Identification of regulatory structure and kinetic parameters of biochemical networks via mixed-integer dynamic optimization.

Background: Recovering the network topology and associated kinetic parameter values from time-series data are central topics in systems biology. Nevertheless, methods that simultaneously do both are few and lack generality.

Results: Here, we present a rigorous approach for simultaneously estimating the parameters and regulatory topology of biochemical networks from time-series data. The parameter estimation task is formulated as a mixed-integer dynamic optimization problem with: (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 approach simultaneously optimizes the Akaike criterion, which captures the trade-off between complexity (measured by the number of parameters), and accuracy of the fitting. This simultaneous optimization mitigates a possible overfitting that could result from addition of spurious regulatory interactions.

Conclusion: The capabilities of our approach were tested in one benchmark problem. Our algorithm is able to identify a set of plausible network topologies with their associated parameters.