Team:UCL/Science/Model

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<ul class="tabs">
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     <li><a href="#view1">Modelling Degradation</a></li>
     <li><a href="#view1">Modelling Degradation</a></li>
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     <li><a href="#view2">Enzymatic Modelling</a></li>
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     <li><a href="#view2">Parameter Inference</a></li>
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     <li><a href="#view3">Characterisation Modelling</a></li>
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     <li><a href="#view3">Flux Balance Analysis</a></li>
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    <li><a href="#view4">Enzyme Kinetics</a></li>
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    <li><a href="#view5">Chemical Mechanism</a></li>
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    <li><a href="#view6">References</a></li>
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<h4>Overview</h4>
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<h3>Overview</h3>
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<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>
<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>
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<img class="imgsizecorrect" src="http://2014.igem.org/wiki/images/5/51/Miriam_Pathway_v3_copy.png">  
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<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>
<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>
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<li> Equations for pathway model.</li>
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Equations for pathway model
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<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>
<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>
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<li>Simulated timecourse data of Acid Orange AzoDye degradation by Azoreductase, Laccase and BsDyP:</li>
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Simulated timecourse data of Acid Orange AzoDye degradation by Azoreductase, Laccase and BsDyP
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<h3>Parameter inference</h3>
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<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 (Liepe, 2014) . </p>  
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<h4>Parameter Inference</h4>
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<p> We wanted to see which part of the pathway is the bottleneck in degrading the AzoDyes and 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 (Liepe, 2014) .</p>  
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<BR>&nbsp;<BR>  
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<br>
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<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>
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<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><br>
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<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>
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<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 AzoDyes and sulfonated AzoDyes over two days. </p>
<BR>&nbsp;<BR>
<BR>&nbsp;<BR>
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<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, 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>
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<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, 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:
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<img src="http://2014.igem.org/wiki/images/8/81/Timecourse.jpg" class="imgsizecorrect">
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The parameter values that gave rise to this final population are called the 'posterior distribution'.</p> <br>
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<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>
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<li>Posterior distribution of model parameters</li>  
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Posterior distribution of model parameters
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<br><br>
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<p>The distribution of values for each parameter are shown in the diagonal. All distributions are between 0 and 1. 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. Three parameters stand out as very constricted, k3, k8, k17 and k18. These are the parameters of the reactions for intake  (k3) and secretion (k8) of AzoDyes as well as the intake (k17) and secretion (k18) of sulfonated AzoDyes by the cell. This shows that the bottleneck happens at those points in our pathway. So if we increase the rate of intake and secretion of AzoDyes and sulfonated AzoDyes in our synthetic pathway, we could speed up the process of degradation! </p>
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<h3> Flux Balance Analysis </h3>
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<h4>Flux Balance Analysis</h4>
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<ul>  
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<p> In order to see whether our xenobiological approach would work we wanted to check whether lack of Ubiquinone would have an effect on the growth rate of the chassis. The literature (Okada 1997 and Soballe, 1999) suggested that Ubiquinone is essential for E.coli growth so we decided to put that to the test! In order to do that we used Flux Balance Analysis (FBA). FBA is a method that uses the metabolism model of E.coli (see below) and calculates the flow of metabolites through that system that is required to maximise a given objective.</p>
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<p> In order to see whether our xenobiological approach would work we wanted to check whether lack of Ubiquinone would have an effect on the growth rate of the chassis. The literature (Okada 1997 and Soballe, 1999) suggested that Ubiquinone is essential for E.coli growth so we decided to put that to the test! In order to do that we used Flux Balance Analysis (FBA). FBA is a method that uses the metabolism model of E.coli (see below) and calculates the flow of metabolites through that system that is required to maximise a given obective </p>
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<br>
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Ecoli metabolism plotted in Cytoscape (Cline, 2007):
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The image below demonstrates the <i>E. coli</i> metabolism plotted in Cytoscape (Cline, 2007):
<img src="http://2014.igem.org/wiki/images/a/a0/Ecoli_hairball.png" class="imgsizecorrect">
<img src="http://2014.igem.org/wiki/images/a/a0/Ecoli_hairball.png" class="imgsizecorrect">
<BR>&nbsp;<BR>
<BR>&nbsp;<BR>
<p> In our case we used growth rate as the objective to maximise. We performed FBA for the core E.coli metabolism with and without Ubiquinone present. With Ubiquinone present the growth rate was calculated to be 0.98 h<sup> -1 </sup>. Without Ubiquione in the system the growth rate was found to be 0  h<sup> -1 </sup>, indicating that E.coli would not grow and survive without ubiquione. This suggested that silencing the essential genes for Ubiquinone production and supplying it externally would give us control over the survival of the chassis and ultimately allow us to contain it.</p>
<p> In our case we used growth rate as the objective to maximise. We performed FBA for the core E.coli metabolism with and without Ubiquinone present. With Ubiquinone present the growth rate was calculated to be 0.98 h<sup> -1 </sup>. Without Ubiquione in the system the growth rate was found to be 0  h<sup> -1 </sup>, indicating that E.coli would not grow and survive without ubiquione. This suggested that silencing the essential genes for Ubiquinone production and supplying it externally would give us control over the survival of the chassis and ultimately allow us to contain it.</p>
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Core metabolism map used for FBA
Core metabolism map used for FBA
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<p> Currently Synthetic biology is primarily based on the use of active modules (usually enzymes) from organisms to create one single organism that can successfully execute a goal. However without understanding the enzymatic action on a molecular scale we are unlikely to ever be able to improve them or design our own. Be believe that this will be the future of SynBio and therefore we have made a special effort to further the understanding of the enzymes we are using via chemical mechanism modelling in conjunction with our chemistry department. </p>
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<h4>Azo Reductase</h4>
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<p>The mechanism of reductive cleavage can either be thought of a step wise addition of H+ ions and electrons or hydride and H+ ions in concert as pictured below
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</p>
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<img src="http://2014.igem.org/wiki/images/d/d4/AzoRMechanism.png">
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<h4>Laccase and Peroxidases</h4>
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<p>Although many papers have touched on these oxidation mechanisms; they tend to skip steps and don’t make entire sense. Examples of this exist in [1]:
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</p>
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<img src="http://2014.igem.org/wiki/images/d/df/Screen_Shot_2014-10-17_at_18.43.08.png">
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<p>It’s issues include radicals gaining electrons and remaining radicals. Protons disappearing and more of the like. We have therefore worked hard to create a mechanism that makes sense.
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</p>
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<img src="http://2014.igem.org/wiki/images/0/06/Oxidising_Azo_Pathway_General.png" width="90%">
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<br>
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<p> Other reactions such as the polymerisation are lacking literature completely and therefore have been modelled as below. The example polymerisation is via the azo reductase product of mordant brown 33. </p>
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<img src="http://2014.igem.org/wiki/images/1/11/Polymerisationreactionlaccase.png" width="90%">
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<h4> References </h4>
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<p> [1] Phenolic Azo Dye Oxidation by Laccase from Pyricularia oryzae, Appl. Environ. Microbiol.December 1995 vol. 61 no. 124374-4377</p>
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<p>Enzyme kinetics are used to further understand reaction parameters of the enzyme. Enzyme kinetics are largely based on the Michaelis-Menten kinetic model that allows us to calculate Vmax (The maximum rate of reaction) and Km (Michaelis Constant: the substrate concentration at which the reaction rate is at half-maximum).
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<img src="http://2014.igem.org/wiki/images/0/01/Screen_Shot_2014-10-18_at_01.26.02.png">
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<p> Where [S]=Substrate concentration and V=Rate of Reaction
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</p>
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<p>The lineweaver burke plot is a double reciprocal plot of 1/[S] against 1/[V] that allows 1/Vmax and -1/Km to be understood via y and x intercepts respectively. We used our data for the decolorisation via enzyme BsDyp (see data page) to create a lineweaver burke plot and hence infer the values of Vmax and Km.
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<img src=http://2014.igem.org/wiki/images/b/b8/Lineweaver_Burke_Plot.png>
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<p>From this we can infer that Vmax=0.0305 mg/mol per hour (4 d.p.) and Km=0.0034 mg/mol (4 d.p.)
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<h3>References</h3>
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<h4>References</h4>
<p> Liepe, J., Kirk, P., Filippi, S., Toni, T., et al. (2014) A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. [Online] 9 (2), 439–456.</p>  
<p> Liepe, J., Kirk, P., Filippi, S., Toni, T., et al. (2014) A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. [Online] 9 (2), 439–456.</p>  
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<p> Orth, J.D., Thiele, I. & Palsson, B.O. (2010) What is flux balance analysis? Nature Biotechnology. [Online] 28 (3), 245–248. </p>
<p> Orth, J.D., Thiele, I. & Palsson, B.O. (2010) What is flux balance analysis? Nature Biotechnology. [Online] 28 (3), 245–248. </p>
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<p> Okada, K., Minehira, M., Zhu, X., Suzuki, K., et al. (1997) The ispB gene encoding octaprenyl diphosphate synthase is essential for growth of Escherichia coli. Journal of bacteriology. 179 (9), 3058–3060. </p>
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<p> Søballe, B. & Poole, R.K. (1999) Microbial ubiquinones: multiple roles in respiration, gene regulation and oxidative stress management. Microbiology (Reading, England). 145 ( Pt 8)1817–1830 </p>
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Latest revision as of 01:33, 18 October 2014

Goodbye Azodye UCL iGEM 2014

Modelling

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 AzoDyes and 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 (Liepe, 2014) .


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 AzoDyes and 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, 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'.


Posterior distribution of model parameters


The distribution of values for each parameter are shown in the diagonal. All distributions are between 0 and 1. 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. Three parameters stand out as very constricted, k3, k8, k17 and k18. These are the parameters of the reactions for intake (k3) and secretion (k8) of AzoDyes as well as the intake (k17) and secretion (k18) of sulfonated AzoDyes by the cell. This shows that the bottleneck happens at those points in our pathway. So if we increase the rate of intake and secretion of AzoDyes and sulfonated AzoDyes in our synthetic pathway, we could speed up the process of degradation!

Flux Balance Analysis

In order to see whether our xenobiological approach would work we wanted to check whether lack of Ubiquinone would have an effect on the growth rate of the chassis. The literature (Okada 1997 and Soballe, 1999) suggested that Ubiquinone is essential for E.coli growth so we decided to put that to the test! In order to do that we used Flux Balance Analysis (FBA). FBA is a method that uses the metabolism model of E.coli (see below) and calculates the flow of metabolites through that system that is required to maximise a given objective.


The image below demonstrates the E. coli metabolism plotted in Cytoscape (Cline, 2007):
 

In our case we used growth rate as the objective to maximise. We performed FBA for the core E.coli metabolism with and without Ubiquinone present. With Ubiquinone present the growth rate was calculated to be 0.98 h -1 . Without Ubiquione in the system the growth rate was found to be 0 h -1 , indicating that E.coli would not grow and survive without ubiquione. This suggested that silencing the essential genes for Ubiquinone production and supplying it externally would give us control over the survival of the chassis and ultimately allow us to contain it.


Core metabolism map used for FBA

Currently Synthetic biology is primarily based on the use of active modules (usually enzymes) from organisms to create one single organism that can successfully execute a goal. However without understanding the enzymatic action on a molecular scale we are unlikely to ever be able to improve them or design our own. Be believe that this will be the future of SynBio and therefore we have made a special effort to further the understanding of the enzymes we are using via chemical mechanism modelling in conjunction with our chemistry department.

Azo Reductase

The mechanism of reductive cleavage can either be thought of a step wise addition of H+ ions and electrons or hydride and H+ ions in concert as pictured below


Laccase and Peroxidases

Although many papers have touched on these oxidation mechanisms; they tend to skip steps and don’t make entire sense. Examples of this exist in [1]:

It’s issues include radicals gaining electrons and remaining radicals. Protons disappearing and more of the like. We have therefore worked hard to create a mechanism that makes sense.


Other reactions such as the polymerisation are lacking literature completely and therefore have been modelled as below. The example polymerisation is via the azo reductase product of mordant brown 33.

References

[1] Phenolic Azo Dye Oxidation by Laccase from Pyricularia oryzae, Appl. Environ. Microbiol.December 1995 vol. 61 no. 124374-4377


Enzyme kinetics are used to further understand reaction parameters of the enzyme. Enzyme kinetics are largely based on the Michaelis-Menten kinetic model that allows us to calculate Vmax (The maximum rate of reaction) and Km (Michaelis Constant: the substrate concentration at which the reaction rate is at half-maximum).

Where [S]=Substrate concentration and V=Rate of Reaction


The lineweaver burke plot is a double reciprocal plot of 1/[S] against 1/[V] that allows 1/Vmax and -1/Km to be understood via y and x intercepts respectively. We used our data for the decolorisation via enzyme BsDyp (see data page) to create a lineweaver burke plot and hence infer the values of Vmax and Km.


From this we can infer that Vmax=0.0305 mg/mol per hour (4 d.p.) and Km=0.0034 mg/mol (4 d.p.)

References

Liepe, J., Kirk, P., Filippi, S., Toni, T., et al. (2014) 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.

Okada, K., Minehira, M., Zhu, X., Suzuki, K., et al. (1997) The ispB gene encoding octaprenyl diphosphate synthase is essential for growth of Escherichia coli. Journal of bacteriology. 179 (9), 3058–3060.

Søballe, B. & Poole, R.K. (1999) Microbial ubiquinones: multiple roles in respiration, gene regulation and oxidative stress management. Microbiology (Reading, England). 145 ( Pt 8)1817–1830

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