Abstract
BackgroundProbabilistic Boolean networks (PBNs) have been proposed for analyzing external control in gene regulatory networks with incorporation of uncertainty. A context-sensitive PBN with perturbation (CS-PBNp), extending a PBN with context-sensitivity to reflect the inherent biological stability and random perturbations to express the impact of external stimuli, is considered to be more suitable for modeling small biological systems intervened by conditions from the outside. In this paper, we apply probabilistic model checking, a formal verification technique, to optimal control for a CS-PBNp that minimizes the expected cost over a finite control horizon.ResultsWe first describe a procedure of modeling a CS-PBNp using the language provided by a widely used probabilistic model checker PRISM. We then analyze the reward-based temporal properties and the computation in probabilistic model checking; based on the analysis, we provide a method to formulate the optimal control problem as minimum reachability reward properties. Furthermore, we incorporate control and state cost information into the PRISM code of a CS-PBNp such that automated model checking a minimum reachability reward property on the code gives the solution to the optimal control problem. We conduct experiments on two examples, an apoptosis network and a WNT5A network. Preliminary experiment results show the feasibility and effectiveness of our approach.ConclusionsThe approach based on probabilistic model checking for optimal control avoids explicit computation of large-size state transition relations associated with PBNs. It enables a natural depiction of the dynamics of gene regulatory networks, and provides a canonical form to formulate optimal control problems using temporal properties that can be automated solved by leveraging the analysis power of underlying model checking engines. This work will be helpful for further utilization of the advances in formal verification techniques in system biology.
Highlights
Probabilistic Boolean networks (PBNs) have been proposed for analyzing external control in gene regulatory networks with incorporation of uncertainty
Unlike other optimal control approaches for PBNs, e.g., [1, 4, 13,14,15], that are usually developed over integer programming and dynamic programming, the method based on probabilistic model checking does not need explicit computation of large-size state transition relations associated with PBNs and offers a framework for flexible specification and analysis
We add control and state cost information into the PRISM code of a context-sensitive PBN with perturbation (CS-PBNp) such that automated model checking a minimum reachability reward property on the code gives the solution to the optimal control problem
Summary
Probabilistic Boolean networks (PBNs) have been proposed for analyzing external control in gene regulatory networks with incorporation of uncertainty. At a given state of the network, by imposing external interventions, e.g., drugs, Probabilistic Boolean networks (PBNs) [2], an extension of Boolean networks (BNs),enable effectively expression of rule-based dependencies between genes and. Wei et al BMC Systems Biology 2017, 11(Suppl 6):104 representation of the switching behaviors of genetic process, and have been been widely used by system biologists in external control for gene regulatory networks with uncertainty [3]. To model uncertainty in realistic biological systems, PBNs have been developed as an extension of BNs. In a PBN, several Boolean functions are defined for each gene, and the functions are chosen randomly with respect to a given probability distribution at each time step. Unlike a BN, such a PBN, called an instantaneously random PBN, is a non-deterministic model, which essentially represents a set of BNs such that a governing one is randomly decided at each time to instantiate the PBN
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
