Team:Manchester/Enzymetest

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.

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.

Objectives

• To build the first kinetic model of fatty acid biosynthesis in E. coli using uncertainty modeling
• To represent the fatty acid production in our system: E.c(oil)i
• To identify areas of the pathway requiring further study in the lab
• To develop a method of modelling that can be used in the absence of a fully characterised pathway

Introduction

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.

Figure 1: Fatty Acid Biosynthesis Pathway, thioesterase reaction (tesA) and Δ 9, Δ12 desaturase reactions.

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 were interested in the concentrations of compounds and their dynamic changes as well as the reactions with the highest control over the fatty acid synthesis pathway. As our analysis would not be possible with a purely constraint-based model, we chose to use a dynamic model. However, to use a dynamic model one needs to know the enzyme kinetic parameters, and these are often unknown or very unreliable for enzymes. Uncertainty can be due to:

experimental uncertainty

in vitro measurements of enzyme kinetics are not always representative of in vivo conditions

compound concentrations often have dynamic changes

We wanted to account for the uncertainty in the fatty acid synthesis pathway parameter data by 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.

Method

Figure 2: Schematic workflow representation for building the dynamic uncertainty model split in 5 successive steps. See text for details.

Collected parameter values from literature

Using the online database BRENDA, we searched for published parameter values for every enzyme in the pathway. In our search we discovered that the published data on the value of parameters in the E. coli fatty acid biosynthesis pathway is limited. Hence, we decided we needed to take this into account in our model.

Categorized parameters into three groups

Group 1: ☑Mean ☑Standard Deviation
Group 2: ☑Mean ☐Standard Deviation
Group 3: ☐Mean ☐Standard Deviation

Filling in the missing information for each parameter

In the case of group one, both the mean and standard deviation were collected from the literature and used to determine the probability distribution. 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. In the case of group three, we used the standard deviation obtained from all enzymes of the same sub-class to create a distribution. Here is a file with the distributions of enzyme classes and subclasses. Below is a spreadsheet of each parameter value. The source of each parameter value is hyperlinked in blue.

Random sampling values from each parameter distribution

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. The rate equations used in our model can be generalised as follows:



We used these rate equations to complete our model of the fatty acid synthesis pathway by adding the thioesterase reactions required for the production of the final fatty acids as well as the reactions catalyzed by FadD. Once our model was complete enough to represent our system we exported this from COPASI in SBML format and converted it to a PySCeS compatible file. PySCeS uses 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. Below is pseudocode of our workflow, the full script to randomly sample the parameters and generate model predictions can be downloaded here.

Creation of 1,000 models with distribution of predictions

We automated the generation of models 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 have a distribution of predictions from a large collection of plausible models.