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Renormalization group approach to the collective behaviour of strongly correlated biological systems

Periodic Reporting for period 2 - RG.BIO (Renormalization group approach to the collective behaviour of strongly correlated biological systems)

Reporting period: 2020-04-01 to 2021-09-30

Collective behaviour in biological systems cuts across spatial and temporal scales, involving organisms that are greatly different at the taxonomic level. Ranging from clusters of bacteria and colonies of cells, up to insect swarms, bird flocks, and vertebrate groups, collective behaviour entails concepts as diverse as coordination, interaction, information transfer, cooperation, and group decision-making. Amid this jumble, though, a striking connection with statistical physics stands out, namely the emergence of large-scale patterns from local interactions between the elements of the system. It is therefore reasonable to describe collective behavior in biology within the same conceptual framework of statistical physics, in the hope to extend to this alley of biology part of the predictive power of theoretical physics. The cornerstones of this program are the concepts of correlation and scaling.

Collective biological systems are correlated to a degree which is unusually strong. On the one hand, we do not fully understand why correlations are so strong, and conjectures about collective response and fluctuation-dissipation relations remain to be proved. On the other hand, strong correlations allow us to study through the same theoretical looking glass systems as diverse as bird flocks, insect swarms and cell colonies: when correlations extend beyond all microscopic length scales of the system, we are led to believe that details cannot matter a lot. An empirical backup to this idea exists, in the form of scaling laws, which have been found to hold both at the static and at the dynamic level. This scenario suggests that the current landscape of scattered concepts (correlation, universality, scaling) can be brought to a theoretical closure through the main tool that physics developed exactly to this aim, namely the Renormalization Group (RG).

By conducting innovative experimental observations on bird flocks, insect swarms and cell colonies, and building on the statistical physics concepts of correlation and scaling, RG.BIO aims at developing a novel RG approach to strongly correlated biological systems.
EXPERIMENTS - The greatest effort in the first 36 months of RG.BIO has been designing the new panning system for 3D tracking in the field. Standard 3D systems have the orientation of the cameras fixed in time, so that the time duration of the acquisitions is restricted to the short interval of time in which animals are in the cameras' common field of view. To overcome this limit we developed a co-moving 3D system, in which cameras are coupled with rotational stages that drive a controlled rotation of all the cameras yet keeping their calibration. Correspondingly, the computer vision unit developed the new tracking algorithms. We successfully collected new data on bird flocks with the new system, which led to a previously unattainable validation of a new marginal theory for flocks correlations. We also successfully tested the new panning system in the set-up for field experiments on insect swarms under perturbation.

Our previous static 3D technology has been transferred to our collaborators at the University of Perugia, who have been setting up the swarming rooms for malaria mosquitoes 3D experiments. Data collection on malaria swarms is well under way. During September 2021, the static 3D technology was also used in Portland (OR) to collect the first set of data on Vaux’s swift flocks. Finally, we set up the time lapse experiment on stem cells in collaboration with our colleagues at the Policlinico Umberto Primo, and we are looking forward to analysing the data.

THEORY - The primary theoretical objective of RG.BIO is to extend the equilibrium RG technique to the off-equilibrium case of strongly correlated biological systems. To pursue this goal we wrote a novel set of field dynamical equations for the description of flocks and swarms. Our first step was to understand the RG crossover between a phase dominated by symmetry and conservation laws on one side, and that ruled by dissipation on the other side. After that, we tackled another crossover, namely that between equilibrium dynamics and active off-equilibrium dynamics. In the last six months we finally managed to tackle the full RG theory with mode-coupling interactions (inertia) and off-equilibrium self-propulsion (activity). The calculation has been extremely complex (with about 80 Feynman diagrams), but in the end we found a new non-trivial RG fixed point.

We also introduced a novel field theory for the description of anomalous correlations in flocks. We find that a marginal speed-restoring force, which fiercely suppresses large speed fluctuations, while leaving virtually free small speed fluctuations, reproduces the experimental data on flocks far better than any previous theory of flocking, as it successfully tames the entropic blow up of the speed fluctuations. In the last six months we have given an RG solution of the marginal theory, discovering that it is asymptotically free in the infrared limit. This is a prediction confirmed by numerical experiments.
EXPERIMENTS - Thanks to our new 3D panning system we are ready to collect new data on flocks of unprecedented time duration, in such a way to be able to measure the relaxation time of flocks and connect it to the correlation length, finally making us in a position to determine the dynamical critical exponent for these systems, an experimental measurement never performed before. We also expect to be able to use this new experimental method to perform perturbation-response experiments in swarms of insects in the field, possibly shedding light on the generalizations of the fluctuation-dissipation theorem in biological systems. The new experimental setup in malaria mosquitoes swarming rooms is unique to our project, and it will allow us to collect new data, especially on mating, that will carry the field considerably beyond the state of the art. At the same time, the time-lapse system in our stem-cells experiment should start producing data at a great rate.

THEORY - The preparatory work of the last two years put us in a unique position to perform a full-fledged RG calculation of the dynamical critical exponent in natural swarms, using a mode-coupling theory with active self-propulsion terms that drive it out of equilibrium. In the last few months we finally managed to bring to conclusion this calculation, and found a novel RG fixed point where both mode-coupling interaction and off-equilibrium self-propulsion are relevant. The extraordinary result is that the dynamical critical exponent at this fixed point is for the first time in fair agreement with the experimental determinations. Thanks to the universality granted by the RG, this result does not depend on any tuning parameter of the theory: there is just one experimental measurement of the critical exponent and one theoretical determination of that same exponent, and the two agree with each other. The major objective of RG.BIO as described in the original proposal, was to produce "quantitatively accurate, and possibly parameter-free matching between theory and experiment in the theoretical physics tradition". We feel that this last calculation of ours fully achieves this objective and carries the crucial endeavour to reconcile theory and experiment in biological active matter significantly beyond the current state of the art.
Roosting place. Piazza dei Cinquecento, one of the biggest and more stable roosting place in Rome.
Experimental set-up. Data on bird flocks are collected during winter (from November to mid-March).
A flock of starling performing a drop formation while chased by a predator.
The co-moving system. A detail of the new experimental apparatus.