Many biological systems at different scales - proteins, cell colonies, bacteria and animal groups- are composed by multiple functional units interacting with each other in a non-trivial way. As a consequence, these systems often display remarkable collective properties, which produce effects that go well beyond the behavior of the single individual.
An archetypical example at the macro scale is flocking, where global coherence and collective motion emerge from inter-individual interactions. Another example at the micro-scale is RNA-based regulation of gene expression. In many such cases, the system as a whole can be schematized as a network of interacting units. From a mechanistic perspective a crucial question is therefore to understand what are the features, in terms of nature of interactions, topology of the network, and individual dynamics, that determine the behavior of the network at collective level. In this project we pursue these issues using concepts and approaches from Statistical Physics. We will exploit our expertise on ordering and out-of-equilibrium phenomena in condensed matter, and our more recent research on living active systems and regulatory networks, to develop novel theoretical models and explain experimental findings.
Let us now discuss the novelty of the proposed research and its expected impact. One remarkable feature of biological systems is that they display efficient large scale behavior - their collective dynamics being often related to some well-defined biological function. Understanding how this can be achieved is therefore an important general open issue.
Theoretical investigations in living active matter have developed along two main directions so far: on the one hand there are numerical works on self-propelled particle models; on the other hand there are hydrodynamic field theories describing the behavior at large scales of 'fluids' of very many of such particles. These approaches allowed to gain an enormous understanding. Still, they have their limits. Many real systems, for example, have finite sizes (below the hydrodynamic limit), with specific boundary conditions, and are far from the idealization of an infinite fluid. Besides, many systems of higher organisms, such as animal groups, have interaction protocols and individual dynamics that are different from the ones assumed in the simplest models: the interaction network is not based on a simple Euclidean metric, and the individual dynamics is inertial on the scales of interest . As a consequence, these systems are able to propagate information through the system in a very efficient way [6] and respond optimally to perturbations. We therefore plan to investigate what could be potential mechanisms leading to such behavior. To this aim, we will study models with different kinds of dynamical rules trying to understand how the dynamics and the interaction typology regulate the collective response of the system. Besides, by exploiting field theory approaches developed on ferromagnetic systems on lattice and off-lattice, we will try to develop a theoretical description of these phenomena. Recent results on midges swarms [7] show that these systems exhibit dynamical scaling, obeying the same kind of dynamical laws observed in condensed matter systems (but with different exponents), and therefore encouraging such an approach. For example, the effect of a perturbation on a moving group (e.g. a predatory attack on a flock) can be modeled as a time dependent external field acting on a ferromagnetic model on a random network [8], and the global response of the network investigated.
Recent research on ferromagnetic systems subject to slowly varying external fields [9] or a time dependent noise [9] can be extremely useful in this respect, indicating how the out of equilibrium effect of the field changes the dynamical scaling of the system [10]. Novel finite-size methods also allow to investigate critical behavior in presence of off-equilibrium dynamics [11].
Another aspect of many active systems, not much explored so far, is related to the non-symmetric nature of interactions between individuals. This asymmetry represents a further source, beyond motility, of non-equilibrium. Recent works [12] showed that it determines a non-trivial response of the system to endogenous fluctuations, enhancing the system's
sensitivity to noise. A schematic way to investigate this problem is to study the fluctuations of a set of orientational degrees of freedom on a direct Euclidean graph. The problem is analogous to the study of the spectra of random Euclidean matrices, which are similar to the Hessian matrices determining the vibrations around the metastable minima of a glassy system, but with direct links. We will try to generalize techniques developed to analyse symmetric Euclidean Random Matrices and their localisation properties to the non-Hermitian case.
In the context of RNA regulation, we have analyzed in some detail the miRNA based post transcriptional, miRNA based regulation network [5,13,14]. We have studied a minimal model of posttranscriptional regulation where the emergence and the nature of the effective interactions can be characterized in detail at steady state. Sensitivity analysis have shown that binding free energies and repression mechanisms are the key ingredients for the cross-talk between ceRNAs to arise. Interactions emerge in specific ranges of repression values, and they can be symmetrical (one ceRNA influences another and vice versa) or asymmetrical (one ceRNA influences another but not the reverse), and may be highly selective, while possibly limited by noise. We have also shown that non trivial correlations among ceRNAs can emerge in experimental readouts due to transcriptional fluctuations even in the absence of miRNA-mediated cross-talk. Our results have had a relevant impact, on a community where the existenced itself of cross-talk phenomena is still a debated issue.