Synchronization, Neuronal Excitability, and Information Flow in Networks of Neuronal Oscillators

Synchronization is an omnipresent phenomenon in the dynamics of complex neuronal networks, emerging between single neurons as the simultaneous generation of action potentials and on larger spatial scales in the collective oscillations of neuronal ensembles. Synchronized neuronal activity is connected to various brain functions, neuronal processing and coding but is also associated with brain diseases. Several regulatory mechanism in the brain act locally by changing the dynamical properties of individual neurons or their synaptic connections. Understanding how local properties affect or even control the collective synchronization dynamics thus may provide helpful insights for the study of e.g. pathological synchronization or information transmission in the brain. In this dissertation, we theoretically and experimentally study how local properties of neurons or groups of neurons affect network wide synchronization, dynamic grouping and information routing. First, we propose and derive a general model of pulse-coupled neuronal threshold units with a partial reset that captures the response of neurons to supra-threshold stimulation. We analytically show that this partial reset controls a sequence of desynchronizing bifurcations that destabilize synchronized groups of neurons in the collective network dynamics. Moreover, we develop a general mathematical formalism to study the phase space structure of pulse-coupled units with delayed interactions and reveal that the partial reset controls a novel type of bifurcation scenario from unstable attractor networks prevalent in units with delayed pulse-coupling to heteroclinic switching dynamics. Second, we show that the excitability type of neurons, i.e. their intrinsic characteristic dynamics of generating action potentials, can be changed dynamically. For the general class of conductance based neuron models we analytically derive the bifurcation structure of the neuronal excitability transition and show that it can be induced by a change in neuronal morphology or in leak conductance. Using dynamic patch clamp experiments we confirm the main theoretical predictions, including a qualitative change in the relation between input current to output spike rate, a transition from integration to resonance properties and a region of bistable dynamics. The results indicate that synaptic activity is sufficient to dynamically induce this neuronal excitability switch, thereby providing a flexible mechanism for the dynamic control of synchronization and grouping of neurons in the collective network dynamics. Third, we study the impact of local changes on the information flow in neuronal networks undergoing collective neuronal oscillations. For the general class of stochastic phase-reduced oscillator networks we derive expressions for the delayed mutual information between clusters as a function of the underlying network structure. We use this theory to reveal how information can be rerouted dynamically by switching between different dynamical states. In hierarchical clustered networks we further show how local changes within a group of neurons control the global inter-cluster information flow. Finally, we confirm these findings in a more biophysical realistic network model of spiking neurons undergoing collective gamma oscillations and extend the results to information transfer in the precisely timed spike patterns.

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