Stability Constraints of Markov State Kinetic Models Based on Routh- Hurwitz Criterion

In computational neuroscience, receptors, channels and more generally signaling pathways are often modeled with Markov state models to represent biochemical reactions, which are then implemented with bilinear equations. One of the goals of these models, once calibrated with experimental results is to predict the dynamics of the biological system they represent in response to molecular perturbations and therefore facilitate and enhance the success rate of drug discovery and development. In order to guarantee model stability during the parameter optimization phase, the authors propose to linearize bilinear kinetic models around an operating point. Considering the model input as piecewise constant, they propose an algorithm based on the Routh-Hurwitz criterion to generate stability constraints on model parameters. As an example, they apply this algorithm to the gamma-aminobutyric acid (GABA) receptor subtype A (GABAA receptor) model, as developed by Pugh and Raman (2005). The results obtained with the Routh-Hurwitz criterion provide constraint equations. The proposed algorithm has also the advantage of being fast and easy to implement.