ReviewInterface focus2022
The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems.
Review in Interface focus, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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Who cites it
15 citing papers in PubMed.
- Decoupling between activation time and steady-state level in input-output responses.PLoS computational biology · 2026Article
- Thermodynamic limits in far-from-equilibrium molecular templating networks.Newton ((New York, N.Y.) · 2026Article
- Algebraic formulas for first-passage times of Markov processes in the linear framework.Bulletin of mathematical biology · 2025Article
- Decoupling between activation time and steady-state level in input-output responses.bioRxiv : the preprint server for biology · 2025Article
- Limits on the computational expressivity of non-equilibrium biophysical processes.Nature communications · 2025Article
- A mathematical model clarifies the ABC Score formula used in enhancer-gene prediction.bioRxiv : the preprint server for biology · 2024Article
- Flexibility and sensitivity in gene regulation out of equilibrium.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Kinetic Diagram Analysis: A Python Library for Calculating Steady-State Observables of Biochemical Systems Analytically.Journal of chemical theory and computation · 2024Article
- Kinetic Diagram Analysis: A Python Library for Calculating Steady-State Observables of Biochemical Systems Analytically.bioRxiv : the preprint server for biology · 2024Article
- 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
- A logic-incorporated gene regulatory network deciphers principles in cell fate decisions.eLife · 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
- Transcriptional kinetic synergy: A complex landscape revealed by integrating modeling and synthetic biology.Cell systems · 2023Article
- The linear framework II: using graph theory to analyse the transient regime of Markov processes.Frontiers in cell and developmental biology · 2023Article
Corrections and comments
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Authors and funding
3 authors.
Funding
Abstract
The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices represent biochemical species or molecular states, edges represent reactions or transitions and labels represent rates. The graph yields a linear dynamics for molecular concentrations or state probabilities, with the graph Laplacian as the operator, and the labels encode the nonlinear interactions between system and environment. The labels can be specified by vertices of other graphs or by conservation laws or, when the environment consists of thermodynamic reservoirs, they may be constants. In the latter case, the graphs correspond to infinitesimal generators of Markov processes. The key advantage of the framework has been that steady states are determined as rational algebraic functions of the labels by the Matrix-Tree theorems of graph theory. When the system is at thermodynamic equilibrium, this prescription recovers equilibrium statistical mechanics but it continues to hold for non-equilibrium steady states. The framework goes beyond other graph-based approaches in treating the graph as a mathematical object, for which general theorems can be formulated that accommodate biomolecular complexity. It has been particularly effective at analysing enzyme-catalysed modification systems and input-output responses.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.