Investigating dynamic causalities in reaction systems

Abstract

Reaction systems are a qualitative formalism for modeling systems of biochemical reactions characterized by the non-permanency of the elements: molecules disappear if not produced by any enabled reaction. Moreover, reaction systems execute in an environment that provides new molecules at each step. Brijder, Ehrenfeucht and Rozenberg investigated dynamic causalities in reaction systems by introducing the idea of predictors. A predictor of a molecule s, for a given n, is the set of molecules to be observed in the environment in order to determine whether s is produced or not by the system at step n.\ud \ud In this paper, we continue the investigation on dynamic causalities by defining an abstract interpretation framework containing three different notions of predictor: Formula based predictors, that is a propositional logic formula that precisely characterizes environments that lead to the production of s after n steps; Multi-step based predictors, that consist of n sets of molecules to be observed in the environment, one for each step; and Set based predictors, that are those proposed by Brijder, Ehrenfeucht and Rozenberg, and consist of a unique set of molecules to be observed in all steps.\ud \ud For each kind of predictor we define an effective operator that allows predictors to be computed for any molecule s and number of steps n. The abstract interpretation framework allows us to compare the three notions of predictor in terms of precision, to relate the three defined operators and to compute minimal predictors. We also discuss a generalization of this approach that allows predictors to be defined independently of the value of n, and a tabling approach for the practical use of predictors on reaction systems models. As an application, we use predictors, generalization and tabling to give theoretical grounds to previously obtained results on a model of gene regulation

Enhancing Reaction Systems: A Process Algebraic Approach

“…The theory of Reaction Systems [9] was born in the field of Natural Computing to model the behaviour of biochemical reactions taking place in living cells. Despite its initial aim, this formalism has shown to be quite useful not only for modeling biological phenomena, but also for the contributions which is giving to computer science [15], theory of computing, mathematics, biology [2,14,1,3], and molecular chemistry [16]. Here we briefly review the basic notions of RSs, see [9] for more details.…”

“…Reaction Systems (RSs) [9] are a rewriting formalism inspired by the way biochemical reactions take place in living cells. This theory has already shown to be relevant in several different fields, such as computer science [15], biology [2,14,1,3], molecular chemistry [16]. Reaction Systems formalise the mechanisms of biochemical systems, such as facilitation and inhibition.…”

Generalized contexts for reaction systems: definition and study of dynamic causalities

“…In [2] we continued the investigation on predictors by introducing the new notion of formula based predictor. A formula based predictor consists in a propositional logic formula to be satisfied by the sequence of (sets of) elements provided by the environment.…”

The Many Roads to the Simulation of Reaction Systems

“…As a arXiv:1904.07445v1 [cs.FL] 15 Apr 2019 computational model, they (and their dynamics) occupy an interesting intermediate position between Boolean Automata Networks [3,4] and Cellular Automata [5,6]. The theoretical exploration is flourishing, with the investigation of combinatorial properties [7,8], complexity of establishing the presence of dynamical behaviours [9,10,11], causal dynamics [12,13,14], and the classification of reaction systems according to the relation of mutual simulability [15]. Reaction systems, however, have also been employed to model real-world systems [16,17].…”