Dynamical-systems and stochastic models of biological processes at the physics-biology interface: master equations, transcriptional bursting, FBA, allometric scaling, agent-based ecological models.
Quantitative Biology
Master equation gene expression (van Kampen)
Stochastic gene expression follows chemical master equation dP(n,t)/dt = Σ W(n'→n)P(n',t) − W(n→n')P(n,t). Two-state model (Peccoud-Ycart…
Transcriptional bursting
Suter-Naef 2011: mRNA produced in discrete bursts of ~size β at rate k_on × p_ON. Burst frequency vs burst size encode regulatory…
Gillespie stochastic simulation algorithm
Gillespie 1976/1977: exact stochastic simulation of chemical-reaction networks. Time to next reaction is exponential with rate Σ_μ a_μ;…
Flux balance analysis / COBRA (Palsson)
Palsson 2004: under stoichiometric quasi-steady-state Sv = 0 with linear constraints (lower/upper bounds on each flux), maximise…
Reaction network theory (Feinberg-Horn-Jackson)
Feinberg 1972 / Horn-Jackson 1972 deficiency-zero theorem: weakly-reversible mass-action networks with deficiency δ=0 have unique stable…
Kleiber 3/4-power allometric scaling (West-Brown-Enquist)
Kleiber 1932: basal metabolic rate B ∝ M^{3/4} across mammals (mouse → elephant). West-Brown-Enquist 1997 derive 3/4 from…
Cell-size control (Amir / Nordon adder model)
Amir 2014 / Nordon 2008: bacteria add constant volume Δ between divisions independent of birth size — the 'adder' model. Yields…
Gene expression noise decomposition (Elowitz-Swain)
Elowitz-Levine-Siggia-Swain 2002: 'intrinsic' vs 'extrinsic' noise decomposed via two-color (CFP+YFP) reporter strain — variance(CFP-YFP)/2…
Synthetic circuit dynamics (Elowitz-Leibler design rules)
Beyond toggle/repressilator: predict circuit dynamics from network topology + part-characterisation. Hill-function rate laws for…
Agent-based ecological models (Grimm-Railsback)
Grimm-Railsback 2005: discrete agents (individuals) with rules + spatial environment → emergent population dynamics. ODD protocol…
Moran process (Moran 1958)
Moran 1958: birth-death population genetics process on N individuals. Each step: one individual duplicates (with mutation/selection bias),…
Metabolic control analysis (Kacser-Burns)
Kacser-Burns 1973 / Heinrich-Rapoport 1974: flux through metabolic pathway controlled distributedly by all enzymes;…
Monod growth (1949)
J Monod 1949 + Schaechter-Maaloe-Kjeldgaard 1958 bacterial-growth-laws; modern Hwa 2015 proteome-allocation.
FBA (Edwards 1999)
Edwards-Palsson 1999 + Orth-Thiele-Palsson 2010 flux-balance-analysis; modern COBRA + GEM-models 100s of organisms.
Noise (Elowitz 2002)
Elowitz 2002 intrinsic + extrinsic noise gene-expression; modern Raj-van Oudenaarden 2008 single-molecule mRNA FISH.
Toggle switch (Gardner 2000)
Gardner-Cantor-Collins 2000 + Elowitz-Leibler 2000 repressilator; foundational synthetic-biology genetic-circuits.
Evolutionary dynamics (Nowak 2006)
M Nowak 2006 'Evolutionary Dynamics'; modern moran-process + replicator-mutator + cooperation.
Network biology (Jeong 2000)
Jeong 2000 + Barabasi-Oltvai 2004 network-biology; scale-free metabolic + protein-interaction networks.