dorsal/arxiv
View SchemaStochastic approach to molecular interactions and computational theory of metabolic and genetic regulations
| Authors | Hidenori Kimura, Hiroyuki Okano, Reiko J. Tanaka |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0612011 |
| URL | https://arxiv.org/abs/q-bio/0612011 |
| DOI | 10.1016/j.jtbi.2007.06.017 |
Abstract
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between transcription factors and the operators of genes and that between ligands and binding sites of allosteric enzymes are typical examples of such molecular interactions. In order to obtain the general mathematical framework of biological regulations, we formulate these interactions as finite Markov processes and establish a computational theory of regulatory activities of macromolecules based mainly on graphical analysis of their state transition diagrams. The contribution is summarized as follows: (1) Stochastic interpretation of Michaelis-Menten equation is given. (2) Notion of \textit{probability flow} is introduced in relation to detailed balance. (3) A stochastic analogy of \textit{Wegscheider condition} is given in relation to loops in the state transition diagram. (4) A simple graphical method of computing the regulatory activity in terms of ligands' concentrations is obtained for Wegscheider cases.
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"abstract": "Binding and unbinding of ligands to specific sites of a macromolecule are one\nof the most elementary molecular interactions inside the cell that embody the\ncomputational processes of biological regulations. The interaction between\ntranscription factors and the operators of genes and that between ligands and\nbinding sites of allosteric enzymes are typical examples of such molecular\ninteractions. In order to obtain the general mathematical framework of\nbiological regulations, we formulate these interactions as finite Markov\nprocesses and establish a computational theory of regulatory activities of\nmacromolecules based mainly on graphical analysis of their state transition\ndiagrams. The contribution is summarized as follows: (1) Stochastic\ninterpretation of Michaelis-Menten equation is given. (2) Notion of\n\\textit{probability flow} is introduced in relation to detailed balance. (3) A\nstochastic analogy of \\textit{Wegscheider condition} is given in relation to\nloops in the state transition diagram. (4) A simple graphical method of\ncomputing the regulatory activity in terms of ligands\u0027 concentrations is\nobtained for Wegscheider cases.",
"arxiv_id": "q-bio/0612011",
"authors": [
"Hidenori Kimura",
"Hiroyuki Okano",
"Reiko J. Tanaka"
],
"categories": [
"q-bio.MN",
"q-bio.QM"
],
"doi": "10.1016/j.jtbi.2007.06.017",
"title": "Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations",
"url": "https://arxiv.org/abs/q-bio/0612011"
},
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