# Team:Manchester/Enzyme

### From 2013.igem.org

** 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

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. **

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.

**Collected parameter values from literature****Categorized parameters into three groups****Filling in the missing information for each parameter****Random sampling values from each parameter distribution****Creation of 1,000 models with distribution of predictions**

** **

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.

**Group 1:**☑Mean ☑Standard Deviation

**Group 2:**☑Mean ☐Standard Deviation

**Group 3:**☐Mean ☐Standard Deviation

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 found in the literature and the standard deviation of all enzymes of the same class or subclass with known kinetic parameters. In the case of group three, we used both the mean and 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. To illustrate the generation of a distribution for plausible values of a parameter, we show an example parameter, DH_OHC4_OHC4, which is involved in the first reaction catalyzed by FabA. As this enzyme was chategorized into group three, we took the mean and standard deviation for the Km values listed in the same subclass (EC 4.2.1) and generated the following distribution of plausible parameters for the Km of DH_OHC4_OHC4:

All reactions and corresponding parameters can be found in the following table. The source of each parameter value is hyperlinked in blue, clicking on the link will direct you to either the literature source or the table from which the BRENDA enzyme class data can be found.

Once each parameter had a probability distribution associated with it, we randomly sampled values from each plausible parameter distribution to use in our model simulation. First we constructed 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 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.

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.

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

** Future Applications: Potentials and Limitations **

We believe that this approach to modelling could have a big impact in terms of how Synthetic Biology is modelled in the future and demonstrates a method in which, by facing the uncertainty of modelling head-on and incorporating this into our approach in a principled manner, it is possible to produce valuable models. This is particularly important in the field of Synthetic Biology, where systems, even if well characterised in one organism, are unlikely to have the same parameters when expressed in another organism.

This approach gives us the ability to model complex and poorly experimentally measured systems, where previous attempts may have produced unrepresentative models. Since the Km values can be sampled from a distribution, the model can be used to determine outcomes that may not be obvious with the use of a single Km value.

However, it is important to note that this method of modelling may not be appropriate in every case. The largest limitation of our use of this method is the inability of some of our simulations to reach steady state. This is likely to be a result of the random combination of parameter values. As the models were not fine-tuned, they will not always work. Although, we consider this as a potential strength as we can clearly highlight possible break points in the system that require further analysis. We show this in our own studies of β-hydroxydecanoyl-ACP dehydrase, described above.

Synthetic Biology operates at the cutting edge of current knowledge. Therefore, it 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 vast range of engineered cellular machines.

The full spreadsheets with reaction rates and species concentrations can be found here:

Reaction Rates

Species Concentrations

**Nomenclature of main metabolites**