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BCCS-Bristol
iGEM 2009

Repressilators coupled by quorum sensing - an agent based approach

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 in a feedback loop such that they repress each other in sequence. This can result in self-sustained oscillations occurring in the network. An example of an analogue in the world of electronics would be a [http://en.wikipedia.org/wiki/Ring_oscillator ring oscillator], in which a number of inverters are connected together in sequence.

Figure 1: Repressilator plasmid [1]

The single repressilator GRN can be simply extended as shown in figure 2(below) to include an autoinducer component. This would theoretically allow repressilators in individual bacteria to communicate with one another via an external chemical field.

Figure 2: Repressilator with autoinducer component for quorum coupling [2]

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

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]

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 A repressilator is a synthetic gene regulatory network, which is generally constructed from three different genes in a feedback loop such that they repress each other in sequence. This can result in self-sustained oscillations occurring in the network. An example of an analogue in the world of electronics would be a [http://en.wikipedia.org/wiki/Ring_oscillator ring oscillator], in which a number of inverters are connected together in sequence.
 [[Image:BCCS-Bristol-Repressilator-elowitz.PNG|frame|Figure 1: Repressilator plasmid [[#ref_elowitz|[1]]] ]]
 The single repressilator GRN can be simply extended as shown in figure 2(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:BCCS-Bristol-Repressilator-quorum.PNG‎|frame|Figure 2: Repressilator with autoinducer component for quorum coupling [[#ref_garcia|[2]]] ]]

Team:BCCS-Bristol/BSim/Case studies/Repressilators