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Team:Manchester/parametertest
From 2013.igem.org
Accomplishments
We have created the first ever model based on uncertainty analysis in iGEM history, and, most importantly, made it functional. This meant we were able to get a series of predictions for the fatty acid biosynthesis pathway, with error bars detailing the extent to which we were able to be confident in our data. Analysis in this area shows that predictions for pathway output are confident. We believe that this method of modelling is an incredibly powerful tool in the investigation
Aim
To use uncertainty modelling to model E.coli fatty acid biosynthesis. Early modelling attempts using traditional methods of modelling were largely unsuccessful, due to the the nature of the fatty acid biosynthesis pathway, and the lack of experimentally defined kinetic values. Rather than use models that were arbitrary or lacked information, we decided to use a less traditional method, based on Monte Carlo sampling, that can give us a clear idea of what the uncertainty of our predictions might be. By embracing this uncertainty, we hoped to create a model with practical, representative results.
We have created the first ever model based on uncertainty analysis in iGEM history, and, most importantly, made it functional. This meant we were able to get a series of predictions for the fatty acid biosynthesis pathway, with error bars detailing the extent to which we were able to be confident in our data. Analysis in this area shows that predictions for pathway output are confident. We believe that this method of modelling is an incredibly powerful tool in the investigation
Aim
To use uncertainty modelling to model E.coli fatty acid biosynthesis. Early modelling attempts using traditional methods of modelling were largely unsuccessful, due to the the nature of the fatty acid biosynthesis pathway, and the lack of experimentally defined kinetic values. Rather than use models that were arbitrary or lacked information, we decided to use a less traditional method, based on Monte Carlo sampling, that can give us a clear idea of what the uncertainty of our predictions might be. By embracing this uncertainty, we hoped to create a model with practical, representative results.
To build our model, we first collected parameters from published literature and the online database BRENDA. In our search we discovered that published data on the value of parameters in the E.coli fatty acid biosynthesis pathway is limited. Hence, we decided to take uncertainty into account by creating probability distribution for each individual parameter. The method used to determine the distribution depended on the information available on that parameter and the parameters were categorised into 2 groups. Group 1 contained parameters with both the mean and standard deviation determined experimentally and published in the literature. In the case of group 1, both the mean and standard deviation were collected to determine the probability distribution. Group 2 contained parameters with neither the means nor the standard deviations available for the enzyme or parameter. In the case of group 2, we used the mean and standard deviation of all enzymes in the same class or subclass with known kinetic parameters. Once each parameter had a probability distribution associated with it, we randomly sampled values from each parameter distribution to run our model simulation.This was done by constructing an initial model in Copasi, using appropriate enzyme kinetic equations, and then exporting this in SBML format to PySCeS, in which a set of non-linear differential equations are used to obtain both structural and kinetic information about the system from these randomly generated kinetic values. This was repeated to create a collection of 1,000 models. From there we were able to determine the uncertainty in our model predictions: instead of a single prediction, we get a distribution of predictions from a large collection of plausible models.
Results
The spreadsheets generated from our script can be found here:
Rates (LINK)
Species (LINK)
The concentrations of the metabolites was outputted in tables, as depicted in Figure XXX. Each line represents one simulation with ten different time points within 100 seconds. The whole data set of all simulations was then attributed with colours according concentration values (Dark Red: >4; Pink: > 2; Light red:> 1; White: 1-0.01; Light yellow: <0.01; Dark yellow: <0.0001). Another table was generated out of this chart according to the ordinal data obtained from colouring the metabolite concentrations. This was done to further improve ease of work and making the data more visual. Figure XXX shows the summary of this qualitative concentration distribution for each metabolite. Again, the brighter green a cell is in colour, the more often simulations rendered metabolite concentrations in the specified concentration interval. For example, the last metabolite in the table C18CoA is bright green, because all 41 simulations rendered between 0.01 - 1 mM. Out of this table, a clear distribution becomes obvious: Except for the first six initial replenishing reactions, all metabolite concentrations are within a small reasonable range mostly between 0.01 - 1 mM. Interestingly, in the reaction towards the end of the pathway, which are responsible for removing the metabolites from the system and therefore give rise to stearic and palmitic acid (our desired products) the range of results appears to be significantly narrower, despite the uncertainty.
The spreadsheets generated from our script can be found here:
Rates (LINK)
Species (LINK)
The concentrations of the metabolites was outputted in tables, as depicted in Figure XXX. Each line represents one simulation with ten different time points within 100 seconds. The whole data set of all simulations was then attributed with colours according concentration values (Dark Red: >4; Pink: > 2; Light red:> 1; White: 1-0.01; Light yellow: <0.01; Dark yellow: <0.0001). Another table was generated out of this chart according to the ordinal data obtained from colouring the metabolite concentrations. This was done to further improve ease of work and making the data more visual. Figure XXX shows the summary of this qualitative concentration distribution for each metabolite. Again, the brighter green a cell is in colour, the more often simulations rendered metabolite concentrations in the specified concentration interval. For example, the last metabolite in the table C18CoA is bright green, because all 41 simulations rendered between 0.01 - 1 mM. Out of this table, a clear distribution becomes obvious: Except for the first six initial replenishing reactions, all metabolite concentrations are within a small reasonable range mostly between 0.01 - 1 mM. Interestingly, in the reaction towards the end of the pathway, which are responsible for removing the metabolites from the system and therefore give rise to stearic and palmitic acid (our desired products) the range of results appears to be significantly narrower, despite the uncertainty.
The analysis of the data shows clearly, that due to a small and reasonable range of metabolite concentrations which stabilises towards the end of the model, a high validity of our functioning model can be safely assumed and demonstrates that the uncertainty is not globally deleterious. Even though the model was working with high uncertainties in data, the output is always within a valid range.
Upon analysing the degree of certainty in our model, and finding that it was at a level that we believe is suitable for further analysis, we were able to create a series of boxplots showing the range of values found within our simulations for species accumulation after 100 seconds. We focused on the longer chain fatty acids, which are the engineering target of our pathway. The order in which the species are shown in the box plots, Figure XXX, is also the order in which they are formed. This is also shown in Figure XXX, where the colour corresponds to the colour of the bar on the box plot.
These results further emphasise that although we created a model based on uncertain parameters, by embracing this uncertainty we have been able to make a model that gives us useful information – and that allows us to specify for every single prediction how certain we can be of getting it right, in particular towards the end of the pathway.
Similar data analysis was carried out on the rates of the reactions. We focused on the reactions we had labelled AAT at the end of our pathway. These are thioesterase reactions directly responsible for the formation of palmitic and stearic acid. We can see that the rates for these reactions also fall within a relatively small range.
Conclusion
Kinetic Pathway modelling demands abundant information of the kinetic parameters. Literature research, however, showed that these were not available sufficiently or involved measurement errors. Hence this knowledge of parameter values often is uncertain. Therefore, we had to choose an approach that is able to deal with these limitations. Uncertainty modelling proved to be the most promising and useful tool for this. Even though the available data was limited, we managed to create a functioning kinetic model of the fatty acid synthesis pathway. This has not been done before and would not have been possible with any traditional approach. A prime example of how our metabolic modelling work directly informed our experimental work is in our decision to biobrick the FabA gene (encoding β-hydroxydecanoyl-ACP dehydrase, shown by the DH_OH reactions in this model). Our uncertainty model had shown us that we would need more kinetic data on key enzymes. The least characterised reaction was catalyzed by the product of the fabA gene, therefore we wished to not only biobrick this gene, but a His-tag to purify the enzyme in order to experimental gauge its activity. However, having taken pains to ensure our model was as realistic as possible, the idea of the insertion of a his-tag that could affect the activity of the enzyme seemed at odds to our overall goal. Therefore, we used further modelling technique to ensure the addition of this his tag would have as little overall bearing on the activity of the enzyme as possible. This can be found here
Kinetic Pathway modelling demands abundant information of the kinetic parameters. Literature research, however, showed that these were not available sufficiently or involved measurement errors. Hence this knowledge of parameter values often is uncertain. Therefore, we had to choose an approach that is able to deal with these limitations. Uncertainty modelling proved to be the most promising and useful tool for this. Even though the available data was limited, we managed to create a functioning kinetic model of the fatty acid synthesis pathway. This has not been done before and would not have been possible with any traditional approach. A prime example of how our metabolic modelling work directly informed our experimental work is in our decision to biobrick the FabA gene (encoding β-hydroxydecanoyl-ACP dehydrase, shown by the DH_OH reactions in this model). Our uncertainty model had shown us that we would need more kinetic data on key enzymes. The least characterised reaction was catalyzed by the product of the fabA gene, therefore we wished to not only biobrick this gene, but a His-tag to purify the enzyme in order to experimental gauge its activity. However, having taken pains to ensure our model was as realistic as possible, the idea of the insertion of a his-tag that could affect the activity of the enzyme seemed at odds to our overall goal. Therefore, we used further modelling technique to ensure the addition of this his tag would have as little overall bearing on the activity of the enzyme as possible. This can be found here
Conclusion
Kinetic Pathway modelling demands abundant information of the kinetic parameters. Literature research, however, showed that these were not available sufficiently or involved measurement errors. Hence this knowledge of parameter values often is uncertain. Therefore, we had to choose an approach that is able to deal with these limitations. Uncertainty modelling proved to be the most promising and useful tool for this. Even though the available data was limited, we managed to create a functioning kinetic model of the fatty acid synthesis pathway. This has not been done before and would not have been possible with any traditional approach. A prime example of how our metabolic modelling work directly informed our experimental work is in our decision to biobrick the FabA gene (encoding β-hydroxydecanoyl-ACP dehydrase, shown by the DH_OH reactions in this model). Our uncertainty model had shown us that we would need more kinetic data on key enzymes. The least characterised reaction was catalyzed by the product of the fabA gene, therefore we wished to not only biobrick this gene, but a His-tag to purify the enzyme in order to experimental gauge its activity. However, having taken pains to ensure our model was as realistic as possible, the idea of the insertion of a his-tag that could affect the activity of the enzyme seemed at odds to our overall goal. Therefore, we used further modelling technique to ensure the addition of this his tag would have as little overall bearing on the activity of the enzyme as possible. This can be found here
Kinetic Pathway modelling demands abundant information of the kinetic parameters. Literature research, however, showed that these were not available sufficiently or involved measurement errors. Hence this knowledge of parameter values often is uncertain. Therefore, we had to choose an approach that is able to deal with these limitations. Uncertainty modelling proved to be the most promising and useful tool for this. Even though the available data was limited, we managed to create a functioning kinetic model of the fatty acid synthesis pathway. This has not been done before and would not have been possible with any traditional approach. A prime example of how our metabolic modelling work directly informed our experimental work is in our decision to biobrick the FabA gene (encoding β-hydroxydecanoyl-ACP dehydrase, shown by the DH_OH reactions in this model). Our uncertainty model had shown us that we would need more kinetic data on key enzymes. The least characterised reaction was catalyzed by the product of the fabA gene, therefore we wished to not only biobrick this gene, but a His-tag to purify the enzyme in order to experimental gauge its activity. However, having taken pains to ensure our model was as realistic as possible, the idea of the insertion of a his-tag that could affect the activity of the enzyme seemed at odds to our overall goal. Therefore, we used further modelling technique to ensure the addition of this his tag would have as little overall bearing on the activity of the enzyme as possible. This can be found here
Useful terminology
Uncertainty:
In synthetic biology two main classes of computational models are commonly used: constraint-based genome-scale models and differential-equation-based dynamic models. In our project, we employed the latter approach, because we are interested in the concentrations of compounds and their dynamic changes, which cannot be predicted using purely constraint-based models. We also wanted to identify the reactions and corresponding enzymes with the highest control over the fatty acid synthesis pathway; again, this is not possible with constraint-based models.
However, for a dynamic model one needs to know the enzyme kinetic parameters, and these are often unknown or very unreliable for enzymes of fatty acid biosynthesis. We wanted to account for the resulting uncertainty using a new “uncertainty modelling” approach, which can potentially serve as a principled approach to handling parameter uncertainty in the future.
Building models with incorporated acknowledgment of uncertainty will produce specified confidence intervals for all model predictions and thus could lead to robust design of engineered cellular machines of fatty acid synthesis and beyond.
Fatty Acid Biosynthesis
Fatty acid biosynthesis is a process that occurs in all living organisms. Glucose is converted into acetyl-CoA through the citric acid cycle, which is fed into the fatty acid biosynthesis pathway. Here it combines with malonyl-CoA to first form a five carbon compound. The five carbon compound is then being converted into a four carbon compound via four successive steps, executed by the enzymes as indicated in Figure XXX . To this resulting C4 body, another malonyl-CoA is added to form a C7 body - which is converted the same manner as the previous C5 body. A number of unchanging enzymes act on the intermediates of this cyclic pathway to ultimately produce fatty acids. From the initial reaction to the end products the whole pathway numbers 43 reactions, about 60 metabolites and 267 parameters.Steady State
The steady state of a metabolic system is the situation where the concentrations of the pathway intermediates remain constant, although there is metabolic flux through the system.
