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 in place 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 and hence refine the model in an effort to produce more accurate predictions and improve our understanding of the system.

The combinations of different rate laws used to model our reactions are as 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

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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, 1000 samples for each reaction were modelled, i.e. the model was simulated with 1000 different sets of kinetic values.
3) Analysed the model by retrieving concentrations at reaction completion for each sample and plotting a histogram as well a ensemble concentration time graphs.
4) Compared experimental data with our model predictions.

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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 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 concentration (mM) after 250 seconds and the predicted plots of concentration vs time for the ensembles parameter sets. 5000 sets of parameters were sampled for each mechanism.

It was decided to run the model for ensemble outputting at 1.6ug/ml 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 close to steady state after 250 seconds. We have three criteria for our model to be considered accurate:

Criteria	Value
250 second concentration	2.5x10-3-3x10-3
Steady State concentration	2.5x10-3-3x10-3
Concentration/Time profile	Similar under visual inspection

The following ensemble outputs are displayed and analyzed for our four possible reaction schemes.

Irrevesible 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 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 mechanism means.

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 does have steady state solutions of the correct shape after 250 seconds, the concentrations are about two thirds of what they should be . Click here For a more detailed explanation of what the mechanism means.

Uni-bi followed by bi-uni 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.

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Conclusions

Two mechanisms appear to give a good fit reversible michaelis menten and uni-bi followed bi-uni with uni-bi bi-uni giving the better fit. If reversible michaelis menten does not fully represent the reaction for two reasons, firstly the creation of GDL as a second product in the first step. Also It does not include abts as a required reagent in the second step. Including the second in the reaction scheme ie reversible followed by bi-uni caused a decrease in the concentration this could be because the ABTS became a limiting reagent. Including GDL as a side product of the first step i.e. uni-bi followed by bi-uni appears to have increased the concentration to the expected value this could be the built up amount of GDL is helping to force the reaction forwards. Any how uni-bi-bi uni takes into account a fuller picture of the reaction mechanism and moves the model close to the experimental data. From this it is concluded that ABTS and GDL both effect the mechanism and must be taken into account. Uni-bi bi-uni best represents the data. Further analysis should be undertaken, looking at further reactions (particularly with regards to GDP), inhibition within the system.

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