Parameter Estimation Using Divide-and-Conquer Methods for Differential Equation Models

In systems biology, a key topic is the elucidation of the dynamic behavior of biological processes that are made up of complex biochemical networks. Statistical modeling is an important to capture the dynamics of biochemical networks such as metabolic networks, signal transduction pathways, and gene regulatory networks. These biochemical models have a set of parameters that represent the physical properties of the systems, such as kinetic constants and reaction rates. In general, the development of these models requires two steps: model structure construction and parameter estimation. The models are often constructed with time derivative expressions, such as ordinary differential equations (ODEs), to describe the change of certain quantities of interest over time [1,2]. The model parameters are then estimated by simulating the actual processes obtained from experimental analyses [3-5]. However, because the differential equation model has many uncertain parameters and limited measurement data, parameter estimation is a major bottleneck in the development of useful biochemical models [6,7].