A universal model for spike-frequency adaptation

Spike-frequency adaptation is a prominent feature of neural dynamics. Among other mechanisms, various ionic currents modulating spike generation cause this type of neural adaptation. Prominent examples are voltage-gated potassium currents (M-type currents), the interplay of calcium currents and intracellular calcium dynamics with calcium-gated potassium channels (AHP-type currents), and the slow recovery from inactivation of the fast sodium current. While recent modeling studies have focused on the effects of specific adaptation currents, we derive a universal model for the firing-frequency dynamics of an adapting neuron that is independent of the specific adaptation process and spike generator. The model is completely defined by the neuron's onset f-I curve, the steady-state f-I curve, and the time constant of adaptation. For a specific neuron, these parameters can be easily determined from electrophysiological measurements without any pharmacological manipulations. At the same time, the simplicity of the model allows one to analyze mathematically how adaptation influences signal processing on the single-neuron level. In particular, we elucidate the specific nature of high-pass filter properties caused by spike-frequency adaptation. The model is limited to firing frequencies higher than the reciprocal adaptation time constant and to moderate fluctuations of the adaptation and the input current. As an extension of the model, we introduce a framework for combining an arbitrary spike generator with a generalized adaptation current

The Utility of Phase Models in Studying Neural Synchronization

Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of coupled neural oscillators. Coupled oscillator theory thus informs the synchronization of spiking neuronal networks. A crucial aspect of coupled oscillator theory is the phase response curve (PRC), which describes the impact of a perturbation to the phase of an oscillator. In neural terms, the perturbation represents an incoming synaptic potential which may either advance or retard the timing of the next spike. The phase response curves and the form of coupling between reciprocally coupled oscillators defines the phase interaction function, which in turn predicts the synchronization outcome (in-phase versus anti-phase) and the rate of convergence. We review the two classes of PRC and demonstrate the utility of the phase model in predicting synchronization in reciprocally coupled neural models. In addition, we compare the rate of convergence for all combinations of reciprocally coupled Class I and Class II oscillators. These findings predict the general synchronization outcomes of broad classes of neurons under both inhibitory and excitatory reciprocal coupling.Comment: 18 pages, 5 figure

Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator

The Hodgkin-Huxley model describes action potential generation in certain types of neurons and is a standard model for conductance-based, excitable cells. Following the early work of Winfree and Best, this paper explores the response of a spontaneously spiking Hodgkin-Huxley neuron model to a periodic pulsatile drive. The response as a function of drive period and amplitude is systematically characterized. A wide range of qualitatively distinct responses are found, including entrainment to the input pulse train and persistent chaos. These observations are consistent with a theory of kicked oscillators developed by Qiudong Wang and Lai-Sang Young. In addition to general features predicted by Wang-Young theory, it is found that most combinations of drive period and amplitude lead to entrainment instead of chaos. This preference for entrainment over chaos is explained by the structure of the Hodgkin-Huxley phase resetting curve.Comment: Minor revisions; modified Fig. 3; added reference

Enhancement of synchronization in a hybrid neural circuit by spike timing dependent plasticity

Synchronization of neural activity is fundamental for many functions of the brain. We demonstrate that spike-timing dependent plasticity (STDP) enhances synchronization (entrainment) in a hybrid circuit composed of a spike generator, a dynamic clamp emulating an excitatory plastic synapse, and a chemically isolated neuron from the Aplysia abdominal ganglion. Fixed-phase entrainment of the Aplysia neuron to the spike generator is possible for a much wider range of frequency ratios and is more precise and more robust with the plastic synapse than with a nonplastic synapse of comparable strength. Further analysis in a computational model of HodgkinHuxley-type neurons reveals the mechanism behind this significant enhancement in synchronization. The experimentally observed STDP plasticity curve appears to be designed to adjust synaptic strength to a value suitable for stable entrainment of the postsynaptic neuron. One functional role of STDP might therefore be to facilitate synchronization or entrainment of nonidentical neurons

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of auditory nerve responses to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe auditory nerve spiking while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of the auditory nerve that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semi-analytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data and explain differences in auditory nerve responses to high and low pulse rate stimulation. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.Comment: 1 title page, 27 manuscript pages, 14 figures, 1 table, 1 appendi