ArticleProceedings of the National Academy of Sciences of the United States of America2018
Structural conditions on complex networks for the Michaelis-Menten input-output response.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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12 citing papers in PubMed.
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- The Hill function is the universal Hopfield barrier for sharpness of input-output responses.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- The Hill function is the universal Hopfield barrier for sharpness of input-output responses.bioRxiv : the preprint server for biology · 2024Article
- Thermodynamic bounds on ultrasensitivity in covalent switching.Biophysical journal · 2023Article
- Size limits the sensitivity of kinetic schemes.Nature communications · 2023Article
- The linear framework II: using graph theory to analyse the transient regime of Markov processes.Frontiers in cell and developmental biology · 2023Article
- The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems.Interface focus · 2022Review
- An optimal growth law for RNA composition and its partial implementation through ribosomal and tRNA gene locations in bacterial genomes.PLoS genetics · 2021Article
- Allosteric conformational ensembles have unlimited capacity for integrating information.eLife · 2021Article
- Bayesian inference and comparison of stochastic transcription elongation models.PLoS computational biology · 2020Article
- Negative reciprocity, not ordered assembly, underlies the interaction of Sox2 and Oct4 on DNA.eLife · 2019Article
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Abstract
The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.
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