Extraction of elementary rate constants from global network analysis of E. coli central metabolism

As computational performance steadily increases, so does interest in extending one-particle-per-molecule models to larger physiological problems. Such models however require elementary rate constants to calculate time-dependent rate coefficients under physiological conditions. Unfortunately, even when in vivo kinetic data is available, it is often in the form of aggregated rate laws (ARL) that do not specify the required elementary rate constants corresponding to mass-action rate laws (MRL). There is therefore a need to develop a method which is capable of automatically transforming ARL kinetic information into more detailed MRL rate constants.

By incorporating proteomic data related to enzyme abundance into an MRL modelling framework, here we present an efficient method operating at a global network level for extracting elementary rate constants from experiment-based aggregated rate law (ARL) models. The method combines two techniques that can be used to overcome the difficult properties in parameterization. The first, a hybrid MRL/ARL modelling technique, is used to divide the parameter estimation problem into sub-problems, so that the parameters of the mass action rate laws for each enzyme are estimated in separate steps. This reduces the number of parameters that have to be optimized simultaneously. The second, a hybrid algebraic-numerical simulation and optimization approach, is used to render some rate constants identifiable, as well as to greatly narrow the bounds of the other rate constants that remain unidentifiable. This is done by incorporating equality constraints derived from the King-Altman and Cleland method into the simulated annealing algorithm. We apply these two techniques to estimate the rate constants of a model of E. coli glycolytic pathways. The simulation and statistical results show that our innovative method performs well in dealing with the issues of high computation cost, stiffness, local minima and uncertainty inherent with large-scale non-convex nonlinear MRL models.

In short, this new hybrid method can ensure the proper solution of a challenging parameter estimation problem of nonlinear dynamic MRL systems, while keeping the computational effort reasonable. Moreover, the work provides us with some optimism that physiological models at the particle scale can be rooted on a firm foundation of parameters generated in the macroscopic regime on an experimental basis. Thus, the proposed method should have applications to multi-scale modelling of the real biological systems allowing for enzyme intermediates, stochastic and spatial effects inside a cell.