Jan Benda

A universal model for spike-frequency adaptation

Spike-frequency adaptation is a prominent feature of neural dynamics. Among other mechanisms, various ionic currents modulating spike generation cause this type of neural adaptation. Prominent examples are voltage-gated potassium currents (M-type currents), the interplay of calcium currents and intracellular calcium dynamics with calcium-gated potassium channels (AHP-type currents), and the slow recovery from inactivation of the fast sodium current. While recent modeling studies have focused on the effects of specific adaptation currents, we derive a universal model for the firing-frequency dynamics of an adapting neuron that is independent of the specific adaptation process and spike generator. The model is completely defined by the neurons onset f-I curve, the steady-state f-I curve, and the time constant of adaptation. For a specific neuron, these parameters can be easily determined from electrophysiological measurements without any pharmacological manipulations. At the same time, the simplicity of the model allows one to analyze mathematically how adaptation influences signal processing on the single-neuron level. In particular, we elucidate the specific nature of high-pass filter properties caused by spike-frequency adaptation. The model is limited to firing frequencies higher than the reciprocal adaptation time constant and to moderate fluctuations of the adaptation and the input current. As an extension of the model, we introduce a framework for combining an arbitrary spike generator with a generalized adaptation current.

Spike-Frequency Adaptation Separates Transient Communication Signals from Background Oscillations

Spike-frequency adaptation is a prominent feature of many neurons. However, little is known about its computational role in processing behaviorally relevant natural stimuli beyond filtering out slow changes in stimulus intensity. Here, we present a more complex example in which we demonstrate how spike-frequency adaptation plays a key role in separating transient signals from slower oscillatory signals. We recorded in vivo from very rapidly adapting electroreceptor afferents of the weakly electric fish Apteronotus leptorhynchus. The firing-frequency response of electroreceptors to fast communication stimuli (“small chirps”) is strongly enhanced compared with the response to slower oscillations (“beats”) arising from interactions of same-sex conspecifics. We are able to accurately predict the electroreceptor afferent response to chirps and beats, using a recently proposed general model for spike-frequency adaptation. The parameters of the model are determined for each neuron individually from the responses to step stimuli. We conclude that the dynamics of the rapid spike-frequency adaptation is sufficient to explain the data. Analysis of additional data from step responses demonstrates that spike-frequency adaptation acts subtractively rather than divisively as expected from depressing synapses. Therefore, the adaptation dynamics is linear and creates a high-pass filter with a cutoff frequency of 23 Hz that separates fast signals from slower changes in input. A similar critical frequency is seen in behavioral data on the probability of a fish emitting chirps as a function of beat frequency. These results demonstrate how spike-frequency adaptation in general can facilitate extraction of signals of different time scales, specifically high-frequency signals embedded in slower oscillations.

A synchronization-desynchronization code for natural communication signals.

Synchronous spiking of neural populations is hypothesized to play important computational roles in forming neural assemblies and solving the binding problem. Although the opposite phenomenon of desynchronization is well known from EEG studies, it is largely neglected on the neuronal level. We here provide an example of in vivo recordings from weakly electric fish demonstrating that, depending on the social context, different types of natural communication signals elicit transient desynchronization as well as synchronization of the electroreceptor population without changing the mean firing rate. We conclude that, in general, both positive and negative changes in the degree of synchrony can be the relevant signals for neural information processing.

The cellular basis for parallel neural transmission of a high-frequency stimulus and its low-frequency envelope

Sensory stimuli often have rich temporal and spatial structure. One class of stimuli that are common to visual and auditory systems and, as we show, the electrosensory system are signals that contain power in a narrow range of temporal (or spatial) frequencies. Characteristic of this class of signals is a slower variation in their amplitude, otherwise known as an envelope. There is evidence suggesting that, in the visual cortex, both narrowband stimuli and their envelopes are coded for in separate and parallel streams. The implementation of this parallel transmission is not well understood at the cellular level. We have identified the cellular basis for the parallel transmission of signal and envelope in the electrosensory system: a two-cell network consisting of an interneuron connected to a pyramidal cell by means of a slow synapse. This circuit could, in principle, be implemented in the auditory or visual cortex by the previously identified biophysics of cortical interneurons.

Linear Versus Nonlinear Signal Transmission in Neuron Models With Adaptation Currents or Dynamic Thresholds

Spike-frequency adaptation is a prominent aspect of neuronal dynamics that shapes a neurons signal processing properties on timescales ranging from about 10 ms to >1 s. For integrate-and-fire model neurons spike-frequency adaptation is incorporated either as an adaptation current or as a dynamic firing threshold. Whether a physiologically observed adaptation mechanism should be modeled as an adaptation current or a dynamic threshold, however, is not known. Here we show that a dynamic threshold has a divisive effect on the onset f-I curve (the initial maximal firing rate following a step increase in an input current) measured at increasing mean threshold levels, i.e., adaptation states. In contrast, an adaptation current subtractively shifts this f-I curve to higher inputs without affecting its slope. As a consequence, an adaptation current acts essentially linearly, resulting in a high-pass filter component of the neurons transfer function for current stimuli. With a dynamic threshold, however, the transfer function strongly depends on the input range because of the multiplicative effect on the f-I curves. Simulations of conductance-based spiking models with adaptation currents, such as afterhyperpolarization (AHP)-type, M-type, and sodium-activated potassium currents, do not show the divisive effects of a dynamic threshold, but agree with the properties of integrate-and-fire neurons with adaptation current. Notably, the effects of slow inactivation of sodium currents cannot be reproduced by either model. Our results suggest that, when lateral shifts of the onset f-I curve are seen in response to adapting inputs, adaptation should be modeled with adaptation currents and not with a dynamic threshold. In contrast, when the slope of onset f-I curves depends on the adaptation state, then adaptation should be modeled with a dynamic threshold. Further, the observation of divisively altered onset f-I curves in adapted neurons with notable variability of their spike threshold could hint to yet known biophysical mechanisms directly affecting the threshold.

From response to stimulus: adaptive sampling in sensory physiology

Sensory systems extract behaviorally relevant information from a continuous stream of complex high-dimensional input signals. Understanding the detailed dynamics and precise neural code, even of a single neuron, is therefore a non-trivial task. Automated closed-loop approaches that integrate data analysis in the experimental design ease the investigation of sensory systems in three directions: First, adaptive sampling speeds up the data acquisition and thus increases the yield of an experiment. Second, model-driven stimulus exploration improves the quality of experimental data needed to discriminate between alternative hypotheses. Third, information-theoretic data analyses open up novel ways to search for those stimuli that are most efficient in driving a given neuron in terms of its firing rate or coding quality. Examples from different sensory systems show that, in all three directions, substantial progress can be achieved once rapid online data analysis, adaptive sampling, and computational modeling are tightly integrated into experiments.

How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.

The effect of difference frequency on electrocommunication: chirp production and encoding in a species of weakly electric fish, Apteronotus leptorhynchus.

The brown ghost knifefish, Apteronotus leptorhynchus, is a model wave-type gymnotiform used extensively in neuroethological studies. As all weakly electric fish, they produce an electric field (electric organ discharge, EOD) and can detect electric signals in their environments using electroreceptors. During social interactions, A. leptorhynchus produce communication signals by modulating the frequency and amplitude of their EOD. The Type 2 chirp, a transient increase in EOD frequency, is the most common modulation type. We will first present a description of A. leptorhynchus chirp production from a behavioural perspective, followed by a discussion of the mechanisms by which chirps are encoded by electroreceptor afferents (P-units). Both the production and encoding of chirps are influenced by the difference in EOD frequency between interacting fish, the so-called beat or difference frequency (Df). Chirps are produced most often when the Df is small, whereas attacks are more common when Dfs are large. Correlation analysis has shown that chirp production induces an echo response in interacting conspecifics and that chirps are produced when attack rates are low. Here we show that both of these relationships are strongest when Dfs are large. Electrophysiological recordings from electroreceptor afferents (P-units) have suggested that small, Type 2 chirps are encoded by increases in electroreceptor synchrony at low Dfs only. How Type 2 chirps are encoded at higher Dfs, where the signals seem to exert the greatest behavioural influence, was unknown. Here, we provide evidence that at higher Dfs, chirps could be encoded by a desynchronization of the P-unit population activity.

Channel Noise from Both Slow Adaptation Currents and Fast Currents Is Required to Explain Spike-Response Variability in a Sensory Neuron

Spike-timing variability has a large effect on neural information processing. However, for many systems little is known about the noise sources causing the spike-response variability. Here we investigate potential sources of spike-response variability in auditory receptor neurons of locusts, a classic insect model system. At low-spike frequencies, our data show negative interspike-interval (ISI) correlations and ISI distributions that match the inverse Gaussian distribution. These findings can be explained by a white-noise source that interacts with an adaptation current. At higher spike frequencies, more strongly peaked distributions and positive ISI correlations appear, as expected from a canonical model of suprathreshold firing driven by temporally correlated (i.e., colored) noise. Simulations of a minimal conductance-based model of the auditory receptor neuron with stochastic ion channels exclude the delayed rectifier as a possible noise source. Our analysis suggests channel noise from an adaptation current and the receptor or sodium current as main sources for the colored and white noise, respectively. By comparing the ISI statistics with generic models, we find strong evidence for two distinct noise sources. Our approach does not involve any dendritic or somatic recordings that may harm the delicate workings of many sensory systems. It could be applied to various other types of neurons, in which channel noise dominates the fluctuations that shape the neurons spike statistics.

Postsynaptic Receptive Field Size and Spike Threshold Determine Encoding of High-Frequency Information Via Sensitivity to Synchronous Presynaptic Activity

Parallel sensory streams carrying distinct information about various stimulus properties have been observed in several sensory systems, including the visual system. What remains unclear is why some of these streams differ in the size of their receptive fields (RFs). In the electrosensory system, neurons with large RFs have short-latency responses and are tuned to high-frequency inputs. Conversely, neurons with small RFs are low-frequency tuned and exhibit longer-latency responses. What principle underlies this organization? We show experimentally that synchronous electroreceptor afferent (P-unit) spike trains selectively encode high-frequency stimulus information from broadband signals. This finding relies on a comparison of stimulus-spike output coherence using output trains obtained by either summing pairs of recorded afferent spike trains or selecting synchronous spike trains based on coincidence within a small time window. We propose a physiologically realistic decoding mechanism, based on postsynaptic RF size and postsynaptic output rate normalization that tunes target pyramidal cells in different electrosensory maps to low- or high-frequency signal components. By driving realistic neuron models with experimentally obtained P-unit spike trains, we show that a small RF is matched with a postsynaptic integration regime leading to responses over a broad range of frequencies, and a large RF with a fluctuation-driven regime that requires synchronous presynaptic input and therefore selectively encodes higher frequencies, confirming recent experimental data. Thus our work reveals that the frequency content of a broadband stimulus extracted by pyramidal cells, from P-unit afferents, depends on the amount of feedforward convergence they receive.