Phase Response Curves in Neuroscience Theory, Experiment, and Analys

Neuronal phase response curves (PRCs) summarize the relationship between the timing of inputs within a neuron’s spike cycle and the consequent shifts in output spike timing.  The form of a neuron’s PRC reflects its mechanism of spike initiation or ex

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Prediction of Network Activity with Phase Response Curves

Introduction The first three parts of this text have introduced the theoretical foundations of phase response analysis; outlined strategies for estimation of neuronal PRCs; detailed the cellular mechanisms underlying phase response properties of a number of neuronal systems of varying complexity and under a variety of conditions representative of diverse neural functions; and in many cases introduced relationships between PRCs and patterning of network behavior. The content of the last part of the book builds upon these earlier materials to extend PRC analysis to a number of current foci in the field. The chapters in Part IV describe uses of PRCs for prediction or interpretation of network activity and tie the network level of neural processing to its cellular substrates. Chapter 14 by Lewis and Skinner considers electrical coupling between pairs of integrate-and-fire models, conductance-based models, and multicompartmental models to address how phase response curves (PRCs) and weakly coupled oscillator theory can be used to understand patterned activity in networks of spiking cortical neurons. In Chap. 15, Hansel et al. extend this analysis to larger networks and consider coupling through both chemical synapses and electrical synapses. They show that synchronization mediated by electrical synapses is more versatile than previously considered and depends on the intrinsic currents and morphology of neurons as well as on the combination of electrical and inhibitory synapses. Inhibitory synapses are ubiquitous in networks of oscillatory neurons, including central pattern-generating circuits. In Chap. 16, Nadim et al. use the concept of a synaptic PRC to examine a possible role of feedback inhibition as a promoter of oscillation stability in the face of extrinsic perturbations. Chapter 17 by Oprisan details how the existence and stability of phase-locked modes in ring networks can be predicted using phase-resetting curves and spike time resetting curves of the individual network components. PRC theory is used by Achuthan et al. in Chap. 18 to analyze phase-locked patterns in pulse-coupled allto-all networks of neurons that receive multiple inputs per cycle. They show that the

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Prediction of Network Activity with Phase Response Curves

existence and stability of synchronous clusters of neurons in the network can to a large extent be explained by factors that influence the slope of the PRC. In Chap. 19, Fink et al. investigate the differential effects of type I and type II PRCs on network synchrony by simulating large-scale networks of Morris– Lecar neurons with excitatory coupling. They demonstrate that as the intrinsic frequency of component neurons is increased, type I phase response properties promote increased network synchrony, while type II properties lead to reduced network synchrony. Finally, Chap. 20 by Zeberg et al. uses a phase-resetting model based on the synaptic phase-resetting function to show how the intrinsic properties of cortical fas