ArticleBiophysical journal2014
The validity of quasi-steady-state approximations in discrete stochastic simulations.
Article in Biophysical journal, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 26 papers.
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Who cites it
26 citing papers in PubMed.
- Exact Formula of the Total Quasi-Steady State Approximation in Competitive Target-Mediated Drug Disposition.Computational and structural biotechnology journal · 2026Article
- How cells tame noise while maintaining ultrasensitive transcriptional responses.PLoS computational biology · 2025Article
- From homogeneity to heterogeneity: Refining stochastic simulations of gene regulation.Computational and structural biotechnology journal · 2025Article
- Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction.Mathematical biosciences · 2024Article
- Beyond homogeneity: Assessing the validity of the Michaelis-Menten rate law in spatially heterogeneous environments.PLoS computational biology · 2024Article
- Theoretical and computational tools to model multistable gene regulatory networks.Reports on progress in physics. Physical Society (Great Britain) · 2023Review
- Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping.iScience · 2023Article
- The effect of microRNA on protein variability and gene expression fidelity.Biophysical journal · 2023Article
- Network design principle for robust oscillatory behaviors with respect to biological noise.eLife · 2022Article
- Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation à la Fenichel.Journal of mathematical biology · 2022Article
- Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression.Nucleic acids research · 2022Article
- On the Validity of the Stochastic Quasi-Steady-State Approximation in Open Enzyme Catalyzed Reactions: Timescale Separation or Singular Perturbation?Bulletin of mathematical biology · 2021Article
- Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities.PLoS computational biology · 2021Article
- Effects of noise and time delay on E2F's expression level in a bistable Rb-E2F gene's regulatory network.IET systems biology · 2021Article
- Misuse of the Michaelis-Menten rate law for protein interaction networks and its remedy.PLoS computational biology · 2020Review
- Basal leakage in oscillation: Coupled transcriptional and translational control using feed-forward loops.PLoS computational biology · 2020Article
- Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach.Journal of mathematical biology · 2020Article
- Bayesian inference of distributed time delay in transcriptional and translational regulation.Bioinformatics (Oxford, England) · 2020Article
- A Systems Biology Approach Identifies Hidden Regulatory Connections Between the Circadian and Cell-Cycle Checkpoints.Frontiers in physiology · 2020Review
- Computational analysis of viable parameter regions in models of synthetic biological systems.Journal of biological engineering · 2019Article
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3 authors.
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Abstract
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.
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