A generalized linear model for estimating spectrotemporal receptive fields from responses to natural sounds

In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF), a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimuli; these algorithms differ in their functional models, cost functions, and regularization methods. Here, we characterize the stimulus-response function of auditory neurons using a generalized linear model (GLM). In this model, each cell's input is described by: 1) a stimulus filter (STRF); and 2) a post-spike filter, which captures dependencies on the neuron's spiking history. The output of the model is given by a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs) and modulation limited (ml) noise. We compare this model to normalized reverse correlation (NRC), the traditional method for STRF estimation, in terms of predictive power and the basic tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs from the two models derived from the same responses can differ substantially and that GLM STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal tuning than does the NRC method when responses to complex sounds are studied in these neurons.     

Nonlinear effects of intrinsic dynamics on temporal encoding in a model of avian auditory cortex

Neurons exhibit diverse intrinsic dynamics, which govern how they integrate synaptic inputs to produce spikes. Intrinsic dynamics are often plastic during development and learning, but the effects of these changes on stimulus encoding properties are not well known. To examine this relationship, we simulated auditory responses to zebra finch song using a linear-dynamical cascade model, which combines a linear spectrotemporal receptive field with a dynamical, conductance-based neuron model, then used generalized linear models to estimate encoding properties from the resulting spike trains. We focused on the effects of a low-threshold potassium current (K_LT) that is present in a subset of cells in the zebra finch caudal mesopallium and is affected by early auditory experience. We found that K_LT affects both spike adaptation and the temporal filtering properties of the receptive field. The direction of the effects depended on the temporal modulation tuning of the linear (input) stage of the cascade model, indicating a strongly nonlinear relationship. These results suggest that small changes in intrinsic dynamics in tandem with differences in synaptic connectivity can have dramatic effects on the tuning of auditory neurons.     

A Normalization Model of Attentional Modulation of Single Unit Responses

Although many studies have shown that attention to a stimulus can enhance the responses of individual cortical sensory neurons, little is known about how attention accomplishes this change in response. Here, we propose that attention-based changes in neuronal responses depend on the same response normalization mechanism that adjusts sensory responses whenever multiple stimuli are present. We have implemented a model of attention that assumes that attention works only through this normalization mechanism, and show that it can replicate key effects of attention. The model successfully explains how attention changes the gain of responses to individual stimuli and also why modulation by attention is more robust and not a simple gain change when multiple stimuli are present inside a neuron''s receptive field. Additionally, the model accounts well for physiological data that measure separately attentional modulation and sensory normalization of the responses of individual neurons in area MT in visual cortex. The proposal that attention works through a normalization mechanism sheds new light a broad range of observations on how attention alters the representation of sensory information in cerebral cortex.     

Receptive field properties of neurons in the electrosensory lateral line lobe of the weakly electric fish, <Emphasis Type="Italic">Gnathonemus petersii</Emphasis>

The receptive field of a sensory neuron is known as that region in sensory space where a stimulus will alter the response of the neuron. We determined the spatial dimensions and the shape of receptive fields of electrosensitive neurons in the medial zone of the electrosensory lateral line lobe of the African weakly electric fish, Gnathonemus petersii, by using single cell recordings. The medial zone receives input from sensory cells which encode the stimulus amplitude. We analysed the receptive fields of 71 neurons. The size and shape of the receptive fields were determined as a function of spike rate and first spike latency and showed differences for the two analysis methods used. Spatial diameters ranged from 2 to 36 mm (spike rate) and from 2.45 to 14.12 mm (first spike latency). Some of the receptive fields were simple consisting only of one uniform centre, whereas most receptive fields showed a complex and antagonistic centre-surround organisation. Several units had a very complex structure with multiple centres and surrounding-areas. While receptive field size did not correlate with peripheral receptor location, the complexity of the receptive fields increased from rostral to caudal along the fish's body.     

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.     

Spike-frequency adaptation generates intensity invariance in a primary auditory interneuron

Adaptation of the spike-frequency response to constant stimulation, as observed on various timescales in many neurons, reflects high-pass filter properties of a neuron's transfer function. Adaptation in general, however, is not sufficient to make a neuron's response independent of the mean intensity of a sensory stimulus, since low frequency components of the stimulus are still transmitted, although with reduced gain. We here show, based on an analytically tractable model, that the response of a neuron is intensity invariant, if the fully adapted steady-state spike-frequency response to constant stimuli is independent of stimulus intensity. Electrophysiological recordings from the AN1, a primary auditory interneuron of crickets, show that for intensities above 60 dB SPL (sound pressure level) the AN1 adapted with a time-constant of approximately 40 ms to a steady-state firing rate of approximately 100 Hz. Using identical random amplitude-modulation stimuli we verified that the AN1's spike-frequency response is indeed invariant to the stimulus' mean intensity above 60 dB SPL. The transfer function of the AN1 is a band pass, resulting from a high-pass filter (cutoff frequency at 4 Hz) due to adaptation and a low-pass filter (100 Hz) determined by the steady-state spike frequency. Thus, fast spike-frequency adaptation can generate intensity invariance already at the first level of neural processing.     

Modeling convergent ON and OFF pathways in the early visual system

For understanding the computation and function of single neurons in sensory systems, one needs to investigate how sensory stimuli are related to a neuron’s response and which biological mechanisms underlie this relationship. Mathematical models of the stimulus–response relationship have proved very useful in approaching these issues in a systematic, quantitative way. A starting point for many such analyses has been provided by phenomenological “linear–nonlinear” (LN) models, which comprise a linear filter followed by a static nonlinear transformation. The linear filter is often associated with the neuron’s receptive field. However, the structure of the receptive field is generally a result of inputs from many presynaptic neurons, which may form parallel signal processing pathways. In the retina, for example, certain ganglion cells receive excitatory inputs from ON-type as well as OFF-type bipolar cells. Recent experiments have shown that the convergence of these pathways leads to intriguing response characteristics that cannot be captured by a single linear filter. One approach to adjust the LN model to the biological circuit structure is to use multiple parallel filters that capture ON and OFF bipolar inputs. Here, we review these new developments in modeling neuronal responses in the early visual system and provide details about one particular technique for obtaining the required sets of parallel filters from experimental data.     

Spectro-temporal receptive fields of auditory neurons in the grassfrog

The nature of the stimulus-response relation for single auditory neurons is reflected in the properties of the Pre-Event Stimulus Ensemble: the ensemble of stimuli, preceding the occurrence of an action potential (neural event). This paper describes methods to analyse the spectro-temporal properties of this ensemble. These methods are based on the analytic signal representation of acoustic signals and functionals derived from it: the instantaneous amplitude and instantaneous frequency and the dynamic power spectrum. The procedures have been applied to a number of extra-cellular single unit recordings from the grassfrog, Rana temporatia L., recorded during presentation of an ensemble of tonal stimuli. The outcome of this analysis describes the spectro-temporal receptive field of the neuron under the present stimulus conditions. The procedure, based on the dynamic power spectrum is applicable to an arbitrary stimulus ensemble, thus allowing a comparison of the spectrotemporal receptive fields for different types of stimuli.     

Sound representation methods for spectro-temporal receptive field estimation

The spectro-temporal receptive field (STRF) of an auditory neuron describes the linear relationship between the sound stimulus in a time-frequency representation and the neural response. Time-frequency representations of a sound in turn require a nonlinear operation on the sound pressure waveform and many different forms for this non-linear transformation are possible. Here, we systematically investigated the effects of four factors in the non-linear step in the STRF model: the choice of logarithmic or linear filter frequency spacing, the time-frequency scale, stimulus amplitude compression and adaptive gain control. We quantified the goodness of fit of these different STRF models on data obtained from auditory neurons in the songbird midbrain and forebrain. We found that adaptive gain control and the correct stimulus amplitude compression scheme are paramount to correctly modelling neurons. The time-frequency scale and frequency spacing also affected the goodness of fit of the model but to a lesser extent and the optimal values were stimulus dependant. Action Editor: Israel Nelken     

Responses of descending neurons to looming stimuli in the praying mantis <Emphasis Type="Italic">Tenodera aridifolia</Emphasis>

Responses to visual stimuli of some neurons that descend the nerve cord from the brain were recorded extracellularly in the mantis Tenodera aridifolia. Most of the recorded neurons showed their largest responses to looming stimuli that simulated a black circle approaching towards the mantis. The neurons showed a transient excitatory response to a gradually darkening or receding circle. The neurons showed sustained excitation to the linearly expanding stimuli, but the spike frequency decreased rapidly. The responses of the neurons were affected by both the diameter and the speed of looming stimuli. Faster or smaller looming stimuli elicited a higher peak frequency. These responses were observed in both recordings from the connective between suboesophageal and prothoracic ganglia and the connective between prothoracic and mesothoracic ganglia. There was a one-to-one correspondence of spike firing between these two recordings with a fixed delay. The neurons had the receptive field on ipsilateral side to its axon at the cervical connective. These results suggest that there is a looming-sensitive descending neuron, with an axon projecting over prothoracic ganglion, in the mantis nervous system.     

Adaptation accentuates responses of fly motion-sensitive visual neurons to sudden stimulus changes

Adaptation in sensory and neuronal systems usually leads to reduced responses to persistent or frequently presented stimuli. In contrast to simple fatigue, adapted neurons often retain their ability to encode changes in stimulus intensity and to respond when novel stimuli appear. We investigated how the level of adaptation of a fly visual motion-sensitive neuron affects its responses to discontinuities in the stimulus, i.e. sudden brief changes in one of the stimulus parameters (velocity, contrast, grating orientation and spatial frequency). Although the neuron''s overall response decreased gradually during ongoing motion stimulation, the response transients elicited by stimulus discontinuities were preserved or even enhanced with adaptation. Moreover, the enhanced sensitivity to velocity changes by adaptation was not restricted to a certain velocity range, but was present regardless of whether the neuron was adapted to a baseline velocity below or above its steady-state velocity optimum. Our results suggest that motion adaptation helps motion-sensitive neurons to preserve their sensitivity to novel stimuli even in the presence of strong tonic stimulation, for example during self-motion.     

Dynamic Alignment Models for Neural Coding

Recently, there have been remarkable advances in modeling the relationships between the sensory environment, neuronal responses, and behavior. However, most models cannot encompass variable stimulus-response relationships such as varying response latencies and state or context dependence of the neural code. Here, we consider response modeling as a dynamic alignment problem and model stimulus and response jointly by a mixed pair hidden Markov model (MPH). In MPHs, multiple stimulus-response relationships (e.g., receptive fields) are represented by different states or groups of states in a Markov chain. Each stimulus-response relationship features temporal flexibility, allowing modeling of variable response latencies, including noisy ones. We derive algorithms for learning of MPH parameters and for inference of spike response probabilities. We show that some linear-nonlinear Poisson cascade (LNP) models are a special case of MPHs. We demonstrate the efficiency and usefulness of MPHs in simulations of both jittered and switching spike responses to white noise and natural stimuli. Furthermore, we apply MPHs to extracellular single and multi-unit data recorded in cortical brain areas of singing birds to showcase a novel method for estimating response lag distributions. MPHs allow simultaneous estimation of receptive fields, latency statistics, and hidden state dynamics and so can help to uncover complex stimulus response relationships that are subject to variable timing and involve diverse neural codes.     

Stimulus change detection in phasic auditory units in the frog midbrain: frequency and ear specific adaptation

Neural adaptation, a reduction in the response to a maintained stimulus, is an important mechanism for detecting stimulus change. Contributing to change detection is the fact that adaptation is often stimulus specific: adaptation to a particular stimulus reduces excitability to a specific subset of stimuli, while the ability to respond to other stimuli is unaffected. Phasic cells (e.g., cells responding to stimulus onset) are good candidates for detecting the most rapid changes in natural auditory scenes, as they exhibit fast and complete adaptation to an initial stimulus presentation. We made recordings of single phasic auditory units in the frog midbrain to determine if adaptation was specific to stimulus frequency and ear of input. In response to an instantaneous frequency step in a tone, 28 % of phasic cells exhibited frequency specific adaptation based on a relative frequency change (delta-f = ±16 %). Frequency specific adaptation was not limited to frequency steps, however, as adaptation was also overcome during continuous frequency modulated stimuli and in response to spectral transients interrupting tones. The results suggest that adaptation is separated for peripheral (e.g., frequency) channels. This was tested directly using dichotic stimuli. In 45 % of binaural phasic units, adaptation was ear specific: adaptation to stimulation of one ear did not affect responses to stimulation of the other ear. Thus, adaptation exhibited specificity for stimulus frequency and lateralization at the level of the midbrain. This mechanism could be employed to detect rapid stimulus change within and between sound sources in complex acoustic environments.     

Spike synchronization of tympanic receptor fibres in a grasshopper (Chorthippus biguttulus L., Acrididae)

In recordings from single tympanic receptor fibres in C. biguttulus, the response to synthesized sounds (rectangularly modulated white noise) interrupted by very brief (a few milliseconds) gaps was examined. In behavioral tests, females of the species respond very differently to such 'model syllables' at moderate intensities, depending on the gap width. If the gaps (in a moderate-intensity syllable) are larger than 2 ms, the stimulus fails to elicit a response, whereas stimuli with gaps smaller than 1 ms are as effective as uninterrupted syllables (D. von Helversen 1972; O. von Helversen 1979). Neither the mean spike count nor the interspike-interval distribution of the single receptor response contains the information sufficient to distinguish uninterrupted syllables from syllables with gaps. On the other hand, examination of the temporal distribution of the spikes reveals that gaps (or the pulse onsets following the gaps) cause spike synchronization. An index of synchronization (IS) was defined as a measure of this gap-induced effect. Analysis of the receptor responses based on IS revealed differences that correspond quantitatively to the abrupt abolition of the behavioral response at a gap-width between 1 and 2 ms. From the hypothesis that such brief gaps are detected by the nervous system by way of spike synchronization in the tympanic nerve, one can predict certain features of the behavioral response to high-intensity stimuli. The gap-induced spike synchronization was more pronounced at higher temperatures. This effect was demonstrated in both summated recordings from the tympanic nerve and single fibre recordings. Experiments with primary auditory fibres of Locusta migratoria showed that the receptors in this species respond very similarly to the same stimuli. That is, the receptors of C. biguttulus are not specially adapted for detecting very brief gaps. Synchronization of the spikes in parallel receptor fibres of the tympanal nerve is probably a general feature of acridids; we infer that in C. biguttulus this gap-induced synchronized activity is detected by special processing in higher auditory centres.     

The Spectro-Temporal Receptive Field

The Spectro-Temporal Receptive Field (STRF) of an auditory neuron has been introduced experimentally on the base of the average spectrotemporal structure of the acoustic stimuli which precede the occurrence of action potentials (Aertsen et al., 1980, 1981). In the present paper the STRF is considered in the general framework of nonlinear system theory, especially in the form of the Volterra integral representation. The STRF is proposed to be formally identified with a linear functional of the second order Volterra kernel. The experimental determination of the STRF leads to a formulation in terms of the Wiener expansion where the kernels can be identified by evaluation of the system's input-output correlations. For a Gaussian stimulus ensemble and a nonlinear system with no even order contributions of order higher than two, it is shown that the second order cross correlation of stimulus and response, normalized with respect to the spectral contents of the stimulus ensemble, leads to the stimulus-invariant spectrotemporal receptive field. The investigation of stimulus-invariance of the STRF for more general nonlinear systems and for stimulus ensembles which can be generated by nonlinear transformations of Gaussian noise involve the evaluation of higher order stimulus-response correlation functions.     

Configurational pattern discrimination responsible for dishabituation in common toads Bufo bufo (L.): Behavioral tests of the predictions of a neural model

Summary Recently, a neural model of visual pattern discrimination for stimulus-specific habituation was developed, based on previous behavioral studies which demonstrated that toads exhibit a dishabituation hierarchy for different worm-like stimuli. The model suggests that visual objects are represented by temporal coding and predicts that the dishabituation hierarchy changes when the stimulus/background contrast direction is reversed or the stimulus size is varied. The behavioral experiments reported in this paper were designed to test these predictions, (1) For a pair of stimuli from the contrast reversal prediction, the experimental results validated the theory. (2) For a pair of stimuli from the size reduction prediction, the experimental results failed to validate the theory. Further experiments concerning size effects suggest that configurai visual pattern discrimination in toads exhibits size invariance. (3) Inspired by the Groves-Thompson account of habituation, we found that dishabituation by a second stimulus has a separate process from habituation to a first stimulus. This paper serves as an example of a fruitful dialogue between experimentation and modeling, crucial for understanding brain functions.Abbreviations a-h worm-like stimulus patterns - AT anterior thalamus - ERF excitatory receptive field - IRF inhibitory receptive field - RF receptive field - R2 to R4 retinal ganglion cell types - vMP posterior ventromedial pallium     

A computational theory of visual receptive fields

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space–time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space–time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space–time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.