Statistical model checking based calibration and analysis of bio-pathway models

Abstract

We present a statistical model checking (SMC) based framework for studying ordinary differential equation (ODE) models of bio-pathways. We address cell-to-cell variability explicitly by using probability distributions to model initial concentrations and kinetic rate values. This implicitly defines a distribution over a set of ODE trajectories, the properties of which are to be characterized. The core component of our framework is an SMC procedure for verifying the dynamical properties of an ODE system accompanied by such prior distributions. To cope with the imprecise nature of biological data, we use a formal specification logic that allows us to encode both qualitative properties and experimental data. Using SMC, we verify such specifications in a tractable way, independent of the system size. This further enables us to develop SMC based parameter estimation and sensitivity analysis procedures. We have evaluated our method on two large pathway models, namely, the segmentation clock network and the thrombin-dependent MLC phosphorylation pathway. The results show that our method scales well and yields good parameter estimates that are robust. Our sensitivity analysis framework leads to interesting insights about the underlying dynamics of these systems. © Springer-Verlag 2013.