Efficient algorithms for ordinary differential equation model identification of biological systems

Abstract

Algorithms for parameter estimation and model selection that identify both the structure and the parameters of an ordinary differential equation model from experimental data are presented. The work presented here focuses on the case of an unknown structure and some time course information available for every variable to be analysed, and this is exploited to make the algorithms as efficient as possible. The algorithms are designed to handle problems of realistic size, where reactions can be nonlinear in the parameters and where data can be sparse and noisy. To achieve computational efficiency, parameters are mostly estimated for one equation at a time, giving a fast and accurate parameter estimation algorithm compared with other algorithms in the literature. The model selection is done with an efficient heuristic search algorithm, where the structure is built incrementally. Two test systems are used that have previously been used to evaluate identification algorithms, a metabolic pathway and a genetic network. Both test systems were successfully identified by using a reasonable amount of simulated data. Besides, measurement noise of realistic levels can be handled. In comparison to other methods that were used for these test systems, the main strengths of the presented algorithms are that a fully specified model, and not only a structure, is identified, and that they are considerably faster compared with other identification algorithms.

Equation discovery for systems biology: finding the structure and dynamics of biological networks from time course data

“…Derivation always starts with the starting symbol S and applies production rules in an iterative manner until an expression that consists of only terminal symbols is reached. Figure 2c shows a CFG that defines a set of ODE structures used by Gennemark and Wedelin [18 ] to model a reaction network due to Arkin and Ross [19](graphically shown in Figure 2a). Figure 2d shows a parse tree for the right-hand side of one of the original equations.…”

“…A metabolic system (a) taken from Arkin and Ross [19] and used by Gennemark and Wedelin [18 ] to evaluate their approach on the task of reconstructing the full dynamics of a system from simulated data. The corresponding ODEs are given in Appendix of [18 ], Eqs.…”

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“…The best design found by the global search is used as initial starting point for the subsequent detailed local search which is characterized by high accuracy but also high computational cost. This approach has been successfully applied previously on similar optimization problems in different fields (21,22). As with all heuristics, a global optimum cannot be guaranteed, and there is a trade-off between the quality of the solution and the computational effort.…”

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“…Nonetheless, the slope estimation strategy is statistically valid [204] and can, at the very least, be used to develop coarse solutions from which to start regular parameter optimization approaches. Reviews of this sub�eld include [68,69,[205][206][207][208][209][210][211][212][213][214].…”