A TOUR OF REACTION SYSTEMS

2011 ◽  
Vol 22 (07) ◽  
pp. 1499-1517 ◽  
Author(s):  
ROBERT BRIJDER ◽  
ANDRZEJ EHRENFEUCHT ◽  
MICHAEL MAIN ◽  
GRZEGORZ ROZENBERG
Keyword(s):  
Biochemical Reactions ◽  
Transition Systems ◽  
Reaction Systems ◽  
Binary Counter ◽  
Research Themes ◽  
Formal Framework

Reaction systems are a formal framework for investigating processes carried out by biochemical reactions. This paper is an introduction to reaction systems. It provides basic notions together with the underlying intuition and motivation as well as two examples (a binary counter and transition systems) of "programming" with reaction systems. It also provides a tour of some research themes.

scholarly journals Facilitation in reaction systems

2020 ◽  
Vol 2 (3) ◽  
pp. 149-161
Author(s):  
Luca Manzoni ◽  
Antonio E. Porreca ◽  
Grzegorz Rozenberg
Keyword(s):  
Structural Properties ◽  
Living Cell ◽  
Formal Model ◽  
Biochemical Reactions ◽  
Reaction Systems ◽  
Model Of Computation ◽  
Dependency Graphs ◽  
Transition Graphs

Abstract Reaction systems is a formal model of computation which originated as a model of interactions between biochemical reactions in the living cell. These interactions are based on two mechanisms, facilitation and inhibition, and this is well reflected in the formulation of reaction systems. In this paper, we investigate the facilitation aspect of reaction systems, where the products of a reaction may facilitate other reactions by providing some of their reactants. This aspect is formalized through positive dependency graphs which depict explicitly such facilitating interactions. The focus of the paper is on demonstrating how structural properties of reaction systems defined through the properties of their positive dependency graphs influence the behavioural properties of (suitable subclasses of) reaction systems, which, as usual, are defined through their transition graphs.

FUNCTIONS DEFINED BY REACTION SYSTEMS

2011 ◽  
Vol 22 (01) ◽  
pp. 167-178 ◽  
Author(s):  
ANDRZEJ EHRENFEUCHT ◽  
MICHAEL MAIN ◽  
GRZEGORZ ROZENBERG
Keyword(s):  
Formal Model ◽  
A Priori ◽  
Reaction System ◽  
Transition Function ◽  
Complex Behavior ◽  
Biochemical Reactions ◽  
Reaction Systems ◽  
Available Resources

Reaction systems are a formal model of interactions between biochemical reactions. They consist of sets of reactions, where each reaction is classified by its set of reactants (needed for the reaction to take place), its set of inhibitors (each of which prevents the reaction from taking place), and its set of products (produced when the reaction takes place) – the set of reactants and inhibitors form the resources of the reaction. Each reaction system defines a (transition) function on its set of states. (States here are subsets of an a priori given set of biochemical entities.) In this paper we investigate properties of functions defined by reaction systems. In particular, we investigate how the power of defining functions depends on available resources, and we demonstrate that with small resources one can define functions exhibiting complex behavior.

scholarly journals Less haste, less waste: on recycling and its limits in strand displacement systems

2012 ◽  
Vol 2 (4) ◽  
pp. 512-521 ◽  
Author(s):  
Anne Condon ◽  
Alan J. Hu ◽  
Ján Maňuch ◽  
Chris Thachuk
Keyword(s):  
Chemical Reaction ◽  
Polynomial Function ◽  
Gray Code ◽  
Strand Displacement ◽  
Reaction Systems ◽  
Chemical Reaction Systems ◽  
Binary Counter ◽  
Dna Strand Displacement ◽  
Dna Strands ◽  
Dna Strand

We study the potential for molecule recycling in chemical reaction systems and their DNA strand displacement realizations. Recycling happens when a product of one reaction is a reactant in a later reaction. Recycling has the benefits of reducing consumption, or waste, of molecules and of avoiding fuel depletion. We present a binary counter that recycles molecules efficiently while incurring just a moderate slowdown compared with alternative counters that do not recycle strands. This counter is an n -bit binary reflecting Gray code counter that advances through 2 n states. In the strand displacement realization of this counter, the waste—total number of nucleotides of the DNA strands consumed—is polynomial in n , the number of bits of the counter, while the waste of alternative counters grows exponentially in n . We also show that our n -bit counter fails to work correctly when many ( Θ ( n )) copies of the species that represent the bits of the counter are present initially. The proof applies more generally to show that in chemical reaction systems where all but one reactant of each reaction are catalysts, computations longer than a polynomial function of the size of the system are not possible when there are polynomially many copies of the system present.

SIMPLE REACTION SYSTEMS AND THEIR CLASSIFICATION

2014 ◽  
Vol 25 (04) ◽  
pp. 441-457 ◽  
Author(s):  
LUCA MANZONI ◽  
DIOGO POÇAS ◽  
ANTONIO E. PORRECA
Keyword(s):  
Equivalence Relation ◽  
Biochemical Reactions ◽  
Reaction Systems ◽  
Model Of Computation ◽  
Simple Reaction ◽  
Boolean Lattices

Reaction systems are a model of computation inspired by biochemical reactions involving reactants, inhibitors and products from a finite background set. We define a notion of multi-step simulation among reaction systems and derive a classification with respect to the amount of resources (reactants and inhibitors) involved in each reaction. We prove that “simple” reaction systems, having at most one reactant and one inhibitor per reaction, suffice in order to simulate arbitrary systems. Finally, we show that the equivalence relation of mutual simulation induces exactly five linearly ordered classes of reaction systems characterizing well-known subclasses of the functions over Boolean lattices, such as the constant, additive (join-semilattice endomorphisms), monotone, and antitone functions.

STABILITY AND CHAOS IN REACTION SYSTEMS

2012 ◽  
Vol 23 (05) ◽  
pp. 1173-1184 ◽  
Author(s):  
ANDRZEJ EHRENFEUCHT ◽  
MICHAEL MAIN ◽  
GRZEGORZ ROZENBERG ◽  
ALLISON THOMPSON BROWN
Keyword(s):  
Experimental Study ◽  
Dynamical Systems ◽  
Living Cell ◽  
Chaotic Behavior ◽  
Discrete Dynamical Systems ◽  
Abstract Model ◽  
Biochemical Reactions ◽  
Initial State ◽  
Small Perturbations ◽  
Reaction Systems

Reaction systems are an abstract model of biochemical reactions in the living cell within a framework of finite (though often large) discrete dynamical systems. In this setting, this paper provides an analytical and experimental study of stability. The notion of stability is defined in terms of the way in which small perturbations to the initial state of a system are likely to change the system's eventual behavior. At the stable end of the spectrum, there is likely to be no change; but at the unstable end, small perturbations take the system into a state that is probabilistically the same as a randomly selected state, similar to chaotic behavior in continuous dynamical systems.

scholarly journals Geometry and symmetry in biochemical reaction systems

2021 ◽  
Author(s):  
Raffaella Mulas ◽  
Rubén J. Sánchez-García ◽  
Ben D. MacArthur
Keyword(s):  
Automorphism Group ◽  
Group Structure ◽  
Biochemical Reaction ◽  
Biochemical Reactions ◽  
Graph Representations ◽  
Reaction Systems ◽  
Pairwise Interactions ◽  
Laplacian Spectra ◽  
Hypergraph Laplacian ◽  
Hypergraph Theory

AbstractComplex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are not well suited to modelling complex sets of reactions that may involve numerous reactants and/or products. Here, we make use of a recently developed hypergraph theory of chemical reactions that naturally allows for higher-order interactions to explore the geometry and quantify functional redundancy in biochemical reactions systems. Our results constitute a general theory of automorphisms for oriented hypergraphs and describe the effect of automorphism group structure on hypergraph Laplacian spectra.

scholarly journals Simulating reversible computation with reaction systems

2020 ◽  
Vol 2 (3) ◽  
pp. 179-193
Author(s):  
Attila Bagossy ◽  
György Vaszil
Keyword(s):  
Environmental Control ◽  
Formal Model ◽  
Living Cells ◽  
Reversible Reaction ◽  
Reversible Systems ◽  
Biochemical Reactions ◽  
Reversible Computation ◽  
Reaction Systems ◽  
Model Of Computation

Abstract Reaction systems are a formal model of computation providing a framework for investigating biochemical reactions inside living cells. We look at the functioning of these systems as a process producing a series of different possible sets of entities representing states which can be changed by the application of reactions, and we study reversibility and its simulation in this framework. Our goal is to establish an Undo-Redo-Do-like semantics of reversibility with environmental control over the direction of the computation following a so-called no-memory approach, that is, without introducing modifications to the model of reaction systems itself. We first establish requirements the systems must satisfy in order to produce processes consisting of states with unique predecessors, then define reversible reaction systems in terms of reversible interactive processes. For such reversible systems, we also construct simulator systems that can traverse between the states of reversible interactive processes back and forth based on the input of a special “rollback” symbol from the environment.

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