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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.03684 |
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| _version_ | 1866910904101109760 |
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| author | Qu, Jiaji Rajbhandari, Malini |
| author_facet | Qu, Jiaji Rajbhandari, Malini |
| contents | Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stochastic fluctuations, particularly at low copy numbers or single-enzyme levels, can profoundly impact reaction outcomes. In this paper, we present a comprehensive view of enzyme kinetics from both deterministic and stochastic perspectives. We begin by deriving the classical Michaelis-Menten equation under the quasi-steady-state assumption (QSSA) and discuss its validity. We then formulate the corresponding stochastic model via the chemical master equation (CME) and illustrate how the Gillespie algorithm can simulate single-molecule events and briefly use Kampen's system-size expansion to justify our simulation methods. Through extended computational analyses -- including variance calculations, phase-plane exploration, and parameter sensitivity -- we highlight how deterministic and stochastic predictions coincide in certain limits but can diverge in small systems. We further incorporate case studies from single-enzyme turnover experiments and cellular contexts to showcase the real-world implications of noise. Taken together, our results underscore the necessity of a multifaceted modeling strategy, whereby one can switch between deterministic methods and stochastic realism to gain a fuller understanding of enzyme kinetics at different scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deterministic and Stochastic Models in Enzyme Kinetics Qu, Jiaji Rajbhandari, Malini Molecular Networks Subcellular Processes Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stochastic fluctuations, particularly at low copy numbers or single-enzyme levels, can profoundly impact reaction outcomes. In this paper, we present a comprehensive view of enzyme kinetics from both deterministic and stochastic perspectives. We begin by deriving the classical Michaelis-Menten equation under the quasi-steady-state assumption (QSSA) and discuss its validity. We then formulate the corresponding stochastic model via the chemical master equation (CME) and illustrate how the Gillespie algorithm can simulate single-molecule events and briefly use Kampen's system-size expansion to justify our simulation methods. Through extended computational analyses -- including variance calculations, phase-plane exploration, and parameter sensitivity -- we highlight how deterministic and stochastic predictions coincide in certain limits but can diverge in small systems. We further incorporate case studies from single-enzyme turnover experiments and cellular contexts to showcase the real-world implications of noise. Taken together, our results underscore the necessity of a multifaceted modeling strategy, whereby one can switch between deterministic methods and stochastic realism to gain a fuller understanding of enzyme kinetics at different scales. |
| title | Deterministic and Stochastic Models in Enzyme Kinetics |
| topic | Molecular Networks Subcellular Processes |
| url | https://arxiv.org/abs/2504.03684 |