Chaotic Neural Circuit Dynamics

Abstract

Information is processed in the brain by the coordinated activity of large neural circuits. Yet, we are still only starting to understand how this high-dimensional complex system gives rise to functions such as processing sensory information, making decisions and controlling behavior. Technological advances such as optogenetics and cellular resolution imaging provide tools to measure and manipulate the activity of many neurons simultaneously. These developments open novel avenues for the interplay of theory and experiment in neuroscience and foster the development of mathematical approaches for the systematic dissection and understanding of cortical information processing. This will undoubtedly allow more systematic and comprehensive insights into the brain's structure, function, dynamics, and plasticity. But given the complexity of neural network dynamics, it is not yet clear to what extent this will also give rise to a better conceptual and quantitative understanding of principles underlying neural circuit information processing. Depending on the specific question, we might need a diversity of theoretical concepts and perspectives. Among these are both mechanistic bottom-up approaches which assemble simplified well-understood units into circuits giving rise to less-understood network dynamics and normative top-down approaches, starting for example from information theoretic, geometric or evolutionary constraints to infer how computations should be performed. How information is encoded, processed and transmitted by neural circuits is intimately related to their collective network dynamics. Therefore, it is desirable to better understand how different factors shape the patterns of activity across neural populations. Prominent factors that shape circuit dynamics include single-cell properties, synaptic features, network topology and external input statistics. In this thesis, we develop novel numerical and analytical techniques from dynamical systems, stochastic processes and information theory to characterize the evoked and spontaneous dynamics and phase space organization of large neural circuit models. Our target is to determine how biophysical properties of neurons and network parameters influence information transmission. We investigate the role and relevance of single-cell properties in the collective network dynamics and study how the statistics of external input spike trains affect the chaoticity and reliability of balanced target circuits. By varying the statistics of the streams of input spike trains and investigating the scaling of properties of the collective dynamics with different network parameters, we identify key parameters that regulate information transmission and the ability to control the activity states in a driven network.