Flux module decomposition for parameter estimation in a multiple-feedback loop model of biochemical networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Since few quantitative values are measured in vivo, the values for unmeasured parameters should be estimated so that the simulation agrees with the experimental data. Considering the sparsity and error rates of experimentally measured data, the first thing is not to find a numerically exact and global solution but to explore a variety of the plausible parameter solutions. To find many plausible parameter solutions without any biases, we developed the two-phase search (TPS) method. However, calculation complexity makes it hard for TPS to optimize a large-scale dynamic model. In this study divide-and-conquer methods are used to solve this problem. The flux module decomposition (FMD) is first proposed that separates a complex, large-scale dynamic model into multiple flux modules without deteriorating its basic control architectures. FMD is combined with TPS, named FMD-TPS, to find many plausible parameter solutions for a dynamic model. To demonstrate the feasibility of FMD-TPS, it is applied to the E. coli ammonia assimilation system that consists of multiple-feedback loops. The variability of the solutions is verified by measuring the space distribution of the parameter solution vectors and by defining the binary vectors checking the consistency with biological behaviors. Compared with non-decomposition methods, FMD-TPS efficiently explored a variety of plausible parameter solutions that reproduce the dynamic behaviors in vivo.