Efficient classification of complete parameter regions based on semidefinite programming

Background: Current approaches to parameter estimation are often inappropriate or inconvenient for the modelling of complex biological systems. For systems described by nonlinear equations, the conventional approach is to first numerically integrate the model, and then, in a second a posteriori step, check for consistency with experimental constraints. Hence, only single parameter sets can be considered at a time. Consequently, it is impossible to conclude that the "best" solution was identified or that no good solution exists, because parameter spaces typically cannot be explored in a reasonable amount of time. Results: We introduce a novel approach based on semidefinite programming to directly identify consistent steady state concentrations for systems consisting of mass action kinetics, i.e., polynomial equations and inequality constraints. The duality properties of semidefinite programming allow to rigorously certify infeasibility for whole regions of parameter space, th...

• Type: Journal
• Year: 2007
• Where: BMCBI
• Authors: Lars Kuepfer, Uwe Sauer, Pablo A. Parrilo
• Keywords: BMCBI 2007, Complex Biological Systems, Parameter, Parameter Sets