Preface -- Part 1; Foundations of Phase Response Analysis -- Introduction to Part 1 -- Chapter 1. The theory of weakly coupled oscillators -- Chapter 2. Phase resetting neural oscillators: Topological theory versus the real world -- Chapter 3. A theoretical framework for the dynamics of multiple intrinsic oscillators in single neurons -- Chapter 4. History of the application of the phase resetting curve to neurons coupled in a pulsatile manner -- Part 2; Estimation of Phase Response Curves -- Introduction to Part 2 -- Chapter 5. Experimentally estimating phase response curves of neurons: Theoretical and practical issues -- Chapter 6. A geometric approach to phase resetting estimation based on mapping temporal to geometric phase -- Chapter 7. PRC estimation with varying width intervals -- Chapter 8. Bayesian approach to estimating phase response curves -- Part 3; Cellular Mechanisms of Neuronal Phase Response Properties -- Introduction to Part 3 -- Chapter 9. Phase response curves to measure ion channel effects on neurons -- Chapter 10. Cellular mechanisms underlying spike-time reliability and stochastic synchronization: Insights and predictions from the phase-response curve -- Chapter 11. Recovery of stimuli encoded with a Hodgkin-Huxley neuron using conditional PRCs -- Chapter 12. Cholinergic neuromodulation controls PRC type in cortical pyramidal neurons -- Chapter 13. Continuum of type I somatic to type II dendritic PRCs; Simulatingin vitro and in vivo phase response properties of a morphologically reconstructed Globus Pallidus neuron model -- Part 4; Prediction of Network Activity with Phase Response Curves -- Introduction to Part4 -- Chapter 14. Understanding activity in electrically coupled networks using PRCs and the theory of weakly coupled oscillators -- Chapter 15. The role of intrinsic cell properties in synchrony of neurons interacting via electrical synapses -- Chapter 16. A PRC description of how inhibitory feedback promotes oscillation stability -- Chapter 17. Existence and stability criteria for phase locked modes in ring networks using phase resetting curves and spike time resetting curves -- Chapter 18. Phase resetting curve analysis of global synchrony, the splay mode and clustering in N neuron all to all pulse-coupled networks -- Chapter 19.  Effects of the frequency dependence of phase response curves on network synchronization -- Chapter 20. Phase-resetting analysis of gamma-frequency synchronization of cortical fast-spiking interneurons using synaptic-like conductance injection.               .

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 excitability as well as other influences of membrane conductances on synaptic integration.  PRCs are efficient encapsulations of the input-output processing of individual neurons to single perturbations and are powerful devices for the prediction and interpretation of patterned neuronal network activity including synchronization phenomena in connected networks or populations receiving shared input.  Thus, application of phase response analysis to neural systems targets the interface of neural computation at the cellular and network levels, one of the most critical and expansive gaps in our understanding of the brain.  This volume surveys the diversity of applications of phase response analysis by many of the prominent theoreticians and experimentalists in the Computational Neurosciences.  Readers will find a thorough introduction to the foundational concepts underlying phase response analysis, advanced techniques for accurate estimation of neuronal PRCs, and impactful illustrations of both the cellular underpinnings of the phase response properties of neurons and the power of phase response analysis to explain network behavior.  Throughout the book, the authors use phase response analysis to elucidate a number of neural systems that are current foci of exciting research in the Computational Neurosciences and are at the forefront of our advancing grasp of the complex mechanisms of brain function and dysfunction.