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-	MODELIZATION OF THE SYNTHETIC ORGANISM	+	{{Template:Paris_menu_modeling}}
		+	<br><br>
-	[[Paris_Modeling_fr|French Page]]	+	=Introduction=
-	What do we want to do ?	+	=== Motivation for Modeling ===
-	The goal is to model the cellular growth, and to prove it is possible, to find the range of paramaters that enables it, and then to optimise the triglycerid production.	+
-	Is it Possible for a cell producing the Amino Acide, to feed at the same time the mother cell, and the triglyciride factory one?  For this, we need to find the good theoritical balance between the different elements of the population. This balance is determined by the firing rate of the cre/lox system, which is genetically engineered	+
-	=Why a modelization ? =	+	We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:
-	==Minimise the biological steps==	+	* so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,
-	Make the system work by finding the possible parameters, and save time when doing wetwork, in order to directly make make the construct the most likely to work. ( For instance, immediately use the good promoters or RBS)	+	* 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.
-	Some might say the system is "simple enough" to build, so that it can be hand crafted. It might work so. But if we don't try to model a simple system, and try to make it stick as much as possible to reality, how can we ever hope to do it for a more complex one?	+
-	==Biosynthetic spirit IGEM==	+
-	If you listen to[https://2007.igem.org/Podcasts Endy],biosynthetic is not making a biological construct. It's HOW you make it, it's the process you use to build it. It's giving the possibility to first virtually create the system before carrying it out: by assembling the biobricks as judiciously as possible, by exactly knowing the link between input and ouput. It has to be reflected in the construction process.	+
		+	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''.
-	==Rythme and organise the biological constructs==	+	=== Questions of Interest ===
		+
		+	The first, most obvious question deals with proving the ''feasibility'' of our system ( [[Paris/Modeling#Proof_of_Principle:_Qualitative_Analysis_of_System.27s_Behavior| Section 2]]). In our case, this amounts to check that the system presents a very simple, qualitative behavior: ''the two cell populations grow''!
		+	Accordingly, we tested whether this property holds under various modeling assumptions.
-	We need to [http://openwetware.org/wiki/Parts_characterization/Characterization_approaches caracterise] the biobricks we're about to use, BEFORE assembling them, so that we can feed the model with parameter values. The We use the model to construct, and see if it fits or not the model, and try to understand why. (It's a new way of research in biology : instead of tearing complicated system a part, you try to first build simple ones, and by observing the difference with theory, a new explanation will sharpen the model
-	=Model WHAT ?=	+	The simplest model that we have considered is a phenomenological ODE model (
-	==Macroscopic Modelization ==	+	[[Paris/Modeling#Exponential_growth_of_cellular_populations:_analytic_analysis_of_an_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.
-	By macroscopique, I mean the modelization at cellular cultur level, with parameter that you can measure outside the cell.	+	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 ([[Paris/Modeling#Potential_macroscopic_effect_of_spatial_aspects_of_Dap_diffusion:_cellular_automaton_on_a_grid| Section 2.2]]), the other incorporating dynamical aspects of cell spatial organization ([[Paris/Modeling#Potential_macroscopic_effect_of_stochastic_and_spatial_aspects_of_Dap_diffusion_and_cell_growth|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]]:
-	We need to get the parameter input and output values of the different elements of the system, introduce them in the model, get the desired cre lox transformation rate, and modifie the cre promoteur, or it's RBS by using caracterised biobricks.	+
-	Parameters to look for in the litterature then to [http://openwetware.org/wiki/Parts_characterization/Measurement_techniques measure] in vitro by ourself :	+	*A SMB with a fixed recombination rate
		+	*A SMB with a recombination rate depending on DAP starvation (feedback)
-	*[AAaborbtion Absorbtion of the vital AA by a cell]	+	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 and tunability ( [[Paris/Modeling#Assessing_robustness_and_tunability_of_two_potential_designs:_numerical_simulations_of_ODE_models|Section 3.1]]). 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 ([[Paris/Modeling#Potential_macroscopic_effect_of_stochastic_phenomena:_stochastic_simulations_with_Gillespie_algorithm|Section 3.2]]).
-	*Production of the vital AA by a cell	+
-	*Diffusion zone of the AA	+
-	*Lethal width of a cell without FTSZ ( for a AA producing cell) (how do you measure it? cell cycle? 4 OR 5 says Ariel. Same cycle speed as for a normal cell (without FTSZ)?	+
-	*Lethal width of a cell without FTSZ ( for a triglyceride producing cell)?	+
-	*Cre lox recombination rate	+
-	Always try to use a reference promoteur or RBS for the caracterisation	+	=Proof of Principle: Qualitative Analysis of System's Behavior=
-	==Microscopique or Genetic Modelization ==	+	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.
-	It's the modelisation of what happens IN the cell : of the genetic network, with the quantity of the different proteins as parameter	+
-	How can we measure the moduls'efficiency? Thanks to [http://parts2.mit.edu/r/parts/htdocs/AbstractionHierarchy/ Pops] and Rips (Ribosome per seconde). We need  reference unity measures. For the [http://partsregistry.org/partsdb/pgroup.cgi?pgroup=RBS Ribosome binding site], we should always compare the RBS used to [http://partsregistry.org/Part:BBa_B0034 this one]. Is it also possible to have a reference promotor?	+	===[[Paris/Continuous_model|Exponential growth of cellular populations: analytic analysis of an ODE model]]===
		+
		+	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.
		+
		+	===[[Paris/Cell_auto|Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid]] [[Image:MGS-inside.png|50px]]===
		+
		+	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.
		+
		+	===[[Paris/Cell_auto_2|Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth]] [[Image:MGS-inside.png|50px]]===
		+
		+	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.
		+
		+	=Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis=
		+
		+	In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.
		+
		+	===[[Paris/Robustness and optimization|Assessing robustness and tunability of two potential designs: numerical simulations of ODE models]]===
		+	In section [https://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.
		+
		+	===[[Paris/Stochastic model|Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm]] [[Image:MGS-inside.png|50px]]===
		+
		+	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.
		+
		+	=Summary=
		+
		+
		+	The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.
		+
		+	In part [[Paris/Modeling#Proof_of_Principle:_Qualitative_Analysis_of_System.27s_Behavior|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.
		+
		+	In part [[Paris/Modeling#Assessing_Robustness_and_Optimizing_System.27s_Behavior:_Quantitative_Analysis|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).
		+
		+	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. This result is not surprising. Intuitively, even if SMB system is heterogeneous (because it is composed of two distinct populations of cells), the spatial distributions of both cells types are uniform; thus, the system evolution is space independent. Nevertheless, we were interested in checking the property using models and simulations. In fact this led us to use and develop original techniques (like [[Paris/Cell_auto_2|Delaunay triangulation]] or [[Paris/Stochastic_model|extended to nested membranes systems Gillespie algorithm]]). From a general point of view, developing such techniques is also of great interest for synthetic biology. Following the concepts of decoupling and abstraction that characterize biosynthetic developments, we have to ideally validate and study designs before constructing them physically. These validations appear at each step of a standard development, at the levels of systems, devices and bricks designing. We tried to follow and contribute to this methodology by considering at first phenomenological and global models, and molecules scaled models at last.
		+
		+	Getting back to SMB, 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...
		+
		+	:'''...all these results corroborate our initial design'''.
		+
		+	=Appendix=
		+
		+	===Tools Description===
		+
		+
		+	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.
		+
		+	====[[Paris/biocham|Biocham]]====
		+	[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.
		+
		+	====[[Paris/mgs|MGS]]====
		+	[[Image:MGS-inside.png|150px|right]]
		+	<br>
		+	[http://mgs.ibisc.univ-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>
		+
		+	===[[Paris/Sources|Sources of MGS and Biocham programs]] [[Image:MGS-inside.png|50px]]===

---

Latest revision as of 10:05, 27 May 2008

Contents 1 Introduction 1.1 Motivation for Modeling 1.2 Questions of Interest 2 Proof of Principle: Qualitative Analysis of System's Behavior 2.1 Exponential growth of cellular populations: analytic analysis of an ODE model 2.2 Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid 2.3 Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth 3 Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis 3.1 Assessing robustness and tunability of two potential designs: numerical simulations of ODE models 3.2 Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm 4 Summary 5 Appendix 5.1 Tools Description 5.1.1 Biocham 5.1.2 MGS 5.2 Sources of MGS and Biocham programs

Introduction

Motivation for Modeling

We want to construct a multicellular bacterial organism made of two co-existing cell types. Brainstorming resulted in proposing the following system:

• so-called soma cells, that produce a metabolite (DAP), and will not be able to divide,
• 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.

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.

Questions of Interest

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! Accordingly, we tested whether this property holds under various modeling assumptions.

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. 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 DESIGN PROCESS:

• A SMB with a fixed recombination rate
• A SMB with a recombination rate depending on DAP starvation (feedback)

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 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 and tunability ( Section 3.1). 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 3.2).

Proof of Principle: Qualitative Analysis of System's Behavior

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.

Exponential growth of cellular populations: analytic analysis of an ODE model

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.

Potential macroscopic effect of spatial aspects of Dap diffusion: cellular automaton on a grid

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.

Potential macroscopic effect of stochastic and spatial aspects of Dap diffusion and cell growth

In this section, we aim at considering SMB as a 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.

Assessing Robustness and Optimizing System's Behavior: Quantitative Analysis

In this section, we focus on more quantitative properties of system's behavior: robustness and optimization capabilities. Two slightly different designs are compared.

Assessing robustness and tunability of two potential designs: numerical simulations of ODE models

In section 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.

Potential macroscopic effect of stochastic phenomena: stochastic simulations with Gillespie algorithm

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.

Summary

The goal of our modeling work was to test our design, mainly to identify potential flaws of the system at early developmental stages.

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.

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).

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. This result is not surprising. Intuitively, even if SMB system is heterogeneous (because it is composed of two distinct populations of cells), the spatial distributions of both cells types are uniform; thus, the system evolution is space independent. Nevertheless, we were interested in checking the property using models and simulations. In fact this led us to use and develop original techniques (like Delaunay triangulation or extended to nested membranes systems Gillespie algorithm). From a general point of view, developing such techniques is also of great interest for synthetic biology. Following the concepts of decoupling and abstraction that characterize biosynthetic developments, we have to ideally validate and study designs before constructing them physically. These validations appear at each step of a standard development, at the levels of systems, devices and bricks designing. We tried to follow and contribute to this methodology by considering at first phenomenological and global models, and molecules scaled models at last.

Getting back to SMB, 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...

...all these results corroborate our initial design.

Appendix

Tools Description

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.

Biocham

[http://contraintes.inria.fr/BIOCHAM/ BIOCHAM] is a programming environment for modeling biochemical systems, making simulations and querying the model in temporal logic.

MGS

[http://mgs.ibisc.univ-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.

Sources of MGS and Biocham programs