Team:Manchester/Model/MechanismUncertainty
Network Mechanism Analysis
Contents
Overview and Motivation Methodology Results ConclusionsOverview 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
Return to top of pageMethodology
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 |
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 |
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.
Return to top of pageConclusions
Two mechanisms appear to give a good fit Reversible Michaelis-Menten(MM) and Uni-Bi MM followed Bi-Uni MM with Uni-Bi MM followed by Bi-Uni MM giving the better fit. Reversible MM 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 MM followed by Bi-Uni MM 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 MM Bi-Uni MM 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 MM Bi-Uni MM best represents the data. Further analysis should be undertaken, looking at further reactions particularly with regards to GDP And asking deeper questions about the mechanism like in what way does the ABTS take part in the second step.
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