Adaptation and selective information transmission in the cricket auditory neuron AN2

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Persistent Firing and Adaptation in Optic-Flow-Sensitive Descending Neurons

A general principle of sensory systems is that they adapt to prolonged stimulation by reducing their response over time. Indeed, in many visual systems, including higher-order motion sensitive neurons in the fly optic lobes and the mammalian visual cortex, a reduction in neural activity following prolonged stimulation occurs. In contrast to this phenomenon, the response of the motor system controlling flight maneuvers persists following the offset of visual motion. It has been suggested that this gap is caused by a lingering calcium signal in the output synapses of fly optic lobe neurons. However, whether this directly affects the responses of the post-synaptic descending neurons, leading to the observed behavioral output, is not known. We use extracellular electrophysiology to record from optic-flow-sensitive descending neurons in response to prolonged wide-field stimulation. We find that, as opposed to most sensory and visual neurons, and in particular to the motion vision sensitive neurons in the brains of both flies and mammals, the descending neurons show little adaption during stimulus motion. In addition, we find that the optic-flow-sensitive descending neurons display persistent firing, or an after-effect, following the cessation of visual stimulation, consistent with the lingering calcium signal hypothesis. However, if the difference in after-effect is compensated for, subsequent presentation of stimuli in a test-adapt-test paradigm reveals adaptation to visual motion. Our results thus show a combination of adaptation and persistent firing in the neurons that project to the thoracic ganglia and thereby control behavioral output.

Online Detection of Multiple Stimulus Changes Based on Single Neuron Interspike Intervals

Nervous systems need to detect stimulus changes based on their neuronal responses without using any additional information on the number, times, and types of stimulus changes. Here, two relatively simple, biologically realistic change point detection methods are compared with two common analysis methods. The four methods are applied to intra- and extracellularly recorded responses of a single cricket interneuron (AN2) to acoustic simulation. Solely based on these recorded responses, the methods should detect an unknown number of different types of sound intensity in- and decreases shortly after their occurrences. For this task, the methods rely on calculating an adjusting interspike interval (ISI). Both simple methods try to separate responses to intensity in- or decreases from activity during constant stimulation. The Pure-ISI method performs this task based on the distribution of the ISI, while the ISI-Ratio method uses the ratio of actual and previous ISI. These methods are compared to the frequently used Moving-Average method, which calculates mean and standard deviation of the instantaneous spike rate in a moving interval. Additionally, a classification method provides the upper limit of the change point detection performance that can be expected for the cricket interneuron responses. The classification learns the statistical properties of the actual and previous ISI during stimulus changes and constant stimulation from a training data set. The main results are: (1) The Moving-Average method requires a stable activity in a long interval to estimate the previous activity, which was not always given in our data set. (2) The Pure-ISI method can reliably detect stimulus intensity increases when the neuron bursts, but it fails to identify intensity decreases. (3) The ISI-Ratio method detects stimulus in- and decreases well, if the spike train is not too noisy. (4) The classification method shows good performance for the detection of stimulus in- and decreases. But due to the statistical learning, this method tends to confuse responses to constant stimulation with responses triggered by a stimulus change. Our results suggest that stimulus change detection does not require computationally costly mechanisms. Simple nervous systems like the cricket's could effectively apply ISI-Ratios to solve this fundamental task.

Quantifying Neuronal Information Flow in Response to Frequency and Intensity Changes in the Auditory Cortex

Studies increasingly show that behavioral relevance alters the population representation of sensory stimuli in the sensory cortices. However, the mechanisms underlying this behavior are incompletely understood. Here, we record neuronal responses in the auditory cortex while a highly trained, awake, normal-hearing gerbil listens passively to target tones of high versus low behavioral relevance. Using an information theoretic framework, we model the overall transmission chain from acoustic input stimulus to recorded cortical response as a communication channel. To quantify how much information core auditory cortex carries about high versus low relevance sound, we then compute the mutual information of the multi-unit neuronal responses. Results show that the output over the stimulus-to-response channel can be modeled as a Poisson mixture. We derive a closed-form fast approximation for the entropy of a mixture of univariate Poisson random variables. A purely rate-code based model reveals reduced information transfer for high relevance compared to low relevance tones, hinting that changes in temporal discharge pattern may encode behavioral relevance.

Context-dependent coding and gain control in the auditory system of crickets

Sensory systems process stimuli that greatly vary in intensity and complexity. To maintain efficient information transmission, neural systems need to adjust their properties to these different sensory contexts, yielding adaptive or stimulus-dependent codes. Here, we demonstrated adaptive spectrotemporal tuning in a small neural network, i.e. the peripheral auditory system of the cricket. We found that tuning of cricket auditory neurons was sharper for complex multi-band than for simple single-band stimuli. Information theoretical considerations revealed that this sharpening improved information transmission by separating the neural representations of individual stimulus components. A network model inspired by the structure of the cricket auditory system suggested two putative mechanisms underlying this adaptive tuning: a saturating peripheral nonlinearity could change the spectral tuning, whereas broad feed-forward inhibition was able to reproduce the observed adaptive sharpening of temporal tuning. Our study revealed a surprisingly dynamic code usually found in more complex nervous systems and suggested that stimulus-dependent codes could be implemented using common neural computations.

Computational themes of peripheral processing in the auditory pathway of insects

Hearing in insects serves to gain information in the context of mate finding, predator avoidance or host localization. For these goals, the auditory pathways of insects represent the computational substrate for object recognition and localization. Before these higher level computations can be executed in more central parts of the nervous system, the signals need to be preprocessed in the auditory periphery. Here, we review peripheral preprocessing along four computational themes rather than discussing specific physiological mechanisms: (1) control of sensitivity by adaptation, (2) recoding of amplitude modulations of an acoustic signal into a labeled-line code (3) frequency processing and (4) conditioning for binaural processing. Along these lines, we review evidence for canonical computations carried out in the peripheral auditory pathway and show that despite the vast diversity of insect hearing, signal processing is governed by common computational motifs and principles.

Bursting neurons and ultrasound avoidance in crickets

Decision making in invertebrates often relies on simple neural circuits composed of only a few identified neurons. The relative simplicity of these circuits makes it possible to identify the key computation and neural properties underlying decisions. In this review, we summarize recent research on the neural basis of ultrasound avoidance in crickets, a response that allows escape from echolocating bats. The key neural property shaping behavioral output is high-frequency bursting of an identified interneuron, AN2, which carries information about ultrasound stimuli from receptor neurons to the brain. AN2's spike train consists of clusters of spikes - bursts - that may be interspersed with isolated, non-burst spikes. AN2 firing is necessary and sufficient to trigger avoidance steering but only high-rate firing, such as occurs in bursts, evokes this response. AN2 bursts are therefore at the core of the computation involved in deciding whether or not to steer away from ultrasound. Bursts in AN2 are triggered by synaptic input from nearly synchronous bursts in ultrasound receptors. Thus the population response at the very first stage of sensory processing - the auditory receptor - already differentiates the features of the stimulus that will trigger a behavioral response from those that will not. Adaptation, both intrinsic to AN2 and within ultrasound receptors, scales the burst-generating features according to the stimulus statistics, thus filtering out background noise and ensuring that bursts occur selectively in response to salient peaks in ultrasound intensity. Furthermore AN2's sensitivity to ultrasound varies adaptively with predation pressure, through both developmental and evolutionary mechanisms. We discuss how this key relationship between bursting and the triggering of avoidance behavior is also observed in other invertebrate systems such as the avoidance of looming visual stimuli in locusts or heat avoidance in beetles.

Power-law inter-spike interval distributions infer a conditional maximization of entropy in cortical neurons

The brain is considered to use a relatively small amount of energy for its efficient information processing. Under a severe restriction on the energy consumption, the maximization of mutual information (MMI), which is adequate for designing artificial processing machines, may not suit for the brain. The MMI attempts to send information as accurate as possible and this usually requires a sufficient energy supply for establishing clearly discretized communication bands. Here, we derive an alternative hypothesis for neural code from the neuronal activities recorded juxtacellularly in the sensorimotor cortex of behaving rats. Our hypothesis states that in vivo cortical neurons maximize the entropy of neuronal firing under two constraints, one limiting the energy consumption (as assumed previously) and one restricting the uncertainty in output spike sequences at given firing rate. Thus, the conditional maximization of firing-rate entropy (CMFE) solves a tradeoff between the energy cost and noise in neuronal response. In short, the CMFE sends a rich variety of information through broader communication bands (i.e., widely distributed firing rates) at the cost of accuracy. We demonstrate that the CMFE is reflected in the long-tailed, typically power law, distributions of inter-spike intervals obtained for the majority of recorded neurons. In other words, the power-law tails are more consistent with the CMFE rather than the MMI. Thus, we propose the mathematical principle by which cortical neurons may represent information about synaptic input into their output spike trains.

Tell me something interesting: context dependent adaptation in somatosensory cortex

It is widely accepted that through a process of adaptation cells adjust their sensitivity in accordance with prevailing stimulus conditions. However, in two recent studies exploring adaptation in the rodent inferior colliculus and somatosensory cortex, neurons did not adapt towards global mean, but rather became most sensitive to inputs that were located towards the edge of the stimulus distribution with greater intensity than the mean. We re-examined electrophysiological data from the somatosensory study with the purpose of exploring the underlying encoding strategies. We found that neural gain tended to decrease as stimulus variance increased. Following adaptation to changes in global mean, neuronal output was scaled such that the relationship between firing rate and local, rather than global, differences in stimulus intensity was maintained. The majority of cells responded to large, positive deviations in stimulus amplitude; with a small number responding to both positive and negative changes in stimulus intensity. Adaptation to global mean was replicated in a model neuron by incorporating both spike-rate adaptation and tonic-inhibition, which increased in proportion to stimulus mean. Adaptation to stimulus variance was replicated by approximating the output of a population of neurons adapted to global mean and using it to drive a layer of recurrently connected depressing synapses. Within the barrel cortex, adaptation ensures that neurons are able to encode both overall levels of variance and large deviations in the input. This is achieved through a combination of gain modulation and a shift in sensitivity to intensity levels that are greater than the mean.

Multiple arithmetic operations in a single neuron: the recruitment of adaptation processes in the cricket auditory pathway depends on sensory context

Sensory pathways process behaviorally relevant signals in various contexts and therefore have to adapt to differing background conditions. Depending on changes in signal statistics, this adjustment might be a combination of two fundamental computational operations: subtractive adaptation shifting a neuron's threshold and divisive gain control scaling its sensitivity. The cricket auditory system has to deal with highly stereotyped conspecific songs at low carrier frequencies, and likely much more variable predator signals at high frequencies. We proposed that due to the differences between the two signal classes, the operation that is implemented by adaptation depends on the carrier frequency. We aimed to identify the biophysical basis underlying the basic computational operations of subtraction and division. We performed in vivo intracellular and extracellular recordings in a first-order auditory interneuron (AN2) that is active in both mate recognition and predator avoidance. We demonstrated subtractive shifts at the carrier frequency of conspecific songs and division at the predator-like carrier frequency. Combined application of current injection and acoustic stimuli for each cell allowed us to demonstrate the subtractive effect of cell-intrinsic adaptation currents. Pharmacological manipulation enabled us to demonstrate that presynaptic inhibition is most likely the source of divisive gain control. We showed that adjustment to the sensory context can depend on the class of signals that are relevant to the animal. We further revealed that presynaptic inhibition is a simple mechanism for divisive operations. Unlike other proposed mechanisms, it is widely available in the sensory periphery of both vertebrates and invertebrates.

Error-probability noise benefits in threshold neural signal detection

Five new theorems and a stochastic learning algorithm show that noise can benefit threshold neural signal detection by reducing the probability of detection error. The first theorem gives a necessary and sufficient condition for such a noise benefit when a threshold neuron performs discrete binary signal detection in the presence of additive scale-family noise. The theorem allows the user to find the optimal noise probability density for several closed-form noise types that include generalized Gaussian noise. The second theorem gives a noise-benefit condition for more general threshold signal detection when the signals have continuous probability densities. The third and fourth theorems reduce this noise benefit to a weighted-derivative comparison of signal probability densities at the detection threshold when the signal densities are continuously differentiable and when the noise is symmetric and comes from a scale family. The fifth theorem shows how collective noise benefits can occur in a parallel array of threshold neurons even when an individual threshold neuron does not itself produce a noise benefit. The stochastic gradient-ascent learning algorithm can find the optimal noise value for noise probability densities that do not have a closed form.