How adaptation currents change threshold, gain and variability of neuronal spiking

Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow $\mathrm{K}^+$-currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in-vivo like fluctuating synaptic input, spike rate output and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current which primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold. A spike-dependent adaptation current alters the I-O curve divisively, thus reducing the response gain. Both types of adaptation currents naturally increase the mean inter-spike interval (ISI), but they can affect ISI variability in opposite ways. A subthreshold current always causes an increase of variability while a spike-triggered current decreases high variability caused by fluctuation-dominated inputs and increases low variability when the average input is large. The effects on I-O curves match those caused by synaptic inhibition in networks with asynchronous irregular activity, for which we find subtractive and divisive changes caused by external and recurrent inhibition, respectively. Synaptic inhibition, however, always increases the ISI variability. We analytically derive expressions for the I-O curve and ISI variability, which demonstrate the robustness of our results. Furthermore, we show how the biophysical parameters of slow $\mathrm{K}^+$-conductances contribute to the two different types of adaptation currents and find that $\mathrm{Ca}^{2+}$-activated $\mathrm{K}^+$-currents are effectively captured by a simple spike-dependent description, while muscarine-sensitive or $\mathrm{Na}^+$-activated $\mathrm{K}^+$-currents show a dominant subthreshold component.Comment: 20 pages, 8 figures; Journal of Neurophysiology (in press

Balanced neural architecture and the idling brain

A signature feature of cortical spike trains is their trial-to-trial variability. This variability is large in the spontaneous state and is reduced when cortex is driven by a stimulus or task. Models of recurrent cortical networks with unstructured, yet balanced, excitation and inhibition generate variability consistent with evoked conditions. However, these models produce spike trains which lack the long timescale fluctuations and large variability exhibited during spontaneous cortical dynamics. We propose that global network architectures which support a large number of stable states (attractor networks) allow balanced networks to capture key features of neural variability in both spontaneous and evoked conditions. We illustrate this using balanced spiking networks with clustered assembly, feedforward chain, and ring structures. By assuming that global network structure is related to stimulus preference, we show that signal correlations are related to the magnitude of correlations in the spontaneous state. Finally, we contrast the impact of stimulation on the trial-to-trial variability in attractor networks with that of strongly coupled spiking networks with chaotic firing rate instabilities, recently investigated by Ostojic (2014). We find that only attractor networks replicate an experimentally observed stimulus-induced quenching of trial-to-trial variability. In total, the comparison of the trial-variable dynamics of single neurons or neuron pairs during spontaneous and evoked activity can be a window into the global structure of balanced cortical networks. © 2014 Doiron and Litwin-Kumar

Learning Contrast-Invariant Cancellation of Redundant Signals in Neural Systems

Cancellation of redundant information is a highly desirable feature of sensory systems, since it would potentially lead to a more efficient detection of novel information. However, biologically plausible mechanisms responsible for such selective cancellation, and especially those robust to realistic variations in the intensity of the redundant signals, are mostly unknown. In this work, we study, via in vivo experimental recordings and computational models, the behavior of a cerebellar-like circuit in the weakly electric fish which is known to perform cancellation of redundant stimuli. We experimentally observe contrast invariance in the cancellation of spatially and temporally redundant stimuli in such a system. Our model, which incorporates heterogeneously-delayed feedback, bursting dynamics and burst-induced STDP, is in agreement with our in vivo observations. In addition, the model gives insight on the activity of granule cells and parallel fibers involved in the feedback pathway, and provides a strong prediction on the parallel fiber potentiation time scale. Finally, our model predicts the existence of an optimal learning contrast around 15% contrast levels, which are commonly experienced by interacting fish

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

Effects of Spike-Driven Feedback on Neural Gain and Pairwise Correlation

Both single neuron and neural population spiking statistics, such as firing rate or temporal patterning, are critical aspects of manyneural codes. Tremendous experimental and theoretical effort has been devoted to understanding how nonlinear membrane dynamics and ambient synaptic activity determine the gain of single neuron firing rate responses. Furthermore, there is increasing experimental evidence that the same manipulationsthat affect firing rate gain also modulate the pairwise correlationbetween neurons. However, there is little understanding of the mechanistic links between rate and correlation modulation. In this thesis, we explore how spike-driven intrinsicfeedback co-modulates firing rate gain and spike traincorrelation. Throughout our study, we focus on excitable LIF neurons subject to Gaussian white noise fluctuations. We first review prior work which develops linear response theory for studying spectral properties of LIF neurons. This theory is used to capture the influence of weak spike driven feedback in single neuron responses. We introduce a concept of "dynamic spike count gain" and study how this property is affected by intrinsic feedback, comparing theoretical results to simulations of stochastic ODE models. We then expand our scope to a pair of such neurons receiving weakly correlated noisy inputs. Extending previous work, we study the correlation between the spike trains of these neurons, comparing theoretical and simulation results. We observe that firing rate gain modulation from feedback is largely time-scale invariant, while correlation modulation exhibits marked temporal dependence. To discern whether these effects can be solely attributed to firing rate changes, we perform a perturbative analysis to derive conditions for correlation modulation over small time scales beyond that expected from rate modulation. We find that correlation is not purely a function of firing rate change; rather it is also influenced by sufficiently fast feedback inputs. These results offer a glimpse into the connections between gain and correlation, indicating that attempts to manipulate either property via firing rates will affect both, and that achievability of modulation targets is constrained by the time scale of spike feedback

The population firing rate in the presence of GABAergic tonic inhibition in single neurons and application to general anaesthesia

International audienceTonic inhibition has been found experimentally in single neurons and a ects the activity of neural populations. This kind of inhibition is supposed to set the background or resting level of neural activity and plays a role in the brains arousal system, e.g. during general anaesthesia. The work shows how to involve tonic inhibition in population rate-coding models by deriving a novel transfer function. The analytical and numerical study of the novel transfer function reveals the impact of tonic inhibition on the population ring rate. Finally, a rst application to a recent neural eld model for general anaesthesia discusses the origin of the loss of consciousness during anaesthesi

The Mechanism of Abrupt Transition between Theta and Hyper-Excitable Spiking Activity in Medial Entorhinal Cortex Layer II Stellate Cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. ‘In vitro’ experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current