Dynamical Probabilistic P Systems: Definitions and Applications

We introduce dynamical probabilistic P systems, a variant where probabilities associated to the rules change during the evolution of the system, as a new approach to the analysis and simulation of the behavior of complex systems. We define the notions for the analysis of the dynamics and we show some applications for the investigation of the properties of the Brusselator (a simple scheme for the Belousov-Zabothinskii reaction), the Lotka-Volterra system and the decay process

Stochastic Approaches in P Systems for Simulating Biological Systems

Different stochastic strategies for modeling biological systems with P systems are reviewed in this paper, such as the multi-compartmental approach and dynamical probabilistic P systems. The respective results obtained from the simulations of a test case study (the quorum sensing phenomena in Vibrio Fischeri colonies) are shown, compared and discussed

Simulating Tritrophic Interactions by Means of P Systems

P systems provide a high level computational modelling framework that combines the structural and dynamical aspects of ecosystems in a compressive and relevant way. The inherent randomness and uncertainty in biological systems is captured by using probabilistic strategies. The design of efficient simulation algorithms in order to reproduce the behavior of these computational models over conventional computers is fundamental for the validation and virtual experimentation processes. In this paper, we describe the modelling framework and two different simulation algorithms. As a case study, a P system based model of an ideal ecosystem with three trophic levels is designed and simulated by both simulation algorithms, providing comparisons of efficiency between them

Toll Based Measures for Dynamical Graphs

Biological networks are one of the most studied object in computational biology. Several methods have been developed for studying qualitative properties of biological networks. Last decade had seen the improvement of molecular techniques that make quantitative analyses reachable. One of the major biological modelling goals is therefore to deal with the quantitative aspect of biological graphs. We propose a probabilistic model that suits with this quantitative aspects. Our model combines graph with several dynamical sources. It emphazises various asymptotic statistical properties that might be useful for giving biological insightsComment: 11 page

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. Although there exist sophisticated algorithms to determine the dynamics of discrete models, their implementations usually require labor-intensive formatting of the model formulation, and they are oftentimes not accessible to users without programming skills. Efficient analysis methods are needed that are accessible to modelers and easy to use. Method: By converting discrete models into algebraic models, tools from computational algebra can be used to analyze their dynamics. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes, and robustness, i.e., small number of attractors