Parameter Relationship Analysis

Contents

Overview 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. However some parameters were often coupled and whilst individually they are 'sloppy' some relationship between them is in fact not. This analysis is to look at and highlight these relationships.

The motivation for this analysis is it can tell you what parameters to focus your literature search on also for our generation of PDF's paramater sloppiness had to be avoided for testing different pdf generators.

Methodology

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

the top 10%, 11%-20% and the rest of model runs were recorded. The parameter sets which generated this data were then stored seperately.

For each combination of the parameters, the data was plotted with the different groupings coloured: green(top 10%) , yellow(11%-20%) and red(the rest) .

The results were normalised to 1 to make trends easier to spot since this analysis is about spotting correlations.

Results

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 It shows that the best parameter sets are at a constant Km,hrp but varying Kcat,hrp. Hence Kcat,HRP is a sloppy variable and Km,HRP is not.

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. It shows both are fairly sloppy parameters and no correlation between rate constants.

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. Kcat,Gox is sloppy and Km,HRP is in the lower end of its pdf.

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. Kcat,HRP is a sloppy parameter and Km,GOx is at the lower end of its pdf.

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. Both rate constants are on the lower end of their Pdf.

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. This is the most interesting parameter analysis. It's Hard to see (verified with model experimentation) but a very steep straight line of the best data points is shown. Hence Kcat/Km is a constant value even though both are sloppy parameters as shown earlier.

Conclusions

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.

Furthermore this type of analysis can find relationships between your parameters. Such as in figure 6. This can lead to Constraints (halfway down linked page.) to further improve the quality of your data set.