AMethods

# Methods of parameter optimization

Mathematical Modelling describes complex biological systems with mathematical equations and concepts. Setting up the initial conditions in the model is not that straight forward. If no experimental data is available, reasonable assumptions based on literature, logic and quantitative analysis need to be made. We believe that the initial assumptions made are crucial to crack the model. Once established, the parameters need to constantly be optimized with experimental data and/or literature data in order to fit reality to its maximum. Parameter optimization adds all the weight to a model's credibility, this is why we decided to approach this in with 2 methods: Sensitivity Analysis and Parameter Sampling.

# Sensitivity Analysis

Sensitivity Analysis is a method which is conventionally used for parameter optimization. A range of independent variables are tested in this technique and their impact on the dependent variable is evaluated. The independent variables which have the greatest influence on the dependant variable are then identified. In our case, we want to optimize the impact the values of specific independent variables have on the rate limiting step of our cellular mechanisms. So, we are evaluating a range of values for each independent variable and analysing which ones optimize the process. We applied this method to the LEGIT and the MOM models.

# Method

1. Identify the dependent variable to be optimized (the rate limiting step in our process)
2. Identify the independent variables that have an impact on this step
3. From literature search/ experimental data, obtain a range of values to be tested for each independent variable
4. Run the model for the range of values tested and identify the optimal condition for the rate limiting step
5. Re-run the initial model to evaluate the impact of the optimized parameters on the overall process, i.e. to determine if the optimized step is prevailed the rate limiting step in the overall cellular mechanism
6. Determine the areas in which research could be performed to further optimize the parameters (Wet Lab contribution)

# Sensitivity Analysis method applied to LEGIT model

Given that transport of intimin to the surface of the E.coli cells is the rate limiting step in the overall process, we are rewriting this ODE in order to simplify the Sensitivity Analysis on this step.

# Parameter Sampling

Parameter Sampling is another technique used to tackle the issue of uncertain and incomplete knowledge of parameter values. It is a method of parameter optimization, which relies on the random sampling of parameter values within a specified range. A probability density function (pdf) determines the distribution of the continuous random variables evaluated in the function. Parameter Sampling considers biological noise, making it a more realistic representation of the behaviour of a biological system.

# Method

1. Identify the dependent variable to be optimized (the rate limiting step in our process)
2. Identify the independent variables that have an impact on the step we are trying to optimize
3. Collect raw data from literature
4. Process raw data by assigning weights to the values depending on the similarity to the to-be-optimized parameter
5. Calculate the weighted mean for all the optimized parameters
6. Generate probability density functions (pdf);input the sample size, standard deviation and weighted mean

# LEGIT model

Assessing the impact of randomly generated discrete variables on the rate of transport of intimin. For this the values of Km and Vmax are evaluated.

Conditions for intimin

• Size: 94 kDa
• Optimal pH conditions: 7
• Native organism: E.coli
• Weighted mean of Km: 0.0147 µM
• Weighted mean of Vmax: 300000 s-1(1 s.f.)

# MOM model

Assessing the impact of randomly generated discrete variables on the rate of translation of RFP. For this the rate of nuclear export of the transcript and the rate of RFP degradation are evaluated.

Conditions for RFP

• Size: 27.9 kDa
• Location of protein: Cytoplasm
• Native organism: CHO cells
• Weighted mean of rate of nuclear export: 1.43 x 10-4 s-1
• Weighted mean of rate of degradation: 8.96 x 10-1 s-1

# Selecting our Programming Languages

This summer we decided to run our models on two different programming languages: MATLAB and Python. Both are high level languages that allowed us to create robust simulations. Upon starting iGEM, everyone on the modelling team wanted to learn a new programming language. Python is an open source software and it is relatively easy to find resources online to help troubleshoot our codes. We also decided to use MATLAB for our models, as we were already familiar with this language from our engineering degrees.

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