The Dynamics of Integrate-and-Fire: Mean vs. Variance Modulations and Dependence on Baseline Parameters

The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low - and moderate-frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. However, the cutoff shows a rapid, supralinear increase with firing rate, with a steeper increase in the case of lower noise. For modulations of the input variance, the gain at high frequency remains finite. Here, we show that the low-frequency responses depend strongly on baseline parameters and derive an analytic condition specifying the parameters at which responses switch from being dominated by low versus high frequencies. Additionally, we show that the resonant responses for variance modulations have properties not expected for common oscillatory resonances: they peak at frequencies higher than the baseline firing rate and persist when oscillatory spiking is disrupted by high noise. Finally, the responses to mean and variance modulations are shown to have a complementary dependence on baseline parameters at higher frequencies, resulting in responses to modulations of Poisson input rates that are independent of baseline input statistics

Complementary responses to mean and variance modulations in the perfect integrate-and-fire model

In the perfect integrate-and-fire model (PIF), the membrane voltage is proportional to the integral of the input current since the time of the previous spike. It has been shown that the firing rate within a noise free ensemble of PIF neurons responds instantaneously to dynamic changes in the input current, whereas in the presence of white noise, model neurons preferentially pass low frequency modulations of the mean current. Here, we prove that when the input variance is perturbed while holding the mean current constant, the PIF responds preferentially to high frequency modulations. Moreover, the linear filters for mean and variance modulations are complementary, adding exactly to one. Since changes in the rate of Poisson distributed inputs lead to proportional changes in the mean and variance, these results imply that an ensemble of PIF neurons transmits a perfect replica of the time-varying input rate for Poisson distributed input. A more general argument shows that this property holds for any signal leading to proportional changes in the mean and variance of the input current

Temporal Processing in the Exponential Integrate-and-Fire Model is Nonlinear

The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocme et al. (2003) as an extension of the standard leaky integrate-and-fire model (LIF). Here, the nonlinearity in the EIF model’s temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for these square-wave inputs indicates that at frequencies above ~40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in isolation

Just Do It: Action-Dependent Learning Allows Sensory Prediction

Sensory-motor learning is commonly considered as a mapping process, whereby sensory information is transformed into the motor commands that drive actions. However, this directional mapping, from inputs to outputs, is part of a loop; sensory stimuli cause actions and vice versa. Here, we explore whether actions affect the understanding of the sensory input that they cause. Using a visuo-motor task in humans, we demonstrate two types of learning-related behavioral effects. Stimulus-dependent effects reflect stimulus-response learning, while action-dependent effects reflect a distinct learning component, allowing the brain to predict the forthcoming sensory outcome of actions. Together, the stimulus-dependent and the action-dependent learning components allow the brain to construct a complete internal representation of the sensory-motor loop

Temporal variability in a synfire chain model of birdsong

https://doi.org/10.1186/1471-2202-9-S1-P2

Disinhibition Bursting of Dopaminergic Neurons

Substantia nigra pars compacta (SNpc) dopaminergic neurons receive strong tonic inputs from GABAergic neurons in the substantia nigra pars reticulata (SNpr) and globus pallidus (GP), and glutamatergic neurons in the subthalamic nucleus. The presence of these tonic inputs raises the possibility that phasic disinhibition may trigger phasic bursts in dopaminergic neurons. We first applied constant NMDA and GABAA conductances onto a two-compartment single cell model of the dopaminergic neuron (Kuznetsov et al., 2006). The model exhibited disinhibition bursting upon stepwise removal of inhibition. A further bifurcation analysis suggests that disinhibition may be more robust than excitation alone in that for most levels of NMDA conductance, the cell remains capable of bursting even after a complete removal of inhibition, whereas too much excitatory input will drive the cell into depolarization block. To investigate the network dynamics of disinhibition, we used a modified version of an integrate-and-fire based model of the basal ganglia (Humphries et al., 2006). Synaptic activity generated in the network was delivered to the two-compartment single cell dopaminergic neuron. Phasic activation of the D1-expressing medium spiny neurons in the striatum (D1STR) produced disinhibition bursts in dopaminergic neurons through the direct pathway (D1STR to SNpr to SNpc). Anatomical studies have shown that D1STR neurons have collaterals that terminate in GP. Adding these collaterals to the model, we found that striatal activation increased the intra-burst firing frequency of the disinhibition burst as the weight of this connection was increased. Our studies suggest that striatal activation is a robust means by which disinhibition bursts can be generated by SNpc dopaminergic neurons, and that recruitment of the indirect pathway via collaterals may enhance disinhibition bursting