A General Procedure for Accurate Parameter Estimation in Dynamic Systems Using New Estimation Errors

The investigation of network dynamics is a major issue in systems and synthetic biology. One of the essential steps in a dynamics investigation is the parameter estimation in the model that expresses biological phenomena. Indeed, various techniques for parameter optimization have been devised and implemented in both free and commercial software. While the computational time for parameter estimation has been greatly reduced, due to improvements in calculation algorithms and the advent of high performance computers, the accuracy of parameter estimation has not been addressed.

We previously proposed an approach for accurate parameter optimization by using Differential Elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system. The equivalent system has the same solution as the original system, and it includes high-order derivatives, which contain information about the form of the observed time-series data. The introduction of an equivalent system into the numerical parameter optimizing procedure resulted in the drastic improvement of the estimation accuracy, since our approach evaluates the difference of not only the values but also the forms between the measured and estimated data, while the classical numerical approach evaluates only the value difference. In this report, we describe the detailed procedure of our approach for accurate parameter estimation in dynamic systems. The ability of our approach is illustrated in terms of the parameter estimation accuracy, in comparison with classical methods.