A Simple Membrane Computing Method for Simulating Bio-Chemical Reactions

There are two formalisms for simulating spatially homogeneous chemical system; the deterministic approach, usually based on differential equations (reaction rate equations) and the stochastic approach which is based on a single differential-difference equation (the master equation). The stochastic approach has a firmer physical basis than the deterministic approach, but the master equation is often mathematically intractable. Thus, a method was proposed to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. However, its drawback remains in great amount of computer time that is often required to simulate a desired amount of system time. A novel method that we propose is Deterministic Abstract Rewriting System on Multisets (DARMS), which is a deterministic approach based on an approximate procedure of an exact stochastic method. DARMS can produce significant gains in simulation speed with acceptable losses in accuracy. DARMS is a class of P Systems in which reaction rules are applied in parallel and deterministically. The feasibility and utility of DARMS are demonstrated by applying it to the Oregonator, which is a well-known model of the Belousov-Zhabotinskii (BZ) reaction. We also consider 1-dimensional and 2-dimensional cellular automata composed of DARMS and confirm that it can exhibit typical pattern formations of the BZ reaction. Since DARMS is a deterministic approach, it ignores the inherent fluctuations and correlations in chemical reactions; they are not so significant in spatially homogeneous chemical reactions but significant in bio-chemical systems. Thus, we also propose a stochastic approach, Stochastic ARMS (SARMS); SARMS is not an exact stochastic approach, but an approximate procedure of the exact stochastic method

The Nondeterministic Waiting Time Algorithm: A Review

We present briefly the Nondeterministic Waiting Time algorithm. Our technique for the simulation of biochemical reaction networks has the ability to mimic the Gillespie Algorithm for some networks and solutions to ordinary differential equations for other networks, depending on the rules of the system, the kinetic rates and numbers of molecules. We provide a full description of the algorithm as well as specifics on its implementation. Some results for two well-known models are reported. We have used the algorithm to explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior