Identification of Regulatory Structure and Kinetic Parameters of Biochemical Networks Via Mixed-Integer Dynamic Optimization

Abstract

Motivation:

The analysis of topological and kinetic information of biochemical networks from data obtained by high throughput techniques is a central topic in systems biology. Intensive researches have focused on estimating kinetic parameters from experimental observations in complete parameterized models. However, the problem of the simultaneous identification of the regulatory topology and model parameters from dynamic profiles has received much less attention to date.

Results:

We present a rigorous approach based on mathematical programming for the parameter estimation of models of biochemical networks that can predict the underlying regulatory structure as well. We formulate the task of identifying this structure along with the values of the kinetic parameters of the associated model as a mixed-integer dynamic optimization (MIDO) problem with two types of variables: (i) binary variables, used to model the existence of regulatory interactions and kinetic effects of metabolites in the network processes; and (ii) continuous variables, denoting metabolites concentrations and kinetic parameters values. The MIDO model seeks to optimize the Akaike criterion, which captures the trade-off between complexity (measured by the number of parameters) and accuracy (quantified by the least square error between experimental observations and in silico predictions) in an attempt to avoid overfitting to the extent possible. This MIDO is reformulated into a mixed-integer nonlinear program (MINLP) using orthogonal collocation on finite elements. The reformulated MINLP is solved via standard optimization tools in an iterative fashion in order to identify a set of plausible network topologies and associated kinetic parameters.

Conclusion:

The capabilities of our approach were tested in one benchmark problem. The example presented in this work, being simple, show that estimating parameters in dynamic kinetic models is far from being an easy task. Our algorithm was able to identify a set of plausible network topologies with their associated parameters that are consistent with the dynamic data available and that can be further refined using additional information and expert knowledge on the system.