A Mathematical Framework for Exploring Protein Folding Dynamics using Probabilistic Model Checking

Protein folding has always been a key problem in the field of computational biology. Several models have been proposed for protein folding in the past. The sequence via which a protein folds has a strong impact on the presence or absence of a disease in an organism. Given their significance to the health of an organism, in this paper, we present a Probabilistic Model Checking (PMC) based approach which provides statistical answers to questions that one may pose about the protein folding process. In such an approach, the protein folding model is represented as a probabilistic state transition system, and the questions are expressed formally in form of temporal properties. The PMC engine provides the probability of satisfying the property, which provides an insight into the protein folding process. Such properties are of several kinds - liveness properties, safety properties and fairness properties. We verify the properties on a probabilistic model checker. In this paper, we present our approach, and demonstrate its applicability by using the protein pro-insulin as our test case. We first express the dynamics of this protein using a probabilistic state transition system. Based on the state transition model we express several liveness, fairness and safety properties which target the folding steps/transitions. The probabilistic model checker tool (Prism [29-32]) is invoked to provide the probability of satisfying each of these queries. We have analyzed the change in the property satisfaction probability as a function of the change in the concentration level of the oxidation and reduction reagents. To the best of the authors’ knowledge, this is the first paper to model protein folding dynamics probabilistically, using Probabilistic Model Checking, a powerful technique from the domain of formal verification of state transition systems.