# Team:Manchester/Model/MechanismUncertainty

Manchester iGEM 2016

Network Mechanism Analysis

Contents

Overview and Motivation
Methodology
Results
Conclusions

Overview and Motivation

During discussions with the experimental team it became clear to us that the exact reaction mechanism was not clearly understood. By modelling a range of different potential mechanisms and comparing the outputs to experimental data we could draw conclusions about the accuracy of the mechanisms. Then we could refine the model in an effort to produce more accurate predictions and improve our understanding of the system.

The combinations of different rate laws we tested are below:

Reaction One (GOx) Reaction Two (HRP)
Irreversible Michaelis-Menten Irreversible Michaelis-Menten
Reversible Michaelis-Menten Reversible Michaelis-Menten
Reversible Michaelis-Menten Bi-Uni Reversible Michaelis-Menten
Uni-Bi Reversible Michaelis-Menten Bi-Uni Reversible Michaelis-Menten

For an explanation of why these four models were chosen click here

Methodology

For each combination of different rate laws used to model our network, the following steps were taken:
1) Generate probability distributions for each kinetic parameter required from our collected data.
2) Simulate the model with different sets of kinetic values that are sampled from probability distributions. In our study, 5000 samples for each reaction were modelled, i.e. the model was simulated with 5000 different sets of kinetic values.
3) Analysed the model by retrieving concentrations at 250 seconds for each sample and plotting a histogram and ensemble concentration time graphs.
4) Compared model predictions with our experimental data.

Results

# Experimental data

The data used uses the initial concentration conditions the data below, everything was run in triplicate.

Glucose /μg ml-1 GOx /μg ml-1 H2O2 /μg ml-1 GDL /μg ml-1 HRP /μg ml-1 ABTS /μg ml-1 ABTSOxidised /μg ml-1
0.5 120 0 0 20 200 0
1 120 0 0 20 200 0
1.25 120 0 0 20 200 0
1.5 120 0 0 20 200 0
1.75 120 0 0 20 200 0
2 120 0 0 20 200 0

These experiments were run in a plate reader and the absorbance of the sample at 420 nm was measured. This was converted to mM using Beer’s law.

Probabilistic composite outputs were then made to test for our exact reaction mechanism. These outputs are the concentration (mM) after 250 seconds and the predicted plots of concentration vs time for 5000 sets of parameters were sampled for each mechanism.

It was decided to use initial conditions of 1.6 ug ml-1 of glucose and evaluate the concentrations after 250 seconds. This was because of the thick band with initial condition of glucose ranging from 1.5 to 2 ug ml-1 attaining steady state at nearly 250 seconds. We have three criteria for our model to be considered accurate:

Criteria Value
250 second concentration $$2.5 \times 10^{-3} \lt C \lt 3\times 10^{-3}$$
Steady State concentration $$2.5 \times 10^{-3} \lt C \lt 3\times 10^{-3}$$
Concentration/Time profile Similar under visual inspection
The following ensemble outputs are displayed and analyzed for our four possible reaction schemes.

## Irreversible Michaelis-Menten

While Irreversible Michaelis-Menten does show a portion (~15% of samples) of iterations which do agree with the 250 second experimental data, it can clearly be seen that the steady state concentration is significantly higher than the experimental results (~3x). This mechanism configuration is therefore inaccurate and excluded from further analysis and the model.

Reversible Michaelis-Menten does have steady state solutions of the correct shape after 250 seconds, the concentrations are slightly too large. Click here for a more detailed explanation of what the mechanisms mean.

Reversible Michaelis-Menten reduces the range of model solutions for 250 seconds however the distribution of this is still particularly spread, the steady state concentration is marginally too large as well.

Reversible Michaelis-Menten followed by Bi-Uni Michaelis-Menten does have steady state solutions of the correct shape after 250 seconds, the steady state concentrations are about two thirds of the experimental value. Click here For a more detailed explanation of what the mechanism means.

Uni-Bi Michaelis-Menten followed by Bi-Uni Michaelis-Menten does have steady state solutions of the correct shape after 250 seconds, the concentrations are inside the expected range. Click here For a more detailed explanation of what the mechanism means.