Team:UCL/Science/Model

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Goodbye Azodye UCL iGEM 2014

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:

Equations for pathway model.

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

Simulated timecourse data of Acid Orange AzoDye degradation by Azoreductase, Laccase and BsDyP:

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!

Posterior distribution of model parameters

Flux Balance Analysis

This was made using cytoscape

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.

@@ Line 12: / Line 12: @@
 <h3>Overview</h3>
-<p> We modelled our synthetic pathway as seen in the figure below:   </p>
+<p> 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):</p>
 <img class="imgsizecorrect" src="https://static.igem.org/mediawiki/2014/5/51/Miriam_Pathway_v3_copy.png">
-<p> Using a sample of parameters we simulated our synthetic pathway, using COPASI. We are showing the pathways for one of the azo-dyes here, methyl red. </p>
+<p> 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: </p>
-<!-- <img src="https://static.igem.org/mediawiki/2014/9/9d/Copasi_screenshot.png" class="imgsizecorrect">-->
-<p>The simulation showed that methyl red is degraded rapidly by laccase (orange) and azoreductase (green). </p>
 <li> Equations for pathway model.</li>
 <img src="https://static.igem.org/mediawiki/2014/c/c1/Reactions.jpg" class="imgsizecorrect">
-<li>Simulated timecourse data of methyl red degradation by azoreductase, laccase and BsDyP. Created using Copasi:</li>
+<p>Using reasonable parameter values, the simulation showed that the AzoDye is degraded within two days (48 hours). This timeframe agrees with the experimental results!</p>
+<li>Simulated timecourse data of Acid Orange AzoDye degradation by Azoreductase, Laccase and BsDyP:</li>
 <img src="https://static.igem.org/mediawiki/2014/f/ff/All_enzymes_copasi.png" class="imgsizecorrect">
 <h3>Parameter inference</h3>
-<p> 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) </p>
+<p> 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/) .  </p>
-<h6> Approximate Bayesian Computation </h6>
-<p> 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 ??. </p>
+<p> 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. </p>
-<p> 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. </p>
+<p> 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. </p>
-<p>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. </p>
+<p>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: </p>
-<p> 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 </p>
+<p>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! </p>
 <li>Posterior distribution of model parameters</li>
-<img src="https://static.igem.org/mediawiki/2014/5/54/Azo_posterior_2.png" class="imgsizecorrect">
+<img src="https://static.igem.org/mediawiki/2014/7/7f/Azo_posterior.png" class="imgsizecorrect">