Abstract
BackgroundThe estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. It is therefore necessary to develop improved methods that are effective, fast, and scalable.ResultsWe show here that alternating regression (AR), applied to S-system models and combined with methods for decoupling systems of differential equations, provides a fast new tool for identifying parameter values from time series data. The key feature of AR is that it dissects the nonlinear 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 no convergence, it is feasible to dedicate some computational effort to identifying suitable start values and search settings, because the method is fast in comparison to conventional methods that the search for suitable initial values is easily recouped. Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well. Specifically, we show with an example from the literature that AR is three to five orders of magnitudes faster than direct structure identifications in systems of nonlinear differential equations.ConclusionAlternating regression provides a strategy for the estimation of parameter values and the identification of structure and regulation in S-systems that is genuinely different from all existing methods. Alternating regression is usually very fast, but its convergence patterns are complex and will require further investigation. In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.
Highlights
The estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems
Novel high-throughput techniques of molecular biology are capable of producing in vivo time series data that are relatively high in quantity and quality
We use a didactic system with four variables that is representative of a small biochemical network [5]
Summary
The estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. The S-system format within Biochemical Systems Theory (BST; [1,2,3,4]) is recognized as a effective modeling framework for both tasks, since it has a mathematically convenient structure and because every parameter has a uniquely defined meaning and role in the biological system. Due to the latter feature, the typically complex identification of the pathway structure reduces to a parameter estimation task, though in a much higherdimensional space. AR is fast and rather stable, and performs structure identification tasks between 1,000 and 50,000 times faster than methods that directly estimate systems of nonlinear differential equations (cf. [6])
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