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Team:BCCS-Bristol/BSim/Case studies/Repressilators
From 2009.igem.org
iGEM 2009
Repressilators coupled by quorum sensing - an agent based approach
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Contents |
Background
The emergence of new GRNs such as the repressilator [1], which may be affected by factors on the population rather than the individual level, has sparked a new interest in modelling GRNs across a bacterial population. Synthetic clocks such as the repressilator may help to provide us with a deeper understanding of oscillatory behaviour in natural systems. Theoretical modelling of such systems across a population is an important step towards better understanding of natural oscillators such as the circadian clock.
What is a repressilator?
A repressilator is a synthetic gene regulatory network, which is generally constructed from three different genes which mutually repress each other in sequence [REFREFREF!]. This can result in self-sustained oscillations occurring in the network.
IMAGE/DIAG-FIG1
The single repressilator GRN can be simply extended as shown in figure XXX (below) to include an autoinducer component. This would theoretically allow repressilators in individual bacteria to communicate with one another via an external chemical field.
IMAGE/DIAG-FIG2
A mathematical description of the repressilator
- GO/strogatz paper
- simplifications present within
Previous work
- well mixed approach
- the strogatz paper
Why we used BSim
Recent mathematical modelling approaches in systems biology tend to model a gene regulatory network in a single cell, and agent based models are considered in a separate context. However, some GRNs such as the repressilator can be coupled across a population of bacteria. In the case of the repressilator the GRNs are coupled by an autoinducer chemical which is free to diffuse in and out of the cell. Previous approaches to modelling this problem (see for example [2]) have all assumed that the chemical is well-mixed across the population. In reality external chemical concentrations will vary across a large space, therefore it is important to consider the effects of a nonuniform chemical field on network dynamics.
In [2] it was shown that communication between cells via quorum sensing can result in population level synchronisation given a large enough cellular density. By bringing together an agent based approach with the standard ordinary differential equation methods used for modelling GRNs we hope to be able to extensively study spatial factors affecting the behaviour of the repressilator in a population.
BSim coupled repressilators
- Strogatz paper
- chemical field (fully spatial/diffusing/decay etc)
Overview
- summarise what we did
- oscillating chemical field
- Images thereof
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Results
The video shows 200 bacteria swimming in a 100x100x100 micron volume. Each bacterium has a system of ODE's inside which model the essential dynamics of a repressilator. In this case, the individual repressilators are coupled via a diffusing autoinducer signal (in this case AHL). The colour of a bacterium represents the level of lacI mRNA in that bacterium (the lacI gene is one of the genes present in the repressilator); the bacterium will change from yellow to red as the internal level of lacI mRNA increases. In the example shown here, all 200 of the individual repressilators are initialised with random conditions, but quickly synchronise due to the effect of the AHL communication.
Frequency
- plots
- as we increase the parameter X the F_coupling/synch etc increases
Phase locking
- Messy trajectory (full trajectory)
- shows the initial randomness, completely unsynchronised
- Followed by different degrees of phase locking
Synchronisation transition
- the parameter we used to measure synch
- increasing diffusion = better synch
- uniform ICs reproduces what was found in Strogatz paper
Further work
- parameters - which are important/relevant - there are many more compared to strogatz etc
- stochasticity
- control - open loop/closed loop - via injection of AI - coupling model to an actual experiment
- better measure of synch - spatial synch
- clustering - effects of control on this
- things
References
- [1] Michael B. Elowitz & Stanislas Leibler - A synthetic oscillatory network of transcriptional regulators | [http://dx.doi.org/doi:10.1073/pnas.0307095101 doi:10.1073/pnas.0307095101]
- [2] J. Garcia-Ojalvo, Michael B. Elowitz, Steven H. Strogatz - Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing | [http://dx.doi.org/doi:10.1038/35002125 doi:10.1038/35002125]
