Reverse engineering of logic-based differential equation models using a mixed-integer dynamic optimisation approach

Motivation: Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters.Results: In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cells.D.H., J.R.B. and J.S.R. acknowledge funding from the EU FP7 projects 'NICHE' (ITN Grant number 289384) and 'BioPreDyn' (KBBE grant number 289434). J.R.B. also acknowledges funding from the Spanish Ministerio de Economia y Competitividad (and the FEDER) through the project MultiScales (DPI2011-28112-C04-03)