Parameter estimation in biochemical systems models with alternating regression

Background: The estimation of parameter values continues to be the bottleneck of thecomputational analysis of biological systems. It is therefore necessary to develop improvedmethods that are effective, fast, and scalable.Results: We show here that alternating regression (AR), applied to S-system models and combinedwith methods for decoupling systems of differential equations, provides a fast new tool foridentifying parameter values from time series data. The key feature of AR is that it dissects thenonlinear inverse problem of estimating parameter values into iterative steps of linear regression.We show with several artificial examples that the method works well in many cases. In cases of noconvergence, it is feasible to dedicate some computational effort to identifying suitable start valuesand search settings, because the method is fast in comparison to conventional methods that thesearch for suitable initial values is easily recouped. Because parameter estimation and theidentification of system structure are closely related in S-system modeling, the AR method isbeneficial for the latter as well. Specifically, we show with an example from the literature that ARis three to five orders of magnitudes faster than direct structure identifications in systems ofnonlinear differential equations.Conclusion: Alternating regression provides a strategy for the estimation of parameter values andthe identification of structure and regulation in S-systems that is genuinely different from all existingmethods. Alternating regression is usually very fast, but its convergence patterns are complex andwill require further investigation. In cases where convergence is an issue, the enormous speed ofthe method renders it feasible to select several initial guesses and search settings as an effectivecountermeasure.