Statistical Model Checking-Based Analysis of Biological Networks

Abstract

We introduce a framework for analyzing ordinary differential equation (ODE) models of biological networks using statistical model checking (SMC). A key aspect of our work is the modeling of single-cell variability by assigning a probability distribution to intervals of initial concentration values and kinetic rate constants. We propagate this distribution through the system dynamics to obtain a distribution over the set of trajectories of the ODEs. This in turn opens the door for performing statistical analysis of the ODE system's behavior. To illustrate this we first encode quantitative data and qualitative trends as bounded linear time temporal logic (BLTL) formulas. Based on this we construct a parameter estimation method using an SMC-driven evaluation procedure applied to the stochastic version of the behavior of the ODE system. We then describe how this SMC framework can be generalized to hybrid automata by exploiting the given distribution over the initial states and the-much more sophisticated-system dynamics to associate a Markov chain with the hybrid automaton. We then establish a strong relationship between the behaviors of the hybrid automaton and its associated Markov chain. Consequently, we sample trajectories from the hybrid automaton in a way that mimics the sampling of the trajectories of the Markov chain. This enables us to verify approximately that the Markov chain meets a BLTL specification with high probability. We have applied these methods to ODE based models of Toll-like receptor signaling and the crosstalk between autophagy and apoptosis, as well as to systems exhibiting hybrid dynamics including the circadian clock pathway and cardiac cell physiology. We

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“…All these observations point to the utility of a thorough study of the feedback regulation between PKA and Atg proteins in human cells. In this context, dynamical modeling approaches promise to offer helpful pointers [11,[107][108][109][110].…”

Mechanisms of Action of Autophagy Modulators Dissected by Quantitative Systems Pharmacology Analysis

“…All these observations point to the utility of a thorough study of the feedback regulation between PKA and ATG proteins in human cells. In this context, dynamical modeling approaches promise to offer helpful pointers [11,[103][104][105][106].…”

On the degradation of forest ecosystems by extreme events: Statistical Model Checking of a hybrid model

“…To investigate these ecological questions, we choose to apply an extension of the Statistical Model Checking framework. This computational approach, which was originally designed for the formal analysis of engineering and industrial systems [20,27,53], has very recently encountered a new success in the study of complex systems arising in life sciences, as in [23,29,32,40] notably. Based on the possibility of producing a great number of simulations of probabilistic models, this technique yields statistical guarantees on the analysis of properties of the model under study.…”

“…This procedure is based on the Statistical Model Checking (SMC) technique [27], a technique whose aim is to estimate the probability that a given model satisfies a given property. This technique has been first developed in the context of computer science models, but has recently been used in the context of life sciences, with a special emphasis on models determined by Ordinary Differential Equations [23,29,32,40]. In essence, the model is equipped with a probability measure on its set of traces, and the aim of SMC is to estimate the measure of the subset of traces that satisfies the property of interest.…”