Modeling biological systems with delays in Bio-PEPA

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Generalized Communicating P Systems Working in Fair Sequential Model

In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition. We show that PP can be seen as a particular variant of GCPS. We also consider a particular stochastic evolution satisfying the fairness condition and obtain that it corresponds to the run of a Gillespie's SSA. This permits to further describe the dynamics of GCPS by a system of ODEs when the population size goes to the infinity.Comment: Presented at MeCBIC 201

Language-based Abstractions for Dynamical Systems

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366

Controlled diffusion processes with markovian switchings for modeling dynamical engineering systems

A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the complexity of these systems by introducing a methodology based on Stochastic Differential Equations (SDE) models. We focus on specific type of complexity derived from unpredictable abrupt and/or structural changes. In this paper an approach based on controlled Stochastic Differential Equations with Markovian Switchings (SDEMS) is proposed. Technical conditions for the existence and uniqueness of the solution of these models are provided. We treat with nonlinear SDEMS that does not have closed solutions. Then, a numerical approximation to the exact solution based on the Euler- Maruyama Method (EM) is proposed. Convergence in strong sense and stability are provided. Promising applications for selected industrial biochemical systems are showed

Markovian Dynamics on Complex Reaction Networks

Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm

Modelling non-Markovian dynamics in biochemical reactions

Biochemical reactions are often modelled as discrete-state continuous-time stochastic processes evolving as memoryless Markov processes. However, in some cases, biochemical systems exhibit non-Markovian dynamics. We propose here a methodology for building stochastic simulation algorithms which model more precisely non-Markovian processes in some specific situations. Our methodology is based on Constraint Programming and is implemented by using Gecode, a state-of-the-art framework for constraint solving

Extended Differential Aggregations in Process Algebra for Performance and Biology

We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required perfect symmetry for exact aggregation, we present approximate fluid lumpability, which makes nearby processes perfectly symmetric after a perturbation of their parameters. We prove that small perturbations yield nearby differential trajectories. Numerically, we show that many heterogeneous processes can be aggregated with negligible errors.Comment: In Proceedings QAPL 2014, arXiv:1406.156