Synchrony measure for a neuron driven by excitatory and inhibitory inputs and its adaptation to experimentally-recorded data

The aim of the current work is twofold: firstly to adapt an existing method measuring the input synchrony of a neuron driven only by excitatory inputs in such a way so as to account for inhibitory inputs as well and secondly to further appropriately adapt this measure so as to be correctly utilised on experimentally-recorded data. The existing method uses the normalized pre-spike slope (NPSS) of the membrane potential, resulting from observing the slope of depolarization of the membrane potential of a neuron prior to the moment of crossing the threshold within a short period of time, to identify the response-relevant input synchrony and through it to infer the operational mode of a neuron. The first adaptation of NPSS is made such that its upper bound calculation accommodates for the higher possible slope values caused by the lower average and minimum membrane potential values due to inhibitory inputs. Results indicate that when the input spike trains arrive randomly, the modified NPSS works as expected inferring that the neuron is operating as a temporal integrator. When the input spike trains arrive in perfect synchrony though, the modified NPSS works as expected only when the level of inhibition is much higher than the level of excitation. This suggests that calculation of the upper bound of the NPSS should be a function of the ratio between excitatory and inhibitory inputs in order to be able to correctly capture perfect synchrony at a neuron's input. In addition, we effectively demonstrate a process which has to be followed when aiming to use the NPSS on real neuron recordings. This process, which relies on empirical observations of the slope of depolarisation for estimating the bounds for the range of observed interspike interval lengths, is successfully applied to experimentally-recorded data showing that through it both a real neuron's operational mode and the amount of input synchrony that caused its firing can be inferred.

Integrator or Coincidence Detector: A Novel Measure Based on the Discrete Reverse Correlation to Determine a Neuron’s Operational Mode

In this letter, we propose a definition of the operational mode of a neuron, that is, whether a neuron integrates over its input or detects coincidences. We complete the range of possible operational modes by a new mode we call gap detection, which means that a neuron responds to gaps in its stimulus. We propose a measure consisting of two scalar values, both ranging from −1 to +1: the neural drive, which indicates whether its stimulus excites the neuron, serves as background noise, or inhibits it; the neural mode, which indicates whether the neuron’s response is the result of integration over its input, of coincidence detection, or of gap detection; with all three modes possible for all neural drive values. This is a pure spike-based measure and can be applied to measure the influence of either all or subset of a neuron’s stimulus. We derive the measure by decomposing the reverse correlation, test it in several artificial and biological settings, and compare it to other measures, finding little or no correlation between them. We relate the results of the measure to neural parameters and investigate the effect of time delay during spike generation. Our results suggest that a neuron can use several different modes simultaneously on different subsets of its stimulus to enable it to respond to its stimulus in a complex manner.

Integrator or coincidence detector --- what shapes the relation of stimulus synchrony and the operational mode of a neuron?

The operational mode of a neuron (i.e., whether a neuron is an integrator or a coincidence detector) is in part determined by the degree of synchrony in the firing of its pre-synaptic neural population. More specifically, it is determined by the degree of synchrony that causes the neuron to fire. In this paper, we investigate the relationship between the input and the operational mode. We compare the response-relevant input synchrony, which measures the operational mode and can be determined using a membrane potential slope-based measure [7], with the spike time distance of the spike trains driving the neuron, which measures spike train synchrony and can be determined using the multivariate SPIKE-distance metric [10]. We discover that the relationship between the two measures changes substantially based on the values of the parameters of the input (firing rate and number of spike trains) and the parameters of the post-synaptic neuron (synaptic weight, membrane leak time constant and spike threshold). More importantly, we determine how the parameters interact to shape the synchrony-operational mode relationship. Our results indicate that the amount of depolarisation caused by a highly synchronous volley of input spikes, is the most influential factor in defining the relationship between input synchrony and operational mode. This is defined by the number of input spikes and the membrane potential depolarisation caused per spike, compared to the spike threshold.

Measuring input synchrony in the Ornstein-Uhlenbeck neuronal model through input parameter estimation

We present a method of estimating the input parameters and through them, the input synchrony, of a stochastic leaky integrate-and-fire neuronal model based on the Ornstein-Uhlenbeck process when it is driven by time-dependent sinusoidal input signal and noise. By driving the neuron using sinusoidal inputs, we simulate the effects of periodic synchrony on the membrane voltage and the firing of the neuron, where the peaks of the sine wave represent volleys of synchronised input spikes. Our estimation methods allow us to measure the degree of synchrony driving the neuron in terms of the input sine wave parameters, using the output spikes of the model and the membrane potential. In particular, by estimating the frequency of the synchronous input volleys and averaging the estimates of the level of input activity at corresponding intervals of the input signal, we obtain fairly accurate estimates of the baseline and peak activity of the input, which in turn define the degrees of synchrony. The same procedure is also successfully applied in estimating the baseline and peak activity of the noise. This article is part of a Special Issue entitled Neural Coding 2012.