ReviewInternational journal of molecular sciences2010
The chemical master equation approach to nonequilibrium steady-state of open biochemical systems: linear single-molecule enzyme kinetics and nonlinear biochemical reaction networks.
Review in International journal of molecular sciences, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- Exploring focal adhesion data: dynamic parameter extraction from FRAP and FLAP experiments using chemical master equation.Frontiers in molecular biosciences · 2025Article
- Critical analysis for nonlinear oscillations by least square HPM.Scientific reports · 2024Article
- Theoretical Tools to Quantify Stochastic Fluctuations in Single-Molecule Catalysis by Enzymes and Nanoparticles.ACS omega · 2022Review
- DNA-Topology Simplification by Topoisomerases.Molecules (Basel, Switzerland) · 2021Review
- Programmable and Chemically Fueled DNA Coacervates by Transient Liquid-Liquid Phase Separation.Chem · 2020Article
- ATP-powered molecular recognition to engineer transient multivalency and self-sorting 4D hierarchical systems.Nature communications · 2020Article
- Automatic error control during forward flux sampling of rare events in master equation models.The Journal of chemical physics · 2020Article
- Stochastic geometry sensing and polarization in a lipid kinase-phosphatase competitive reaction.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- Review
- Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters.Journal of the Royal Society, Interface · 2017Review
- Challenges in structural approaches to cell modeling.Journal of molecular biology · 2016Review
- Active Degradation Explains the Distribution of Nuclear Proteins during Cellular Senescence.PloS one · 2015Article
- Discrete-state stochastic models of calcium-regulated calcium influx and subspace dynamics are not well-approximated by ODEs that neglect concentration fluctuations.Computational and mathematical methods in medicine · 2012Article
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Abstract
We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a "punctuated equilibrium" manner.
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