ArticleBulletin of mathematical biology2016
State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation.
Article in Bulletin of mathematical biology, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 23 papers.
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23 citing papers in PubMed.
- Truncating the time-evolving discrete chemical master equation for stochastic biological networks.Biophysical journal · 2026Article
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- Tensor product algorithms for inference of contact network from epidemiological data.BMC bioinformatics · 2024Article
- Distilling dynamical knowledge from stochastic reaction networks.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Gene expression model inference from snapshot RNA data using Bayesian non-parametrics.Nature computational science · 2023Article
- Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise.Frontiers in cell and developmental biology · 2023Article
- Inferring initial state of the ancestral network of cellular fate decision: a case study of phage lambda.Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference · 2021Article
- Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry.Molecular biology of the cell · 2021Article
- Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality.Frontiers in genetics · 2021Article
- Effects of niche overlap on coexistence, fixation and invasion in a population of two interacting species.Royal Society open science · 2020Article
- BAYESIAN INFERENCE OF STOCHASTIC REACTION NETWORKS USING MULTIFIDELITY SEQUENTIAL TEMPERED MARKOV CHAIN MONTE CARLO.International journal for uncertainty quantification · 2020Article
- Discrete and continuous models of probability flux of switching dynamics: Uncovering stochastic oscillations in a toggle-switch system.The Journal of chemical physics · 2019Article
- Sensitivities of Regulation Intensities in Feed-Forward Loops with Multistability.Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference · 2019Article
- Evolution of Coagulation-Fragmentation Stochastic Processes Using Accurate Chemical Master Equation Approach.Communications in information and systems · 2019Article
- Probabilistic control of HIV latency and transactivation by the Tat gene circuit.Proceedings of the National Academy of Sciences of the United States of America · 2018Article
- Discrete flux and velocity fields of probability and their global maps in reaction systems.The Journal of chemical physics · 2018Article
- Nonlatching positive feedback enables robust bimodality by decoupling expression noise from the mean.PLoS biology · 2017Article
- PRODIGEN: visualizing the probability landscape of stochastic gene regulatory networks in state and time space.BMC bioinformatics · 2017Article
- Mechanisms of stochastic focusing and defocusing in biological reaction networks: insight from accurate chemical master equation (ACME) solutions.Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference · 2016Article
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Abstract
The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.
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