Theta and gamma rhythmic coding through two spike output modes in the hippocampus during spatial navigation.

Hippocampal CA1 neurons generate single spikes and stereotyped bursts of spikes. However, it is unclear how individual neurons dynamically switch between these output modes and whether these two spiking outputs relay distinct information. We performed extracellular recordings in spatially navigating rats and cellular voltage imaging and optogenetics in awake mice. We found that spike bursts are preferentially linked to cellular and network theta rhythms (3-12 Hz) and encode an animal's position via theta phase precession, particularly as animals are entering a place field. In contrast, single spikes exhibit additional coupling to gamma rhythms (30-100 Hz), particularly as animals leave a place field. Biophysical modeling suggests that intracellular properties alone are sufficient to explain the observed input frequency-dependent spike coding. Thus, hippocampal neurons regulate the generation of bursts and single spikes according to frequency-specific network and intracellular dynamics, suggesting that these spiking modes perform distinct computations to support spatial behavior.

Low-dimensional models of single neurons: a review.

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.