Team:UCL/Science/Model

Overview

There are three ways we can degrade azodyes: using Azoreductase (AzoR), Laccase (Lac) or BsDyp. Azoreductase breaks down AzoDye (AzoD) into two products Laccase breaks down AzoDye as well as the products of the reaction of Azoreductase with AzoDye. BsDyP acts on sulfonated AzoDyes (sAzoD):

In order to model this system we used COPASI. We included equations for gene expression and degradation for each gene in our pathway, as well as the intake and excretion of AzoDyes and sulfonated AzoDyes. The equations we included as well as the parameter assigned to each one are shown below:

Using reasonable parameter values, the simulation showed that the AzoDye is degraded within two days (48 hours). This timeframe agrees with the experimental results!

Parameter inference

We wanted to see which part of the pathway is the bottleneck in degrading the sulfonated AzoDyes. 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 in the future in order to speed up the degradation. To do that we used ABC-SysBio (http://www.theosysbio.bio.ic.ac.uk/resources/abc-sysbio) .

Approximate Bayesian Computation (ABC) is a method that utilises Bayesian statistics for parameter inference in synthetic biology. Given a model and data form that model, it computes the most likely parameters that could give rise to that data. We used the model and simulated data we had in order to find out which parameters are restricted in the values they can have in order to achieve that behaviour.

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 prior distributions consist of a range of values for each parameter, from which the algorithm will sample values. The input file also contains the data from the degradation of sulfonated AzoDyes over two days.

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 data 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 the distance between the data and the simulations is minimised. The parameter values that gave rise to this final population are called the 'posterior distribution'. This is shown in the figure below:

The distribution of values for each parameter are shown in the diagonal. Then drawing a straight line from one parameter to the other, 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, k17 and k18. These are the parameters of the reactions for intake (k13) and secretion (k18) of sulfonated AzoDyes by the cell. This shows that the bottleneck happens at those two points in our pathway. So if we increase the rate of intake and secretion of AzoDyes in our synthetic pathway, we could speed up the process of AzoDye degradation!

Flux Balance Analysis

Ecoli metabolism

This was made using cytoscape

Core metabolism map used for FBA

References

Liepe, J., Kirk, P., Filippi, S., Toni, T., et al. (n.d.) A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. [Online] 9 (2), 439–456.

Hoops S., Sahle S., Gauges R., Lee C., Pahle J., Simus N., Singhal M., Xu L., Mendes P. and Kummer U. (2006). COPASI: a COmplex PAthway SImulator. Bioinformatics 22, 3067-74.

Cline, M.S., Smoot, M., Cerami, E., Kuchinsky, A., et al. (2007) Integration of biological networks and gene expression data using Cytoscape. Nature Protocols. [Online] 2 (10), 2366–2382.

Orth, J.D., Thiele, I. & Palsson, B.O. (2010) What is flux balance analysis? Nature Biotechnology. [Online] 28 (3), 245–248.