Warwick Tucker
Department of Mathematics
Uppsala University
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 nontrivial 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 talk we present a completely deterministic method for parameter reconstruction based on
interval analysis. We illustrate its utility by applying it to reconstruct metabolic networks.
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.