7 research outputs found
Fixed points and attractors of additive reaction systems
Reaction systems are discrete dynamical systems that simulate biological processes within living cells through finite sets of
reactants, inhibitors, and products. In this paper, we study the computational complexity of deciding on the existence of
fixed points and attractors in the restricted class of additive reaction systems, in which each reaction involves at most one
reactant and no inhibitors. We prove that all the considered problems, that are known to be hard for other classes of
reaction systems, are polynomially solvable in additive systems. To arrive at these results, we provide several non-trivial
reductions to problems on a polynomially computable graph representation of reaction systems that might prove useful for
addressing other related problems in the future
SOS Rules for Equivalences of Reaction Systems
Reaction Systems (RSs) are a successful computational framework inspired by
biological systems. A RS pairs a set of entities with a set of reactions over
them. Entities can be used to enable or inhibit each reaction, and are produced
by reactions. Entities can also be provided by an external context. RS
semantics is defined in terms of an (unlabelled) rewrite system: given the
current set of entities, a rewrite step consists of the application of all and
only the enabled reactions. In this paper we define, for the first time, a
labelled transition system for RSs in the structural operational semantics
(SOS) style. This is achieved by distilling a signature whose operators
directly correspond to the ingredients of RSs and by defining some simple SOS
inference rules for any such operator to define the behaviour of the RS in a
compositional way. The rich information recorded in the labels allows us to
define an assertion language to tailor behavioural equivalences on some
specific properties or entities. The SOS approach is suited to drive additional
enhancements of RSs along features such as quantitative measurements of
entities and communication between RSs. The SOS rules have been also exploited
to design a prototype implementation in logic programming.Comment: Part of WFLP 2020 pre-proceeding
Fixed Points and Attractors of Reactantless and Inhibitorless Reaction Systems
Reaction systems are discrete dynamical systems that model biochemical
processes in living cells using finite sets of reactants, inhibitors, and
products. We investigate the computational complexity of a comprehensive set of
problems related to the existence of fixed points and attractors in two
constrained classes of reaction systems, in which either reactants or
inhibitors are disallowed. These problems have biological relevance and have
been extensively studied in the unconstrained case; however, they remain
unexplored in the context of reactantless or inhibitorless systems.
Interestingly, we demonstrate that although the absence of reactants or
inhibitors simplifies the system's dynamics, it does not always lead to a
reduction in the complexity of the considered problems.Comment: 29 page
Fixed points and attractors of reactantless and inhibitorless reaction systems
Reaction systems are discrete dynamical systems that model biochemical processes in living
cells using finite sets of reactants, inhibitors, and products. We investigate the computational
complexity of a comprehensive set of problems related to the existence of fixed points and
attractors in two constrained classes of reaction systems, in which either reactants or inhibitors
are disallowed. These problems have biological relevance and have been extensively studied
in the unconstrained case; however, they remain unexplored in the context of reactantless
or inhibitorless systems. Interestingly, we demonstrate that although the absence of reactants
or inhibitors simplifies the system’s dynamics, it does not always lead to a reduction in the
complexity of the considered problems
Modeling and Analyzing Reaction Systems in Maude
Reaction Systems (RSs) are a successful computational framework for modeling systems inspired by biochemistry. An RS defines a set of rules (reactions) over a finite set of entities (e.g., molecules, proteins, genes, etc.). A computation in this system is performed by rewriting a finite set of entities (a computation state) using all the enabled reactions in the RS, thereby producing a new set of entities (a new computation state). The number of entities in the reactions and in the computation states can be large, making the analysis of RS behavior difficult without a proper automated support. In this paper, we use the Maude language—a programming language based on rewriting logic—to define a formal executable semantics for RSs, which can be used to precisely simulate the system behavior as well as to perform reachability analysis over the system computation space. Then, by enriching the proposed semantics, we formalize a forward slicer algorithm for RSs that allows us to observe the evolution of the system on both the initial input and a fragment of it (the slicing criterion), thus facilitating the detection of forward causality and influence relations due to the absence/presence of some entities in the slicing criterion. The pursued approach is illustrated by a biological reaction system that models a gene regulation network for controlling the process of differentiation of T helper lymphocytes