Novel mechanisms for phase transitions and self-organization in living systems

Zusammenfassung

ABSTRACT In the study of collective phenomena, phase transitions and self-organized criticality have attracted particular attention. Furthermore, during the last decade, it has been conjectured, based on several empirical evidences, that living systems might benefit from having attributes akin to criticality, such as a large repertoire of dynamical responses, a high sensitivity to environmental changes and an efficient management of the information. First, we focus on such empirical evidence about criticality in living systems. Given the diversity and heterogeneity between such systems, with examples ranging from brain activity to flock dynamics, a general theory for understanding why and how living systems could dynamically tune themselves to be poised in the vicinity of a critical point is lacking. Employing tools from statistical mechanics and information theory, we show that complex adaptive or evolutionary systems can be much more efficient in coping with diverse heterogeneous environmental conditions when operating at criticality, while they remain non-critical for simple and predictable environments [1]. A more robust convergence to criticality emerges in co-evolutionary and co-adaptive set-ups in which individuals aim to represent other agents in the community with fidelity, and the environment is composed, essentially, by the community itself. While, initially, this population consists of simple individuals, complexity emerges as a global attractor of the dynamics, and the community ends to be highly heterogeneous. This result could apply to some bacterial communities and viral populations for which a huge phenotypic variability has been empirically observed. Such a large diversification can be seen as a form of ``bet hedging'', an adaptive survival strategy analogous to stock-market portfolio management, which turns out to be a straightforward consequence of individuals in the community being critical. The second part of this thesis focuses on the study of bet-hedging strategies in the context of population dynamics. Here we analyze a simple model of a community of individuals reproducing by means of two different strategies: a poor but safe strategy or a better but risky (environment-dependent) one. Our main finding is that the benefits of developing bet-hedging strategies are strongly enhanced in highly fluctuating environments, as well as for low-dimensional systems, where intrinsic fluctuations play a key role. A specific case of bet-hedging corresponds to hybrid dispersal strategies developed by certain plants, which have evolved to two spread their offspring by meas of two kind of seeds. We study a simple model of population dynamics equipped with some realistic features typical from these ecosystems, such as inbreeding depression, and we analyze under which conditions hybrid strategies provide a significant gain respect to the pure strategies, and therefore, are more likely to be developed. Finally, we dedicate the last part of this thesis to the study of neural dynamics, in particular to the so-called Up and Down states, a specific case of cortical oscillations in which the activity switches from intense activity intervals (Up) to quiescent periods (Down); additionally, Up and Down states have been related to exhibit fingerprints of self-organized criticality. We focus on the experimental evidence that a class of spontaneous oscillations can emerge within the Up states, but not for Down states. By using different computational models, we show that the collective phenomenon of ``stochastic amplification of fluctuations'', previously described in other contexts such as Ecology and Epidemiology, explains in an elegant manner, beyond model details, this extra-rhythm emerging only in Up states but not in Downs [2]. Summing up, by using different tools from statistical mechanics, information theory, game theory and stochastic processes, this thesis has tried to identify several underlying mechanisms which allow biological systems to successfully operate in their everyday life. Given their general character, it might be expected that living systems in nature have learned, throughout the course of adaptation and evolution, to take advantage of these mechanisms in a wide range of different contexts.