Critical fluctuations in biological systems

Half a century ago, Ken Wilson and Leo Kadanoff introduced the renormalization-group framework for understanding systems with emergent, fractal scale invariance. For five decades, statistical physicists have applied these techniques to equilibrium phase transitions, avalanche models, glasses and disordered systems, the onset of chaos, plastic flow in crystals, surface morphologies, fracture, … But these tools have not made a substantial impact in engineering or biology.
Even now we do not have a clear understanding of the singularity at the critical point for even the traditional equilibrium phase transitions – we know the critical exponents for these transitions to high precision but are missing complete understanding of the universal scaling functions. Also, we have not developed the tools to extend our predictions of the asymptotic behavior to a systematic approximation of the phase diagrams – analytic corrections to scaling. For non-equilibrium and active-matter phase transitions of interest to biology, both exponents and scaling functions may be needed, often with the cell or tissue being close to many interacting transitions.
We will begin with a brief discussion of how universality and scaling may be important to understand systems in physics and biology systems: ‘lipid rafts’ in cell membranes using Ising models, rigidity transitions in physics (granular materials and glasses) and biology (cellular cytoskeletons, intercellular actin and other networks), avalanches in magnets and in neural activity in the brain. We will then embark on a more technical discussion of how well our methods work in models we understand well – Ising models and model rigidity transitions.