Parameter estimation in modulated, unbranched reaction chains within biochemical systems

Modern biology is increasingly developing techniques for measuring time series of global gene expression and of many simultaneous proteins or metabolites. These data contain valuable information on the dynamics of cells, which has to be extracted with computational means. Given a suitable mathematical model, this extraction is in principle a straightforward regression task, but the complexity and nonlinearity of the differential equations that describe biological systems cause severe difficulties when the systems are of realistic size. We propose a method of stepwise regression that can be applied effectively to linear portions of pathways. The method may be combined with other estimation methods and either directly yields reasonable parameter estimates or at least provides appropriate start values for subsequent nonlinear search algorithms. We illustrate the method with the analysis of in vivo NMR data describing the dynamics of glycolytic metabolites in Lactococcus lactis.