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 mixedinteger 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.The authors acknowledges the financial support of the following institutions: Spanish Ministry of Education and Science (CTQ2009-14420-C02, CTQ2012-37039-C02, DPI2012-37154-C02-02, BFU2008-00196/BMC, BFU2010-17704, SGR2009-0809 and ENE 2011-28269-CO3-03), Spanish Ministry of External Affairs (projects PHB 2008-0090-PC), and European Commission (Marie Curie Actions - IAPP program - FP7/251298)