Lin-log Model of E. coli Central Metabolism.

Mathematical models of dynamics of metabolic pathways are used for analysis of complex regulations of biochemical reactions as an intrinsic property of a metabolism. The models are derived under assumptions of kinetic rate functions and usually result in simplification in view of the model theoretical scope and/or its practical application. The main obstacle in kinetic modeling is the dimensionality of the parametric space, its nonlinearity and ill-conditioned relations for kinetic parameter estimation. In this work these problems are effectively resolved by use of an approximate linear-logarithmic (Lin-log) applied in analysis of regulation of Escherichia coli central metabolism. Complex multiplicative Michaelis-Menten kinetic rate expressions are transformed into simple in parameter linear functions and non-linear logarithmic dependencies on concentrations of substrates, and cofactors. The Lin-log kinetic rates enable direct estimation of rate elasticities which are the key parameters in metabolic control analysis (MCA). Due to in the parameter linearity, the estimation problem is solved in a non-iterative least square algorithm. Applied is singular value decomposition (SVD) algorithm for system matrix pseudoinversion with the eigenvalue cut-off threshold at 0.01. The results are presented as parameters of enzyme activities and reaction elasticities. Evaluated activities and elasticities provided insight into the fluxes regulation. Comparison of the simulation results by Lin-log and Michaelis-Menten model reveals that errors are of the same order of magnitude.