This article is part of the supplement: Problems and tools in the systems biology of the neuronal cell
Parameter estimate of signal transduction pathways
1 European Brain Research Institute, Via Fosso del Fiorano 64, Roma, Italy
2 Lay Line Genomics SpA, S.Raffaele Science Park, Castel Romano, Italy
3 International School of Advanced Studies (SISSA/ISAS), Biophysics Dept., Via Beirut 2-4, Trieste, Italy
4 ENEA, Casaccia Research Center, Computing and Modelling Unit, Via Anguillarese 301, S.Maria di Galeria, Italy
5 Ylichron Srl, c/o ENEA, Casaccia Research Center, Via Anguillarese 301, S.Maria di Galeria, Italy
BMC Neuroscience 2006, 7(Suppl 1):S6 doi:10.1186/1471-2202-7-S1-S6Published: 30 October 2006
The "inverse" problem is related to the determination of unknown causes on the bases of the observation of their effects. This is the opposite of the corresponding "direct" problem, which relates to the prediction of the effects generated by a complete description of some agencies. The solution of an inverse problem entails the construction of a mathematical model and takes the moves from a number of experimental data. In this respect, inverse problems are often ill-conditioned as the amount of experimental conditions available are often insufficient to unambiguously solve the mathematical model. Several approaches to solving inverse problems are possible, both computational and experimental, some of which are mentioned in this article. In this work, we will describe in details the attempt to solve an inverse problem which arose in the study of an intracellular signaling pathway.
Using the Genetic Algorithm to find the sub-optimal solution to the optimization problem, we have estimated a set of unknown parameters describing a kinetic model of a signaling pathway in the neuronal cell. The model is composed of mass action ordinary differential equations, where the kinetic parameters describe protein-protein interactions, protein synthesis and degradation. The algorithm has been implemented on a parallel platform. Several potential solutions of the problem have been computed, each solution being a set of model parameters. A sub-set of parameters has been selected on the basis on their small coefficient of variation across the ensemble of solutions.
Despite the lack of sufficiently reliable and homogeneous experimental data, the genetic algorithm approach has allowed to estimate the approximate value of a number of model parameters in a kinetic model of a signaling pathway: these parameters have been assessed to be relevant for the reproduction of the available experimental data.