Team:Manchester/Model/ParameterRelationships
Parameter Relationshpis Analysis
Contents
Overview and Motivation Methodology Results ConclusionsOverview and Motivation
During the early experimental phase of the model production, it was noticed that for some parameters the actual value did not matter too much, these 'sloppy' parameters could have a large range of values with minimal impact on the main model predictions. Instead it was notices that these parameters were often grouped and whilst individually they are 'sloppy' some relationship between them is in fact not. This analysis is to look at and highlight these realtionships.
Return to top of pageMethodology
The model was run many times, the concentration vs time data was then compared with experimental data.
The data was assessed using a mean squared error
$$MSE = n^{-1}{\sum_{i=1}^n(y_{i,experimental}-y_{i,model})^2}$$the top 10% of model runs were recorded. The parameter sets which generated this data was then stored. This process was repeated and the data which provided the 11% - 20% best results was also stored leaving the remaining data stored.
For each combination of the parameters, the data was plotted with the different groupings coloured: green, yellow and red respectively.
The results were normalised to 1 to make trends easier to spot since this analysis is qualitative not quantitive.
Return to top of pageResults
Figure 1 shows Kcat vs Km for HRP. Green indicates values that scored the top 10% when compared to experimental data. Yellow indicated 11%-20% and red indicated the remainder
Figure 2 shows Kcat for HRP vs Kcat for GOx. Green indicates values that scored the top 10% when compared to experimental data. Yellow indicated 11%-20% and red indicated the remainder
Figure 3 shows Km for HRP vs Kcat for GOx. Green indicates values that scored the top 10% when compared to experimental data. Yellow indicated 11%-20% and red indicated the remainder
Figure 4 shows Kcat for HRP vs Km for GOx. Green indicates values that scored the top 10% when compared to experimental data. Yellow indicated 11%-20% and red indicated the remainder
Figure 5 shows Km for HRP vs Km for GOx. Green indicates values that scored the top 10% when compared to experimental data. Yellow indicated 11%-20% and red indicated the remainder
Figure 6 shows Km vs Kcat for GOx. Green indicates values that scored the top 10% when compared to experimental data. Yellow indicated 11%-20% and red indicated the remainder
Return to top of pageConclusions
From the graphs it is quite clear that some parameters have no relationship, as shown by the random distribution of green and yellow points amongst the red points. For other parameter combinations there are clear relationships shown by a band of green, bounded by bands of yellow amongst the red points. This validates our decision to provide a constraint in the suitable parameter values selected from certain PDFs. This analysis was only undertaken using irreversible Michaelis-Menten kinetics. Further analysis should be performed using other rate laws and more complicated relationships, rather than the ratio explored here, for example in systems with multiple pathways to the same point this could indicate if one pathway is heavily limiting the overall network compared to another. Accuracy of the analysis could be improved by using more experimental data for comparison.
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