The response of cortical neurons to in vivo-like input current: theory and experiment

Abstract

The study of several aspects of the collective dynamics of interacting neurons can be highly simplified if one assumes that the statistics of the synaptic input is the same for a large population of similarly behaving neurons (mean field approach). In particular, under such an assumption, it is possible to determine and study all the equilibrium points of the network dynamics when the neuronal response to noisy, in vivo-like, synaptic currents is known. The response function can be computed analytically for simple integrate-and-fire neuron models and it can be measured directly in experiments in vitro. Here we review theoretical and experimental results about the neural response to noisy inputs with stationary statistics. These response functions are important to characterize the collective neural dynamics that are proposed to be the neural substrate of working memory, decision making and other cognitive functions. Applications to the case of time-varying inputs are reviewed in a companion paper (Giugliano et al. in Biol Cybern, 2008). We conclude that modified integrate-and-fire neuron models are good enough to reproduce faithfully many of the relevant dynamical aspects of the neuronal response measured in experiments on real neurons in vitro.

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

“…Our results suggest a smoother transition in this non-linear region (Figure 3A), which is in agreement with other in vivo data (Priebe et al, 2004) and in vitro data stimulating the neurons with in vivo like inputs (La Camera et al, 2008), both obtained from neocortical neurons. It is possible that this property is more pronounced in an in vivo setting such as ours with an intense synaptic background activity as compared to in vitro since previous simulation work has suggested that the background level of stochastic synaptic input changes the dynamics of spike firing (Jaeger and Bower, 1999; Gauck and Jaeger, 2000, 2003; Destexhe et al, 2001; Salinas and Sejnowski, 2002; Fellous et al, 2003; Suter and Jaeger, 2004), especially close to the threshold (La Camera et al, 2008). A suitable description of the spike firing statistics should therefore be capable of featuring both a sharp and a smooth threshold in this region.…”

“…The relationship between the input current and the spike firing frequency is frequently reported to be linear (Nowak et al, 2003; Mckay and Turner, 2005; Molineux et al, 2005; Meehan et al, 2010; Zhong et al, 2010). However, as the firing frequency of a neuron approaches zero the linearity inevitably disappears, either by a sharp threshold or by a smoother transition between zero and non-zero firing, also shown theoretically using leaky integrate-and-fire (LIF) neuron models (Fourcaud-Trocme et al, 2003; La Camera et al, 2008). Our results suggest a smoother transition in this non-linear region (Figure 3A), which is in agreement with other in vivo data (Priebe et al, 2004) and in vitro data stimulating the neurons with in vivo like inputs (La Camera et al, 2008), both obtained from neocortical neurons.…”

“…However, as the firing frequency of a neuron approaches zero the linearity inevitably disappears, either by a sharp threshold or by a smoother transition between zero and non-zero firing, also shown theoretically using leaky integrate-and-fire (LIF) neuron models (Fourcaud-Trocme et al, 2003; La Camera et al, 2008). Our results suggest a smoother transition in this non-linear region (Figure 3A), which is in agreement with other in vivo data (Priebe et al, 2004) and in vitro data stimulating the neurons with in vivo like inputs (La Camera et al, 2008), both obtained from neocortical neurons. It is possible that this property is more pronounced in an in vivo setting such as ours with an intense synaptic background activity as compared to in vitro since previous simulation work has suggested that the background level of stochastic synaptic input changes the dynamics of spike firing (Jaeger and Bower, 1999; Gauck and Jaeger, 2000, 2003; Destexhe et al, 2001; Salinas and Sejnowski, 2002; Fellous et al, 2003; Suter and Jaeger, 2004), especially close to the threshold (La Camera et al, 2008).…”

Diminished Activity-Dependent Brain-Derived Neurotrophic Factor Expression Underlies Cortical Neuron Microcircuit Hypoconnectivity Resulting from Exposure to Mutant Huntingtin Fragments

“…A simplified spike-rate model accounting for the patterned electrical activity emerging in populations of cultured neurons was defined and computersimulated to interpret the electrophysiological recordings. We described the firing rate, R(t), of the ensemble of cortical neurons in terms of the single-cell f-I curve and recurrent connectivity La Camera et al, 2008). The model replicates some of the features characterizing the population bursts as transient irregular outbursts in R(t).…”

Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity

“…1a, respectively) are more or less excitable, respectively. Gain functions have been worked out for several integrate-and-fire (IF) neurons and synaptic transmission models (see for review Burkitt 2006;La Camera et al 2008). Here we use a U(m) derived in (Fusi and Mattia 1999) for a simplified IF neuron model.…”