A new error-control for initial value solvers
Proceedings of the conference on Numerical ordinary differential equations
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
| Hi-index | 0.00 |
Recently, there has been growing interest in the modelling and simulation of biological systems. Such systems are often modelled in terms of coupled ordinary differential equations that involve parameters whose (often unknown) values correspond to certain fundamental properties of the system. For example, in metabolic modelling, concentrations of metabolites can be described by such equations, where parameters correspond to the kinetic rates of the underlying chemical reactions. Within this framework, the increasing availability of time series data opens up the attractive possibility of reconstructing approximate parameter values, thus enabling the in silico exploration of the behaviour of complex dynamical systems. The parameter reconstruction problem, however, is very challenging – a fact that has resulted in a plethora of heuristics methods designed to fit parameters to the given data. In this paper we propose a completely deterministic method for parameter reconstruction that is based on interval analysis. We illustrate its utility by applying it to reconstruct metabolic networks using S-systems. Our method not only estimates the parameters very precisely, it also determines the appropriate network topologies. A major strength of the proposed method is that it proves that large portions of parameter space can be disregarded, thereby avoiding spurious solutions.