Divisive gain modulation with dynamic stimuli in integrate-and-fire neurons

Divisive gain modulation enables flexible and rapid entrainment in a neocortical microcircuit model

Neocortical circuits exhibit a rich dynamic repertoire, and their ability to achieve entrainment (adjustment of their frequency to match the input frequency) is thought to support many cognitive functions and indicate functional flexibility. Although previous studies have explored the influence of various circuit properties on this phenomenon, the role of divisive gain modulation (or divisive inhibition) is unknown. This gain control mechanism is thought to be delivered mainly by the soma-targeting interneurons in neocortical microcircuits. In this study, we use a neural mass model of the neocortical microcircuit (extended Wilson-Cowan model) featuring both soma-targeting and dendrite-targeting interneuronal subpopulations to investigate the role of divisive gain modulation in entrainment. Our results demonstrate that the presence of divisive inhibition in the microcircuit, as delivered by the soma-targeting interneurons, enables its entrainment to a wider range of input frequencies. Divisive inhibition also promotes a faster entrainment, with the microcircuit needing less time to converge to the fully entrained state. We suggest that divisive inhibition, working alongside subtractive inhibition, allows for more adaptive oscillatory responses in neocortical circuits and, thus, supports healthy brain functioning.NEW & NOTEWORTHY We introduce a computational neocortical microcircuit model that features two inhibitory neural populations, with one providing subtractive and the other divisive inhibition to the excitatory population. We demonstrate that divisive inhibition widens the range of input frequencies to which the microcircuit can become entrained and diminishes the time needed to reach full entrainment. We suggest that divisive inhibition enables more adaptive oscillatory activity, with important implications for both normal and pathological brain function.

Mechanisms underlying gain modulation in the cortex

Cortical gain regulation allows neurons to respond adaptively to changing inputs. Neural gain is modulated by internal and external influences, including attentional and arousal states, motor activity and neuromodulatory input. These influences converge to a common set of mechanisms for gain modulation, including GABAergic inhibition, synaptically driven fluctuations in membrane potential, changes in cellular conductance and changes in other biophysical neural properties. Recent work has identified GABAergic interneurons as targets of neuromodulatory input and mediators of state-dependent gain modulation. Here, we review the engagement and effects of gain modulation in the cortex. We highlight key recent findings that link phenomenological observations of gain modulation to underlying cellular and circuit-level mechanisms. Finally, we place these cellular and circuit interactions in the larger context of their impact on perception and cognition.

Conductance-Based Refractory Density Approach for a Population of Bursting Neurons

The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modelling interacting populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study, we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting population model makes use of slow-fast analysis, which leads to a novel methodology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explorations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).

Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models

Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces are considered. By assuming quasi-steady-state activity, one can neglect the complex temporal dynamics; however, in many cases the quasi-steady-state assumption fails. Here, we develop a new reduction method for a general heterogeneous firing-rate model receiving background correlated noisy inputs that accurately handles highly non-equilibrium statistics and interactions of heterogeneous cells. Our method involves solving an efficient set of nonlinear ODEs, rather than time-consuming Monte Carlo simulations or high-dimensional PDEs, and it captures the entire set of first and second order statistics while allowing significant heterogeneity in all model parameters.

Nitric Oxide Orchestrates a Power-Law Modulation of Sympathetic Firing Behaviors in Neonatal Rat Spinal Cords

Nitric oxide (NO) is a diffusible gas and has multifarious effects on both pre- and postsynaptic events. As a consequence of complex excitatory and inhibitory integrations, NO effects on neuronal activities are heterogeneous. Using in vitro preparations of neonatal rats that retain the splanchnic sympathetic nerves and the thoracic spinal cord as an experimental model, we report here that either enhancement or attenuation of NO production in the neonatal rat spinal cords could increase, decrease, or not change the spontaneous firing behaviors recorded from splanchnic sympathetic single fibers. To elucidate the mathematical features of NO-mediated heterogeneous responses, the ratios of changes in firing were plotted against their original firing rates. In log-log plots, a linear data distribution demonstrated that NO-mediated heterogeneity in sympathetic firing responses was well described by a power function. Selective antagonists were applied to test if glycinergic, GABAergic, glutamatergic, and cholinergic neurotransmission in the spinal cord are involved in NO-mediated power-law firing modulations (plFM). NO-mediated plFM diminished in the presence of mecamylamine (an open-channel blocker of nicotinic cholinergic receptors), indicating that endogenous nicotinic receptor activities were essential for plFM. Applications of strychnine (a glycine receptor blocker), gabazine (a GABA_A receptor blocker), or kynurenate (a broad-spectrum ionotropic glutamate receptor blocker) also caused plFM. However, strychnine- or kynurenate-induced plFM was diminished by L-NAME (an NO synthase inhibitor) pretreatments, indicating that the involvements of glycine or ionotropic glutamate receptor activities in plFM were secondary to NO signaling. To recapitulate the arithmetic natures of the plFM, the plFM were simulated by firing changes in two components: a step increment and a fractional reduction of their basal firing activities. Ionotropic glutamate receptor activities were found to participate in plFM by both components. In contrast, GABA_A receptor activities are involved in the component of fractional reduction only. These findings suggest that NO orchestrates a repertoire of excitatory and inhibitory neurotransmissions, incurs a shunting effect on postsynaptic membrane properties, and thus, alters sympathetic firing in a manner of plFM. We propose that the plFM mediated by NO forms a basic scheme of differential controls for heterogeneous sympathetic regulation of visceral functions.

Inhibition in the auditory brainstem enhances signal representation and regulates gain in complex acoustic environments

Inhibition plays a crucial role in neural signal processing, shaping and limiting responses. In the auditory system, inhibition already modulates second order neurons in the cochlear nucleus, e.g. spherical bushy cells (SBCs). While the physiological basis of inhibition and excitation is well described, their functional interaction in signal processing remains elusive. Using a combination of in vivo loose-patch recordings, iontophoretic drug application, and detailed signal analysis in the Mongolian Gerbil, we demonstrate that inhibition is widely co-tuned with excitation, and leads only to minor sharpening of the spectral response properties. Combinations of complex stimuli and neuronal input-output analysis based on spectrotemporal receptive fields revealed inhibition to render the neuronal output temporally sparser and more reproducible than the input. Overall, inhibition plays a central role in improving the temporal response fidelity of SBCs across a wide range of input intensities and thereby provides the basis for high-fidelity signal processing.

Subtractive, divisive and non-monotonic gain control in feedforward nets linearized by noise and delays

The control of input-to-output mappings, or gain control, is one of the main strategies used by neural networks for the processing and gating of information. Using a spiking neural network model, we studied the gain control induced by a form of inhibitory feedforward circuitry-also known as "open-loop feedback"-, which has been experimentally observed in a cerebellum-like structure in weakly electric fish. We found, both analytically and numerically, that this network displays three different regimes of gain control: subtractive, divisive, and non-monotonic. Subtractive gain control was obtained when noise is very low in the network. Also, it was possible to change from divisive to non-monotonic gain control by simply modulating the strength of the feedforward inhibition, which may be achieved via long-term synaptic plasticity. The particular case of divisive gain control has been previously observed in vivo in weakly electric fish. These gain control regimes were robust to the presence of temporal delays in the inhibitory feedforward pathway, which were found to linearize the input-to-output mappings (or f-I curves) via a novel variability-increasing mechanism. Our findings highlight the feedforward-induced gain control analyzed here as a highly versatile mechanism of information gating in the brain.

Binaural gain modulation of spectrotemporal tuning in the interaural level difference-coding pathway

In the brainstem, the auditory system diverges into two pathways that process different sound localization cues, interaural time differences (ITDs) and level differences (ILDs). We investigated the site where ILD is detected in the auditory system of barn owls, the posterior part of the lateral lemniscus (LLDp). This structure is equivalent to the lateral superior olive in mammals. The LLDp is unique in that it is the first place of binaural convergence in the brainstem where monaural excitatory and inhibitory inputs converge. Using binaurally uncorrelated noise and a generalized linear model, we were able to estimate the spectrotemporal tuning of excitatory and inhibitory inputs to these cells. We show that the response of LLDp neurons is highly locked to the stimulus envelope. Our data demonstrate that spectrotemporally tuned, temporally delayed inhibition enhances the reliability of envelope locking by modulating the gain of LLDp neurons' responses. The dependence of gain modulation on ILD shown here constitutes a means for space-dependent coding of stimulus identity by the initial stages of the auditory pathway.

A principled dimension-reduction method for the population density approach to modeling networks of neurons with synaptic dynamics

The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons (i.e., Monte Carlo). It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic (i.e., higher-dimensional) neural networks.

Balanced synaptic input shapes the correlation between neural spike trains

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states.

Combined LTP and LTD of modulatory inputs controls neuronal processing of primary sensory inputs

A hallmark of brain organization is the integration of primary and modulatory pathways by principal neurons. However, the pathway interactions that shape primary input processing remain unknown. We investigated this problem in mouse dorsal cochlear nucleus (DCN) where principal cells integrate primary, auditory nerve input with modulatory, parallel fiber input. Using a combined experimental and computational approach, we show that combined LTP and LTD of parallel fiber inputs to DCN principal cells and interneurons, respectively, broaden the time window within which synaptic inputs summate. Enhanced summation depolarizes the resting membrane potential and thus lowers the response threshold to auditory nerve inputs. Combined LTP and LTD, by preserving the variance of membrane potential fluctuations and the membrane time constant, fixes response gain and spike latency as threshold is lowered. Our data reveal a novel mechanism mediating adaptive and concomitant homeostatic regulation of distinct features of neuronal processing of sensory inputs.

Slope-based stochastic resonance: how noise enables phasic neurons to encode slow signals

Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal's rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.

Principal brain cells, called neurons, show a tremendous amount of diversity in their responses to driving stimuli. A widely present but understudied class of neurons prefers to respond to high-frequency inputs and neglect slow variations; these cells are called phasic neurons. Although phasic neurons do not normally respond to slow signals, we show that noise, a ubiquitous neural input, can enable them to respond to distinct features of slow signals. We emphasize the fact that, in the presence of noise, they are still sensitive to the change in stimulus, rather than to the constant part of the slow inputs, just as they are for fast inputs without noise. This feature distinguishes the response of phasic neurons from those of other neurons, which show more sensitivity to the amplitude of their inputs. We believe that our study has significantly broadened the understanding about the information-processing ability and functional roles of phasic neurons.