(490e) 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.