Team:Manchester/Enzymetest

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Summary

Working with a pathway as large and uncharacterised as the fatty acid biosynthesis presented many challenges, the most important of which was the lack of reliable, experimentally established kinetic values for many of the key reactions. Our solution was to create a model that explicitly acknowledges this lack of data and the resulting uncertainty, using Monte Carlo sampling from plausible parameter value distributions -- enabling us to produce model predictions with confidence intervals. We believe that this unusual and innovative modelling strategy can potentially serve as a general principled approach to handling parameter uncertainty in the future. Synthetic Biology will always operate at the cutting edge of current knowledge and thus will unavoidably face the challenge of uncertainty. Building models with incorporated acknowledgment of uncertainty will yield model predictions with specified confidence intervals, and thus will lead to more robust design strategies for a wide range of engineered cellular machines.

Objectives

  • To build the first kinetic model of fatty acid biosynthesis in E. coli
  • To predict fatty acid production

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.

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 Synthesis

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 reacts with malonyl-CoA to form a four carbon compound. The four carbon compound is then reduced and dehydrated via four successive steps, executed, with the help of NADPH, by the enzymes as indicated in Figure 1. To this resulting C4 body, another malonyl-CoA reacts to form a C6 body - which is converted the same manner as the previous C4 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.

Approach

To build our model(Figure 2), 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 three groups. Group one contained parameters with both the mean and standard deviation determined experimentally and published in the literature. In the case of group one, both the mean and standard deviation were collected to determine the probability distribution. Group two contained parameters with neither the means nor the standard deviations available for the parameter. In the case of group two, we used the mean and standard deviation of all enzymes of the same class or subclass with known kinetic parameters. Group three consisted of parameters with known mean parameter value, but without standard deviation. In the case of group three, we used the standard deviation obtained from all enzymes of the same sub-class to create a distribution. The means and standard deviation of enzyme classes and sub-classes are defined in the following file
.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.