Criticality in living systems

Research summary

One paper, summarised for reference. Colloquium: Criticality and dynamical scaling in living systems — Miguel A. Muñoz, Rev. Mod. Phys. (2018) 90, 031001 (arXiv:1712.04499). doi:10.1103/RevModPhys.90.031001.

The hypothesis, and the framing

The authoritative review of the criticality hypothesis: that biological systems — parts, aspects, or groups of them — may draw functional benefits from operating near the critical point of a continuous phase transition, balancing robustness (order) against flexibility (disorder) while gaining maximal sensitivity, large dynamical repertoires, and optimal computation. Muñoz deliberately takes the dynamical / non-equilibrium view (there is an underlying process poised near a transition), as distinct from the statistical-criticality view (analyse the statistics of configurations), and reviews the evidence with pointed skepticism — the signatures are appealing but there is “no smoking gun.”

The vocabulary of criticality

• Scale invariance = power laws. $P(x)=Ax^{-\alpha}$ is the only distribution unchanged under rescaling; the statistical trademark of criticality (versus a characteristic scale).
• The contact / branching process (the prototype absorbing-state transition): active nodes die at unit rate and spawn neighbours at rate $\lambda$; a mean-field bifurcation at $\lambda_c=1$ separates a quiescent (absorbing) phase from an active one. At criticality: critical slowing down ($\rho(t)\sim t^{-1}$), diverging susceptibility, and avalanches with power-law sizes ($P(S)\sim S^{-\tau}$, $\tau=3/2$) and durations ($\sim T^{-2}$) — the mean-field (Galton–Watson) branching exponents. Finite systems obey finite-size scaling $P(S,N)\sim S^{-\tau}G(S/N)$.
• Damage spreading — evolve two replicas differing by one perturbation; it grows (chaotic), shrinks (ordered), or is marginal (critical), gauging the dynamical regime.
• Self-organized criticality (SOC) — the sandpile: a feedback loop between activity and a slowly-driven control parameter (slow drive + fast dissipation) self-tunes to the critical point if timescales separate infinitely and dynamics conserve. Otherwise → self-organized quasi-criticality (hovering around the point with excursions) or nothing. Also adaptive criticality (network rewiring).
• Generic scale invariance (Grinstein) — scaling across extended regions without tuning, via broken continuous symmetry, quenched disorder → Griffiths phases, or neutral dynamics.
• Statistical criticality — maximum-entropy Ising-like models inferred from data (retina, flocks, immune repertoire) sit at $\beta_c\approx1$; but this can be an artifact of marginalising hidden variables / of fitting feature-rich data (Schwab, Marsili).

Functional advantages

• Sensory criticality (the clean case). Inner-ear hair cells sit at a Hopf bifurcation: the response goes nonlinear, $R\sim F^{1/3}$, so the gain $R/F\sim F^{-2/3}$ diverges for tiny signals at the characteristic frequency — extreme sensitivity plus sharp frequency selectivity; coupling many Hopf oscillators (cochlea) yields a genuine critical point.
• Maximal sensitivity / dynamic range (Kinouchi–Copelli — peaks at $\lambda_c$), large correlations (coordination), critical slowing down (long memories), and a maximal dynamical repertoire (variability of patterns).
• Computation at the edge of chaos (Langton) — optimal trade-off between information storage and transmission (Turing’s two ingredients). This is the basis of reservoir computing (echo-state networks, liquid-state machines), which performs best near a critical point.

The empirical tour (in brief)

• Neural — spontaneous cortical activity; neuronal avalanches (Beggs–Plenz: $\tau\approx3/2$, $\alpha\approx2$, a universal avalanche shape); edges of synchronization, global stability, percolation, and a thermodynamic (retinal maxent) transition; criticality fades in seizure, anaesthesia, and sleep.
• Gene regulatory networks — RBNs critical near $\langle K\rangle=2$ (Derrida $\zeta=1$); damage-spreading best-fits real microarray data at criticality; Zipf’s law in gene expression.
• Collective motion — flocks with scale-free correlations (speed fluctuations not explained by a Goldstone mode → tuning to a critical point); insect swarms regulating density (finite-size scaling); sheep herds’ intermittent packing; ant foraging poised between exploration and recruitment.

Why it’s collected here

This is the reference the other papers hang off, and it is unusually concrete for this lab: it is the canonical statement of reservoir computing at criticality, of branching/avalanche exponents ($\tau=3/2$), and of self-organized quasi-criticality (the honest alternative to a clean rate-clamp); and its section on the thresholding, time-binning, and sub-sampling pitfalls of avalanche measurement — plus the “causally-defined vs time-binned avalanches” gap — is a direct checklist for any cluster / avalanche analysis run on the harness.

The skeptic’s caution

Avalanche evidence is dogged by thresholding, time-binning, and sub-sampling artifacts (which can manufacture exponents), and rarely spans more than 2–3 decades. A deeper worry is a near-tautology: feature-rich, multi-scale data are best fit by a model tuned near its critical point simply because that is the only regime generating multi-scale patterns. Hence the open dichotomy — is biological criticality a real organizing principle, or a reflection of our models’ limits? Finite systems are never truly critical (do finite-size analysis; name the two phases), and generic scale invariance / Griffiths phases may supply the scaling without fine-tuning.

References

Muñoz (2018), Rev. Mod. Phys. 90, 031001 · Mora & Bialek (2011), J. Stat. Phys. 144, 268 · Beggs & Plenz (2003), J. Neurosci. 23, 11167 · Bak, Tang & Wiesenfeld (1987), Phys. Rev. Lett. 59, 381 · Kinouchi & Copelli (2006), Nat. Phys. 2, 348 · Langton (1990), Physica D 42, 12 · Bonachela & Muñoz (2009), J. Stat. Mech., P09009 · Schwab, Nemenman & Mehta (2014), Phys. Rev. Lett. 113, 068102 · Clauset, Shalizi & Newman (2009), SIAM Rev. 51, 661 · Cavagna et al. (2010), PNAS 107, 11865.