Polynomial Systems Arising in the Study of Biochemical Reaction Networks
summary
Mass-action kinetics produce autonomous polynomial ODEs whose reaction graph forces conservation relations and integer-exponent monomials; for many enzymatic networks a combinatorial criterion makes the steady-state ideal binomial (toric) so positive steady states match nonzero complex solutions, letting algebraic geometry count and parametrize them. Example: a two‑component osmoregulation model fixes one species concentration (x7) for all positive steady states, independent of rate constants. Methods: combinatorics, binomial ideals, semi‑algebraic parameter decomposition.
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chapters (8)
- 0:00Polynomial systems in biochemistry
- 1:24Polynomial systems from networks
- 8:30Bacterial signaling with mass action
- 13:30Enzymatic networks and Michaelis-Menten
- 17:45Conservation relations and steady states
- 21:34Key questions in network analysis
- 26:31Stability and biological observations
- 29:02Stable states and irreversibility
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