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

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

Reaction Systems and Synchronous Digital Circuits

A reaction system is a modeling framework for investigating the functioning of the living cell, focused on capturing cause-effect relationships in biochemical environments. Biochemical processes in this framework are seen to interact with each other by producing the ingredients enabling and/or inhibiting other reactions. They can also be influenced by the environment seen as a systematic driver of the processes through the ingredients brought into the cellular environment. In this paper, the first attempt is made to implement reaction systems in the hardware. We first show a tight relation between reaction systems and synchronous digital circuits, generally used for digital electronics design. We describe the algorithms allowing us to translate one model to the other one, while keeping the same behavior and similar size. We also develop a compiler translating a reaction systems description into hardware circuit description using field-programming gate arrays (FPGA) technology, leading to high performance, hardware-based simulations of reaction systems. This work also opens a novel interesting perspective of analyzing the behavior of biological systems using established industrial tools from electronic circuits design

Comparing reactions in reaction systems

Originally, reaction systems were introduced to describe in a formal way the interactions between biochemical reactions taking place in living cells. They are also investigated as an abstract model of interactive computation. A reaction system is determined by a finite background set of entities and a finite set of reactions. Each reaction specifies the entities that it needs to be able to occur, the entities which block its execution, and the entities that it produces if it occurs. Based on the entities available in a state of the system, all reactions of the system that are enabled take place and together produce the entities that form the next state. In this paper we compare reactions in terms of their enabledness and results. We investigate three partial orders on reactions that build on two definitions of equivalence of (sets of) reactions. It is demonstrated how each partial order defines a lattice (with greatest lower bounds and least upper bounds) for all nontrivial reactions. Together, these orders provide an insight in possible redundancies and (re)combinations of the reactions of a reaction system. (C) 2020 Elsevier B.V. All rights reserved.Algorithms and the Foundations of Software technolog