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Team:Edinburgh/Modelling/Signalling
From 2010.igem.org
Overview: Modelling intercellular bacterial BRIDGEs
During the intracellular modelling of bacterial BRIDGEs, it became apparent that perturbations alone would not suffice to demonstrate the interactions of light based communication between bacteria. What was needed was modelling of entire colonies of bacteria. The goals of this modelling would be to demonstrate in-silico the light based communication between bacteria that we are trying to develop, and to establish whether light based communication is feasible given the few in-vitro measurements we are able to make.
The ideal is to be able to simulate a colony in an initial random state spontaneously synchronising. Realistically, however, this is a very difficult problem. The computational complexity of simply replicating the intracellular model for lots of individual cells and simulating them all together is prohibitive (especially given the hardware we have available). Also, there are a lot of unknowns that will have to be dealt with:
- How is the light output from one bacterium converted into signal input by a neighbouring bacterium?
- What is the distribution of the light sensing molecules in the receiving bacterium?
- How is the light attenuated by distance between the bacteria?
- How is the light attenuated by passing through two cell membranes?
- Will motility of the bacteria be an important factor?
- How much light from other bacteria will be required to not be swamped by the light output of the receiving bacterium itself?
- How will a bacterium cope with multiple con icting signals from neighbouring bacteria?
- Will the light emission within a single bacterium be homogeneous, or will there be multiple different outputs from different regions within the bacterium?
The Model
The proposed plan is to simplify the intracellular model. The aim would be to produce a model which produces the three light outputs and reacts to varying levels of three light inputs in exactly the same way as the current, full intracellular model. This is a non-trivial task: first, 'exact' is difficult to define with stochastic modelling - no two simulation runs will be the same. The simplest approach would be to run the simulation repeatedly and compute both the mean and standard deviation for the observables (light output), for each of a number of test profiles (light input). Then we somehow develop a simplified model which matches output for each of these profiles. Again, 'matching' needs to be defined as some means of scoring.
The development of this model will be automated, since there is not the time available to redevelop the simplified model every time the full intracellular model is refined with new experimental data. Either mathematical analysis or evolutionary model development through genetic algorithms can thus be used to accomplish this; both are difficult tasks, but genetic algorithms may be within our capabilities.
With a simplified intracellular model, we can think about intercellular communication. There are two elements here; how we represent the interaction of neighbouring cells over time, and how we transform the light output of one cell into the light input of its neighbours (and itself), taking into account attenuation, multiple conflicting signals, etc.
Our proposed solution is to create a simulation based on both stochastic modelling and cellular automata. For the initial implementation we will make the simplifying assumptions that the cells are non-motile, and regularly packed into a two-dimensional hexagonal mesh. Each cell will receive input from its six nearest neighbours (and itself).
Figure 1: The two-dimensional hexagonal mesh that forms the underlying structure of our proposed intercellular model.
The stochastic model will hold a representation of a colony laid out in the above hexagonal mesh. Each cell will have an individual representation of the simplified intra-cellular model. The model will be run stochastically with each cell effectively operating independently. After every time interval delta-t has elapsed, the values of each of the three light inputs in a cell is calculated based on the observed light output at that timepoint of the cell itself and its 6 closest neighbours:
inputgreen = fgreen(outputcell; (outputneighbour - i : i = 1::6))
inputblue = fblue(outputcell; (outputneighbour - i : i = 1::6))
The functions fred, fgreen, and fblue have yet to be defined, but will hopefully be based on experimental data.
After updating the input value of all cells in the mesh, stochastic simulation is resumed. The cycle then repeats after every delta-t time units. This should give us a basis for the simulation of bacterial colony synchronisation.
