Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

Neuronal precision and the limits for acoustic signal recognition in a small neuronal network

Recognition of acoustic signals may be impeded by two factors: extrinsic noise, which degrades sounds before they arrive at the receiver’s ears, and intrinsic neuronal noise, which reveals itself in the trial-to-trial variability of the responses to identical sounds. Here we analyzed how these two noise sources affect the recognition of acoustic signals from potential mates in grasshoppers. By progressively corrupting the envelope of a female song, we determined the critical degradation level at which males failed to recognize a courtship call in behavioral experiments. Using the same stimuli, we recorded intracellularly from auditory neurons at three different processing levels, and quantified the corresponding changes in spike train patterns by a spike train metric, which assigns a distance between spike trains. Unexpectedly, for most neurons, intrinsic variability accounted for the main part of the metric distance between spike trains, even at the strongest degradation levels. At consecutive levels of processing, intrinsic variability increased, while the sensitivity to external noise decreased. We followed two approaches to determine critical degradation levels from spike train dissimilarities, and compared the results with the limits of signal recognition measured in behaving animals.     

Neural Coding with Graded Membrane Potential Changes and Spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.     

Spike-timing in primary sensory neurons: a model of somatosensory transduction in the rat

In previous work, we constructed a simple electro-mechanical model of transduction in the rat mystacial follicle that was able to replicate primary afferent response profiles to a variety of whisker deflection stimuli. Here, we update that model to fit newly available spike-timing response data, and demonstrate that the new model produces appropriate responses to richer stimuli, including pseudo white noise and natural textures, at a spike-timing level of detail. Additionally, we demonstrate reliable distributed encoding of multi-component oscillatory signals. No modifications were necessary to the mechanical model of the physical components of the follicle–sinus complex, supporting its generality. We conclude that this model, and its continued development, will aid the understanding both of somatosensory systems in general, and of physiological results from higher (e.g. thalamocortical) systems by accurately characterising the signals on which they operate.     

Mixed Signal Learning by Spike Correlation Propagation in Feedback Inhibitory Circuits

The brain can learn and detect mixed input signals masked by various types of noise, and spike-timing-dependent plasticity (STDP) is the candidate synaptic level mechanism. Because sensory inputs typically have spike correlation, and local circuits have dense feedback connections, input spikes cause the propagation of spike correlation in lateral circuits; however, it is largely unknown how this secondary correlation generated by lateral circuits influences learning processes through STDP, or whether it is beneficial to achieve efficient spike-based learning from uncertain stimuli. To explore the answers to these questions, we construct models of feedforward networks with lateral inhibitory circuits and study how propagated correlation influences STDP learning, and what kind of learning algorithm such circuits achieve. We derive analytical conditions at which neurons detect minor signals with STDP, and show that depending on the origin of the noise, different correlation timescales are useful for learning. In particular, we show that non-precise spike correlation is beneficial for learning in the presence of cross-talk noise. We also show that by considering excitatory and inhibitory STDP at lateral connections, the circuit can acquire a lateral structure optimal for signal detection. In addition, we demonstrate that the model performs blind source separation in a manner similar to the sequential sampling approximation of the Bayesian independent component analysis algorithm. Our results provide a basic understanding of STDP learning in feedback circuits by integrating analyses from both dynamical systems and information theory.     

A field test of the audibility of urban versus rural songs in mountain chickadees

Anthropogenic noise can mask avian vocalizations, and several urban‐dwelling species adjust frequency or amplitude of vocalizations in ways that appear to compensate for increased noise levels. Playback studies have investigated whether receivers differentiate between signals produced by rural and urban males, but it is difficult to determine whether differential response to stimulus reflects differences in audibility versus perceived differences in male signals/condition that result from urban settlement. Here, we performed paired‐playback trials to determine whether mountain chickadees (Poecile gambeli) differentiate urban versus rural songs when both stimuli were broadcast within noise. For each playback, stimuli were played in short bouts starting at a low signal‐to‐noise ratio and increasing in relative amplitude with each successive bout. If the primary function of adjusted urban songs is propagation in noise, we hypothesized that focal males would respond sooner to urban versus rural playbacks (detect at lower signal‐to‐noise ratios). If urban songs solely encode information about the male's condition (such as increased aggression), then we predicted only a differential aggressive response to playbacks once detected. If urban songs both increase propagation and embed information on male condition, we predicted a combination of both response types. We found no difference in latency to first response in urban versus rural songs, but some evidence for differential aggression to playback dependent on both stimulus type (urban vs. rural) and local ambient noise levels; focal males in noisy (urban) sites responded aggressively to both stimulus types, whereas focal males in quiet (rural) sites responded more aggressively to urban than to rural stimuli. This context‐dependent discrimination may be the result of increased aggression in urban habitats, improved communication in noisy habitats by urban signallers and receivers, or some combination of the two.     

The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short () timescales while simultaneously reducing correlations at long () timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs.     

Probing real sensory worlds of receivers with unsupervised clustering

The task of an organism to extract information about the external environment from sensory signals is based entirely on the analysis of ongoing afferent spike activity provided by the sense organs. We investigate the processing of auditory stimuli by an acoustic interneuron of insects. In contrast to most previous work we do this by using stimuli and neurophysiological recordings directly in the nocturnal tropical rainforest, where the insect communicates. Different from typical recordings in sound proof laboratories, strong environmental noise from multiple sound sources interferes with the perception of acoustic signals in these realistic scenarios. We apply a recently developed unsupervised machine learning algorithm based on probabilistic inference to find frequently occurring firing patterns in the response of the acoustic interneuron. We can thus ask how much information the central nervous system of the receiver can extract from bursts without ever being told which type and which variants of bursts are characteristic for particular stimuli. Our results show that the reliability of burst coding in the time domain is so high that identical stimuli lead to extremely similar spike pattern responses, even for different preparations on different dates, and even if one of the preparations is recorded outdoors and the other one in the sound proof lab. Simultaneous recordings in two preparations exposed to the same acoustic environment reveal that characteristics of burst patterns are largely preserved among individuals of the same species. Our study shows that burst coding can provide a reliable mechanism for acoustic insects to classify and discriminate signals under very noisy real-world conditions. This gives new insights into the neural mechanisms potentially used by bushcrickets to discriminate conspecific songs from sounds of predators in similar carrier frequency bands.     

Regional admixture mapping and structured association testing: conceptual unification and an extensible general linear model

Individual genetic admixture estimates, determined both across the genome and at specific genomic regions, have been proposed for use in identifying specific genomic regions harboring loci influencing phenotypes in regional admixture mapping (RAM). Estimates of individual ancestry can be used in structured association tests (SAT) to reduce confounding induced by various forms of population substructure. Although presented as two distinct approaches, we provide a conceptual framework in which both RAM and SAT are special cases of a more general linear model. We clarify which variables are sufficient to condition upon in order to prevent spurious associations and also provide a simple closed form “semiparametric” method of evaluating the reliability of individual admixture estimates. An estimate of the reliability of individual admixture estimates is required to make an inherent errors-in-variables problem tractable. Casting RAM and SAT methods as a general linear model offers enormous flexibility enabling application to a rich set of phenotypes, populations, covariates, and situations, including interaction terms and multilocus models. This approach should allow far wider use of RAM and SAT, often using standard software, in addressing admixture as either a confounder of association studies or a tool for finding loci influencing complex phenotypes in species as diverse as plants, humans, and nonhuman animals.     

The refractory periods and threshold potentials of sequential spikes measured by whole-cell recording

Neurons in the central nervous system are thought to program neural language via firing sequential spikes for guiding animal behaviors. The quantitative profiles of spike intrinsic properties are critically important to understand spike programming. We developed approaches with whole-cell recordings to measure the threshold potentials and refractory periods (RPs) of sequential spikes, and to analyze the relationships of these factors with spike timing precision and capacity at the regular-spiking and fast-spiking neurons in cortical slice. The RPs and threshold potentials of sequential spikes at these two groups of neurons are different and are linearly correlated with spike timing precision and capacity. These data suggest that RPs and threshold potentials essentially navigate the spike programming for the precise and loyal encoding of meaningful neural signals. Our study provides the avenues for decoding the spectrum of the neural signals quantitatively.     

Evolutionarily conserved coding properties of auditory neurons across grasshopper species

We investigated encoding properties of identified auditory interneurons in two not closely related grasshopper species (Acrididae). The neurons can be homologized on the basis of their similar morphologies and physiologies. As test stimuli, we used the species-specific stridulation signals of Chorthippus biguttulus, which evidently are not relevant for the other species, Locusta migratoria. We recorded spike trains produced in response to these signals from several neuron types at the first levels of the auditory pathway in both species. Using a spike train metric to quantify differences between neuronal responses, we found a high similarity in the responses of homologous neurons: interspecific differences between the responses of homologous neurons in the two species were not significantly larger than intraspecific differences (between several specimens of a neuron in one species). These results suggest that the elements of the thoracic auditory pathway have been strongly conserved during the evolutionary divergence of these species. According to the 'efficient coding' hypothesis, an adaptation of the thoracic auditory pathway to the specific needs of acoustic communication could be expected. We conclude that there must have been stabilizing selective forces at work that conserved coding characteristics and prevented such an adaptation.     

Encoding Stimulus Information by Spike Numbers and Mean Response Time in Primary Auditory Cortex

Neurons can transmit information about sensory stimuli via their firing rate, spike latency, or by the occurrence of complex spike patterns. Identifying which aspects of the neural responses actually encode sensory information remains a fundamental question in neuroscience. Here we compared various approaches for estimating the information transmitted by neurons in auditory cortex in two very different experimental paradigms, one measuring spatial tuning and the other responses to complex natural stimuli. We demonstrate that, in both cases, spike counts and mean response times jointly carry essentially all the available information about the stimuli. Thus, in auditory cortex, whereas spike counts carry only partial information about stimulus identity or location, the additional availability of relatively coarse temporal information is sufficient in order to extract essentially all the sensory information available in the spike discharge pattern, at least for the relatively short stimuli (< ∼ 100 ms) commonly used in auditory research.     

What Do Contrast Threshold Equivalent Noise Studies Actually Measure? Noise vs. Nonlinearity in Different Masking Paradigms

The internal noise present in a linear system can be quantified by the equivalent noise method. By measuring the effect that applying external noise to the system’s input has on its output one can estimate the variance of this internal noise. By applying this simple “linear amplifier” model to the human visual system, one can entirely explain an observer’s detection performance by a combination of the internal noise variance and their efficiency relative to an ideal observer. Studies using this method rely on two crucial factors: firstly that the external noise in their stimuli behaves like the visual system’s internal noise in the dimension of interest, and secondly that the assumptions underlying their model are correct (e.g. linearity). Here we explore the effects of these two factors while applying the equivalent noise method to investigate the contrast sensitivity function (CSF). We compare the results at 0.5 and 6 c/deg from the equivalent noise method against those we would expect based on pedestal masking data collected from the same observers. We find that the loss of sensitivity with increasing spatial frequency results from changes in the saturation constant of the gain control nonlinearity, and that this only masquerades as a change in internal noise under the equivalent noise method. Part of the effect we find can be attributed to the optical transfer function of the eye. The remainder can be explained by either changes in effective input gain, divisive suppression, or a combination of the two. Given these effects the efficiency of our observers approaches the ideal level. We show the importance of considering these factors in equivalent noise studies.     

Tuning curves, neuronal variability, and sensory coding

Tuning curves are widely used to characterize the responses of sensory neurons to external stimuli, but there is an ongoing debate as to their role in sensory processing. Commonly, it is assumed that a neuron's role is to encode the stimulus at the tuning curve peak, because high firing rates are the neuron's most distinct responses. In contrast, many theoretical and empirical studies have noted that nearby stimuli are most easily discriminated in high-slope regions of the tuning curve. Here, we demonstrate that both intuitions are correct, but that their relative importance depends on the experimental context and the level of variability in the neuronal response. Using three different information-based measures of encoding applied to experimentally measured sensory neurons, we show how the best-encoded stimulus can transition from high-slope to high-firing-rate regions of the tuning curve with increasing noise level. We further show that our results are consistent with recent experimental findings that correlate neuronal sensitivities with perception and behavior. This study illustrates the importance of the noise level in determining the encoding properties of sensory neurons and provides a unified framework for interpreting how the tuning curve and neuronal variability relate to the overall role of the neuron in sensory encoding.     

Spike generating dynamics and the conditions for spike-time precision in cortical neurons

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.     

Effects of binaural decorrelation on neural and behavioral processing of interaural level differences in the barn owl (Tyto alba)

The effect of binaural decorrelation on the processing of interaural level difference cues in the barn owl (Tyto alba) was examined behaviorally and electrophysiologically. The electrophysiology experiment measured the effect of variations in binaural correlation on the first stage of interaural level difference encoding in the central nervous system. The responses of single neurons in the posterior part of the ventral nucleus of the lateral lemniscus were recorded to stimulation with binaurally correlated and binaurally uncorrelated noise. No significant differences in interaural level difference sensitivity were found between conditions. Neurons in the posterior part of the ventral nucleus of the lateral lemniscus encode the interaural level difference of binaurally correlated and binaurally uncorrelated noise with equal accuracy and precision. This nucleus therefore supplies higher auditory centers with an undegraded interaural level difference signal for sound stimuli that lack a coherent interaural time difference. The behavioral experiment measured auditory saccades in response to interaural level differences presented in binaurally correlated and binaurally uncorrelated noise. The precision and accuracy of sound localization based on interaural level difference was reduced but not eliminated for binaurally uncorrelated signals. The observation that barn owls continue to vary auditory saccades with the interaural level difference of binaurally uncorrelated stimuli suggests that neurons that drive head saccades can be activated by incomplete auditory spatial information.     

Simple model for encoding natural images by retinal ganglion cells with nonlinear spatial integration

A central goal in sensory neuroscience is to understand the neuronal signal processing involved in the encoding of natural stimuli. A critical step towards this goal is the development of successful computational encoding models. For ganglion cells in the vertebrate retina, the development of satisfactory models for responses to natural visual scenes is an ongoing challenge. Standard models typically apply linear integration of visual stimuli over space, yet many ganglion cells are known to show nonlinear spatial integration, in particular when stimulated with contrast-reversing gratings. We here study the influence of spatial nonlinearities in the encoding of natural images by ganglion cells, using multielectrode-array recordings from isolated salamander and mouse retinas. We assess how responses to natural images depend on first- and second-order statistics of spatial patterns inside the receptive field. This leads us to a simple extension of current standard ganglion cell models. We show that taking not only the weighted average of light intensity inside the receptive field into account but also its variance over space can partly account for nonlinear integration and substantially improve response predictions of responses to novel images. For salamander ganglion cells, we find that response predictions for cell classes with large receptive fields profit most from including spatial contrast information. Finally, we demonstrate how this model framework can be used to assess the spatial scale of nonlinear integration. Our results underscore that nonlinear spatial stimulus integration translates to stimulation with natural images. Furthermore, the introduced model framework provides a simple, yet powerful extension of standard models and may serve as a benchmark for the development of more detailed models of the nonlinear structure of receptive fields.     

Changes in response latencies of the mouse inferior colliculus neurons depending on the position and movement direction of the spectral contrast

Variability of response latency of neurons in the mouse inferior colliculus of (Mus musculus) to signals of notch noise and of noise band with regular varying of the notch/band center frequencies, have been studied. Plots of latency and spike count versus notch/band center frequency were constructed (latency functions and spike count functions). Spectral notch/noise band motion crossing boundaries of excitatory areas in the neurons frequency receptive field could produce latency function shifts (and appropriate to this spike count function shifts). Direction-dependent latency function and spike count function shifts were mostly seen for primary-like and V-shape neurons. The most interesting feature of directional sensitivity of inhibitory-dominated neurons was the selective shortening of latency and selective synchronization of the initial spikes (with appropriate to this spike count rise). The dynamic properties of inhibitory-dominated neurons can be explained on the basis of their selective sensitivity to position of spectral contrast in frequency receptive field, connected with disinhibition, and of the character of distribution of excitatory and inhibitory inputs. Manifestation of motion effects was influenced by spectral shape of noise signal and notch width.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.