A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays
arXiv:0708.0370 · doi:10.1063/1.2799998
Abstract
Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie Algorithm or the Next Reaction Method. In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified Next Reaction Method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays.
25 pages, 1 figure. Some minor changes made to add clarity
References in corpus (1)
Cited by in corpus (104)
- Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
- Simulating the evolution of soot mixing state with a particle-resolved aerosol model
- Pooling single-cell recordings: Scalable inference through heterogeneous kinetics
- The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data
- Incorporating postleap checks in tau-leaping
- Temporal Gillespie algorithm: Fast simulation of contagion processes on time-varying networks
- Simulating non-Markovian stochastic processes
- Master equations and the theory of stochastic path integrals
- Markovian Dynamics on Complex Reaction Networks
- Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
- Stochastic Simulation of Biomolecular Networks in Dynamic Environments
- A Gillespie algorithm for non-Markovian stochastic processes
- Error analysis of tau-leap simulation methods
- Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation
- Stochastic amplification in an epidemic model with seasonal forcing
- Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics
- Limit cycles, complex Floquet multipliers and intrinsic noise
- The interplay of intrinsic and extrinsic bounded noises in genetic networks
- Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments
- Population Dynamics in a Changing Environment: Random versus Periodic Switching
- Intrinsic fluctuations in stochastic delay systems: theoretical description and application to a simple model of gene regulation
- Hybrid framework for the simulation of stochastic chemical kinetics
- Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics
- Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes
- Impact of environmental colored noise in single-species population dynamics
- An adaptive multi-level simulation algorithm for stochastic biological systems
- Model reduction for stochastic chemical systems with abundant species
- Attempt-time Monte Carlo: an alternative for simulation of stochastic jump processes with time-dependent transition rates
- Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise
- Extending the multi-level method for the simulation of stochastic biological systems
- Stochastic effects in a seasonally forced epidemic model
- Topological time-series analysis with delay-variant embedding
- Gillespie algorithms for stochastic multiagent dynamics in populations and network
- Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system
- Has wild poliovirus been eliminated from Nigeria?
- Marginal process framework: A model reduction tool for Markov jump processes
- State and parameter estimation from exact partial state observation in stochastic reaction networks
- Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise
- Modeling the long term dynamics of pre-vaccination pertussis
- Using tensor network states for multi-particle Brownian ratchets
- Efficient Finite Difference Method for Computing Sensitivities of Biochemical Reactions
- On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems
- Maximizing Information Gain for the Characterization of Biomolecular Circuits
- Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes
- Physical approaches to the dynamics of genetic circuits: A tutorial
- Analytical and numerical treatment of continuous ageing in the voter model
- Constant-complexity Stochastic Simulation Algorithm with Optimal Binning
- A new approach to simulating stochastic delayed systems
- Anomalous diffusion and long-range memory in the scaled voter model
- Computing time-periodic steady-state currents via the time evolution of tensor network states
- Multilevel Hybrid Split-Step Implicit Tau-Leap
- Quasi-Monte Carlo methods applied to tau-leaping in stochastic biological systems
- Population Extinction under Bursty Reproduction in a Time Modulated Environment
- Importance sampling for partially observed temporal epidemic models
- On the motion of kinesin in a viscoelastic medium
- Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
- Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size
- Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronised oscillations in the presomitic mesoderm
- Population switching under a time-varying environment
- Stochastic Averaging and Sensitivity Analysis for Two Scale Reaction Networks
- Uniformisation techniques for stochastic simulation of chemical reaction networks
- Robustly simulating biochemical reaction kinetics using multi-level Monte Carlo approaches
- Mean-field models for non-Markovian epidemics on networks: from edge-based compartmental to pairwise models
- A finite state projection method for steady-state sensitivity analysis of stochastic reaction networks
- Efficient parameter sensitivity computation for spatially-extended reaction networks
- Delayed interactions in the noisy voter model through the periodic polling mechanism
- Inference of plasmid copy number mean and noise from single cell gene expression data
- Bending fluctuations in semiflexible, inextensible, slender filaments in Stokes flow: towards a spectral discretization
- Stochastic reaction networks within interacting compartments
- Direct numerical method for counting statistics in stochastic processes
- Stochastic fluctuations and quasi-pattern formation in reaction-diffusion systems with anomalous transport
- Learning-Based Importance Sampling via Stochastic Optimal Control for Stochastic Reaction Networks
- Boundary value for a nonlinear transport equation emerging from a stochastic coagulation-fragmentation type model
- Low variance couplings for stochastic models of intracellular processes with time-dependent rate functions
- A new twist for the simulation of hybrid systems using the true jump method
- Stochastic Modeling and Statistical Inference of Intrinsic Noise in Gene Regulation System via Chemical Master Equation
- Weak error analysis of numerical methods for stochastic models of population processes
- Stochastic Filtering of Reaction Networks Partially Observed in Time Snapshots
- Automated Importance Sampling via Optimal Control for Stochastic Reaction Networks: A Markovian Projection-based Approach
- Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control
- Multilevel Hybrid Chernoff Tau-leap
- An Efficient Forward-Reverse Expectation-Maximization Algorithm for Statistical Inference in Stochastic Reaction Networks
- Importance sampling for a robust and efficient multilevel Monte Carlo estimator for stochastic reaction networks
- A Diffusion-Based Embedding of the Stochastic Simulation Algorithm in Continuous Space
- Some network conditions for positive recurrence of stochastically modeled reaction networks
- Computational complexity analysis for Monte Carlo approximations of classically scaled population processes
- Generating functionals and Gaussian approximations for interruptible delay reactions
- Markov-bridge generation of transition paths and its application to cell-fate choice
- Hybrid Pathwise Sensitivity Methods for Discrete Stochastic Models of Chemical Reaction Systems
- Complexity of Multilevel Monte Carlo Tau-Leaping
- Stochastic filters based on hybrid approximations of multiscale stochastic reaction networks
- An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains
- Product-form stationary distributions for deficiency zero chemical reaction networks
- Conditions for Extinction Events in Chemical Reaction Networks with Discrete State Spaces
- Stochastic simulation of biochemical systems with randomly fluctuating rate constants
- Stochastic analysis of biochemical reaction networks with absolute concentration robustness
- Demon with dementia - the deterioration of information transcription
- Fast reactions with non-interacting species in stochastic reaction networks
- An asymptotic relationship between coupling methods for stochastically modeled population processes
- Variance of finite difference methods for reaction networks with non-Lipschitz rate functions
- Efficient simulation techniques for biochemical reaction networks
- Characterizing the dynamics of rubella relative to measles: the role of stochasticity
- Discrete Stochastic Models in Continuous Time for Ecology
- Effect Of Site Selective Ion Channel Blocking on Action Potential