Spike generation estimated from stationary spike trains in a variety of neurons in vivo.

Anton Spanne,Pontus Geborek,Henrik Jã¶Rntell,Fredrik Bengtsson

doi:10.3389/fncel.2014.00199

Abstract

To any model of brain function, the variability of neuronal spike firing is a problem that needs to be taken into account. Whereas the synaptic integration can be described in terms of the original Hodgkin-Huxley (H-H) formulations of conductance-based electrical signaling, the transformation of the resulting membrane potential into patterns of spike output is subjected to stochasticity that may not be captured with standard single neuron H-H models. The dynamics of the spike output is dependent on the normal background synaptic noise present in vivo, but the neuronal spike firing variability in vivo is not well studied. In the present study, we made long-term whole cell patch clamp recordings of stationary spike firing states across a range of membrane potentials from a variety of subcortical neurons in the non-anesthetized, decerebrated state in vivo. Based on the data, we formulated a simple, phenomenological model of the properties of the spike generation in each neuron that accurately captured the stationary spike firing statistics across all membrane potentials. The model consists of a parametric relationship between the mean and standard deviation of the inter-spike intervals, where the parameter is linearly related to the injected current over the membrane. This enabled it to generate accurate approximations of spike firing also under inhomogeneous conditions with input that varies over time. The parameters describing the spike firing statistics for different neuron types overlapped extensively, suggesting that the spike generation had similar properties across neurons.

Highlights

Synaptic integration, i.e., the process by which a neuron summates and transforms the information it receives from other neurons, has been extensively studied both in vitro and in vivo and can be described as variations of the original Hodgkin-Huxley formulations for conductance-based electrical signaling (Stemmler and Koch, 1999; Goldwyn and Shea-Brown, 2011; Drion et al, 2012)
DATA APPROXIMATIONS Our first aim was to analyze the distribution of the inter-spike intervals (ISIs) across the operative range of firing frequencies that these types of cells have previously been described to display under behavior (Edgley and Lidierth, 1987, 1988; Prut and Fetz, 1999; Pasalar et al, 2006; Takei and Seki, 2010, 2013; Badura et al, 2013)
In particular the long tail of distributions of the threshold crossing events in Figure 1D, which was absent in the ISIs, strongly suggests that the statistics of the spike generation was determined by other factors in addition to the synaptic inputs and the absolute value of the membrane potential

Summary

Introduction

I.e., the process by which a neuron summates and transforms the information it receives from other neurons, has been extensively studied both in vitro and in vivo and can be described as variations of the original Hodgkin-Huxley formulations for conductance-based electrical signaling (Stemmler and Koch, 1999; Goldwyn and Shea-Brown, 2011; Drion et al, 2012). There are two different views, one that this process is deterministic and can be calculated with high precision using variations of the original integrate-and-fire principle, and another one where the concept of stochastic noise in the spike generation per se is providing a stochastic contribution to the times of spike initiation. We aimed to provide such approximations based on long-term intracellular recordings from a variety of neuron types in vivo

Objectives

Methods

Results

Conclusion