The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries \(A_{i,j}\) and \(A_{j,i}\) are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology.

During their life, because of transients, fluctuations and environmental stresses, proteins undergo several conformational transitions that challenge their ability to reach and maintain their native, functional state. Cells have evolved an array of molecular machines, collectively called chaperones, that are able, through ATP hydrolysis, thus by energy consumption, to move proteins in a non-equilibrium steady state where the populations of the different conformations do not necessarily correlate with their thermodynamic stability.

The continuous development of theoretical models and computational methods has contributed to an unprecedented arsenal of different and/or complementary approaches aimed at the investigation of nature. However, only the comparison between model predictions and experimental data can ultimately assess the quality of the chosen model of reference. In this respect, biological materials constitute a challenging yet paradigmatic benchmark for the application of theoretical physics in an integrative approach that takes into account also the particularities of the involved disciplines. In this talk, I will present case studies in which theoretical models and computational methods allowed us to interpret experimental data and elucidate observed puzzling phenomena. In each presented case, the questions posed by the experimental investigations dictated the choice of the interpretative model that, in turn, lead to a progress in the understanding of the observed behavior. This could not have been achieved without a close collaboration and a continuous exchange of information between scientists with most diverse backgrounds. However, this integrative approach requires a great amount of patience and a rather uncommon versatility in dealing with different jargons and views. These epistemological aspects will be highlighted in each of the presented case studies, with the conviction in that they represent the key to achieve excellence in this intriguing field of research.

We will review the results obtained from the study of a two-dimensional system of active dumbbells, introduced as a paradigmatic example of a system of non symmetrical brownian particles with self-propulsion. Each dumbbell is composed by two colloids permanently kept together, with an excluded volume interaction modeled through a Weeks-Chandler-Anderson (WCA) potential. They are immersed in an implicit solvent modeled by the Langevin equation. The activity or self-propulsion is represented by a constant force acting on the principal direction of the dumbbell. We find that activity triggers a nonequilibrium phase separation between a gaseous phase and a phase with clusters. We study the kinetics of the aggregates of dumbbells in the phase separated region. The clusters spontaneously break chiral symmetry and rotate; they also display a nematic ordering with spiral patterns. We will also relate this phase separation to the transitions occurring in the system without activity. On the other hand, for the phase without aggregation, we determine the translational and rotational diffusion properties. Different regimes can be observed, depending on the combination of the random noise, activity and density of the system. Unusual increase with density of the rotational diffusion coefficient is found and explained as due to clustering. Fluctuations have been also examined from the point of view of large deviation theory. The rate function for the active work on each particle has been determined showing non-singular behaviour interpreted as a condensation transition.

The relationships between the core-periphery architecture of the species interaction network and the mechanisms ensuring the stability in mutualistic ecological communities are still unclear. In particular, most studies have focused their attention on asymptotic resilience or persistence, neglecting how perturbations propagate through the system. Here we develop a theoretical framework to evaluate the relationship between the architecture of the interaction networks and the impact of perturbations by studying localization, a measure describing the ability of the perturbation to propagate through the network. We show that mutualistic ecological communities are localized, and localization reduces perturbation propagation and attenuates its impact on species abundance. Localization depends on the topology of the interaction networks, and it positively correlates with the variance of the weighted degree distribution, a signature of the network topological heterogeneity. Our re sults provide a different perspective on the interplay between the architecture of interaction networks in mutualistic communities and their stability.
NATURE COMMUNICATIONS | 6:10179 | DOI: 10.1038/ncomms10179 |
www.nature.com/naturecommunications

The finite-size scaling method was originally developed to analyse the properties of physical systems near phase transitions, allowing to compute the values of the critical exponents and their relations, and to precisely define the notion of universality. Allometric relationships have also been found in many biological and ecological systems, and scaling laws have been successfully used to provide a unified description to seemingly unrelated empirical patterns. The most famous scaling relationship in biology is probably Kleiber's law that relates an organism's metabolic rate with its mass: for animals and plants spanning more than ten orders of magnitude in body size, the metabolic rate scales approximately as the mass to the power 3/4. Quarter power scaling with body mass is also observed for many characteristic times and rates, such as life times and heart rates. The universality of these exponents suggests that there might be a general explanation for them that only relies on few fundamental features common to such a diverse range of systems. In this talk I will present a framework based on finite-size scaling and optimisation principles that can provide a general explanation to Kleiber's law and a consistent description of the structure of many biological and ecological systems, focusing in particular on river basins and tropical forests. I will also discuss the possibility to use a similar framework to describe the patterns of population distribution observed in urban systems.

Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal distributions of activity in neuroscience and other fields, we propose and analyze a theory for the self-organization to the point of phase-coexistence in systems exhibiting a first-order phase transition. It explains the emergence of regular avalanches with attributes of scale-invariance which coexist with huge anomalous ones, with realizations in many fields, including neuroscience.