Regularization Techniques for Biochemical Reaction Networks

Models of biochemical reaction networks often contain a large number of parameters that cannot all be estimated from the limited amount of noisy experimental data usually available. Therefore, many of the nominal parameter values must be obtained from the open scientific literature. Differences in cell type, organism, etc. add large amounts of uncertainty to these literature-sourced parameters for use in the particular system to be modeled. There clearly is a need to estimate at least some of the parameter values from experimental data, however, the small amount of available data and the large number of parameters commonly found in these types of models, require the use of regularization techniques to avoid over-fitting. Parameter set selection comprises a group of related methods that seek to choose only a small subset of model parameters for estimation that will best represent the current data set and predict future ones. Parameter set selection achieves model reduction by retaining the less important parameters at their nominal values, thereby reducing the number of variable parameters in the model. A parameter sensitivity technique employing local sensitivity analysis and hierarchical clustering will be presented, along with more advanced extensions to explicitly incorporate parameter uncertainties. These techniques will then be evaluated on two biochemical reaction networks: a signal transduction example and a pharmacokinetic/pharmacodynamic type 1 diabetes example.