Team:Manchester/Model/Constraints
Constraints
Improve data motivation, What we used
In some situations there are constraints (representing physical limitations) that can be applied to the parameters to further improve your data set. One such example is the haldane relationship which relates kinetic parameters to the equilibrium constant.
For our system we noticed the Kcat/Km ratio was reported so this was used.
As such only parameters consistent with this ratio were used.
In doing this kind of step you not only save computer time but also can provide a tighter prediction on what you would expect to observe if the model is accurate.
Below you will find a figure showing the difference to the simulation using a filtered data set and a unfiltered data set.
The above figures illustrate the difference in simulation results when applying constraints to your parameters. Left is a concentration graph with no constraints applied, Right is a concentration graph with constraints applied. As you can see the constrained simulation produces less results that take much longer to reach steady state, this was consistent with experimental data.
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Illustration of concept
Below some imaginary constraints are given by the 2 blue curves. Any point which falls between the 2 curves would be accepted (in green) and any point which lies outside these bounds is rejected (in red). This is repeated until enough suitable points are generated.
How code works and Git
Relevant github link. All files discussed here are available for reference
The code works not exactly like you would expect from the theory explanation. Specifically the constraint is not applied to the original pdfs to create a new pdf consistent with the constraint, to do this you need to look into multivariate distributions. We actually took the much easier to code option of while running the simulation sampling from both Kcat and Km distributions (kcat/km is the constraint). Only keeping values that are within 0.5 standard deviations of the kcat/km value where standard deviation was calculated from the literature ratio.
The downside of our simpler method is that we waste computer time. As we only had one constraint this wasn’t much of a problem, however if you have many constraints you will have to look into multivariate techniques, or overcome the slowness with high performance computing (supercomputers).
