Skip to main content

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

Periodic Reporting for period 1 - RG.BIO (Renormalization group approach to the collective behaviour of strongly correlated biological systems)

Reporting period: 2018-10-01 to 2020-03-31

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 and which would require fine tuning at the physical level. Strong correlations are at the same time the mystery of collective behaviour and the key to unlock this mystery. On the one hand, we do not fully understand why correlations are so strong, and conjectures about collective response and fluctuation-dissipation relations are to be proved. On the other hand, strong correlations allow us to study and compare 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. In absence of any empirical backup, this may look like wishful thinking. But an empirical backup does exist, 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 half a century ago exactly to this aim, namely the renormalization group.

By conducting innovative experimental observations on bird flocks (starlings, swifts), insect swarms (midges, mosquitoes) and cell colonies, and building on the statistical physics concepts of correlation and scaling, RG.BIO aims at developing a novel renormalization group approach to strongly correlated biological systems, with the purpose of classifying into new universality classes the collective phenomena of life.
EXPERIMENTS. The greatest effort in the first 18 months of RG.BIO has been invested into designing and building the new dynamic apparatus for 3D tracking of animal groups in the field. Standard 3D stereo systems are designed in a static fashion with the orientation and the position of the cameras fixed in time, thus with a fixed field of view. The limitation of this set-up is that the time duration of the collected data is restricted only 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 camera system inspired by the human ability to follow the trajectory of a flock with a coordinate movement of the eyes. In the new co-moving system cameras are coupled with rotational stages that drive a controlled rotation of all the cameras in the same direction and with the same rotational speed, actively adapting the field of view to the animal's motion. The introduction of the rotational stages makes the external parameters of the system time-dependent quantities that have to be calibrated frame by frame. This affects not only the experiment that has to be designed to guarantee an easy procedure for the calibration in the field, but also the tracking process that needs to take into account the movement of the cameras. The design of the system, its calibration and the tests on consistency and accuracy in the 3D reconstruction took most of the time of the experimental team, while the computer vision unit developed and tested the new tracking algorithm. We successfully carried out a first pilot experimental campaign on bird flocks, which confirmed the feasibility of the experiment with the new system, which is easy to mount and easy to calibrate, hence it is well-suited for field experiments. These pilot data were also extremely valuable for the development and the debugging of the new 3D tracking algorithm.

THEORY. One of the central ideas inspiring my theoretical understanding of biological collective behaviour, is that the social forces appearing into the equations of motion cannot act directly on the velocities of the animals, but have to be mediated by the spin, namely the generator of the rotations of the velocity itself. This change of perspective allowed our lab to reconcile theory with experiments regarding the propagation of information in bird flocks and the shape of the dynamical correlation functions in insect swarms. In the light of this, our first theoretical effort within RG.BIO has been to perform an RG calculation of a model in which non-dissipative terms coupling the velocity and the spin modes coexisted with the dissipative terms typical of any biological system. We discovered that for low enough dissipation, or small enough groups, dissipation is ineffective, so that the critical exponent ruling the dynamics has a value much closer to the experimental one than previous estimates. We are now studying how these mode-coupling terms impact on hydrodynamics theories with explicit terms of self-propulsion. Finally, we have developed a new marginal field theory, able to explain the scale-free correlations of the speed found in bird flocks as a phenomenon due to the vicinity to a zero temperature critical point, hence avoiding the need to tune any parameter to criticality.
EXPERIMENTS. The current limitation of the new dynamic system is that the rotation of the cameras is manually controlled via a joypad (one joypad controls all the cameras). We plan to develop a LIDAR automatic control of the system. LIDARs are essentially laser-based 3D scanners that retrieve the 3D position of a target by directly measuring the time of flight of the emitted light. At the current state, their accuracy is too low for individual 3D tracking, but it is sufficient to obtain information on the group 3D position. We plan to calibrate the system LIDAR-camera to estimate, from the 3D information gathered with the LIDAR, the 2D velocity of the target group on the 2D sensors of the cameras and automatically adapt the system field of view to follow the group motion.

THEORY. The central theoretical idea of RG.BIO is that the only way to develop a predictive theoretical physics of biological collective phenomena is through a novel renormalization group (RG) approach. The long-term objective of the project is to develop a new RG perturbative theory based on separation of time scales, using correlations and scaling laws as empirical anchors of theoretical work. These results will be tested against the experimental arm of the project, exploring the validity of an RG classification of collective biological phenomena into universality classes. Quantitatively accurate, and possibly parameter-free matching between theory and experiment, in the theoretical physics tradition, will be a major concern of RG.BIO.
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.