Glasgow/Modeling

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= Summary =
Synthetic biology has been used to describe an approach to biology
which attempts to design and construct deliberate biological systems
that can be investigated experimentally, which are otherwise very
expensive and practically challenging. One of the central features
of synthetic biology is the appreciation of the knowledge from
science and engineering disciplines for the better design and
understanding of synthetic networks. Here we have engineered a
bacterial biosensor with the involvement of the construction of two
new reporter genes PhzM and PhzS to detect polluting
chemicals, which has the potential to provide an inexpensive and
easy-to-use method of detecting industrial pollution. We explored
a variety of computational approaches to study the behaviour of
three synthetic systems: simple reporter system, positive feedback
reporter system and '''[...]'''. We developed deterministic
and stochastic models that quantitatively describe the graded
signal-response property of the simple reporter system, and also
showed that models can be expanded and used to qualitatively predict
the ''in vivo'' behaviour of the complicated systems. The dynamics
is further studied via the application of qualitative modelling
methods. Simulations reveal that the model with positive feedback
loop has higher output level than that from the intact model '''[...]''' This work shows that by integrating engineering
techniques with scientific methodologies, we can gain a new insights
into the genetic regulation and should become the reference framework
for the design and construction of biochemical networks in synthetic
biology.

= Framework =
We have used a framework which unifies the qualitative,
stochastic and continuous worlds, as a basis for our overall approach to
modelling
and analysing the biochemical pathways.
Each perspective adds its
contribution to the understanding of the system, thus the three
approaches do not compete, but complement each other.  
Qualitative descriptions are abstractions over
stochastic or continuous descriptions, and the stochastic
and continuous models approximate each other.  
Note: this framework is based on 
(Gilbert et al 2007).

Our overall framework is illustrated in
Figure 1 that relates the three major ways of
modelling and analysing biochemical networks that we have used:
qualitative, stochastic and continuous.

The most abstract representation of a biochemical network is 
qualitative and is minimally described by its topology.  Initial descriptions
can be obtained from biochemists, and are often in some semiformal
representation.  These can easily be transformed into
a formal description at this stage which is usually
a bipartite directed graph with nodes representing biochemical
entities or reactions, or in Petri net terminology places
and transitions - see [https://2007.igem.org/Glasgow/Modeling#Petri_Net_Modelling Petri net section]'''.  
<center>[[Image: FrameworkSlide.png |frame| Figure 1. Conceptual modelling framework]]</center>
The qualitative description can be further enhanced by the abstract
representation of discrete quantities of species, achieved in Petri
nets by the use of tokens at places.  These can represent the number
of molecules, or the level of concentration, of a species.  A
particular arrangement of tokens over a network is called a 
marking.  The standard semantics for these qualitative Petri
nets (QPN) does not associate a time with transitions or the sojourn
of tokens at places, and thus these descriptions are time-free.
The qualitative analysis considers however all possible behaviour
of the system under any timing.  
The behaviour of such a net forms a discrete state
space. 

Timed information can be added to the qualitative description in
two ways -- stochastic and continuous.  
The continuous model replaces the discrete values of species with
continuous values, and hence is not able to describe the behaviour
of species at the level of individual molecules, but only the overall
behaviour via concentrations.  We can regard the discrete description
of concentration levels as abstracting over the continuous description
of concentrations.  Timed information is introduced by the association
of a particular deterministic rate information with each transition,
permitting the continuous model to be represented as a set of
ordinary differential equations (ODEs) - see [https://2007.igem.org/Glasgow/Modeling#Model_Evolution Model Evolution].  
The concentration of a
particular species in such a model will have the same value at each
point of time for repeated experiments.  The state space of such
models is continuous and linear. 
It is also possible to linearise ODE descriptions, by for example Laplace transforms, in an attempt to increase modularity in the system description and hence to facilitate model construction - see [[Glasgow/Modeling#BioBrick_library |BioBrick library]].  This approach results in transformations from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain.

The stochastic Petri net (SPN) description preserves the discrete state
description,
but in addition associates a particular stochastic rate information
with each reaction, permitting the stochastic model to be regarded as a 
Markov process with a discrete state space.
The time-evolution of such a process can be described by 
the Chemical Master Equation (CME), which is equivalent to Kolmorogov's forward equation
(Wilkinson 2006).
It is quite straightforward to simulate such a system, and this is usually
done with the standard discrete event simulation procedure known as "the
Gillespie algorithm" (Gillespie, 1977) - see  [[Glasgow/Modeling#Stochastic_Modelling |Stochastic Modelling]].
The QPN is an abstraction of
the SPN, sharing the same state space and transition relation with
the stochastic model, with the probabilistic information removed.
All qualitative properties valid in the QPN are also valid in the
SPN, and vice versa.


In summary, the qualitative
time-free description is the most basic,  with discrete values
representing numbers of molecules or levels of concentrations.
The qualitative description abstracts over two timed, quantitative models.
In the stochastic description, discrete values for the amounts of species
are retained, but a stochastic rate is associated with each reaction.  The continuous model describes amounts of species using continuous values
and associates a deterministic rate with each reaction.
These two time-dependent models can be mutually approximated by hazard
functions belonging to the stochastic world.

'''References'''

D. Gilbert, M. Heiner and S. Lehrack (2007). [[Media:Edinburgh_proceedings.pdf | "A Unifying
Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets"]]. In
proceedings Computational Methods in Systems Biology CMSB 2007 (Computational Methods in Systems Biology),
Springer-Verlag LNCS/LNBI Volume 4695, pp. 200-216.

D.T. Gillespie (1977). Exact stochastic simulation of coupled chemical reactions.  Journal of Physical Chemistry, 1977.  81:25 pp 2340-2361

D.J. Wilkinson (2006).  Stochastic modelling for systems biology.  Chapman & Hall / CRC.

= Model design and analysis: outline=

[[Image: Glasgow_design_small.png|frame|Figure 2. Design of our system. The intermediate compound is 5-
methylphenazine-1-carboxylic acid betaine.]]
The biochemists constructed an initial diagram to describe the system, using a fairly informal graphical syntax.  This used a generic form of the transcription factor ('tf' for the gene, and 'TF' for the protein product) which represented both XylR (BTEX detecting) and DntR (Salicylate detecting).  In outline, the steps that we used to develop and refine our model were:

# Simplification by abstracting away the mRNA, thus combining transcription and translation.  
# Combining the PhzM and PhzS components to give one step from PCA to PYO
# We also developed a variant of the model with a positive feedback loop 



The descriptions (with and without the positive feedback loop) were then transformed into Qualitative Petri Nets (QPN) - see [https://2007.igem.org/Glasgow/Modeling#Petri_Net_Modelling Petri net section].
We derived the [https://2007.igem.org/Glasgow/Modeling#Parameter_searching_and_refinement  rate parameters], and wrote down descriptions and simulated the models in 
[https://2007.igem.org/Glasgow/Modeling#Model_design:_detailed Ordinary Differential Equations], as well as in [https://2007.igem.org/Glasgow/Modeling#Petri_Net_Modelling Continuous Petri Nets] (CPN).  We performed 
model analysis to refine the rate parameters using [https://2007.igem.org/Glasgow/Modeling#Minicap_Sensitivity_Analysis_Program_Package our implementation of the the MPSA algorithm] and [https://2007.igem.org/Glasgow/Modeling#Comparative_Model_Analysis model comparison].  
Simulation of the continuous model was performed in MatLab and [http://www.bionessie.org BioNessie].
Finally we constructed and simulated 
[https://2007.igem.org/Glasgow/Modeling#Stochastic_Modelling stochastic models] in MatLab and 
[https://2007.igem.org/Glasgow/Modeling#Stochastic_Modelling_vs._ODE_Modelling  compared the results] of from the continuous (ODE-based) and stochastic approaches.

A more detailed description of the model design process is as follows:

= Model design: detailed=
[[Image: Glasgow_simple_small.png|frame|Figure 3. The simple model]]
The basic design of our system is shown in Figure 2. The sensing protein TF is produced constitutively. TF stands for one of the sensing proteins that were used in the implemented system - DntR or XylR. TF that is always present in the system binds the signal (pollutant) compound. The TF|S complex promotes expression of the PhzM and PhzS protein coding regions. These proteins catalyse transformation of PCA compound that is available in the system into pyocyanin (PYO).

Two slightly different designs of our system were investigated in the course of the project. The latter is a modification that includes a positive feedback loop in order to enhance system's response to the signal.

In our modelling effort we have simplified the representation of our design to ease modelling. Firstly, we have omitted the intermediate mRNA production
and represented gene expression in one step instead. The resulting
model contains less parameters, thus is easier to analyse. Also, there are less
parameters that need to be found or estimate. In fact, gene expression rate
is often measured disregarding mRNA production.

Production of MPCAB (our working name for 5-methylphenazine-1-carboxylic
acid betaine - the intermediate compound) has been dropped as well. A study
which aimed to characterise this part of the pathway [5] revealed that it is
very hard to characterise the PCA -> MPCAB and MPCAB -> PYO
reactions separately. This is probably due to instability of MPCAB. The
composite reaction PCA -> PYO was characterised instead. Therefore, the
MPCAB has been completely removed from the model and the PhzM and
PhzS proteins have been joined together into PhzMS.

The basic model is shown on the Figure 3. The equations we have developed for it are shown below.

[[Image: Equations1_wiki.png|center]]

[[Image: Glasgow_feedback_small.png|frame| Figure 4. Model with positive feedback]]

The positive feedback model (Figure 4) includes additional coding region for TF protein placed after PhzMS coding. Once the pollutant is present and expression of reporter proteins is started also more TF is produced. Our assumption was that increased concentration of TF will cause more pollutant molecules to be bound into TF|S complex and, in turn, expression at the TF|S promoter would be enhanced further. The equations we have developed for the positive feedback loop model are as follows.

[[Image: Equations2_wiki.png|center]]

[[Image: Glasgow_comparison_plot.png|frame| Figure 5. Comparison of responses of the simple model and feedback loop model (bold line). Pyocyanin curve is light blue, PhzMS curve is red.]]

To see the full PDF report [[https://static.igem.org/mediawiki/2007/a/ad/Glasgow_modelling.pdf click here]].

= Petri Net Modelling =
[[Image: Glasgow_petri.png|400px|right]]
[http://en.wikipedia.org/wiki/Petri_nets Petri nets] are used to describe discrete distributed systems that 
have concurrent processes, and provide users with an intuitive
and easy-to-understand graphical representation of systems. During
the iGEM project, we explored the use of Petri nets for the construction 
and analysis of synthetic biological networks, with a focus on facilitating the  experimental design. We started off
with the construction of ''qualitative'' petri-net models using the [http://www-dssz.informatik.tu-cottbus.de/index.html?/software/snoopy.html Snoopy] tool.
A major advantage of the Qualitative Petri net (QPN) approach is that it enables us to perform network
analysis in the absence of prior knowledge of the system parameters.
We achieved this using the Charlie tool (available from [http://www-dssz.informatik.tu-cottbus.de/index.html?/software/tutorial_biopn.html Monika Heiner], where we identified the
subsets of the Petri net models covered by certain properties with
T-invariants (cyclic behaviour) and P-invariants (constant output
in amount). We also studied various suggestions for the system's
possible structures using the ''token game'' with different initial markings. Based on the observation
of possible flows and discussions with biochemists, we examined and
validated the models in terms of the boundedness, for example.
Although Petri Nets were initially designed for qualitative analysis
they have been extended to permit other forms of analysis including
the quantitative form which is known as a Continuous Petri Net (CPN) which has an ODE-based semantics (see [https://2007.igem.org/Glasgow/Modeling#Framework framework]). We
investigated the dynamics of the systems quantitatively using
the parameters retrieved from the literature (for details, please
refer to the section on Parameter Searching), and simulated the behaviour using [http://www-dssz.informatik.tu-cottbus.de/index.html?/software/snoopy.html Snoopy] which can handle continuous Petri nets and has
inbuilt ODE solvers.
These results were consistent with those
generated by the pure [https://2007.igem.org/Glasgow/Modeling#Model_Evolution ODE approach].

See the full [http://compbio.dcs.gla.ac.uk/iGEM2007/petrinet_report.pdf Petri net report].

= Parameter searching and refinement =


Parameter searching using Google Scholar, PubMed and biomedical databases 
was carried out by Christine and Xu under the direction of Dr David Leader. The
task was largely steered by the discussions with, and the suggestions
given by Emma Travis.  We applied the [https://2007.igem.org/Glasgow/Modeling#Minicap_Sensitivity_Analysis_Program_Package Minicap program], and [https://2007.igem.org/Glasgow/Modeling#Comparative_Model_Analysis model comparison], both developed as part of the project, in order to help us identify sensible ranges associated with the parameters.   A
complete table containing either exact or constrained values for
each of the system parameters was produced, as shown in the [Parameters.png parameter
table], where parameters are annotated with their type,
values and supporting data sources.

[[Image: Glasgow_Constants.png|center]]


== Minicap Sensitivity Analysis Program Package ==
The Multi-Parametric and Initial Concentration Sensitivity analysis package is a Matlab function which executes a chosen Dynamic or Stochastic ''System Function'' for a defined number of different variable values across any desired range. The ''subject'' of analysis can either be constants in the user's system eg. parameters in a biological system (MPSA) or initial values of the variables in the user's system eg. initial substrate concentrations (ISCSA). The program will output a plot for each variable showing a comparison of ''acceptable'' and ''unacceptable'' samples across the subject's range with 3 calculated quantitative comparison figures: the ''Correlation Coefficient'', the ''Area'' between acceptable and unacceptable curves, and the ''Standard Deviation of the gradient'' of the acceptable plot. The comparative and intrinsic sensitivity of each chosen subject is thus highlighted. A plot showing the trend of the ''Substrate of Interest'' over time is also displayed. 

As well as this report, the Minicap package contains a User Manual in html, a number of example codes and all the novel (i.e. not ode15s) function and text files required to run Minicap.

Downloads:

The MatLab code is available as [http://compbio.dcs.gla.ac.uk/iGEM2007/Minicap_Sensitivity_Analysis_Program_Package.zip server (Minicap)]. 
To see the full PDF report on Minicap [[https://static.igem.org/mediawiki/2007/f/fb/Minicap.pdf  click here]].

== Comparative Model Analysis ==
[[Image: Glasgow_Comparison.png|400px|right]]
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= Stochastic Modelling =
[[Image:1_cell_titled.png|400px|right]] 
[[Image:Rangegamma_10cells.png|400px|right]] 

A stochastic model for a general biosensor was constructed by students and simulated using Gillespie algorithm in MATLAB. Modelling biological systems in terms of ordinary differential equations is often not enough as cells are intrinsically noisy due to low numbers of molecules that participate in reactions. This can lead to significant statistical fluctuations in reaction rates and, the systems behaviour can differ from that predicted by a deterministic model.  In this case, the system of interest was a single cell or bacteria of a bacterial whole cell biosensor.

In this study the concept of stochastic simulation was introduced using a computational approach called Gillespie algorithm. The Gillespie algorithm allows a discrete and stochastic simulation with few reactants because every reaction is individually simulated. It takes into account a number of parameters that contribute to the model in a random manner, rather than assuming everything can be predicted.
The goal of this study was to construct a stochastic model based on a deterministic one and to investigate the amount of noise (measured by the Fano factor and the coefficient of variation). Simulations were performed for several of cells and repeated for many runs to find representative behaviour. Noise was expected to decrease as the number of cells increased. However, in this study it was found that the coefficient of variation stayed roughly the same as the number of cells increased.

We also aimed to study whether generic features predicted by other modelling approaches can be repeated by stochastic simulations. The effects of leakiness of the promoter was also observed in the system. Leakiness had a detrimental effect on the reliability of the system.  It provides a higher output of the protein which in turn gives a false indication of the level of signal being detected. 
[[Media:GlasgowStochasticModelling.pdf|Full report on stochastic modelling]]

= Stochastic Modelling vs. ODE Modelling = 

~~ the four pictures here ~~

= BioBrick library  =
[[Image:BioBricks.JPG|right|400px]]

BioBrickLibrary is an add on Library to Simulink for modelling dynamical biological systems at Brick (Gene) level. Simulink is a program dedicated for dynamical system simulation, however in depth knowledge of dynamics is needed if one is to simulate system mentioned above. The BioBrick library has all the blocks as well as GUI (Graphical User Interface) needed to do the job without understanding how Simulink works. It uses drag and drop system and shares all constants in Matlab’s .m file, so it is easy to store and update them.

BioBrick library’s main aim is to tell whether and how different topology will influence the output of the system. If actual rate constants are known it can be used instead or as complimentary to ODE modelling. However it must be noted that ODE rate constants ARE NOT TRANSFERABLE to BioBrick library. 

Downloads:

The software is available as [http://compbio.dcs.gla.ac.uk/iGEM2007/BioBricklibrary.zip BioBrickLibrary.zip].
More information about the package can be found in [[Media:ElectrEcoBluSimulinkManual.pdf|ElectrEcoBluSimulinkManual]] document.
See full [[Media:Report.pdf|Technical Report (''BioBrick Type Modeling'')]] for concept evolution and justification.

= Microbial Fuel Cell Evaluation =
[[Image:MFC.jpg|right|150px]]
During the course of the project some introductory work has been done with microbial fuel cells in order to prepare us for the envisaged final stage of the project. We have had three fuel cells at our disposition supplied by the UK's NCBE. The experience we have gained and some of the results have been aggregated in this short work. 

= Download Models and Software =

== Model files ==

'''Qualitative''':

Qualitative Petri net : [http://compbio.dcs.gla.ac.uk/iGEM2007/QPN_simple.spped Simple model] and
[http://compbio.dcs.gla.ac.uk/iGEM2007/QPN_feedback.spped Feedback version].

'''Continuous''': 

Continuous Petri net : [http://compbio.dcs.gla.ac.uk/iGEM2007/CPN_simple.spcontped Simple model] and
[http://compbio.dcs.gla.ac.uk/iGEM2007/CPN_feedback.spcontped Feedback version].

SBML : [http://compbio.dcs.gla.ac.uk/iGEM2007/iGEM_SimpleReporter.xml Simple model] and [http://compbio.dcs.gla.ac.uk/iGEM2007/iGEM_PositiveFeedbackReporter.xml Feedback version].

Matlab : [http://compbio.dcs.gla.ac.uk/iGEM2007/ODE_Basic.zip Simple model] and [http://compbio.dcs.gla.ac.uk/iGEM2007/ODE_Feedback Feedback version].

'''Stochastic''': 

Matlab: [http://compbio.dcs.gla.ac.uk/iGEM2007/stochastic_code.zip stochastic code library]

== Software ==

Minicap program: [http://compbio.dcs.gla.ac.uk/iGEM2007/Minicap_Sensitivity_Analysis_Program_Package.zip matLab code], and  [https://static.igem.org/mediawiki/2007/f/fb/Minicap.pdf  report].

BioBribrick library: [http://compbio.dcs.gla.ac.uk/iGEM2007/BioBricklibrary.zip software], 
[[Media:ElectrEcoBluSimulinkManual.pdf|ElectrEcoBluSimulinkManual]], and 
[[Media:Report.pdf|Technical Report (''BioBrick Type Modeling'')]].

BioNessie: [http://www.bionessie.org package] (a biochemical network editor, simulator and analyser for SBML descriptions, developed at the Bioinformatics Research Centre Glasgow, outwith the iGEM project).

Snoopy: [http://www-dssz.informatik.tu-cottbus.de/index.html?/software/snoopy.html package] (A Petri net tool, developed at the Brandenburg university of technology Cottbus, outwith the iGEM project).

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