Spike-timing prediction in cortical neurons with active dendrites

Abstract

A complete single-neuron model must correctly reproduce the firing of spikes and bursts. We present a study of a simplified model of deep pyramidal cells of the cortex with active dendrites. We hypothesized that we can model the soma and its apical dendrite with only two compartments, without significant loss in the accuracy of spike-timing predictions. The model is based on experimentally measurable impulse-response functions, which transfer the effect of current injected in one compartment to current reaching the other. Each compartment was modeled with a pair of non-linear differential equations and a small number of parameters that approximate the Hodgkin-and-Huxley equations. The predictive power of this model was tested on electrophysiological experiments where noisy current was injected in both the soma and the apical dendrite simultaneously. We conclude that a simple two-compartment model can predict spike times of pyramidal cells stimulated in the soma and dendrites simultaneously. Our results support that regenerating activity in the apical dendritic is required to properly account for the dynamics of layer 5 pyramidal cells under in-vivo-like conditions.

Global, multiplexed dendritic computations under in vivo-like conditions

“…While in cortical pyramidal cells NMDA receptor activation has been shown to be the primary influence on neuronal responses in vivo (Lavzin et al, 2012;Smith et al, 2013;Palmer et al, 2014;Schmidt-Hieber et al, 2017), which our hLN model captures accurately, future developments of the hLN approach could improve its ability to capture events such as the initiation and the propagation of dendritic Na + -spikes. This could be done, for example, by extending the static non-linearities employed here with simplified dynamical models of spike generation and propagation along the network of the hierarchical subunits as proposed recently to model spike responses of neurons with dendritic calcium spikes (Naud et al, 2014). Interestingly, our results also suggest that Na + -and NMDA-related non-linearities may involve drastically different hierarchical processing within the dendritic tree, akin to multiplexing inputs to a slow channel with a single global non-linearity and a fast channel with local non-linear interactions and multiple hierarchical steps.…”

Action potential initiation in a two-compartment model of pyramidal neuron mediated by dendritic Ca2+ spike

“…But they may fail to provide greater insights into the mechanism underlying AP initiation than the experiments upon which they are based, since they include so many extraneous details. There are also theoretical studies using simple two-compartment models to describe the Ca 2+ activity of dendrites for pyramidal cell383940414243. However, none of them has provided a satisfied interpretation of how dendritic Ca 2+ spike participates in the initiating dynamics of somatic/axonal APs.…”

“…There are also studies that use two compartments to model pyramidal neurons with dendritic Ca 2+ channel. Such simple point-neuron models have been adopted to study their firing patterns383940, spike-timing predictions41, spike timing-dependent plasticity42, and spike-frequency adaptation43. However, it has attracted little attention about the somatic/axonal AP initiation associated with dendritic Ca 2+ spike.…”

Sparse Bursts Optimize Information Transmission in a Multiplexed Neural Code

“…S1a-d 27 ), a critical frequency for an after-spike depolarization ( Fig. S1e-h 42 ), and the spiking response of TPNs to complex stimuli in vitro 43 . In addition to the shared alternating signals, each cell in the population receives independent background noise to reproduce the high variability of recurrent excitatory networks balanced by inhibition, as well as low burst fraction and the typical membrane potential standard deviation observed in vivo [44][45][46] (see Materials and Methods).…”