http://2007.igem.org/wiki/index.php?title=Special:Contributions/Vieira&feed=atom&limit=50&target=Vieira&year=&month=2007.igem.org - User contributions [en]2019-11-20T12:17:22ZFrom 2007.igem.orgMediaWiki 1.16.5http://2007.igem.org/wiki/index.php/Template:Paris_video_modeling2Template:Paris video modeling22007-10-27T00:29:58Z<p>Vieira: </p>
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= Experimental results =<br />
<br />
== SMB related experiments ==<br />
<br />
=== dapA deletant growth ===<br />
<br />
We expect the somatic cells to excrete only a limited amount of DAP, it would thus be nice if our auxotroph strain could grow on limited amount of metabolite. Over night culture were diluted 100 time in LB suplemented with different amount of DAP.<br />
<br />
=== Survival of dapA deleted strain and Co-culture experiments ===<br />
<br />
<br />
If we want our system to be robust, the germ line cells should be able to live as long as possible when deprived of DAP. They may indeed face such a feat within our system if their is not enough somatic cells at a given time.<br />
<br />
Our dapA deleted strain was grown over night in LB + 300µM DAP. A culture was then launched diluting 100 time the ON culture in LB (+ Kanamycin). 100µL were plated each hour and the number of clone determined.<br />
<br />
We also want to know if the soma of our synthetic organism will be able to feed the germ line. Unfortunatly, this cannot properly be done without the final construct. Nevertheless, we can already check if in similar situations, dapA deleted strain can survive. <br />
<br />
Two different co-culture experiments were performed: <br />
* In the first one, the dapA deleted strain is grown with a prototroph strain. In this case, we know for sure that the prototroph cells will take the population over. Nervertheless it is interesting to see if dapA deleted strain survive longer in this condition than if alone and without DAP.<br />
<br />
[[Image:Paris_DapASurvival.jpg]]<br />
<br />
(the experiment has only been done once, and would be worth repeating to confirm the results)<br />
<br />
We can draw from this curves two important conclusions:<br />
<br />
1. Most of the cells die within the first 2 hours of culture, but a small fraction of the cells are still alive after 8 hours. A part of the dapA deleted cells can thus survive for quite long, which is a good point for us.<br />
<br />
2. When in coculture with a prototroph cell, around 100 time more cells have a long term survival. This means that the dapA deleted strain benefits a bit from the prototroph cell presence and its DAP production capacities.<br />
<br />
* In the second coculture experiment, the dapA deleted strain is grown with a strain bearing an auxotrophy to another metabolite. This experiment reproduces cross-feeding works done on the yeast by Shou W et al. (Synthetic cooperation in engineered yeast populations, PNAS). In this coculture there is a mutual dependence of each strain for the other. If this works, then we know for sure that dapA deleted strain can be rescued by a strain producing DAP!<br />
<br />
Our dapA- strain was grown with a tryptophan operon deleted strain. The culture was plated to check the presence of both strains after 8H. They were both present in concentration above 5*10^4 CFU/Ml. This clearly means that DAP is a good choice as our auxotrophy metabolite !<br />
<br />
=== DAP excretion by prototroph cells ===<br />
<br />
We want to know if prototroph cells are excreting DAP and in what amount. Instead of doing proper chemical dosages which are expensive, we had the idea to make a biological measurements. If we want to quantify DAP concentration of a given medium, we might be able to do so simply by looking at how well a dapA- strain grows into it.<br />
<br />
<br />
Prototroph MG1655 strain was grown in LB, and the medium was recovered at different stages of the culture and purified. The dapA deleted strain was then grown in the recovered medium. What we observed is that no enough DAP is present for any growth to happen. From this point we decided to had little concentration of DAP into the recovered medium, to see what is the minimum amount to add to obtain growth. If this amount is small then it means that there is already quite a lot of DAP present into the medium. Typically if we need to add 10µM of DAP to get a growth similar to LB supplemented with 20µM, we can estimate that the initial concentration is around 10µM.<br />
<br />
<br />
More rigorously, what we measure isn't really the DAP concentration of the medium, but rather what we could call DAP equivalents. This is mainly due to two points. First, dapA gene is the first out of 5 genes making the steps from aspartate-semialdehyde to DAP. So we measure in fact the sum of all intermediaries of the pathway that may be present in the medium and imported by the cells. This is not a problem for us since we do not really care with what exact compound the soma feeds the germline. Second, the recovered medium isn't really LB anymore, so it is not perfectly rigorous to compare it with LB. There might be other compounds excreted during growth, compensating for the DAP starvation. But we do not really care either if this is the case. What we really want to see is how much the excretions of a prototroph cell can favor the growth of a dapA- strain (regardless of what excreted compound matters). And we measure this as DAP equivalents.<br />
<br />
<br />
Here are representative results of what we got from this experiments:<br />
<br />
Medium recovered from MG1655 culture broth are annotated S0.2, S0.4, S0.6, S0.8 and were recovered at optical densities of respectively 0.2, 0.4, 0.6 and 0.8. The added DAP concentration is given.<br />
<br />
[[Image:Paris_Graph1_w121_070707.jpg|800px]]<br />
[[Image:Paris_Graph2_w121_070707.jpg|800px]]<br />
<br />
We clearly see that the latter we recover the medium in the prototroph growth, the less DAP we need to add to obtain growth. This is one more hint that DAP is a good choice for the SMB and we can also try to estimate DAP equivalents for our media. For instance the growth in S0.2 with 25µM of added DAP seems equivalent to the growth in LB with 37.5µM added DAP. This means that S0.2 contains around 12.5µM of DAP equivalents. Nevertheless it was quite hard to retrieve any reliable data from this experiment.<br />
<br />
Here are estimates of DAP equivalents gathered from several experiments:<br />
* S0.2=<br />
* S0.4=<br />
* S0.6=<br />
* S0.8=<br />
<br />
=== Recombination frequency measurements ===<br />
<br />
In the section “Design Process”, the question of the recombination frequency has been discussed. G to S differentiation frequency, and thus lox recombination frequency on which it is based, is a key aspect of our system. Indeed, optimal overall differentiation frequency lies somewhere between 0 and 50% per generation.<br />
<br />
We would like to have tuneable recombination device in order to find the optimal frequency, which lies somewhere between 0 and 50% of recombination per generation. We should be able to tune the recombination frequency by modulating the Cre recombinase expression. In order to do this, we have cloned Cre under the control of the pBAD promoter. We then wanted to characterize our "Cre generator device", and determine the relation between Cre expression level and recombination frequency.<br />
<br />
Three types of experiments were planned and partially performed in this regard:<br />
<br />
* Experiments using FX85 strain harbouring lox-KmR-lox casstte: indirectly measuring recombination frequency by plating on Kan plates after Cre expression assays.<br />
* Experiments using FX85 strain harbouring lox-KmR-lox casstte: indirectly measuring recombination frequency by studying growthrates.<br />
* Experiments using the recombination measurement biodevice.<br />
<br />
<br />
A) Experiments using FX85 strain harbouring lox-KmR-lox casstte: indirectly measuring<br />
<br />
We used FX85 strain (provided by Francois-Xavier Barre) carrying the cassette: lox-KmR-lox inserted into its chromosome. We transformed this strain with our pBad-Cre construct (carried by an Ampiciline resistance plasmid: pSB1A2). Inducing of Cre expression with different arabinose levels was performed. The last step is then spreading on selective plates (Amp or Amp+Kan). The ratio between the number of clones on the two types of plates should give us an estimate of the recombination frequency. When we tried to do this, we did not get any clones on the Amp+Kan plates, even without Cre induction. But this doesn't mean that the recombination frequency is 100%. In fact, if recombination frequency is around 50% per generation or higher, no colonies can grow on kan plates, simply because half or more of the cells will die at each generation (those who recombine are not resistant to Kanamycin any more after little time). <br />
<br />
This means that our Cre generator is quite leaky and gives quite high recombination rates without induction. <br />
<br />
B) Experiments using FX85 strain harbouring lox-KmR-lox casstte: indirectly measuring recombination frequency by studying growthrates.<br />
<br />
If recombination frequency is two high in owr experimental system, then no growth can be seen on Ampicilline (plasmid selection antibiotic)+ Kanamycin (screens against recombiants: cells having excised lox-kanR from their genome). We tested an alternative strategy in order to circumvent this problem.<br />
In order to approximately determine what recombination rate we had, we performed another experiment. FX85 strain was transformed with our pBad-Cre construct. Directly after transformation, liquid cultures were launched with either Amp or Amp+Kan. 100µl of the cultures were regularly plated on LB+Amp, giving the following growth curves:<br />
<br />
C) The third strategy is based on a more direct observation of recombination rate. <br />
We have constructed a “Recombination frequency measurement” device. The schematic structure of this genetic construct is as follows:<br />
<br />
[[Image: recombi frequency.jpg|center|500px]]<br />
<br />
This consctruct has been generated, [[Recombination frequency device|SEE HERE]] the steps of it’s construction.<br />
<br />
This construct has yet to be inserted in the genome. Cre induced recombination frequency measurements will then be performed.<br />
Using this system, an event of recombination is accompanied by a switch in fluorescence from GFP to mRFP wich can be followed under microscope on small E.coli populations.<br />
<br />
=== dapAp characterisation ===<br />
<br />
=== pBAD characterisation ===<br />
<br />
<br />
=== Comparing of dapA genes of E.coli & B.subtilis ===<br />
<br />
== DGAT cloning and triglyceride synthesis in E. Coli ==<br />
<br />
*'''TG synthesis experiment'''<br />
<br />
1. We transformed chemically competent E.coli (DH5alpha) with pBluescript SK minus vector (Stratagene) (ampicilline resistance and pLac promoter) baring DGAT gene (pKS::DGAT). In this vector, dgat transcription is induced by IPTG. <br />
<br />
Nile Red fluorescence dye was used, at a concentration of 5µg/mL to monitor lipid inclusions in different conditions of DGAT expression and fatty acid availability:<br />
<br />
(0.4mM IPTG induction in LB medium with or without sodium oleate 2mM). Results are shown below.<br />
<br />
[[Image: Coli dgat 07232007.jpg|center|900px]]<br />
<br />
Line 1 represents E.coli transformed with pKS::DGAT; and Line 2 the negative control (E.coli transformed by part B0015). Columns 1 and 2 are LB medium without sodium oleate supplementation; columns 3 and 4 are LB with sodium oleate supplementation (2mM). Columns 1 and 3 are without IPTG; columns 3 and 4 with IPTG induction (0.4mM). <br><br />
'''We can observe lipid inclusion into E.coli transformed by pKS::DGAT with IPTG induction'''. <br />
<br>No significant difference is seen between the +/- oleate cells. <br><br />
<br />
2. To exclude that the fluorescence observed is due to DGAT induced cell death. A cell death marker (green) is used. It can be seen below that cell death is not increased upon DGAT expression.<br />
<br />
[[Image: Coli_dgat_death_07232007.jpg|center|800px]]<br />
<br />
3. We started creating DGAT biobrick <bbpart>BBa_I718002</bbpart>: <br />
<br />
*PCR based mutagenesis was performed to eliminate a PstI site in dgat coding sequence. <br />
* We attempted adding biobrick prefix and suffix sites to dgat but have yet to finish the cloning process :-(<br />
<br />
<br />
<br />
= Modeling results =</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-26T17:50:22Z<p>Vieira: /* Biocham */</p>
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<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for Modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to ''an exponential growth of the two coexisting cell types''. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, ''each adapted to a particular problem''.<br />
<br />
=== Questions of Interest ===<br />
<br />
The first, most obvious question deals with proving the ''feasibility'' of our system (Section 2). In our case, this amounts to check that the system presents a very simple, qualitative behavior: ''the two cell populations grow''!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in this model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=Proof of Principle: Qualitative Analysis of System's Behavior=<br />
<br />
In this section, we develop models to test the feasibility of our system. We focus on a simple, essential qualitative property: the growth of the two coexisting cell types. This property is investigated under various modeling assumptions.<br />
<br />
===[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]===<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
===[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
===[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this section, we aim at considering SMB as a [[Paris/mgs#Dynamical_Systems_with_a_Dynamical_Structure|dynamical system with a dynamical structure]] and studying the impact of the cells organization on the future of the population. In order to achieve this goal, we have developed a mechanistic model based on a masses/springs system, that will allow cell to divide and die.<br />
<br />
=Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis=<br />
<br />
In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.<br />
<br />
===[[Paris/Robustness and optimization|Assessing robustness and tunability of two potential designs: numerical simulations of ODE models]]=== <br />
In section [http://2007.igem.org/Paris/DesignProcess#Optimization_through_feedback Design process] two designs have been proposed. The only difference is that one of them incorporates a negative feedback of cre recombinase by dap. We developed simple models to evaluate the relative benefits of both designs in term of robustness and optimization capabilities.<br />
<br />
===[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this last part, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria. We were able to achieve this goal by proposing an optimized extension of the Gillespie algorithm.<br />
<br />
=Summary=<br />
<br />
<br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part 2, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part 3, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
:'''…all these results corroborate our initial design'''.<br />
<br />
=Appendix=<br />
<br />
===Tools Description===<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
====[[Paris/biocham|Biocham]]====<br />
[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.<br><br />
[http://biosynthetique.free.fr/model/AMFI.xml Sbml source]<br />
<br />
====[[Paris/mgs|MGS]]====<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
[http://mgs.ibisc.unive-evry.fr/ MGS] is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
===[[Paris/Sources|Sources of the MGS programs]] [[Image:MGS-inside.png|50px]]===</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-26T17:48:14Z<p>Vieira: /* Biocham */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for Modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to ''an exponential growth of the two coexisting cell types''. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, ''each adapted to a particular problem''.<br />
<br />
=== Questions of Interest ===<br />
<br />
The first, most obvious question deals with proving the ''feasibility'' of our system (Section 2). In our case, this amounts to check that the system presents a very simple, qualitative behavior: ''the two cell populations grow''!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in this model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=Proof of Principle: Qualitative Analysis of System's Behavior=<br />
<br />
In this section, we develop models to test the feasibility of our system. We focus on a simple, essential qualitative property: the growth of the two coexisting cell types. This property is investigated under various modeling assumptions.<br />
<br />
===[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]===<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
===[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
===[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this section, we aim at considering SMB as a [[Paris/mgs#Dynamical_Systems_with_a_Dynamical_Structure|dynamical system with a dynamical structure]] and studying the impact of the cells organization on the future of the population. In order to achieve this goal, we have developed a mechanistic model based on a masses/springs system, that will allow cell to divide and die.<br />
<br />
=Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis=<br />
<br />
In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.<br />
<br />
===[[Paris/Robustness and optimization|Assessing robustness and tunability of two potential designs: numerical simulations of ODE models]]=== <br />
In section [http://2007.igem.org/Paris/DesignProcess#Optimization_through_feedback Design process] two designs have been proposed. The only difference is that one of them incorporates a negative feedback of cre recombinase by dap. We developed simple models to evaluate the relative benefits of both designs in term of robustness and optimization capabilities.<br />
<br />
===[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this last part, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria. We were able to achieve this goal by proposing an optimized extension of the Gillespie algorithm.<br />
<br />
=Summary=<br />
<br />
<br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part 2, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part 3, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
:'''…all these results corroborate our initial design'''.<br />
<br />
=Appendix=<br />
<br />
===Tools Description===<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
====[[Paris/biocham|Biocham]]====<br />
[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.<br />
[http://biosynthetique.free.fr/model/AMFI.xml Sbml source]<br />
<br />
====[[Paris/mgs|MGS]]====<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
[http://mgs.ibisc.unive-evry.fr/ MGS] is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
===[[Paris/Sources|Sources of the MGS programs]] [[Image:MGS-inside.png|50px]]===</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-26T17:46:16Z<p>Vieira: /* Biocham */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for Modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to ''an exponential growth of the two coexisting cell types''. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, ''each adapted to a particular problem''.<br />
<br />
=== Questions of Interest ===<br />
<br />
The first, most obvious question deals with proving the ''feasibility'' of our system (Section 2). In our case, this amounts to check that the system presents a very simple, qualitative behavior: ''the two cell populations grow''!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in this model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=Proof of Principle: Qualitative Analysis of System's Behavior=<br />
<br />
In this section, we develop models to test the feasibility of our system. We focus on a simple, essential qualitative property: the growth of the two coexisting cell types. This property is investigated under various modeling assumptions.<br />
<br />
===[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]===<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
===[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
===[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this section, we aim at considering SMB as a [[Paris/mgs#Dynamical_Systems_with_a_Dynamical_Structure|dynamical system with a dynamical structure]] and studying the impact of the cells organization on the future of the population. In order to achieve this goal, we have developed a mechanistic model based on a masses/springs system, that will allow cell to divide and die.<br />
<br />
=Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis=<br />
<br />
In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.<br />
<br />
===[[Paris/Robustness and optimization|Assessing robustness and tunability of two potential designs: numerical simulations of ODE models]]=== <br />
In section [http://2007.igem.org/Paris/DesignProcess#Optimization_through_feedback Design process] two designs have been proposed. The only difference is that one of them incorporates a negative feedback of cre recombinase by dap. We developed simple models to evaluate the relative benefits of both designs in term of robustness and optimization capabilities.<br />
<br />
===[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this last part, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria. We were able to achieve this goal by proposing an optimized extension of the Gillespie algorithm.<br />
<br />
=Summary=<br />
<br />
<br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part 2, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part 3, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
:'''…all these results corroborate our initial design'''.<br />
<br />
=Appendix=<br />
<br />
===Tools Description===<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
====[[Paris/biocham|Biocham]]====<br />
[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.<br />
<br />
[http://biosynthetique.free.fr/model/AMFI.xml]<br />
<br />
====[[Paris/mgs|MGS]]====<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
[http://mgs.ibisc.unive-evry.fr/ MGS] is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
===[[Paris/Sources|Sources of the MGS programs]] [[Image:MGS-inside.png|50px]]===</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-26T17:44:48Z<p>Vieira: /* Biocham */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for Modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to ''an exponential growth of the two coexisting cell types''. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, ''each adapted to a particular problem''.<br />
<br />
=== Questions of Interest ===<br />
<br />
The first, most obvious question deals with proving the ''feasibility'' of our system (Section 2). In our case, this amounts to check that the system presents a very simple, qualitative behavior: ''the two cell populations grow''!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in this model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=Proof of Principle: Qualitative Analysis of System's Behavior=<br />
<br />
In this section, we develop models to test the feasibility of our system. We focus on a simple, essential qualitative property: the growth of the two coexisting cell types. This property is investigated under various modeling assumptions.<br />
<br />
===[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]===<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
===[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
===[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this section, we aim at considering SMB as a [[Paris/mgs#Dynamical_Systems_with_a_Dynamical_Structure|dynamical system with a dynamical structure]] and studying the impact of the cells organization on the future of the population. In order to achieve this goal, we have developed a mechanistic model based on a masses/springs system, that will allow cell to divide and die.<br />
<br />
=Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis=<br />
<br />
In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.<br />
<br />
===[[Paris/Robustness and optimization|Assessing robustness and tunability of two potential designs: numerical simulations of ODE models]]=== <br />
In section [http://2007.igem.org/Paris/DesignProcess#Optimization_through_feedback Design process] two designs have been proposed. The only difference is that one of them incorporates a negative feedback of cre recombinase by dap. We developed simple models to evaluate the relative benefits of both designs in term of robustness and optimization capabilities.<br />
<br />
===[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this last part, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria. We were able to achieve this goal by proposing an optimized extension of the Gillespie algorithm.<br />
<br />
=Summary=<br />
<br />
<br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part 2, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part 3, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
:'''…all these results corroborate our initial design'''.<br />
<br />
=Appendix=<br />
<br />
===Tools Description===<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
====[[Paris/biocham|Biocham]]====<br />
[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.<br />
<br />
[ftp://biosynthetique.free.fr/modele/AMFI.xml]<br />
<br />
====[[Paris/mgs|MGS]]====<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
[http://mgs.ibisc.unive-evry.fr/ MGS] is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
===[[Paris/Sources|Sources of the MGS programs]] [[Image:MGS-inside.png|50px]]===</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-26T17:44:17Z<p>Vieira: /* Biocham */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for Modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to ''an exponential growth of the two coexisting cell types''. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, ''each adapted to a particular problem''.<br />
<br />
=== Questions of Interest ===<br />
<br />
The first, most obvious question deals with proving the ''feasibility'' of our system (Section 2). In our case, this amounts to check that the system presents a very simple, qualitative behavior: ''the two cell populations grow''!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in this model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=Proof of Principle: Qualitative Analysis of System's Behavior=<br />
<br />
In this section, we develop models to test the feasibility of our system. We focus on a simple, essential qualitative property: the growth of the two coexisting cell types. This property is investigated under various modeling assumptions.<br />
<br />
===[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]===<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
===[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
===[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this section, we aim at considering SMB as a [[Paris/mgs#Dynamical_Systems_with_a_Dynamical_Structure|dynamical system with a dynamical structure]] and studying the impact of the cells organization on the future of the population. In order to achieve this goal, we have developed a mechanistic model based on a masses/springs system, that will allow cell to divide and die.<br />
<br />
=Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis=<br />
<br />
In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.<br />
<br />
===[[Paris/Robustness and optimization|Assessing robustness and tunability of two potential designs: numerical simulations of ODE models]]=== <br />
In section [http://2007.igem.org/Paris/DesignProcess#Optimization_through_feedback Design process] two designs have been proposed. The only difference is that one of them incorporates a negative feedback of cre recombinase by dap. We developed simple models to evaluate the relative benefits of both designs in term of robustness and optimization capabilities.<br />
<br />
===[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]] [[Image:MGS-inside.png|50px]]===<br />
<br />
In this last part, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria. We were able to achieve this goal by proposing an optimized extension of the Gillespie algorithm.<br />
<br />
=Summary=<br />
<br />
<br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part 2, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part 3, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
:'''…all these results corroborate our initial design'''.<br />
<br />
=Appendix=<br />
<br />
===Tools Description===<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
====[[Paris/biocham|Biocham]]====<br />
[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.<br />
<br />
[ http://biosynthetique.free.fr/modele/AMFI.xml]<br />
<br />
====[[Paris/mgs|MGS]]====<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
[http://mgs.ibisc.unive-evry.fr/ MGS] is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
===[[Paris/Sources|Sources of the MGS programs]] [[Image:MGS-inside.png|50px]]===</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/AcknowledgmentsParis/Acknowledgments2007-10-26T17:37:35Z<p>Vieira: /* People who helped us */</p>
<hr />
<div>{{Template:Paris_menu}}<br />
<br />
<br />
==Bibliography==<br />
<br />
<br />
* Relation Between Excreted Lipopolysaccharide Complexes and Surface Structures of a Lysine-Limited Culture of Escherichia coli K. W. KNOX,' MARET VESK,2 AND ELIZABETH WORK<br />
<br />
* Soybean DapA mutations encoding lysine-insensitive dihydrodipicolinate synthase Gregg W. Silk and Benjamin F. Matthews<br />
<br />
* Expression from the Escherichia coli dapA promoter is regulated by intracellular levels of diaminopimelic acid. Acord J, Masters M (2004), FEMS Microbiol Lett 235(1);131-7. PMID: 15158272 <br />
<br />
==People who helped us==<br />
We are extremely grateful to all the people who helped us in a way or an other during this project: <br />
<br />
* the TaMaRa Lab (www.necker.fr/tamara/), for their help, material and intellectual support. And especially Marjorie, Marie Flo, Michelle, Béatrice, Marina, Marianne, Mederick and all the lab people without whom we could have done nothing.<br />
<br />
* Francois Xavier Barre, for interesting discussions that influenced our project a lot, and for divers strains.<br />
<br />
* Cedric Auffray, for FACS facility</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/AcknowledgmentsParis/Acknowledgments2007-10-26T17:37:07Z<p>Vieira: /* People who helped us */</p>
<hr />
<div>{{Template:Paris_menu}}<br />
<br />
<br />
==Bibliography==<br />
<br />
<br />
* Relation Between Excreted Lipopolysaccharide Complexes and Surface Structures of a Lysine-Limited Culture of Escherichia coli K. W. KNOX,' MARET VESK,2 AND ELIZABETH WORK<br />
<br />
* Soybean DapA mutations encoding lysine-insensitive dihydrodipicolinate synthase Gregg W. Silk and Benjamin F. Matthews<br />
<br />
* Expression from the Escherichia coli dapA promoter is regulated by intracellular levels of diaminopimelic acid. Acord J, Masters M (2004), FEMS Microbiol Lett 235(1);131-7. PMID: 15158272 <br />
<br />
==People who helped us==<br />
We are extremely grateful to all the people who helped us in a way or an other during this project: <br />
<br />
* the TaMaRa Lab (www.necker.fr/tamara/), for their help, material and intellectual support. And especially Marjorie, Marie Flo, Michelle, Béatrice, Marina, Marianne, Mederick and all the lab people without whom we could have done nothing.<br />
<br />
* Francois Xavier Barre, for interesting discussions that influenced our project a lot, and for divers strains.<br />
<br />
* Our mothers and the hot girls in red dress <br />
<br />
* Cedric Auffray, for FACS facility</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-26T12:14:24Z<p>Vieira: /* Results */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br />
<br><br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
<br><br />
<br />
= Introduction =<br />
<br />
DAP feeding between somatic and germ cells is based on an indirect communication process: soma cells produce DAP and release it in the environment; DAP molecules freely diffuse outside until they are captured by a germ cell. As the diffusion takes place in the environment, a somatic cell feed first the germ cells that are close to it. Then an well mixed hypothesis as the one used in the our [[Paris/Continuous_model|growth of population analysis]] is hard to assume. We are interesting here in the case where the differentiation of a germ into a soma is DAP dependent. In order to figure out the relation between DAP diffusion and differentiation we propose a simple cellular automaton on square grid. Each cell of the automaton contains a bacterium. We first detail some hypotheses used in this model, then we specify the local behavior rules following by each automaton cell. Finally, the generated simulation is presented.<br />
<br />
= Hypotheses =<br />
<br />
The chosen approach consists in observing the DAP diffusion and differentiation frontwaves. In order to focus on these phenomenon, we work on a ''constant'' population (no death, no division). So we assume that without DAP in its surrounding, a germ cell does not die but remain in passive state (we can imagine that they are at a stationary phase or between to division cycle). It will seem that DAP ''wake up'' bacteria but it's just an artifact due to this assumption.<br />
<br />
It may happen that a germ cell as enough DAP to evolve (typically when it is touched by a DAP diffusion front) but we assume that the contribution is not enough for the cell to divide.<br />
<br />
Finally, we assume then that DAP is produced in somatic cells only and consumed by germ cells. The communication is done by distinguishing in the automaton intra and extra cellular DAP (respectively named DAPi and DAPe).<br />
<br />
= Model Description =<br />
<br />
In this we focus on the elaboration of the cellular automaton.<br />
<br />
== Structure ==<br />
<br />
As we have previously announced, we design cellular automaton on a square grid. More precisely, in order to avoid boundary effects, we assume that the grid is actually wrapped in such a way the grid topology is a 2D torus. Each cell of the automaton contains a bacterium, either germ or somatic, together with the external DAP concentration. So we represent the different states of the automaton cell by tuple of values <code>{DAPe,DAPi,Type}</code>:<br />
<br />
* <code>DAPe</code> is the external DAP concentration,<br />
<br />
* <code>DAPi</code> is the internal DAP concentration in the bacterium,<br />
<br />
* <code>Type</code> represents if the bacterium is differentiated or not; it can take two values <code>BactG</code> and <code>BactS</code>.<br />
<br />
== Dynamics ==<br />
<br />
The following rules specify the local evolution of each cell of the automaton. We distinguished to evolution laws depending on what kind of bacterium is in the cell:<br />
<br />
*<html><u>In the case of a BactS cell</u></html>: we have to consider the diffusion of <code>DAPe</code> between the considered cell and its neighbors, the export of DAP from the inside to the outside, and finally the production of <code>DAPi</code>. The rule can be presented as follows:<br />
<br />
DAPe <- DAPe + (DAPe diffused in the neighborhood) + (DAPi lost by export)<br />
DAPi <- DAPi + (DAPi produced) - (DAPi lost by export)<br />
Type <- BactS<br />
<br />
*<html><u>In the case of a BactG cell</u></html>: we have to consider the diffusion of <code>DAPe</code> between the considered cell and its neighbors, the import of DAP from the outside to the inside, the consumption of <code>DAPi</code>, and finally the differentiation when DAP concentration reaches a right range of values. The rule can be presented as follows:<br />
<br />
DAPe <- DAPe + (DAPe diffused in the neighborhood) - (DAPi gain by import)<br />
DAPi <- DAPi - (DAPi consumed) + (DAPi gain by import)<br />
Type <- '''if''' (min_threshold) < DAPi < (max_threshold) '''then''' BactS '''else''' BactG<br />
<br />
== Parameters ==<br />
<br />
We consider 8 parameters. They are used with some noise during the evolution to avoid a deterministic behavior.<br />
<br />
* In <code>BactS</code> cells:<br />
<br />
:* Dap export rate in somatic bacteria<br />
<br />
:* Dap import rate in somatic bacteria<br />
<br />
:* Dap production rate of somatic bacteria<br />
<br />
* In <code>BactG</code> cells:<br />
<br />
:* Dap export rate in germ bacteria<br />
<br />
:* Dap import rate in germ bacteria<br />
<br />
:* Dap consummation rate of germ bacteria<br />
<br />
:* Minimal threshold for differentiation<br />
<br />
:* Maximal threshold for differentiation<br />
<br />
== Initial state ==<br />
<br />
Our initial state is 30x30 2D toric cellular automaton where all cells are initialized by value <code>{DAPe=0,DAPi=0,Type=BactG}</code> but four <code>{DAPe=0,DAPi=0,Type=BactS}</code> are randomly placed in the grid.<br />
<br />
<br />
<br />
= Output [[Image:MGS-inside.png|50px]]=<br />
<br />
Our implementation was done in [[Paris/mgs|MGS]] and the output was generated by [http://www.sciences.univ-nantes.fr/info/perso/permanents/cohen/SOFTWARE/GBVIEW/index.html GBView].<br />
<br />
The output is two animated pictures: the first one shows the differentiation, the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
<br />
*The first picture shows the diffusion of DAP: the front wave is figured in light blue; the dark blue area corresponds to stable parts of the system where concentration do not evolve anymore.<br />
<br />
*The second picture presents the differentiation: red and blue cells are respectively germ and somatic bacteria.<br />
<br />
= Results =<br />
<br />
As we can see, the differentiation and DAP diffusion wave fronts are superposed. This simulation is obviously out of reality but the underlying model have been developed in order to consider that low concentration of DAP induces differentiation (cells become green - dark blue), while with high DAP concentration, the differentiation is inhibited. Without this second threshold, all cells would differentiate. But some germ cells remain because they are enough fed to stay over the threshold. This property is of course crucial as only germ cells can reproduce.<br />
<br />
In the considered model of the system, the inhibition must be strong and effective for not all the cells differentiate. Bad thresholds make the system collapse: a too strong inhibition prevents germ cells to differentiate, and on the opposite, a too weak inhibition make all them switch to a somatic state.<br />
<br />
We also played with the constants of diffusion and found that the 3 mechanisms(export, import, diffusion in space), are important factors. For a few entities of DAP imported, there is a important amount of DAP produced, this amount is given by the neighbors BactS and to keep a coherent rate of production, a BactG must be surrounded by BactS, we can't have a ratio of 1:1.<br />
<br />
= [[Paris\Sources#Cell auto|Sources]] =</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-26T11:42:44Z<p>Vieira: /* Dynamics */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br />
<br><br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
<br><br />
<br />
= Introduction =<br />
<br />
DAP feeding between somatic and germ cells is based on an indirect communication process: soma cells produce DAP and release it in the environment; DAP molecules freely diffuse outside until they are captured by a germ cell. As the diffusion takes place in the environment, a somatic cell feed first the germ cells that are close to it. Then an well mixed hypothesis as the one used in the our [[Paris/Continuous_model|growth of population analysis]] is hard to assume. We are interesting here in the case where the differentiation of a germ into a soma is DAP dependent. In order to figure out the relation between DAP diffusion and differentiation we propose a simple cellular automaton on square grid. Each cell of the automaton contains a bacterium. We first detail some hypotheses used in this model, then we specify the local behavior rules following by each automaton cell. Finally, the generated simulation is presented.<br />
<br />
= Hypotheses =<br />
<br />
The chosen approach consists in observing the DAP diffusion and differentiation frontwaves. In order to focus on these phenomenon, we work on a ''constant'' population (no death, no division). So we assume that without DAP in its surrounding, a germ cell does not die but remain in passive state (we can imagine that they are at a stationary phase or between to division cycle). It will seem that DAP ''wake up'' bacteria but it's just an artifact due to this assumption.<br />
<br />
It may happen that a germ cell as enough DAP to evolve (typically when it is touched by a DAP diffusion front) but we assume that the contribution is not enough for the cell to divide.<br />
<br />
Finally, we assume then that DAP is produced in somatic cells only and consumed by germ cells. The communication is done by distinguishing in the automaton intra and extra cellular DAP (respectively named DAPi and DAPe).<br />
<br />
= Model Description =<br />
<br />
In this we focus on the elaboration of the cellular automaton.<br />
<br />
== Structure ==<br />
<br />
As we have previously announced, we design cellular automaton on a square grid. More precisely, in order to avoid boundary effects, we assume that the grid is actually wrapped in such a way the grid topology is a 2D torus. Each cell of the automaton contains a bacterium, either germ or somatic, together with the external DAP concentration. So we represent the different states of the automaton cell by tuple of values <code>{DAPe,DAPi,Type}</code>:<br />
<br />
* <code>DAPe</code> is the external DAP concentration,<br />
<br />
* <code>DAPi</code> is the internal DAP concentration in the bacterium,<br />
<br />
* <code>Type</code> represents if the bacterium is differentiated or not; it can take two values <code>BactG</code> and <code>BactS</code>.<br />
<br />
== Dynamics ==<br />
<br />
The following rules specify the local evolution of each cell of the automaton. We distinguished to evolution laws depending on what kind of bacterium is in the cell:<br />
<br />
*<html><u>In the case of a BactS cell</u></html>: we have to consider the diffusion of <code>DAPe</code> between the considered cell and its neighbors, the export of DAP from the inside to the outside, and finally the production of <code>DAPi</code>. The rule can be presented as follows:<br />
<br />
DAPe <- DAPe + (DAPe diffused in the neighborhood) + (DAPi lost by export)<br />
DAPi <- DAPi + (DAPi produced) - (DAPi lost by export)<br />
Type <- BactS<br />
<br />
*<html><u>In the case of a BactG cell</u></html>: we have to consider the diffusion of <code>DAPe</code> between the considered cell and its neighbors, the import of DAP from the outside to the inside, the consumption of <code>DAPi</code>, and finally the differentiation when DAP concentration reaches a right range of values. The rule can be presented as follows:<br />
<br />
DAPe <- DAPe + (DAPe diffused in the neighborhood) - (DAPi gain by import)<br />
DAPi <- DAPi - (DAPi consumed) + (DAPi gain by import)<br />
Type <- '''if''' (min_threshold) < DAPi < (max_threshold) '''then''' BactS '''else''' BactG<br />
<br />
== Parameters ==<br />
<br />
We consider 8 parameters. They are used with some noise during the evolution to avoid a deterministic behavior.<br />
<br />
* In <code>BactS</code> cells:<br />
<br />
:* Dap export rate in somatic bacteria<br />
<br />
:* Dap import rate in somatic bacteria<br />
<br />
:* Dap production rate of somatic bacteria<br />
<br />
* In <code>BactG</code> cells:<br />
<br />
:* Dap export rate in germ bacteria<br />
<br />
:* Dap import rate in germ bacteria<br />
<br />
:* Dap consummation rate of germ bacteria<br />
<br />
:* Minimal threshold for differentiation<br />
<br />
:* Maximal threshold for differentiation<br />
<br />
== Initial state ==<br />
<br />
Our initial state is 30x30 2D toric cellular automaton where all cells are initialized by value <code>{DAPe=0,DAPi=0,Type=BactG}</code> but four <code>{DAPe=0,DAPi=0,Type=BactS}</code> are randomly placed in the grid.<br />
<br />
<br />
<br />
= Output [[Image:MGS-inside.png|50px]]=<br />
<br />
Our implementation was done in [[Paris/mgs|MGS]] and the output was generated by [http://www.sciences.univ-nantes.fr/info/perso/permanents/cohen/SOFTWARE/GBVIEW/index.html GBView].<br />
<br />
The output is two animated pictures: the first one shows the differentiation, the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
<br />
*The first picture shows the diffusion of DAP: the front wave is figured in light blue; the dark blue area corresponds to stable parts of the system where concentration do not evolve anymore.<br />
<br />
*The second picture presents the differentiation: red and blue cells are respectively germ and somatic bacteria.<br />
<br />
= Results =<br />
<br />
As we can see, the differentiation and DAP diffusion wave fronts are superposed. This simulation is obviously out of reality but the underlying model have been developed in order to consider that low concentration of DAP induces differentiation (cells become green - dark blue), while with high DAP concentration, the differentiation is inhibited. Without this second threshold, all cells would differentiate. But some germ cells remain because they are enough fed to stay over the threshold. This property is of course crucial as only germ cells can reproduce.<br />
<br />
In the considered model of the system, the inhibition must be strong and effective for not all the cells differentiate. Bad thresholds make the system collapse: a too strong inhibition prevents germ cells to differentiate, and on the opposite, a too weak inhibition make all them switch to a somatic state.<br />
<br />
= [[Paris\Sources#Cell auto|Sources]] =</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-26T11:40:50Z<p>Vieira: /* Dynamics */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br />
<br><br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
<br><br />
<br />
= Introduction =<br />
<br />
DAP feeding between somatic and germ cells is based on an indirect communication process: soma cells produce DAP and release it in the environment; DAP molecules freely diffuse outside until they are captured by a germ cell. As the diffusion takes place in the environment, a somatic cell feed first the germ cells that are close to it. Then an well mixed hypothesis as the one used in the our [[Paris/Continuous_model|growth of population analysis]] is hard to assume. We are interesting here in the case where the differentiation of a germ into a soma is DAP dependent. In order to figure out the relation between DAP diffusion and differentiation we propose a simple cellular automaton on square grid. Each cell of the automaton contains a bacterium. We first detail some hypotheses used in this model, then we specify the local behavior rules following by each automaton cell. Finally, the generated simulation is presented.<br />
<br />
= Hypotheses =<br />
<br />
The chosen approach consists in observing the DAP diffusion and differentiation frontwaves. In order to focus on these phenomenon, we work on a ''constant'' population (no death, no division). So we assume that without DAP in its surrounding, a germ cell does not die but remain in passive state (we can imagine that they are at a stationary phase or between to division cycle). It will seem that DAP ''wake up'' bacteria but it's just an artifact due to this assumption.<br />
<br />
It may happen that a germ cell as enough DAP to evolve (typically when it is touched by a DAP diffusion front) but we assume that the contribution is not enough for the cell to divide.<br />
<br />
Finally, we assume then that DAP is produced in somatic cells only and consumed by germ cells. The communication is done by distinguishing in the automaton intra and extra cellular DAP (respectively named DAPi and DAPe).<br />
<br />
= Model Description =<br />
<br />
In this we focus on the elaboration of the cellular automaton.<br />
<br />
== Structure ==<br />
<br />
As we have previously announced, we design cellular automaton on a square grid. More precisely, in order to avoid boundary effects, we assume that the grid is actually wrapped in such a way the grid topology is a 2D torus. Each cell of the automaton contains a bacterium, either germ or somatic, together with the external DAP concentration. So we represent the different states of the automaton cell by tuple of values <code>{DAPe,DAPi,Type}</code>:<br />
<br />
* <code>DAPe</code> is the external DAP concentration,<br />
<br />
* <code>DAPi</code> is the internal DAP concentration in the bacterium,<br />
<br />
* <code>Type</code> represents if the bacterium is differentiated or not; it can take two values <code>BactG</code> and <code>BactS</code>.<br />
<br />
== Dynamics ==<br />
<br />
The following rules specify the local evolution of each cell of the automaton. We distinguished to evolution laws depending on what kind of bacterium is in the cell:<br />
<br />
* In the case of a <code>'''BactS'''</code> cell: we have to consider the diffusion of <code>DAPe</code> between the considered cell and its neighbors, the export of DAP from the inside to the outside, and finally the production of <code>DAPi</code>. The rule can be presented as follows:<br />
<br />
DAPe <- DAPe + (DAPe diffused in the neighborhood) + (DAPi lost by export)<br />
DAPi <- DAPi + (DAPi produced) - (DAPi lost by export)<br />
Type <- BactS<br />
<br />
* In the case of a <code>'''BactG'''</code> cell: we have to consider the diffusion of <code>DAPe</code> between the considered cell and its neighbors, the import of DAP from the outside to the inside, the consumption of <code>DAPi</code>, and finally the differentiation when DAP concentration reaches a right range of values. The rule can be presented as follows:<br />
<br />
DAPe <- DAPe + (DAPe diffused in the neighborhood) - (DAPi gain by import)<br />
DAPi <- DAPi - (DAPi consumed) + (DAPi gain by import)<br />
Type <- '''if''' (min_threshold) < DAPi < (max_threshold) '''then''' BactS '''else''' BactG<br />
<br />
== Parameters ==<br />
<br />
We consider 8 parameters. They are used with some noise during the evolution to avoid a deterministic behavior.<br />
<br />
* In <code>BactS</code> cells:<br />
<br />
:* Dap export rate in somatic bacteria<br />
<br />
:* Dap import rate in somatic bacteria<br />
<br />
:* Dap production rate of somatic bacteria<br />
<br />
* In <code>BactG</code> cells:<br />
<br />
:* Dap export rate in germ bacteria<br />
<br />
:* Dap import rate in germ bacteria<br />
<br />
:* Dap consummation rate of germ bacteria<br />
<br />
:* Minimal threshold for differentiation<br />
<br />
:* Maximal threshold for differentiation<br />
<br />
== Initial state ==<br />
<br />
Our initial state is 30x30 2D toric cellular automaton where all cells are initialized by value <code>{DAPe=0,DAPi=0,Type=BactG}</code> but four <code>{DAPe=0,DAPi=0,Type=BactS}</code> are randomly placed in the grid.<br />
<br />
<br />
<br />
= Output [[Image:MGS-inside.png|50px]]=<br />
<br />
Our implementation was done in [[Paris/mgs|MGS]] and the output was generated by [http://www.sciences.univ-nantes.fr/info/perso/permanents/cohen/SOFTWARE/GBVIEW/index.html GBView].<br />
<br />
The output is two animated pictures: the first one shows the differentiation, the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
<br />
*The first picture shows the diffusion of DAP: the front wave is figured in light blue; the dark blue area corresponds to stable parts of the system where concentration do not evolve anymore.<br />
<br />
*The second picture presents the differentiation: red and blue cells are respectively germ and somatic bacteria.<br />
<br />
= Results =<br />
<br />
As we can see, the differentiation and DAP diffusion wave fronts are superposed. This simulation is obviously out of reality but the underlying model have been developed in order to consider that low concentration of DAP induces differentiation (cells become green - dark blue), while with high DAP concentration, the differentiation is inhibited. Without this second threshold, all cells would differentiate. But some germ cells remain because they are enough fed to stay over the threshold. This property is of course crucial as only germ cells can reproduce.<br />
<br />
In the considered model of the system, the inhibition must be strong and effective for not all the cells differentiate. Bad thresholds make the system collapse: a too strong inhibition prevents germ cells to differentiate, and on the opposite, a too weak inhibition make all them switch to a somatic state.<br />
<br />
= [[Paris\Sources#Cell auto|Sources]] =</div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modeling2Template:Paris video modeling22007-10-25T23:01:00Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://biosynthetique.free.fr/images/preview.jpg&autostart=false&file=http://biosynthetique.free.fr/videos/finalv4.flv" /><br />
<param name="quality" value="high" /><br />
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<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://biosynthetique.free.fr/images/preview.jpg&autostart=false&file=http://biosynthetique.free.fr/videos/finalv4.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_menu_modelingTemplate:Paris menu modeling2007-10-25T16:43:50Z<p>Vieira: </p>
<hr />
<div><html><br />
<style type="text/css"><br />
#navmenu ul{<br />
list-style: none;<br />
}<br />
#navmenu ul li{<br />
display: inline;<br />
padding: 5px 5px 3px 5px;<br />
border: thin solid black;<br />
background-color: Lavender ;<br />
}<br />
#navmenu a {<br />
font-size: 10pt;<br />
font-family: "Lucida Grande", Verdana, arial, sans-serif;<br />
text-decoration: none;<br />
color: DarkBlue;<br />
}<br />
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color: #FF6633;<br />
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#navmenu img {<br />
height: 100px;<br />
width: 150px;<br />
}<br />
</style><br />
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<div id=navmenu><br />
<br />
<center><a href='http://2007.igem.org/Paris'><br />
<ul><br />
<li><a href='http://2007.igem.org/Paris/Project_Description'> Project Description</a></li><br />
<li><a href='http://2007.igem.org/Paris/Modeling'> Introduction</a></li><br />
<li><a href='http://2007.igem.org/Paris/Macroscopic Models'> Proof of principle</a></li><br />
<li><a href='http://2007.igem.org/Paris/Quantitative aspects'> Quantitative aspects</a></li><br />
<li><a href='http://2007.igem.org/Paris/summary'>Summary</a></li><br />
<li><a href='http://2007.igem.org/Paris/models tools'>Appendix</a></li><br />
</ul><br />
<br />
</div><br />
</center><br />
</html></div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-25T16:39:55Z<p>Vieira: </p>
<hr />
<div>{{Template:Paris_menu}}<br><br><br />
{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to an exponential growth of the two coexisting cell types. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, each adapted to a particular problem.<br />
<br />
<br />
=== The questions of interest ===<br />
<br />
The first, most obvious question deals with proving the feasibility of our system (Section II). In our case, this amounts to check that the system presents a very simple, qualitative behavior: the two cell populations grow!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in the previous model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in Section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in Section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=[[Paris/Macroscopic_Models|Proof of principle: qualitative analysis of system's behavior]]=<br />
<br />
Those models are at macroscopic scale. They are focused on the evolution of the population, with global rules avoiding description of all the microscopic mechanisms. We present tree different works, with different approaches (ODE, automaton)...<br />
<br />
==[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]==<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
==[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]]==<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
==[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth: cellular automaton in 3D]]==<br />
<br />
We try with this work to characterize the effect on the cells, of the DAP diffusion in a free space where cells can divide or die.<br><br />
We have a growing culture with germinal cells and somatic cells.<br><br />
We want to see if we can have different kinds of evolution for our cells.<br><br />
as we can see in the [[Paris/Cell_auto|DAP diffusion automaton]] the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.<br />
<br />
=[[Paris/Microscopic_Models|Assessing robustness and optimizing system's behavior: quantitative analysis]]=<br />
<br />
==Problem description==<br />
==[[Paris/Continuous modelb|Assessing robustness of two potential designs: numerical simulations of ODE models]]==<br />
==[[Paris/Continuous modelb|Assessing tunability of two potential designs: numerical simulations of ODE models]]== <br />
This model aims at describing the dynamic evolution of populations of germen and soma type bacteria.<br />
It is based on a set of differential equations describing DAP synthesis, DAP transport,<br />
differentiation of germen bacteria into soma and bacteria death.<br />
<br />
==[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]]==<br />
=Summary=<br />
<br />
=Appendix=<br />
<br />
==[[Paris/models_tools|Tools description]]==<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
===[[Paris/biocham|Biocham]]===<br />
<br />
<br />
===[[Paris/mgs|MGS]]===<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
MGS is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
==[[Paris/Sources| Models, Initial Conditions Files and Sources]]==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-25T16:39:37Z<p>Vieira: </p>
<hr />
<div>{{Template:Paris_menu}}<br><br><br />
{{Template:Paris_menu_modeling}<br />
<br><br><br />
<br />
=Introduction=<br />
<br />
=== Motivation for modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to an exponential growth of the two coexisting cell types. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, each adapted to a particular problem.<br />
<br />
<br />
=== The questions of interest ===<br />
<br />
The first, most obvious question deals with proving the feasibility of our system (Section II). In our case, this amounts to check that the system presents a very simple, qualitative behavior: the two cell populations grow!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in the previous model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in Section [[Paris/DesignProcess#Optimization_through_feedback|Design process]].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in Section [[Paris/DesignProcess#Optimization_through_feedback|Design process]]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=[[Paris/Macroscopic_Models|Proof of principle: qualitative analysis of system's behavior]]=<br />
<br />
Those models are at macroscopic scale. They are focused on the evolution of the population, with global rules avoiding description of all the microscopic mechanisms. We present tree different works, with different approaches (ODE, automaton)...<br />
<br />
==[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]==<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
==[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]]==<br />
<br />
In this part of our work, we aim at characterizing the diffusion of the DAP and the effect on the cells differentiation. This study consists in observing by simulation, the diffusion of DAP in a lawn of germ cells with some isolated somatic cells using a cellular automaton.<br />
<br />
==[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth: cellular automaton in 3D]]==<br />
<br />
We try with this work to characterize the effect on the cells, of the DAP diffusion in a free space where cells can divide or die.<br><br />
We have a growing culture with germinal cells and somatic cells.<br><br />
We want to see if we can have different kinds of evolution for our cells.<br><br />
as we can see in the [[Paris/Cell_auto|DAP diffusion automaton]] the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.<br />
<br />
=[[Paris/Microscopic_Models|Assessing robustness and optimizing system's behavior: quantitative analysis]]=<br />
<br />
==Problem description==<br />
==[[Paris/Continuous modelb|Assessing robustness of two potential designs: numerical simulations of ODE models]]==<br />
==[[Paris/Continuous modelb|Assessing tunability of two potential designs: numerical simulations of ODE models]]== <br />
This model aims at describing the dynamic evolution of populations of germen and soma type bacteria.<br />
It is based on a set of differential equations describing DAP synthesis, DAP transport,<br />
differentiation of germen bacteria into soma and bacteria death.<br />
<br />
==[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]]==<br />
=Summary=<br />
<br />
=Appendix=<br />
<br />
==[[Paris/models_tools|Tools description]]==<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
===[[Paris/biocham|Biocham]]===<br />
<br />
<br />
===[[Paris/mgs|MGS]]===<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
MGS is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
==[[Paris/Sources| Models, Initial Conditions Files and Sources]]==</div>Vieirahttp://2007.igem.org/wiki/index.php/ParisParis2007-10-25T16:34:46Z<p>Vieira: </p>
<hr />
<div><font size=16><center>The SMB: Synthetic Multicellular Bacterium</center></font> <br><br />
<br />
<br><br />
{{Paris_MainMenu}}<br />
<br><br />
{{paris_video_modeling2}}<br />
<br><br />
<br />
The aim of our project is to engineer the first synthetic multicellular bacterium, the SMB. This new organism is a new tool for the engineering of complex biological systems. It consists in two interdependent cell lines. The first one, dedicated to reproduction will be called the germ line (red cells). It is able to differentiate into the second line: the soma (green cells), which is sterile and dedicated to support the germ line. The germ line is auxotroph for DAP (diaminopimelate) which is provided by the soma. There is thus an interdependency relationship. The soma, being sterile, doesn't exist without the germ line to generate it, and the germ line needs the soma to complement its auxotrophy. We provide here experimental and computational evidences that this system can work, as well as the almost complete construction of the SMB.<br />
<br />
<div align="center" ><br />
{| cellspacing="2px" cellpadding="5" border="2" style="padding: 0px; width: 780px; color: black; background-color: white;"<br />
|-valign="top"<br />
|width=189.25px style="padding: 10px; background-color: lightblue; border: 2px solid black;" |<br />
<br />
<center><h3>Members</h3><br />
<br />
'''Student Members'''<br />
<br />
[[User:Aurelien.rizk|Aurélien Rizk]]<br><br />
[[User:David.bikard|David Bikard]]<br><br />
[[User:Davidoff|David Guegan]]<br><br />
[[User:Davidpz|David Puyraimond]]<br><br />
[[User:Eismoustique|Eimad Shotar]]<br><br />
[[User:Vieira|Gilles Vieira]]<br><br />
[[User:Nicolas C.|Nicolas Chiaruttini]]<br><br />
[[User:Thomasclozel|Thomas Clozel]]<br><br />
[[User:Landrain|Thomas Landrain]]<br><br />
<br />
<br />
'''Instructors'''<br />
<br />
[[User:Ablindner|Ariel Lindner]]<br><br />
[[User:Alfonso|Alfonso Jaramillo]]<br><br />
[[User:Delapla|Franck Delaplace]]<br><br />
[[User:Kepes|Francois Kepes]]<br><br />
[[User:Vschachter|Vincent Schachter]]<br><br />
[[User:Bottani|Samuel Bottani]]<br><br />
<br />
'''Advisors'''<br />
<br />
[[User:Chettaoui|Chafika Chettaoui|]]<br><br />
[[User:Spicher|Antoine Spicher]]<br><br />
[[User:flefevre|Francois Le Fevre]]<br><br />
[[User:PTortosa|Pablo Tortosa]]<br><br />
[[User:maria|Maria Suarez]]<br><br />
[[User:SMIDTAS|Serge Smidtas]]<br><br />
<br />
</center><br />
<br />
|width=189.25px style="padding:10px; background-color: #ffffff; border: 2px solid black;" |<br />
<br />
<center><h3>Informations</h3></center><br />
<br><br><br />
'''[[Summary of the teachers|Summary of the teachers workshop]] '''<br />
<br><br><br />
<br />
'''Schedule'''<br />
* '''Next meeting : Wednesday october 24th'''<br />
Results, Conclusions, Wiki<br />
<br />
Wiki freezing: D-5 !!<br />
<br><br><br />
<br />
'''Links'''<br />
* [http://biosynthetique.free.fr/index.php5?title=Accueil Our French wiki (SB 2006/06 journal club)]<br />
* [http://partsregistry.org/Main_Page The registry]<br />
* [http://partsregistry.org/Help:Contents Biobricks and Registry Tutorials]<br />
* [http://en.wikipedia.org/wiki/Help:Wikitext_examples Wiki Formatting Guide]<br />
<br><br><br><br />
<center>[[Image:Tour eiffel.gif|60px]]</center><br />
|width=189.25px style="padding: 10px; background-color: #FF6666; border: 2px solid black;" |<br />
<br />
<center><h3>Project</h3></center><br />
<br />
<br />
* '''[[Paris/Project Description| Project Description]]'''<br />
<br />
<br />
'''Life in the Lab'''<br />
* [[Paris/Constructs| Molecular biology constructs]]<br />
<br />
* [[Paris/Notebook_Calendar| Team Notebook]]<br />
<br />
* [[Paris/Oligos| Oligos]]<br />
<br />
* [[Paris/PROTOCOLS| Protocols]]<br />
<br />
* [[Paris/Freezer| Freezer]]<br />
<br />
* [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2007&group=Paris Our parts at the registry]<br />
<br />
<br />
* [[Paris/DISCUSSION| Forum]]<br />
<br />
<br />
[[Paris/The team at work|The team at work]]<br />
<br />
|}<br />
<br />
<html><br />
From October 17th 2007:<br><br />
<a href="http://www3.clustrmaps.com/counter/maps.php?url=http://2007.igem.org/Paris" id="clustrMapsLink"><img src="http://www3.clustrmaps.com/counter/index2.php?url=http://2007.igem.org/Paris" style="border:0px;" alt="Locations of visitors to this page" title="Locations of visitors to this page" id="clustrMapsImg" onError="this.onError=null; this.src='http://www2.clustrmaps.com/images/clustrmaps-back-soon.jpg'; document.getElementById('clustrMapsLink').href='http://www2.clustrmaps.com'" /><br />
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<a href="http://www.easycounter.com/"><br />
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border="0" alt="Web Counters"></a><br />
<br><a href="http://www.easycounter.com/FreeCounter3.html">Hit Counters</a><br />
</html><br />
<br />
<br />
We are extremely grateful to the following organisations for their support of our project:<br />
<br />
<table><tr><td><br />
<br />
</td><td><br />
[[Image:Paris_Sponsors.jpg]]<br />
</td><td><br />
Fondation Bettencourt<br />
<br />
[http://www.fondationbs.org/ www.fondationbs.org]<br />
<br />
<br />
Sofinnova<br />
<br />
[http://www.sofinnova.fr www.sofinnova.fr]<br />
<br />
<br />
Ambassade de France aux Etats Unis<br />
<br />
[http://www.ambafrance-us.org/ www.ambafrance-us.org]<br />
<br />
<br />
Synbiocomm<br />
<br />
[http://www.syntheticbiology.ethz.ch/synbiocomm/index www.syntheticbiology.ethz.ch]<br />
</td></tr></table></div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-25T14:36:40Z<p>Vieira: /* Spatial simulation */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
Coming soon<br />
<br />
=Introduction=<br />
<br />
=== Motivation for modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to an exponential growth of the two coexisting cell types. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, each adapted to a particular problem.<br />
<br />
<br />
=== The questions of interest ===<br />
<br />
The first, most obvious question deals with proving the feasibility of our system (Section II). In our case, this amounts to check that the system presents a very simple, qualitative behavior: the two cell populations grow!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in the previous model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in Section Blah[add link to corresponding section].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in Section Blah[add link to corresponding section]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=[[Paris/Macroscopic_Models|Proof of principle: qualitative analysis of system's behavior]]=<br />
<br />
Those models are at macroscopic scale. They are focused on the evolution of the population, with global rules avoiding description of all the microscopic mechanisms. We present tree different works, with different approaches (ODE, automaton)...<br />
<br />
==[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]==<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
==[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]]==<br />
<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br />
<br />
==[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth: cellular automaton in 3D]]==<br />
<br />
We try with this work to characterize the effect on the cells, of the DAP diffusion in a free space where cells can divide or die.<br><br />
We have a growing culture with germinal cells and somatic cells.<br><br />
We want to see if we can have different kinds of evolution for our cells.<br><br />
as we can see in the [[Paris/Cell_auto|DAP diffusion automaton]] the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.<br />
<br />
=[[Paris/Microscopic_Models|Assessing robustness and optimizing system's behavior: quantitative analysis]]=<br />
<br />
==Problem description==<br />
==[[Paris/Continuous modelb|Assessing robustness of two potential designs: numerical simulations of ODE models]]==<br />
==[[Paris/Continuous modelb|Assessing tunability of two potential designs: numerical simulations of ODE models]]== <br />
This model aims at describing the dynamic evolution of populations of germen and soma type bacteria.<br />
It is based on a set of differential equations describing DAP synthesis, DAP transport,<br />
differentiation of germen bacteria into soma and bacteria death. This approach differs form the precedents one by the level of description of the model<br />
and the numerical analysis done on the model.<br />
<br />
==[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]]==<br />
=Summary= <br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part II, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part III, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
…all these results corroborate our initial design.<br />
=Appendix=<br />
<br />
==[[Paris/models_tools|Tools description]]==<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
===[[Paris/biocham|Biocham]]===<br />
<br />
<br />
===[[Paris/mgs|MGS]]===<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
MGS is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
==[[Paris/Sources| Models, Initial Conditions Files and Sources]]==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-25T14:35:46Z<p>Vieira: /* Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth: cellular automaton in 3D */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
Coming soon<br />
<br />
=Introduction=<br />
<br />
=== Motivation for modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to an exponential growth of the two coexisting cell types. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, each adapted to a particular problem.<br />
<br />
<br />
=== The questions of interest ===<br />
<br />
The first, most obvious question deals with proving the feasibility of our system (Section II). In our case, this amounts to check that the system presents a very simple, qualitative behavior: the two cell populations grow!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in the previous model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in Section Blah[add link to corresponding section].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in Section Blah[add link to corresponding section]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=[[Paris/Macroscopic_Models|Proof of principle: qualitative analysis of system's behavior]]=<br />
<br />
Those models are at macroscopic scale. They are focused on the evolution of the population, with global rules avoiding description of all the microscopic mechanisms. We present tree different works, with different approaches (ODE, automaton)...<br />
<br />
==[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]==<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
==[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]]==<br />
<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br />
<br />
==[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth: cellular automaton in 3D]]==<br />
<br />
==Spatial simulation==<br />
We try with this work to characterize the effect on the cells, of the DAP diffusion in a free space where cells can divide or die.<br><br />
We have a growing culture with germinal cells and somatic cells.<br><br />
We want to see if we can have different kinds of evolution for our cells.<br><br />
as we can see in the [[Paris/Cell_auto|DAP diffusion automaton]] the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.<br />
<br />
=[[Paris/Microscopic_Models|Assessing robustness and optimizing system's behavior: quantitative analysis]]=<br />
<br />
==Problem description==<br />
==[[Paris/Continuous modelb|Assessing robustness of two potential designs: numerical simulations of ODE models]]==<br />
==[[Paris/Continuous modelb|Assessing tunability of two potential designs: numerical simulations of ODE models]]== <br />
This model aims at describing the dynamic evolution of populations of germen and soma type bacteria.<br />
It is based on a set of differential equations describing DAP synthesis, DAP transport,<br />
differentiation of germen bacteria into soma and bacteria death. This approach differs form the precedents one by the level of description of the model<br />
and the numerical analysis done on the model.<br />
<br />
==[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]]==<br />
=Summary= <br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part II, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part III, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
…all these results corroborate our initial design.<br />
=Appendix=<br />
<br />
==[[Paris/models_tools|Tools description]]==<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
===[[Paris/biocham|Biocham]]===<br />
<br />
<br />
===[[Paris/mgs|MGS]]===<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
MGS is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
==[[Paris/Sources| Models, Initial Conditions Files and Sources]]==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/ModelingParis/Modeling2007-10-25T14:34:21Z<p>Vieira: /* Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br><br />
<br />
Coming soon<br />
<br />
=Introduction=<br />
<br />
=== Motivation for modeling ===<br />
<br />
We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:<br />
* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,<br />
* so-called germ cells that are able to grow, but only in presence of (sufficient quantities of ) DAP, and are able to differentiate into soma cells.<br />
<br />
Informal reasoning indicate that this design should be correct, in the sense that it leads to an exponential growth of the two coexisting cell types. However, before actually constructing this system, we would like to assess the quality of our design using modeling approaches. Since different questions needed to be answered, we developed different types of models, each adapted to a particular problem.<br />
<br />
<br />
=== The questions of interest ===<br />
<br />
The first, most obvious question deals with proving the feasibility of our system (Section II). In our case, this amounts to check that the system presents a very simple, qualitative behavior: the two cell populations grow!<br />
Accordingly, we tested whether this property holds under various modeling assumptions.<br />
<br />
<br />
The simplest model that we have considered is a phenomenological ODE model (Section 2.1). Being very simple, analytic analysis is possible and the stability of equilibria can be investigated under mild assumptions on parameters.<br />
However, a number of phenomena that might play an important role are neglected in the previous model. By assuming that cellular and molecular concentrations evolve continuously and that the solution is well-mixed, noise and space-related issues may have been overlooked. To test whether these phenomena may affect the qualitative behavior of the system (i.e. growth), we developed two models, one focusing on spatial aspects of Dap diffusion on cell differentiation (Section 2.2), the other incorporating dynamical aspects of cell spatial organization (Section 2.3). These results are rather general, in the sense that the level of abstraction of these models does not allow to distinguish between the two slightly different designs proposed in Section Blah[add link to corresponding section].<br />
<br />
<br />
In addition to feasibility, robustness and tunability of the system are also of prime interest. More precisely, we would like to find an objective criteria to discriminate between the two competing designs proposed in Section Blah[add link to corresponding section]. The two designs differ by the presence or absence of a negative regulation of cre recombinase expression by Dap. To address this problem, we developed two numerical ODE models and investigated their relative robustness (Section 3.1) and tunability (Section 3.2). Finally, it is also important to check that stochastic phenomena that are neglected in ODE models do not affect the macroscopic behavior. Stated differently we checked whether the deterministic models and their stochastic counterparts present globally the same behavior (Section 3.3).<br />
<br />
=[[Paris/Macroscopic_Models|Proof of principle: qualitative analysis of system's behavior]]=<br />
<br />
Those models are at macroscopic scale. They are focused on the evolution of the population, with global rules avoiding description of all the microscopic mechanisms. We present tree different works, with different approaches (ODE, automaton)...<br />
<br />
==[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]==<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space in this analysis and we follow only the variation of the different cell lines concentrations in the culture volume.<br />
<br />
==[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]]==<br />
<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br />
<br />
==[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth: cellular automaton in 3D]]==<br />
<br />
We try with this model to see the effect of DAP on the cells. We have a growing culture with germinal cells and somatic cells.<br />
We want to see if we can have different kinds of evolution for our cells.<br />
as we can see in the simple automaton the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.<br />
=[[Paris/Microscopic_Models|Assessing robustness and optimizing system's behavior: quantitative analysis]]=<br />
<br />
==Problem description==<br />
==[[Paris/Continuous modelb|Assessing robustness of two potential designs: numerical simulations of ODE models]]==<br />
==[[Paris/Continuous modelb|Assessing tunability of two potential designs: numerical simulations of ODE models]]== <br />
This model aims at describing the dynamic evolution of populations of germen and soma type bacteria.<br />
It is based on a set of differential equations describing DAP synthesis, DAP transport,<br />
differentiation of germen bacteria into soma and bacteria death. This approach differs form the precedents one by the level of description of the model<br />
and the numerical analysis done on the model.<br />
<br />
==[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]]==<br />
=Summary= <br />
The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.<br />
<br />
In part II, we showed that the system can present – at least qualitatively – the desired behaviour: an exponential growth of the two populations of coexisting cellular types.<br />
<br />
In part III, our results indicated that the system’s behavior should be reasonably robust, and provided arguments in favour of the design having a negative regulation of recombinase expression by Dap (increased robustness and tunability).<br />
<br />
In all cases, models incorporating additional details, related to space and/or stochasticity, indicated that these phenomena should not affect the global behavior of the system. So previous conclusions, obtained using deterministic models, should remain valid despite the fact that we neglected noise- and space-related issues. <br />
<br />
We would like to stress here that these results should be taken with great care, given the extreme simplicity of our models and the lack of data to provide information on parameter values and initial conditions. But still, globally…<br />
<br />
…all these results corroborate our initial design.<br />
=Appendix=<br />
<br />
==[[Paris/models_tools|Tools description]]==<br />
<br />
<br />
For our simulations we used unusual tools, Biocham and MGS. Thanks to their specificities and capacities, we were able to simulate ''easily'' the mechanisms that we wanted to focus on.<br />
<br />
===[[Paris/biocham|Biocham]]===<br />
<br />
<br />
===[[Paris/mgs|MGS]]===<br />
[[Image:MGS-inside.png|150px|right]]<br />
<br><br />
MGS is an experimental programming language developed at the university of Evry and dedicated to the modeling and the simulation of dynamical systems with a dynamical structure. We briefly present in this section the philosophy of MGS programming.<br />
<br><br><br><br><br />
<br />
==[[Paris/Sources| Models, Initial Conditions Files and Sources]]==</div>Vieirahttp://2007.igem.org/wiki/index.php/User:VieiraUser:Vieira2007-10-25T12:49:39Z<p>Vieira: </p>
<hr />
<div>Vieira Gilles<br>[[Image:Gvieira.jpg|right|160px]]<br />
24 years<br><br />
Student in 2dn year of Master degrees of bioinformatics & biostatistics at Paris XI University<br><br />
Center of interests:<br><br />
Metabolic Network Modelling, biotechnology & synthetic biology</div>Vieirahttp://2007.igem.org/wiki/index.php/File:Gvieira.jpgFile:Gvieira.jpg2007-10-25T12:48:21Z<p>Vieira: </p>
<hr />
<div></div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Project_DescriptionParis/Project Description2007-10-25T12:42:07Z<p>Vieira: </p>
<hr />
<div>{{Template:Paris_menu}}<br />
<br />
<br />
== <center>The SMB: Synthetic Multicellular Bacterium</center> == <br><br />
<br />
The aim of our project is to engineer the first synthetic multicellular bacterium, the SMB. This new organism is a new tool for the engineering of complex biological systems. It consists in two interdependent cell lines. The first one, dedicated to reproduction will be called the germ line (red cells). It is able to differentiate into the second line: the soma (green cells), which is sterile and dedicated to support the germ line. The germ line is auxotroph for DAP (diaminopimelate) which is provided by the soma. There is thus an interdependency relationship. The soma, being sterile, doesn't exist without the germ line to generate it, and the germ line needs the soma to complement its auxotrophy. We provide here experimental and computational evidences that this system can work, as well as the almost complete construction of the SMB.<br />
<br />
<br />
{{Paris_video_modeling2}}</div>Vieirahttp://2007.igem.org/wiki/index.php/ParisParis2007-10-25T12:36:07Z<p>Vieira: </p>
<hr />
<div>{{paris_video_modeling2}}<br />
<br />
<font size=16><center>The SMB: Synthetic Multicellular Bacterium</center></font> <br><br />
<br />
<br><br />
{{Paris_MainMenu}}<br />
<br><br />
<br />
The aim of our project is to engineer the first synthetic multicellular bacterium, the SMB. This new organism is a new tool for the engineering of complex biological systems. It consists in two interdependent cell lines. The first one, dedicated to reproduction will be called the germ line (red cells). It is able to differentiate into the second line: the soma (green cells), which is sterile and dedicated to support the germ line. The germ line is auxotroph for DAP (diaminopimelate) which is provided by the soma. There is thus an interdependency relationship. The soma, being sterile, doesn't exist without the germ line to generate it, and the germ line needs the soma to complement its auxotrophy. We provide here experimental and computational evidences that this system can work, as well as the almost complete construction of the SMB.<br />
<br />
<div align="center" ><br />
{| cellspacing="2px" cellpadding="5" border="2" style="padding: 0px; width: 780px; color: black; background-color: white;"<br />
|-valign="top"<br />
|width=189.25px style="padding: 10px; background-color: lightblue; border: 2px solid black;" |<br />
<br />
<center><h3>Members</h3><br />
<br />
'''Student Members'''<br />
<br />
[[User:Aurelien.rizk|Aurélien Rizk]]<br><br />
[[User:David.bikard|David Bikard]]<br><br />
[[User:Davidoff|David Guegan]]<br><br />
[[User:Davidpz|David Puyraimond]]<br><br />
[[User:Eismoustique|Eimad Shotar]]<br><br />
[[User:Vieira|Gilles Vieira]]<br><br />
[[User:Nicolas C.|Nicolas Chiaruttini]]<br><br />
[[User:Thomasclozel|Thomas Clozel]]<br><br />
[[User:Landrain|Thomas Landrain]]<br><br />
<br />
<br />
'''Instructors'''<br />
<br />
[[User:Ablindner|Ariel Lindner]]<br><br />
[[User:Alfonso|Alfonso Jaramillo]]<br><br />
[[User:Delapla|Franck Delaplace]]<br><br />
[[User:Kepes|Francois Kepes]]<br><br />
[[User:Vschachter|Vincent Schachter]]<br><br />
[[User:Bottani|Samuel Bottani]]<br><br />
<br />
'''Advisors'''<br />
<br />
[[User:Chettaoui|Chafika Chettaoui|]]<br><br />
[[User:Spicher|Antoine Spicher]]<br><br />
[[User:flefevre|Francois Le Fevre]]<br><br />
[[User:PTortosa|Pablo Tortosa]]<br><br />
[[User:maria|Maria Suarez]]<br><br />
[[User:SMIDTAS|Serge Smidtas]]<br><br />
<br />
</center><br />
<br />
|width=189.25px style="padding:10px; background-color: #ffffff; border: 2px solid black;" |<br />
<br />
<center><h3>Informations</h3></center><br />
<br><br><br />
'''[[Summary of the teachers|Summary of the teachers workshop]] '''<br />
<br><br><br />
<br />
'''Schedule'''<br />
* '''Next meeting : Wednesday october 24th'''<br />
Results, Conclusions, Wiki<br />
<br />
Wiki freezing: D-5 !!<br />
<br><br><br />
<br />
'''Links'''<br />
* [http://biosynthetique.free.fr/index.php5?title=Accueil Our French wiki (SB 2006/06 journal club)]<br />
* [http://partsregistry.org/Main_Page The registry]<br />
* [http://partsregistry.org/Help:Contents Biobricks and Registry Tutorials]<br />
* [http://en.wikipedia.org/wiki/Help:Wikitext_examples Wiki Formatting Guide]<br />
<br><br><br><br />
<center>[[Image:Tour eiffel.gif|60px]]</center><br />
|width=189.25px style="padding: 10px; background-color: #FF6666; border: 2px solid black;" |<br />
<br />
<center><h3>Project</h3></center><br />
<br />
<br />
* '''[[Paris/Project Description| Project Description]]'''<br />
<br />
<br />
'''Life in the Lab'''<br />
* [[Paris/Constructs| Molecular biology constructs]]<br />
<br />
* [[Paris/Notebook_Calendar| Team Notebook]]<br />
<br />
* [[Paris/Oligos| Oligos]]<br />
<br />
* [[Paris/PROTOCOLS| Protocols]]<br />
<br />
* [[Paris/Freezer| Freezer]]<br />
<br />
* [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2007&group=Paris Our parts at the registry]<br />
<br />
<br />
* [[Paris/DISCUSSION| Forum]]<br />
<br />
<br />
[[Paris/The team at work|The team at work]]<br />
<br />
|}<br />
<br />
<html><br />
From October 17th 2007:<br><br />
<a href="http://www3.clustrmaps.com/counter/maps.php?url=http://2007.igem.org/Paris" id="clustrMapsLink"><img src="http://www3.clustrmaps.com/counter/index2.php?url=http://2007.igem.org/Paris" style="border:0px;" alt="Locations of visitors to this page" title="Locations of visitors to this page" id="clustrMapsImg" onError="this.onError=null; this.src='http://www2.clustrmaps.com/images/clustrmaps-back-soon.jpg'; document.getElementById('clustrMapsLink').href='http://www2.clustrmaps.com'" /><br />
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border="0" alt="Web Counters"></a><br />
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<br />
<br />
We are extremely grateful to the following organisations for their support of our project:<br />
<br />
<table><tr><td><br />
<br />
</td><td><br />
[[Image:Paris_Sponsors.jpg]]<br />
</td><td><br />
Fondation Bettencourt<br />
<br />
[http://www.fondationbs.org/ www.fondationbs.org]<br />
<br />
<br />
Sofinnova<br />
<br />
[http://www.sofinnova.fr www.sofinnova.fr]<br />
<br />
<br />
Ambassade de France aux Etats Unis<br />
<br />
[http://www.ambafrance-us.org/ www.ambafrance-us.org]<br />
<br />
<br />
Synbiocomm<br />
<br />
[http://www.syntheticbiology.ethz.ch/synbiocomm/index www.syntheticbiology.ethz.ch]<br />
</td></tr></table></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modeling2Template:Paris video modeling22007-10-25T12:32:55Z<p>Vieira: </p>
<hr />
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</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:54:39Z<p>Vieira: </p>
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<noembed><br />
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<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://biosynthetique.free.fr/images/3/39/Mawarningb.gif&autostart=false&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://biosynthetique.free.fr/images/3/39/Mawarningb.gif&autostart=false&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:51:46Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://2007.igem.org/Image:ParisLogoIGEM.jpg&autostart=false&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://2007.igem.org/Image:ParisLogoIGEM.jpg&autostart=false&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:51:16Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://2007.igem.org/Image:ParisLogoIGEM.jpg&autostart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?image=http://2007.igem.org/Image:ParisLogoIGEM.jpg&autostart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:48:14Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autostart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autostart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:47:24Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autostart=true&image=http://2007.igem.org/Image:ParisLogoIGEM.jpg&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autostart=true&image=http://2007.igem.org/Image:ParisLogoIGEM.jpg&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:45:02Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autostart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autostart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:41:56Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:41:33Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autoStart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?autoStart=true&file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true" /><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/Template:Paris_video_modelingTemplate:Paris video modeling2007-10-25T08:39:06Z<p>Vieira: </p>
<hr />
<div><html><br />
<center><br />
<head><br />
<title>modeling</title><br />
</head><br />
<body><br />
<noembed><br />
<object style="width:640px;height:480px"><br />
<param name="movie" value="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?file=http://biosynthetique.free.fr/videos/finalv2.flv" /><br />
<param name="quality" value="high" /><br />
</object> <br />
</noembed><br />
<embed width="640" height="480" src="http://biosynthetique.free.fr/videos/flv_player/flvplayer.swf?file=http://biosynthetique.free.fr/videos/finalv2.flv" quality="high" type="application/x-shockwave-flash" allowfullscreen="true"/><br />
</body><br />
<br />
</center><br />
</html><br></div>Vieirahttp://2007.igem.org/wiki/index.php/ParisParis2007-10-25T08:32:06Z<p>Vieira: </p>
<hr />
<div><center><html><br />
<embed style="width:250px; height:200px;" id="VideoPlayback" type="application/x-shockwave-flash" src="http://video.google.com/googleplayer.swf?docid=2422231061053866723&hl=en" flashvars=""; > </embed></html><br />
[[Image:ParisLogoIGEM.jpg|400px]]<html><br />
<embed style="width:250px; height:200px;" id="VideoPlayback" type="application/x-shockwave-flash" src="http://video.google.com/googleplayer.swf?docid=2051019221671269340&hl=en=en =en" flashvars=""> </embed></html></center><br />
<br><br />
{{Paris_menu}}<br />
<br />
<br />
<div align="center" ><br />
{| cellspacing="2px" cellpadding="5" border="2" style="padding: 0px; width: 780px; color: black; background-color: white;"<br />
|-valign="top"<br />
|width=189.25px style="padding: 10px; background-color: lightblue; border: 2px solid black;" |<br />
<br />
<center><h3>Members</h3><br />
<br />
'''Student Members'''<br />
<br />
[[User:Aurelien.rizk|Aurélien Rizk]]<br><br />
[[User:David.bikard|David Bikard]]<br><br />
[[User:Davidoff|David Guegan]]<br><br />
[[User:Davidpz|David Puyraimond]]<br><br />
[[User:Eismoustique|Eimad Shotar]]<br><br />
[[User:Vieira|Gilles Vieira]]<br><br />
[[User:Nicolas C.|Nicolas Chiaruttini]]<br><br />
[[User:Thomasclozel|Thomas Clozel]]<br><br />
[[User:Landrain|Thomas Landrain]]<br><br />
<br />
<br />
'''Instructors'''<br />
<br />
[[User:Ablindner|Ariel Lindner]]<br><br />
[[User:Alfonso|Alfonso Jaramillo]]<br><br />
[[User:Delapla|Franck Delaplace]]<br><br />
[[User:Kepes|Francois Kepes]]<br><br />
[[User:Vschachter|Vincent Schachter]]<br><br />
[[User:Bottani|Samuel Bottani]]<br><br />
<br />
'''Advisors'''<br />
<br />
[[User:Chettaoui|Chafika Chettaoui|]]<br><br />
[[User:Spicher|Antoine Spicher]]<br><br />
[[User:flefevre|Francois Le Fevre]]<br><br />
[[User:PTortosa|Pablo Tortosa]]<br><br />
[[User:maria|Maria Suarez]]<br><br />
[[User:SMIDTAS|Serge Smidtas]]<br><br />
<br />
</center><br />
<br />
|width=189.25px style="padding:10px; background-color: #ffffff; border: 2px solid black;" |<br />
<br />
<center><h3>Informations</h3></center><br />
<br><br><br />
'''[[Summary of the teachers|Summary of the teachers workshop]] '''<br />
<br><br><br />
<br />
'''Schedule'''<br />
* '''Next meeting : Wednesday october 24th'''<br />
Results, Conclusions, Wiki<br />
<br />
Wiki freezing: D-5 !!<br />
<br><br><br />
<br />
'''Links'''<br />
* [http://biosynthetique.free.fr/index.php5?title=Accueil Our French wiki (SB 2006/06 journal club)]<br />
* [http://partsregistry.org/Main_Page The registry]<br />
* [http://partsregistry.org/Help:Contents Biobricks and Registry Tutorials]<br />
* [http://en.wikipedia.org/wiki/Help:Wikitext_examples Wiki Formatting Guide]<br />
<br><br><br><br />
<center>[[Image:Tour eiffel.gif|60px]]</center><br />
|width=189.25px style="padding: 10px; background-color: #FF6666; border: 2px solid black;" |<br />
<br />
<center><h3>Project</h3></center><br />
<br />
<br />
* '''[[Paris/Project Description| Project Description]]'''<br />
<br />
<br />
'''Life in the Lab'''<br />
* [[Paris/Constructs| Molecular biology constructs]]<br />
<br />
* [[Paris/Notebook_Calendar| Team Notebook]]<br />
<br />
* [[Paris/Oligos| Oligos]]<br />
<br />
* [[Paris/PROTOCOLS| Protocols]]<br />
<br />
* [[Paris/Freezer| Freezer]]<br />
<br />
* [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2007&group=Paris Our parts at the registry]<br />
<br />
<br />
* [[Paris/DISCUSSION| Forum]]<br />
<br />
<br />
[[Paris/The team at work|The team at work]]<br />
<br />
|}<br />
<br />
<html><br />
From October 17th 2007:<br><br />
<a href="http://www3.clustrmaps.com/counter/maps.php?url=http://2007.igem.org/Paris" id="clustrMapsLink"><img src="http://www3.clustrmaps.com/counter/index2.php?url=http://2007.igem.org/Paris" style="border:0px;" alt="Locations of visitors to this page" title="Locations of visitors to this page" id="clustrMapsImg" onError="this.onError=null; this.src='http://www2.clustrmaps.com/images/clustrmaps-back-soon.jpg'; document.getElementById('clustrMapsLink').href='http://www2.clustrmaps.com'" /><br />
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border="0" alt="Web Counters"></a><br />
<br><a href="http://www.easycounter.com/FreeCounter3.html">Hit Counters</a><br />
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<br />
<br />
We are extremely grateful to the following organisations for their support of our project:<br />
<br />
<table><tr><td><br />
<br />
</td><td><br />
[[Image:Paris_Sponsors.jpg]]<br />
</td><td><br />
Fondation Bettencourt<br />
<br />
[http://www.fondationbs.org/ www.fondationbs.org]<br />
<br />
<br />
Sofinnova<br />
<br />
[http://www.sofinnova.fr www.sofinnova.fr]<br />
<br />
<br />
Ambassade de France aux Etats Unis<br />
<br />
[http://www.ambafrance-us.org/ www.ambafrance-us.org]<br />
<br />
<br />
Synbiocomm<br />
<br />
[http://www.syntheticbiology.ethz.ch/synbiocomm/index www.syntheticbiology.ethz.ch]<br />
</td></tr></table></div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_auto_2Paris/Cell auto 22007-10-25T08:19:15Z<p>Vieira: /* Spatial simulation */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the effect on the cells, of the DAP diffusion in a free space where cells can divide or die.<br><br />
We have a growing culture with germinal cells and somatic cells.<br><br />
We want to see if we can have different kinds of evolution for our cells.<br><br />
as we can see in the [[Paris/Cell_auto|simple automaton]] the diffusion mechanism and the effect on differentiation can be describe more accurately, so for the moment we just ignore the diffusion putting a black box on it and just focused on the total number of DAP entities.<br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''evolving population''' ( death for BactS and division BactG).<br><br />
*Case 1 : The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
*Case 2 : The differentiation has a''' constant rate''', it will be the same rate for each division cycle<br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
We consider a global variable DAP (no internal/external DAP)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
All the cells grow<br />
<br />
=='''''We have 3 bags and 1 entity in our model'''''==<br />
*bag <br><br />
Bact it has a concentration internal of DAP and a radius. It's a cell in our automaton<br><br />
BactS is a Bact which produce DAP and can grow<br><br />
BactG is a Bact which consume DAP and can divide or differentiate <br><br />
*entity<br><br />
DAP Value of DAP<br><br><br><br />
<br />
='''Case 1'''=<br />
<br />
=='''''We produce this set of rules'''''==<br />
<br />
<br><br />
Mechanic forces<br><br />
* We create a spring between the center of each Bact, then we compute the forces related to this spring and we update the position of the cells (adding noise to it)<br><br />
For bactS<br><br />
*if random < Probability of death then<br />
BactS=null<br><br />
else <br />
if random < probability to grow & size < max cell size then <br />
BactS=BactS+{new size=size+delta} <br />
else <br />
nothing<br><br />
*Produce DAP<br />
<br><br />
For BactG<br><br />
*DAP'=DAP - self consumed DAP - diffused DAP<br />
*if enough DAP then<br />
if random< probability of differentiation then<br />
BactG=BactS<br />
else<br />
BactG= BactG+{DAP'}<br />
else<br />
if size > max size then<br />
if probability to divide > random & DAP'> minimal needed to divide then<br />
BactG = 2 BactG with minimal size <br />
else <br />
BactG= BactG +{DAP=DAP'}<br />
else<br />
if random < probability to grow then<br />
BactG = BactG + {new size= size + delta}<br />
else<br />
nothing<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
4 BactS and a BactG in the middle <br />
<br><br><br><br />
<br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can had noise for each of them.<br><br />
'''Mechanic'''<br><br />
*DT time step<br><br />
*K constant of the spring<br><br />
*Mu variation of position<br><br />
*R0_Gm minimal size of a BactG (after division)<br />
*R0_G maximal size of a BactG (before division)<br />
*R0_S maximal size of BactS <br />
<br><br />
'''In Bact'''<br><br />
*Diff diffusion constant<br><br />
<br><br />
'''In BactS:'''<br><br />
*Diffp probability of differentiation<br><br />
*DEPOT production of DAP<br><br />
*DeathSP probability of death <br><br />
*CroitS probability of growth <br><br />
<br><br />
'''In BactG:'''<br><br />
*CONS Dap consumed<br><br />
*DivG probability of division<br><br />
*CroitG probability of growth<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use imoview to generate those movies''<br />
<br><br><br />
The output is two videos showing the evolution of the organism<br><br />
<br />
<center><br />
<html><br />
<embed style="width:350px; height:300px;" id="VideoPlayback" type="application/x-shockwave-flash" src="http://video.google.com/googleplayer.swf?docid=2051019221671269340&hl=en" flashvars=""; > </embed><br />
<embed style="width:350px; height:300px;" id="VideoPlayback" type="application/x-shockwave-flash" src="http://video.google.com/googleplayer.swf?docid=2422231061053866723&hl=en=en =en" flashvars=""> </embed></html></center><br />
*The first video show a first comportment<br />
:Red : BactG<br />
:Green : BactS <br />
:dark<->light Bact : low<->high DAP<br />
:The number of bacteria (G or S) increase with the time <br />
*The second video show a second comportment<br />
:Red BactG<br />
:Green BactS<br />
:dark<->light Bact : low<->high DAP<br />
:The number of cells is constant and maintains itself <br />
<br />
After playing with the parameters we can isolate 4 kinds of comportment.<br><br />
2 of them are not really interested the system doesn't evolve or collapse (all the bacteria become S type).<br><br />
The other 2 comportment show that our system can lead to an evolving organism developing itself and colonizing the environment or it can stay stable like a tissue or an organ.<br />
<br />
='''Case 2'''=<br />
<br />
=='''''We produce this set of rules'''''==<br />
<br />
<br><br />
Mechanic forces<br><br />
* We create a spring between the center of each Bact, then we compute the forces related to this spring and we update the position of the cells (adding noise to it)<br><br />
For bactS<br><br />
*if random < Probability of death then<br />
BactS=null<br><br />
else <br />
if random < probability to grow & size < max cell size then <br />
BactS=BactS+{new size=size+delta} <br />
else <br />
nothing<br><br />
*Produce DAP<br />
<br><br />
For BactG<br><br />
*DAP'=DAP - self consumed DAP - diffused DAP<br />
*if random< probability of differentiation then<br />
BactG=BactS<br />
else<br />
if size > max size then<br />
if probability to divide > random & DAP'> minimal needed to divide then<br />
BactG = 2 BactG with minimal size <br />
else <br />
if random < probability to grow then<br />
BactG = BactG + {new size= size + delta}<br />
else<br />
nothing<br />
else<br />
BactG = BactG + {DAP=DAP'}<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
6 BactS and a BactG in the middle for the first result<br />
5 BactS and 2 BactG for the second result<br />
<br><br><br><br />
<br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can had noise for each of them.<br><br />
'''Mechanic'''<br><br />
*DT time step<br><br />
*K constant of the spring<br><br />
*Mu variation of position<br><br />
*R0_Gm minimal size of a BactG (after division)<br />
*R0_G maximal size of a BactG (before division)<br />
*R0_S maximal size of BactS <br />
<br><br />
'''In Bact'''<br><br />
*Diff diffusion constant<br><br />
<br><br />
'''In BactS:'''<br><br />
*Diffp probability of differentiation<br><br />
*DEPOT production of DAP<br><br />
*DeathSP probability of death <br><br />
*CroitS probability of growth <br><br />
<br><br />
'''In BactG:'''<br><br />
*CONS Dap consumed<br><br />
*DivG probability of division<br><br />
*CroitG probability of growth<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use imoview to generate those movies''<br />
<br><br><br />
The output is two videos showing the evolution of the organism<br><br />
<br />
<center><br />
<html><br />
<embed style="width:350px; height:300px;" id="VideoPlayback" type="application/x-shockwave-flash" src="http://video.google.com/googleplayer.swf?docid=-193608487106391911&hl=en" flashvars=""; > </embed><br />
<embed style="width:350px; height:300px;" id="VideoPlayback" type="application/x-shockwave-flash" src="http://video.google.com/googleplayer.swf?docid=4619339118096511087&hl=en" flashvars=""> </embed></html></center><br />
*The first video show a first comportment<br />
:Red : BactG<br />
:Green : BactS <br />
:dark<->light Bact : low<->high DAP<br />
:The number of bacteria (G or S) increase with the time <br />
*The second video show a second comportment<br />
:Red BactG<br />
:Green BactS<br />
:dark<->light Bact : low<->high DAP<br />
:The number of cells is constant and maintains itself <br />
<br />
After playing with the parameters we can isolate 4 kinds of comportment.<br><br />
2 of them are not really interested the system doesn't evolve or collapse (all the bacteria become S type).<br><br />
The other 2 comportment show that our system can lead to an evolving organism developing itself and colonizing the environment or it can stay stable like a tissue or an organ.<br />
<br />
=[[Paris/Sources#Cell auto 2|Sources]]=</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:16:04Z<p>Vieira: /* '''''Output''''' */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
'''Without DAP a cell can't do anything''', so it seems that DAP ''wake up'' bacteria but it's just an artifact.<br><br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
<br><br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br />
<br><br><br />
'''In reality this phenomenon''' does not exist, but this model show that the low concentration of DAP induces differentiation (cells become green)(dark blue),then with high concentration of DAP, the differentiation is inhibited. That why some cells stay in red <br><br />
We can also note that the population can be stabilized, and the level of DAP remains constant in these areas, the color of the cells doesn't change anymore and the concentration of DAP doesn't change too.<br />
<br><br><br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:15:40Z<p>Vieira: /* '''''Output''''' */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
'''Without DAP a cell can't do anything''', so it seems that DAP ''wake up'' bacteria but it's just an artifact.<br><br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
<br><br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br />
<br><br><br />
'''In reality this phenomenon''' does not exist, but this model show that the low concentration of DAP induces differentiation (cells become green)(dark blue),then with high concentration of DAP, the differentiation is inhibited. That why some cells stay in red <br><br />
We can also note that the population can be stabilized, and the level of DAP remains constant in these areas, the color of the cells don't change anymore and the concentration of DAP doesn't change too.<br />
<br><br><br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:13:40Z<p>Vieira: /* '''''Output''''' */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
'''Without DAP a cell can't do anything''', so it seems that DAP ''wake up'' bacteria but it's just an artifact.<br><br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
<br><br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br />
<br><br><br />
'''In reality this phenomenon''' does not exist, but this model show that the low concentration of DAP induces differentiation (dark blue) and with high concentration of DAP, the differentiation is inhibited. <br><br />
We can also note that the population can be stabilized, and the level of DAP remains constant in these areas.<br />
<br><br><br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:13:24Z<p>Vieira: /* '''''Output''''' */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
'''Without DAP a cell can't do anything''', so it seems that DAP ''wake up'' bacteria but it's just an artifact.<br><br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
<br><br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br><br />
<br><br><br />
'''In reality this phenomenon''' does not exist, but this model show that the low concentration of DAP induces differentiation (dark blue) and with high concentration of DAP, the differentiation is inhibited. <br><br />
We can also note that the population can be stabilized, and the level of DAP remains constant in these areas.<br />
<br><br><br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:04:49Z<p>Vieira: /* '''''We make some hypothesis:''''' */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
'''Without DAP a cell can't do anything''', so it seems that DAP ''wake up'' bacteria but it's just an artifact.<br><br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br><br />
<br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:04:20Z<p>Vieira: /* '''''We make some hypothesis:''''' */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
'''Without DAP a cell can't do anything.''', so it seems that DAP ''wake up'' bacteria but it's just an artifact<br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br><br />
<br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Cell_autoParis/Cell auto2007-10-25T08:02:09Z<p>Vieira: /* Spatial simulation */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br><br />
==Spatial simulation==<br />
We try with this work to characterize the diffusion of the DAP and the effect on the cells. We have a lawn of bacterias with germinal cells and some somatic cells, we also introduce a spatial localisation for the cells.<br><br />
<br />
=='''''We make some hypothesis:'''''==<br />
<br />
We work with a '''constant population''' (no death and no division), we can imagine that we are a stationary phase or between to division cycle.<br><br />
Without DAP a cell can't do anything.<br />
The differentiation is '''DAP dependent''', it's append when the cell as enough DAP to evolve but not enough to divide.<br><br />
The '''DAP is made in bacteria S''', the production rate is the difference between the total production and self consummation<br><br />
The DAP can be under two types intra/extra cellular (DAPi/DAPe)<br><br />
The '''DAP is consumed in bacteria G''' <br><br><br><br />
<br />
=='''''We have 3 bags and 2 entities in our model'''''==<br />
*bag<br><br />
Bact it has a concentration internal of DAP ('''DAPi''') and external ('''DAPe'''). It's a cell in our automaton<br><br />
BactS is a Bact which produce DAPi<br><br />
BactG is a Bact which consume DAPi <br><br />
*entity<br><br />
DAPi internal value of DAP<br><br />
DAPe external value of DAP<br />
<br><br><br><br />
=='''''We produce this set of rules'''''==<br />
<br><br />
For bactS<br><br />
*DAPe = DAPe + DAPe_diffused_in_neighborhood + DAPi_diffused_from_the_BactS<br><br />
*DAPi= DAPi +DAPi_produced - DAPi_diffused_from_the_BactS<br><br />
<br><br />
For BactG<br><br />
*DAPe=DAPe + DAPe_diffused_in_neighborhood - DAPi_diffused_from_the_BactG<br><br />
*DAPi= DAPi -DAPi_consummate + DAPi_diffused_from_the_BactG<br><br />
*BactG = if minimal DAPi for differentiation < DAPi < maximal DAPi for differentiation BactS else stay BactG<br />
<br><br><br><br />
<br />
=='''''Initial state'''''==<br />
<br><br />
We use a 30x30 cells automaton.<br />
All cells are BactG excepted 4 BactS which are placed randomly on the automaton<br />
<br><br><br><br />
=='''''Parameters'''''==<br />
<br><br />
We have 8 parameters and we can add noise for each of them.<br><br />
'''In BactS:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap production<br><br />
<br><br />
'''In BactG:'''<br><br />
*Dap export<br><br />
*Dap import<br><br />
*Dap consummation<br><br />
*Minimal Dap needed for differentiation<br><br />
*Maximal Dap needed for differentiation<br><br />
<br><br><br><br />
<br />
=='''''Output'''''==<br />
<br><br />
''We use gbview to generate those pictures''<br />
<br><br><br />
The output is two animated pictures one show the differentiation the other the diffusion of DAPe<br><br />
<center>[[Image:Paris\Diff_DAP.gif|Dap diffusion]][[Image:Paris\Diffe.gif|Bact differentiation]]</center><br><br />
*The first picture show the diffusion of DAP<br />
:We can see a front wave in light blue after that there is a dark blue area in which the systeme is stable the concentration doesn't evolve.<br />
*The second picture show the differentiation<br />
:Red BactG<br />
:Green BactS<br />
:The differentiation follow the wave front<br><br />
<br />
After playing with the parameters, we can deduct 2 important things:<br />
*The inhibition most be strong and effective (we play with the minimal and maximal value of DAP for differentiation)<br />
:if it isn't the case the system collapse all the bactG stay BactG if the inhibition is too strong or switch to BactS if the inhibition is not enough strong.<br />
*The production and diffusion of DAP will be a critical factor<br />
:The DAP has to be produce then he will be exported, it will diffuse in the medium and will be imported<br />
:There is no proof of a special system to import or export DAP, so for each step there is a large amount of DAP lost.<br />
<br />
=='''''[[Paris\Sources#Cell auto|Sources]]'''''==</div>Vieirahttp://2007.igem.org/wiki/index.php/Paris/Continuous_modelParis/Continuous model2007-10-25T07:50:26Z<p>Vieira: /* Derivation of the model */</p>
<hr />
<div>{{Template:Paris_menu_modeling}}<br />
<br><br />
<br />
=Well mixed population model =<br />
<br />
We present here a theoretical approach based on population dynamics. We consider here <br />
the case of a well mixed, homogeneous, culture of the SMB organism, i.e. there is no space <br />
in this analysis and we follow only the variation of the different cell lines concentrations <br />
in the culture volume. <br />
<br />
<br />
== Derivation of the model ==<br />
<br />
Let the variables ''g, s'' and ''d'' describe respectively the concentrations of germinal and somatic cells and the concentration of DAP, then we can write for our system :<br />
<br />
<br clear="all" /><br />
[[Image:eq1.jpg|right]]<br />
<br clear="all" /><br />
<br />
Equation (1a) describes the growth of the germinal cell population in presence of sufficient <br />
DAP (interaction represented by the Michaelis-Menten function) ; the term proportional <br />
to α2 is the differentiation into somatic cells by recombination of the CRE/LOX box, and <br />
the last term proportional to α3 is the germinal cells’ death. Equation (1b) is the variation <br />
of the somatic cells’ population, with the term proportional to α4 for somatic cells’ death. <br />
The last line describes DAP production by the somatic cells, and includes a degradation <br />
term. In absence of any quantitative details on assimilation of DAP by germinal cells and <br />
response to DAP levels, n and k are are to be considered as arbitrary phenomenological <br />
parameters. We take however in the following n = 1 neglecting potential saturation related non-linearities for high DAP concentrations. The value of k corresponds to the DAP <br />
concentration for half-maximal growth rate, and could set experimentally. <br />
We simplify the previous system by assuming that the evolution of d is rapid compared to <br />
the cellular growth, so that at this time scale we can take d' = 0 and write d = s α5/ <br />
α6 . This gives the two-variable system :<br />
<br />
<br clear="all" /><br />
[[Image:eq2.jpg|right]]<br />
<br clear="all" /><br />
<br />
Redefinition of parameters k → kα6 /α5 and α3 → α2 + α3 leads to the simpler writing :<br />
<br />
<br clear="all" /><br />
[[Image:eq3.jpg|right]]<br />
<br clear="all" /><br />
<br />
Let us do some rewriting : <br />
<br />
<br clear="all" /><br />
[[Image:eq4.jpg|right]]<br />
<br clear="all" /><br />
<br />
and by redefining the time and most of the parameters we get : <br />
<br />
<br clear="all" /><br />
[[Image:eq5.jpg|right]]<br />
<br clear="all" /><br />
<br />
The fixed points are (g = 0, s = 0) and the solution of :<br />
<br clear="all" /><br />
[[Image:eq6.jpg|right]]<br />
<br clear="all" /><br />
<br />
==Analysis of stability ==<br />
<br />
=== Fixed point at the origin ===<br />
<br />
Let us linearize the system (5a) close to the origin. For small perturbations <br />
around (g = 0, s = 0) (5a) is equivalent to : <br />
<br clear="all" /><br />
[[Image:eq7.jpg|right]]<br />
<br clear="all" /><br />
We look for a solution of the form [[Image:inline7.jpg]] , with [[Image:inline8.jpg]] an arbitrary vector. The values of λ are the eigenvalues of the matrix in (7) and can be obtain here straightforwardly by <br />
the characteristic polynomial : λ1 = −b, λ2 = −1, with respectively the eigenvectors [[Image:inline9.jpg]].<br />
<br />
The two eigenvalues are always negative : the origin is therefore <br />
always an attractive fixed point. For too weak initial concentrations of the two cellular <br />
types, the system is always going to die out.<br />
<br />
===Second fixed point, out of the origin ===<br />
Let (g0 := β s0 , s0 := k/(α−1) ) be the non trivial solution of (6a). We can simplify the (5a) by <br />
dividing the two equations respectively by g0 et s0 and by taking as new variables G := g/g0 <br />
and S := s/s0: <br />
<br clear="all" /><br />
[[Image:eq8.jpg|right]]<br />
<br clear="all" /><br />
<br />
and with μ := α−1 = α1/α2− 1 : <br />
<br clear="all" /><br />
[[Image:eq9.jpg|right]]<br />
<br clear="all" /><br />
<br />
The fixed point is now (G0=1,S0=1). We linearize system (9a) around this point and <br />
look for a solution close to it. Take x := G−G0 and y := S−S0 , close to (G0,S0) we can <br />
write by keeping only the first order term of (9a) : <br />
<br />
<br clear="all" /><br />
[[Image:eq10.jpg|right]]<br />
<br clear="all" /><br />
<br />
Looking for a solution of the form [[Image:inline7.jpg]], we need to find the eigenvalues of the matrix in <br />
(10). Solving the characteristic polynomial gives :<br />
<br />
<br clear="all" /><br />
[[Image:eq1112.jpg|right]]<br />
<br clear="all" /><br />
<br />
In order to determine the stability of the fixed point, let us examine the signs of the <br />
eigenvalues : λ1 is always negative, while λ2 is positive if μ/1+μ > 0. That is, by returning <br />
to the original parameters of (1) if α1 > α2 (more growth than recombination). In this <br />
case (which is expected) the fixed point (G0, S0) is unstable and the populations of the <br />
two cell lines diverge. <br />
<br />
==Conclusion==<br />
If we put together the results on the two fixed points we get the situation represented on <br />
the following diagram : <br />
<br />
<center>[[Image:diagram.jpg]]</center><br />
<br />
For a region around the origin and below some line passing through (G0, S0) any initial <br />
conditions converges to the origin. For higher values of the initial conditions we always <br />
expect exponential growth of the populations.</div>Vieira