Static analysis of Biological Regulatory Networks dynamics using abstract interpretation

Abstract

<jats:p>The analysis of the dynamics of Biological Regulatory Networks (BRNs) requires innovative methods to cope with the state-space explosion. This paper settles an original approach for deciding reachability properties based on<jats:italic>Process Hitting</jats:italic>, which is a framework suitable for modelling dynamical complex systems. In particular, Process Hitting has been shown to be of interest in providing compact models of the dynamics of BRNs with discrete values. Process Hitting splits a finite number of processes into so-called sorts and describes the way each process is able to act upon (that is, to ‘hit’) another one (or itself) in order to ‘bounce’ it as another process of the same sort with further actions.</jats:p><jats:p>By using complementary abstract interpretations of the succession of actions in Process Hitting, we build a very efficient static analysis to over- and under-approximate reachability properties, which avoids the need to build the underlying states graph. The analysis is proved to have a low theoretical complexity, in particular when the number of processes per sorts is limited, while a very large number of sorts can be managed.</jats:p><jats:p>This makes such an approach very promising for the scalable analysis of abstract complex systems. We illustrate this through the analysis of a large BRN of 94 components. Our method replies quasi-instantaneously to reachability questions, while standard model-checking techniques regularly fail because of the combinatoric explosion of behaviours.</jats:p>

Pint: A Static Analyzer for Transient Dynamics of Qualitative Networks with IPython Interface

“…Reachability verification is a PSPACE-complete problem and its resolution often explodes on large networks. Pint implements over-and under-approximation of reachability [21,9] which allow tackling large models, although being potentially inconclusive when the over-approximation is satisfied but not the under-approximation. In such cases, one should fall back to classical model-checking.…”

Concretizing the Process Hitting into Biological Regulatory Networks

“…For instance, if b 1 , c 1 , and d 1 cooperate, one can create a cooperative sort bc with 4 processes reflecting the presence of b 1 and c 1 , and a cooperative sort bcd with 4 processes reflecting the presence of bc 11 and d 1 . Such constructions are helpful in PH as the static analysis of dynamics developed in [11] does not suffer from the number of sorts, but on the number of processes within a single sort.…”

“…This framework can be seen as a special class of formalisms like Petri Nets or Communicating Finite State Machines, where the causality between actions is restricted. Thanks to the particular structure of interactions within a PH, very efficient static analysis methods have been developed to over-and under-approximate reachability properties making tractable the formal analysis of BRNs with hundreds of components [11].…”

“…This framework can be seen as a special class of formalisms like Petri Nets or Communicating Finite State Machines, where the causality between actions is restricted. Thanks to the particular structure of interactions within a PH, very efficient static analysis methods have been developed to over-and under-approximate reachability properties making tractable the formal analysis of BRNs with hundreds of components [11].PH is suitable to model BRNs with different levels of abstraction in the specification of cooperations (associated influences) between components. This allows to model BRNs with a partial knowledge on precise evolution functions for components by capturing the largest (the most general) dynamics.…”

“…For instance, if b 1 , c 1 , and d 1 cooperate, one can create a cooperative sort bc with 4 processes reflecting the presence of b 1 and c 1 , and a cooperative sort bcd with 4 processes reflecting the presence of bc 11 and d 1 . Such constructions are helpful in PH as the static analysis of dynamics developed in [11] does not suffer from the number of sorts, but on the number of processes within a single sort.While the construction of cooperation in PH allows to encode any boolean functions between cooperating processes [10], it is worth noticing they introduce a temporal shift in their application. This allows the existence of interleaving of actions leading to a cooperative sort representing a past sub-state of the presence of the cooperative processes.…”