Modeling and Simulating Biological Processes with Stochastic Multiset Rewriting

Membrane systems were originally introduced as models of computation inspired by the structure and the functioning of living cells. More recently, membrane systems have been shown to be suitable also to model cellular processes. Inspired by brane calculi, a new model of membrane system with peripheral proteins has been recently introduced. Such model has compartments (enclosed by membranes), floating objects, and objects attached to the internal and external surfaces of the membranes. The objects can be processed/transported inside/across the compartments and the transport is regulated by opportune objects attached to the membranes surfaces. We present a stochastic simulator of this model, with a style of syntax based on chemical reactions. We show that the simulator can be particularly useful in modelling biological processes that involve compartments, surface and integral membrane proteins, transport and processing of chemical substances. As examples we present the simulation of circadian clock and the G-protein cycle in yeast

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

Membrane Computing as a Modeling Framework. Cellular Systems Case Studies

Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of the living cell, and from the way cells cooperate in tissues, organs, or other populations of cells. This research area developed very fast, both at the theoretical level and in what concerns the applications. After a very short description of the domain, we mention here the main areas where membrane computing was used as a framework for devising models (biology and bio-medicine, linguistics, economics, computer science, etc.), then we discuss in a certain detail the possibility of using membrane computing as a high level computational modeling framework for addressing structural and dynamical aspects of cellular systems. We close with a comprehensive bibliography of membrane computing applications

Parallel Graph Rewriting Systems

In this paper we introduce a new theoretical paradigm, called PGR systems, which can be used to model in a discrete manner some natural phenomena occurring in-vivo/in-vitro en- vironments. PGR systems make use of graphs to describe the spatial structure of space of individuals, while the system dynamics caused by the movement/interaction of individuals is captured by the parallel applications of some graph rewriting rules. In this frame, an il- lustrative example is studied and based on it, an eloquent comparison between the abstract rewriting machines and PGR systems is done. Several further ideas to overcome the global computational effort needed for simulations, but still maintaining the overall ability for mod- eling are finally proposed

Frontiers of Membrane Computing: Open Problems and Research Topics

This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing

On Designing Multicore-aware Simulators for Biological Systems

The stochastic simulation of biological systems is an increasingly popular technique in bioinformatics. It often is an enlightening technique, which may however result in being computational expensive. We discuss the main opportunities to speed it up on multi-core platforms, which pose new challenges for parallelisation techniques. These opportunities are developed in two general families of solutions involving both the single simulation and a bulk of independent simulations (either replicas of derived from parameter sweep). Proposed solutions are tested on the parallelisation of the CWC simulator (Calculus of Wrapped Compartments) that is carried out according to proposed solutions by way of the FastFlow programming framework making possible fast development and efficient execution on multi-cores.Comment: 19 pages + cover pag

Deterministic and stochastic P systems for modelling cellular processes

This paper presents two approaches based on metabolic and stochastic P systems, together with their associated analysis methods, for modelling biological sys- tems and illustrates their use through two case studies.Kingdom's Engineering and Physical Sciences Research Council EP/ E017215/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/D019613/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/F01855X/

Reaction Cycles in Membrane Systems and Molecular Dynamics

We are considering molecular dynamics and (sequential) membrane systems from the viewpoint of Markov chain theory. The first step is to understand the structure of the configuration space, with respect to communicating classes. Instead of a reachability analysis by traditional methods, we use the explicit monoidal structure of this space with respect to rule applications. This leads to the notion of precycle, which is an element of the integer kernel of the stoichiometric matrix. The generators of the set of precycles can be effectively computed by an incremental algorithm due to Contejean and Devie. To arrive at a characterization of cycles, we introduce the notion of defect, which is a set of geometric constraints on a configuration to allow a precycle to be enabled, that is, be a cycle. An important open problem is the effcient calculation of the defects. We also discuss aspects of asymptotic behavior and connectivity, as well as give a biological example, showing the usefulness of the method for model checking

Towards Probabilistic Model Checking on P Systems Using PRISM

This paper presents the use of P systems and π-calculus to model interacting molecular entities and how they are translated into a probabilistic and symbolic model checker called PRISM.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58