Synchronous and asynchronous dynamics in neuroscience: a statistical physics approach

Resumen

Understanding emergence, evolution and organization of natural systems is one of the main objective of science. Statisical physics has played a prominent role shedding light on the processes underlying order and complexity present in biological systems from a bottomup approach, i.e. recovering the observed collective properties from our knowledge of the elementary components and their interactions. These ideas revolutionized our conception of science during the 20th century, and in the last decades they have become important in areas such as biology or neuroscience, leading to some exciting discoveries and hypotheses that are still in debate. One of the most powerful conceptual ideas is the theory of selforganized criticality proposed by Bak and collaborators in 1987, which proposes that natural systems might be self tuned to the vicinity of a critical point, which would allow them to take advantage of characteristic critical properties such us long-range correlations, large susceptibility, or increased capacity for computation and information processing. Today there is experimental evidence that this the case for some systems in biology. In 2003 Beggs and Plenz observed, in an experimental breakthrough, power-law distributed avalanches, which are usually manifested by critical systems, suggesting that the brain could also work at the edge of a critical phase transition in the universality class of the unbiased branching process, where activity does not grow nor shrink, on average. Almost twenty years later, there is still no conclusive evidence to close the debate on whether the brain, or at least some parts or it, are critical or not. The rich dynamical repertoire of the brain (including bistability, oscillations in several spectral ranges, large irregular outbursts...) has eluded a complete theoretical description in terms of simple models, and even recent experimental data is not completely conclusive on this respect. It has been recently proposed that a way to bring together scale-free avalanches with brain rhythms is to consider synchronization phase transitions and their associated critical points. In this thesis, the criticality hypothesis in the brain is studied from the perspective of synchronization phenomena, discussing under which circumstances synchronization transitions can generate power-law distributed avalanches, as well as their relation with other experimentally-observed aspects of the cortical dynamics such as the balance between excitation and inhibition or bistability. The thesis is organized in the following way: Chapter 1 presents some basics concepts dynamical systems, and critical phenomena, as well as a summary of the issue of criticality in the brain and related philosophical aspects. Chapter 2 is a review of theoretical models for neural and synaptic dynamics, as well as mesoscopic models describing whole regions in an effective way. Relevant concepts from synchronization theory are also sketched here. Chapter 3 introduces the concept of “Jensen’s force” by studying a discrete model that sheds light on the role on inhibition and sparsity in neural networks, and the effect of excitation-inhibition balance. Chapter 4 presents the concept of hybrid synchronization, a novel regime where both partial synchronization and scale-free avalanches can be found together. Chapter 5 presents a review of self-organization theory, including the new concept of self-organized bistability. These concepts are later applied to assess the relationship between self-organization and collective oscillations in cortical dynamics. Chapter 6 sketches future work to develop from here on, including preliminary analyses of more realistic systems. Chapter 7 includes a discussion on the thesis’ results, as well as the conclusions.