Markovian Dynamics on Complex Reaction Networks

Abstract

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.

52 pages, 11 figures, for freely available MATLAB software, see http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.html

References in corpus (23)

• Evolutionary games on graphs
• Adaptive Coevolutionary Networks: A Review
• Nonequilibrium phase transition in the coevolution of networks and opinions
• Social Balance on Networks: The Dynamics of Friendship and Enmity
• Sensitivity, robustness and identifiability in stochastic chemical kinetics models
• Stochastic thermodynamics of chemical reaction networks
• Noise bridges dynamical correlation and topology in coupled oscillator networks
• Incorporating postleap checks in tau-leaping
• Heterogeneous Voter Models
• How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
• Amplified biochemical oscillations in cellular systems
• Phenomenological Models of Socio-Economic Network Dynamics
• Coarse graining of master equations with fast and slow states
• Van Kampen's expansion approach in an opinion formation model
• Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models
• Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
• Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics
• Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting
• Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics
• Noise Effects in Nonlinear Biochemical Signaling
• Quantifying Stochastic Effects in Biochemical Reaction Networks using Partitioned Leaping
• An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm
• A Hierarchical Exact Accelerated Stochastic Simulation Algorithm

Cited by in corpus (19)

• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• A scalable computational framework for establishing long-term behavior of stochastic reaction networks
• Multiple-scale stochastic processes: decimation, averaging and beyond
• Adaptive Hybrid Simulations for Multiscale Stochastic Reaction Networks
• A stochastic and dynamical view of pluripotency in mouse embryonic stem cells
• Heterogeneous continuous time random walks
• Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm
• Gillespie algorithms for stochastic multiagent dynamics in populations and network
• Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos
• Stationary distributions via decomposition of stochastic reaction networks
• Stochastic Distinguishability of Markovian Trajectories
• The theory of individual based discrete-time processes
• Rejection-Based Simulation of Non-Markovian Agents on Complex Networks
• Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties
• Biased versus unbiased numerical methods for stochastic simulations
• Chemical master equation parameter exploration using DMRG
• An algebraic approach to product-form stationary distributions for some reaction networks
• Small Open Chemical Systems Theory and Its Implications to Darwinian Evolutionary Dynamics, Complex Self-Organization and Beyond
• Discreteness-induced transitions in multi-body reaction systems