Complexity of model checking for reaction systems

Reaction systems are a new mathematical formalism inspired by the living cell and driven by only two basic mechanisms: facilitation and inhibition. As a modeling framework, they differ from the traditional approaches based on ODEs and CTMCs in two fundamental aspects: their qualitative character and the non-permanency of resources. In this article we introduce to reaction systems several notions of central interest in biomodeling: mass conservation, invariants, steady states, stationary processes, elementary fluxes, and periodicity. We prove that the decision problems related to these properties span a number of complexity classes from P to NP- and coNP-complete to PSPACE-complete.

[1]  Wojciech Penczek,et al.  Model checking temporal properties of reaction systems , 2015, Inf. Sci..

[2]  R. Voellmy,et al.  Chaperone regulation of the heat shock protein response. , 2007, Advances in experimental medicine and biology.

[3]  Neil Immerman,et al.  Descriptive Complexity , 1999, Graduate Texts in Computer Science.

[4]  Andrzej Ehrenfeucht,et al.  A Tour of reaction Systems , 2011, Int. J. Found. Comput. Sci..

[5]  Ion Petre,et al.  Reaction System Models for the Heat Shock Response , 2014, Fundam. Informaticae.

[6]  Axel Kowald,et al.  Systems Biology in Practice: Concepts, Implementation and Application , 2005 .

[7]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[8]  Andrzej Ehrenfeucht,et al.  Functions Defined by Reaction Systems , 2011, Int. J. Found. Comput. Sci..

[9]  Enrico Formenti,et al.  Fixed Points and Attractors of Reaction Systems , 2014, CiE.

[10]  Arto Salomaa.  Functions and sequences generated by reaction systems , 2012, Theor. Comput. Sci..

[11]  Giancarlo Mauri,et al.  An excursion in reaction systems: From computer science to biology , 2012, Theor. Comput. Sci..

[12]  Wojciech Penczek,et al.  Model checking temporal properties of reaction systems , 2015, Inf. Sci..

[13]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[14]  Ion Petre,et al.  A simple mass-action model for the eukaryotic heat shock response and its mathematical validation , 2011, Natural Computing.

[15]  Enrico Formenti,et al.  Cycles and Global Attractors of Reaction Systems , 2014, DCFS.

[16]  Arto Salomaa,et al.  Functional Constructions between reaction Systems and Propositional Logic , 2013, Int. J. Found. Comput. Sci..

[17]  Andrzej Ehrenfeucht,et al.  Reaction Systems , 2007, Fundam. Informaticae.