Team:UCL/Science/Model

Overview

We modelled our synthetic pathway as seen in Fig. ??.

Using a sample of parameters we simulated our synthetic pathway, using COPASI (Figure ??). We are showing the pathways for one of the azo-dyes here, methyl red. The simulation showed that methyl red is degraded rapidly by laccase (orange) and azoreductase (green).

Parameter inference

We wanted to see which part of the pathway is the bottleneck in degrading the azo-dyes as fast as possible. So we analysed the parameters of our model to see which one is the most constrained, which could give us an insight on which one to tweak experimentally. To do that we used ABC-SysBio (Barnes, 2011)

Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) is a method that utilises Bayesian statistics for parameter inference in synthetic biology. An overview of the way it works can be found in Figure ??.

To use ABC-SysBio we had to make an SBML file describing our model and write an xml input file. The input file contains values for initial conditions of each species in our model, as well as prior distributions for each parameter. The priors consist of a range of values for each parameter, from which the algorithm will sample values. The input file also contains the time course of one of the species involved, against which each simulation will be compared. We used the simulation results of methyl red degradation.

ABC-SysBio samples a value for each parameter from the priors and using the initial conditions provided, simulates the model. The resulting time course is compared to the desired behaviour provided, and if the distance between the two is greater than a threshold e, the sampled parameter set is rejected. This is repeated for 100 sets of samples, consisting of one population. The sets that were accepted are then perturbed by a small amount and then a new population is sampled from the perturbed sets. This process is repeated until a final e is reached, when the distance between the simulated and desired time courses is minimal. The parameter values that gave rise to this final population are called the 'posterior distribution', and is a subset of the prior distribution defined initially.

The results of ABC-SysBio are shown in Figure ??. The distribution of values for each parameter are shown in the diagonal. At the point where the two meet, the two parameters have been plotted against each other in a density contour plot. Two parameters stand out as very constricted, k3 and k8. These are the parameters of the reactions for intake (k3) and secretion (k8) of methyl red by the cell. This shows that the bottleneck happens at those two points in our pathway. So if we were two increase the rate of intake and secretion of azo-dye in our synthetic pathway, we could increase the efficiency of azo-dye degradation

Flux Balance Analysis

• Parameter estimations for pathway model have been found for desired behaviours (using approximate Bayesian computation, ABC SysBio).
• Graphs of results.