Parameter estimation with term-wise decomposition in biochemical network GMA models by hybrid regularized Least Squares-Particle Swarm Optimization

High-throughput analytical techniques such as nuclear magnetic resonance, protein kinase phosphorylation, and mass spectroscopic methods generate time dense profiles of metabolites or proteins that are replete with structural and kinetic information about the underlying system that produced them. Experimentalists are in urgent need of computational tools that will allow efficient extraction of this information from these time series data. A new parameter estimation method for biochemical systems formulated as Generalized Mass Action (GMA) models known to capture the nonlinear dynamics of complex biological systems such as gene regulatory, signal transduction and metabolic networks, is described. For such models, it is known that parameter estimation algorithm performance deteriorates rapidly with increasing network size. We propose a decomposition strategy that breaks up the system equations into terms whose rate constants and kinetic order parameters are estimated one term at a time resulting in dramatic parameter space dimensionality reductions. This approach is demonstrated in a hybrid algorithm based on Regularized Least Squares Regression and Multi-objective Particle Swarm Optimization. We validate our proposed strategy through the efficient and accurate extraction of GMA model parameter values from noise-free and noisy simulated data for Saccharomyces cerevisiae and actual Nuclear Magnetic Resonance (NMR) data for Lactoccocus lactis.