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.     

The Essential Complexity of Auditory Receptive Fields

Encoding properties of sensory neurons are commonly modeled using linear finite impulse response (FIR) filters. For the auditory system, the FIR filter is instantiated in the spectro-temporal receptive field (STRF), often in the framework of the generalized linear model. Despite widespread use of the FIR STRF, numerous formulations for linear filters are possible that require many fewer parameters, potentially permitting more efficient and accurate model estimates. To explore these alternative STRF architectures, we recorded single-unit neural activity from auditory cortex of awake ferrets during presentation of natural sound stimuli. We compared performance of > 1000 linear STRF architectures, evaluating their ability to predict neural responses to a novel natural stimulus. Many were able to outperform the FIR filter. Two basic constraints on the architecture lead to the improved performance: (1) factorization of the STRF matrix into a small number of spectral and temporal filters and (2) low-dimensional parameterization of the factorized filters. The best parameterized model was able to outperform the full FIR filter in both primary and secondary auditory cortex, despite requiring fewer than 30 parameters, about 10% of the number required by the FIR filter. After accounting for noise from finite data sampling, these STRFs were able to explain an average of 40% of A1 response variance. The simpler models permitted more straightforward interpretation of sensory tuning properties. They also showed greater benefit from incorporating nonlinear terms, such as short term plasticity, that provide theoretical advances over the linear model. Architectures that minimize parameter count while maintaining maximum predictive power provide insight into the essential degrees of freedom governing auditory cortical function. They also maximize statistical power available for characterizing additional nonlinear properties that limit current auditory models.     

A new method for adjusting neural response jitter in the STRF obtained by spike-trigger averaging

Sensitivity of central auditory neurons to frequency modulated (FM) sound is often characterized based on spectro-temporal receptive field (STRF), which is generated by spike-trigger averaging a random stimulus. Due to the inherent property of time variability in neural response, this method erroneously represents the response jitter as stimulus jitter in the STRF. To reveal the trigger features more clearly, we have implemented a method that minimizes this error. Neural spikes from the brainstem of urethane-anesthetized rats were first recorded in response to two sets of FM stimuli: (a) a random FM tone for the generation of STRF and (b) a family of linear FM ramps for the determination of FM 'trigger point'. Based on the first dataset, STRFs were generated using spike-trigger averaging. Individual modulating waveforms were then matched with respect to their mean waveform at time-windows of a systematically varied length. A stable or optimal variance time profile was found at a particular window length. At this optimal window length, we performed delay adjustments. A marked sharpening in the FM bands in the STRF was found. Results were consistent with the FM 'trigger point' as estimated by the linear FM ramps. We concluded that the present approach of adjusting response jitter was effective in delineating FM trigger features in the STRF.     

Fine frequency-modulation trigger features of midbrain auditory neurons extracted by the progressive thresholding method--a preliminary study

Spectro-temporal receptive fields (STRFs) are commonly used to characterize response properties of central auditory neurons and for visualizing 'trigger features'. However, trigger features in STRF maps typically have a blurry appearance. Therefore it is unclear what details could be embedded in them. To investigate this, we developed a new method called 'progressive thresholding' to resolve fine structures in the STRFs, and applied the method to FM responses recorded from single units at the auditory midbrain of anesthetized rats. Random FM tones of a narrow frequency range (approximately 0.5 octave) were first presented to evoked spike responses at the cell's best frequency. Perispike modulating time waveforms collected (50 msec long, n = 1500 to 4000 tracings) were used to generate STRF based on spike-triggered-averaging. After supra-threshold areas of pixel counts had been determined through a step of progressive thresholding in the map, those peri-spike modulating waveforms passing through each area were dejittered systematically. At what seemed to be an optimal threshold, multiple trigger features (up to a maximum of 4 fine bands) were extracted from the initially simple-looking STRF. Results show that fine FM trigger features are present in STRFs and that they can be resolved with the present method of analysis.     

Sparse Spectro-Temporal Receptive Fields Based on Multi-Unit and High-Gamma Responses in Human Auditory Cortex

Spectro-Temporal Receptive Fields (STRFs) were estimated from both multi-unit sorted clusters and high-gamma power responses in human auditory cortex. Intracranial electrophysiological recordings were used to measure responses to a random chord sequence of Gammatone stimuli. Traditional methods for estimating STRFs from single-unit recordings, such as spike-triggered-averages, tend to be noisy and are less robust to other response signals such as local field potentials. We present an extension to recently advanced methods for estimating STRFs from generalized linear models (GLM). A new variant of regression using regularization that penalizes non-zero coefficients is described, which results in a sparse solution. The frequency-time structure of the STRF tends toward grouping in different areas of frequency-time and we demonstrate that group sparsity-inducing penalties applied to GLM estimates of STRFs reduces the background noise while preserving the complex internal structure. The contribution of local spiking activity to the high-gamma power signal was factored out of the STRF using the GLM method, and this contribution was significant in 85 percent of the cases. Although the GLM methods have been used to estimate STRFs in animals, this study examines the detailed structure directly from auditory cortex in the awake human brain. We used this approach to identify an abrupt change in the best frequency of estimated STRFs along posteromedial-to-anterolateral recording locations along the long axis of Heschl’s gyrus. This change correlates well with a proposed transition from core to non-core auditory fields previously identified using the temporal response properties of Heschl’s gyrus recordings elicited by click-train stimuli.     

Discriminative Learning of Receptive Fields from Responses to Non-Gaussian Stimulus Ensembles

Analysis of sensory neurons'' processing characteristics requires simultaneous measurement of presented stimuli and concurrent spike responses. The functional transformation from high-dimensional stimulus space to the binary space of spike and non-spike responses is commonly described with linear-nonlinear models, whose linear filter component describes the neuron''s receptive field. From a machine learning perspective, this corresponds to the binary classification problem of discriminating spike-eliciting from non-spike-eliciting stimulus examples. The classification-based receptive field (CbRF) estimation method proposed here adapts a linear large-margin classifier to optimally predict experimental stimulus-response data and subsequently interprets learned classifier weights as the neuron''s receptive field filter. Computational learning theory provides a theoretical framework for learning from data and guarantees optimality in the sense that the risk of erroneously assigning a spike-eliciting stimulus example to the non-spike class (and vice versa) is minimized. Efficacy of the CbRF method is validated with simulations and for auditory spectro-temporal receptive field (STRF) estimation from experimental recordings in the auditory midbrain of Mongolian gerbils. Acoustic stimulation is performed with frequency-modulated tone complexes that mimic properties of natural stimuli, specifically non-Gaussian amplitude distribution and higher-order correlations. Results demonstrate that the proposed approach successfully identifies correct underlying STRFs, even in cases where second-order methods based on the spike-triggered average (STA) do not. Applied to small data samples, the method is shown to converge on smaller amounts of experimental recordings and with lower estimation variance than the generalized linear model and recent information theoretic methods. Thus, CbRF estimation may prove useful for investigation of neuronal processes in response to natural stimuli and in settings where rapid adaptation is induced by experimental design.     

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     

Columnar Connectivity and Laminar Processing in Cat Primary Auditory Cortex

Background

Radial intra- and interlaminar connections form a basic microcircuit in primary auditory cortex (AI) that extracts acoustic information and distributes it to cortical and subcortical networks. Though the structure of this microcircuit is known, we do not know how the functional connectivity between layers relates to laminar processing.

Methodology/Principal Findings

We studied the relationships between functional connectivity and receptive field properties in this columnar microcircuit by simultaneously recording from single neurons in cat AI in response to broadband dynamic moving ripple stimuli. We used spectrotemporal receptive fields (STRFs) to estimate the relationship between receptive field parameters and the functional connectivity between pairs of neurons. Interlaminar connectivity obtained through cross-covariance analysis reflected a consistent pattern of information flow from thalamic input layers to cortical output layers. Connection strength and STRF similarity were greatest for intralaminar neuron pairs and in supragranular layers and weaker for interlaminar projections. Interlaminar connection strength co-varied with several STRF parameters: feature selectivity, phase locking to the stimulus envelope, best temporal modulation frequency, and best spectral modulation frequency. Connectivity properties and receptive field relationships differed for vertical and horizontal connections.

Conclusions/Significance

Thus, the mode of local processing in supragranular layers differs from that in infragranular layers. Therefore, specific connectivity patterns in the auditory cortex shape the flow of information and constrain how spectrotemporal processing transformations progress in the canonical columnar auditory microcircuit.     

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.     

Differences between Spectro-Temporal Receptive Fields Derived from Artificial and Natural Stimuli in the Auditory Cortex

Spectro-temporal properties of auditory cortex neurons have been extensively studied with artificial sounds but it is still unclear whether they help in understanding neuronal responses to communication sounds. Here, we directly compared spectro-temporal receptive fields (STRFs) obtained from the same neurons using both artificial stimuli (dynamic moving ripples, DMRs) and natural stimuli (conspecific vocalizations) that were matched in terms of spectral content, average power and modulation spectrum. On a population of auditory cortex neurons exhibiting reliable tuning curves when tested with pure tones, significant STRFs were obtained for 62% of the cells with vocalizations and 68% with DMR. However, for many cells with significant vocalization-derived STRFs (STRF_voc) and DMR-derived STRFs (STRF_dmr), the BF, latency, bandwidth and global STRFs shape differed more than what would be predicted by spiking responses simulated by a linear model based on a non-homogenous Poisson process. Moreover STRF_voc predicted neural responses to vocalizations more accurately than STRF_dmr predicted neural response to DMRs, despite similar spike-timing reliability for both sets of stimuli. Cortical bursts, which potentially introduce nonlinearities in evoked responses, did not explain the differences between STRF_voc and STRF_dmr. Altogether, these results suggest that the nonlinearity of auditory cortical responses makes it difficult to predict responses to communication sounds from STRFs computed from artificial stimuli.     

Multiple-band trigger features of midbrain auditory neurons revealed in composite spectro-temporal receptive fields

Receptive fields of single units in the auditory midbrain of anesthetized rats were studied using random FM-tone stimuli of narrow frequency-ranges. Peri-spike averaging of the modulating waveform first produced a spectro-temporal receptive field (STRF). Combining STRFs obtained from the same unit at different frequency regions generated a composite receptive field covering a wider frequency range of 2 to 3 octaves. About 20% of the composite STRFs (26/122) showed a pattern of multiple-bands which were not clear in the non-composite maps. Multiple-bands in a given composite map were often oriented in the same direction (representing upward or downward FM ramp) separated at rather regular frequency intervals. They reflect multiple FM trigger features in the stimulus rather than repetitive firing to a single trigger feature. Results showed that the subcortical auditory pathways are capable of detecting multiple FM features and such sensitivity could be useful in detecting multiple-harmonic FM bands present in the vocalization sounds.     

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.     

To Burst or Not to Burst?

It is well known that some neurons tend to fire packets of action potentials followed by periods of quiescence (bursts) while others within the same stage of sensory processing fire in a tonic manner. However, the respective computational advantages of bursting and tonic neurons for encoding time varying signals largely remain a mystery. Weakly electric fish use cutaneous electroreceptors to convey information about sensory stimuli and it has been shown that some electroreceptors exhibit bursting dynamics while others do not. In this study, we compare the neural coding capabilities of tonically firing and bursting electroreceptor model neurons using information theoretic measures. We find that both bursting and tonically firing model neurons efficiently transmit information about the stimulus. However, the decoding mechanisms that must be used for each differ greatly: a non-linear decoder would be required to extract all the available information transmitted by the bursting model neuron whereas a linear one might suffice for the tonically firing model neuron. Further investigations using stimulus reconstruction techniques reveal that, unlike the tonically firing model neuron, the bursting model neuron does not encode the detailed time course of the stimulus. A novel measure of feature detection reveals that the bursting neuron signals certain stimulus features. Finally, we show that feature extraction and stimulus estimation are mutually exclusive computations occurring in bursting and tonically firing model neurons, respectively. Our results therefore suggest that stimulus estimation and feature extraction might be parallel computations in certain sensory systems rather than being sequential as has been previously proposed.     

Spectrotemporal processing in spectral tuning modules of cat primary auditory cortex

Spectral integration properties show topographical order in cat primary auditory cortex (AI). Along the iso-frequency domain, regions with predominantly narrowly tuned (NT) neurons are segregated from regions with more broadly tuned (BT) neurons, forming distinct processing modules. Despite their prominent spatial segregation, spectrotemporal processing has not been compared for these regions. We identified these NT and BT regions with broad-band ripple stimuli and characterized processing differences between them using both spectrotemporal receptive fields (STRFs) and nonlinear stimulus/firing rate transformations. The durations of STRF excitatory and inhibitory subfields were shorter and the best temporal modulation frequencies were higher for BT neurons than for NT neurons. For NT neurons, the bandwidth of excitatory and inhibitory subfields was matched, whereas for BT neurons it was not. Phase locking and feature selectivity were higher for NT neurons. Properties of the nonlinearities showed only slight differences across the bandwidth modules. These results indicate fundamental differences in spectrotemporal preferences--and thus distinct physiological functions--for neurons in BT and NT spectral integration modules. However, some global processing aspects, such as spectrotemporal interactions and nonlinear input/output behavior, appear to be similar for both neuronal subgroups. The findings suggest that spectral integration modules in AI differ in what specific stimulus aspects are processed, but they are similar in the manner in which stimulus information is processed.     

Orientation sensitive properties of visually driven neurons in extrastriate area 21a of cat cortex

Orientation sensitive properties of extrastriate area 21a neurons were investigated. Special attention was paid to the qualitative characteristics of neuron responses to the different orientations of visual stimulus motion across neuron classical receptive fields (CRF). The results of experiments have shown that a group of neurons (31%) in area 21a with specialized responses to moving visual stimuli changed their direction selective (DS) characteristics depending on the orientation of the stimulus movement. Some neurons reveal an abrupt drop of the direction sensitivity index (DI) to certain orientation (58%), and some show significant increase of DI at one of applied orientations of stimulus motion (22%). Detailed investigation of response patterns of non-directional neurons to different orientations of stimulus motion have revealed clear-cut qualitative differences, such as different regularities in the distribution of inter-peak inhibitory intervals in the response pattern in dependence of the orientation of stimulus motion. The investigation of neuron CRF stationary functional organization did not reveal correlations between RF's spatial functional organization, and that of qualitative modulations of neuron response patterns. A suggestion was put forward, that visual information central processing of orientation discrimination is a complex integrative process that includes quantitative as well as qualitative transformations of neuron activity.     

Nonlinear cross-frequency interactions in primary auditory cortex spectrotemporal receptive fields: a Wiener–Volterra analysis

The effects of nonlinear interactions between different sound frequencies on the responses of neurons in primary auditory cortex (AI) have only been investigated using two-tone paradigms. Here we stimulated with relatively dense, Poisson-distributed trains of tone pips (with frequency ranges spanning five octaves, 16 frequencies /octave, and mean rates of 20 or 120 pips /s), and examined within-frequency (or auto-frequency) and cross-frequency interactions in three types of AI unit responses by computing second-order “Poisson-Wiener” auto- and cross-kernels. Units were classified on the basis of their spectrotemporal receptive fields (STRFs) as “double-peaked”, “single-peaked” or “peak-valley”. Second-order interactions were investigated between the two bands of excitatory frequencies on double-peaked STRFs, between an excitatory band and various non-excitatory bands on single-peaked STRFs, and between an excitatory band and an inhibitory sideband on peak-valley STRFs. We found that auto-frequency interactions (i.e., those within a single excitatory band) were always characterized by a strong depression of (first-order) excitation that decayed with the interstimulus lag up to ～200 ms. That depression was weaker in cross-frequency compared to auto-frequency interactions for ～25% of dual-peaked STRFs, evidence of “combination sensitivity” for the two bands. Non-excitatory and inhibitory frequencies (on single-peaked and peak-valley STRFs, respectively) typically weakly depressed the excitatory response at short interstimulus lags (<50 ms), but weakly facilitated it at longer lags (～50–200 ms). Both the depression and especially the facilitation were stronger for interactions with inhibitory frequencies rather than just non-excitatory ones. Finally, facilitation in single-peaked and peak-valley units decreased with increasing stimulus density. Our results indicate that the strong combination sensitivity and cross-frequency facilitation suggested by previous two-tone-paradigm studies are much less pronounced when using more temporally-dense stimuli.     

Searching for optimal stimuli: ascending a neuron’s response function

Many methods used to analyze neuronal response assume that neuronal activity has a fundamentally linear relationship to the stimulus. However, some neurons are strongly sensitive to multiple directions in stimulus space and have a highly nonlinear response. It can be difficult to find optimal stimuli for these neurons. We demonstrate how successive linear approximations of neuronal response can effectively carry out gradient ascent and move through stimulus space towards local maxima of the response. We demonstrate search results for a simple model neuron and two models of a highly selective neuron.     

Implementation of an elaborated neuromorphic model of a biological photoreceptor

We describe here an elaborated neuromorphic model based on the photoreceptors of flies and realised in both software simulation and hardware using discrete circuit components. The design of the model is based on optimisations and further elaborations to the mathematical model initially developed by van Hateren and Snippe that has been shown to accurately simulate biological responses in simulations under both steady-state and limited dynamic conditions. The model includes an adaptive time constant, nonlinear adaptive gain control, logarithmic saturation and a nonlinear adaptive frequency response mechanism. It consists of a linear phototransduction stage, a dynamic filter stage, two divisive feedback loops and a static nonlinearity. In order to test the biological accuracy of the model, impulses and step responses were used to test and evaluate the steady-state characteristics of both the biological (fly) and artificial (new neuromorphic model) photoreceptors. These tests showed that the model has faithfully captured most of the essential characteristics of the insect photoreceptor cells. The model showed a decreasing response to impulsive stimuli when the background intensity was increased, indicating that the circuit adapted to background luminance in order to improve the overall operating range and better encode the contrast of the stimulus rather than luminance. The model also showed the same change in its frequency response characteristics as the biological photoreceptors over a luminance range of 70,000 cd/m², with the corner frequency of the circuit ranging from 10 to 90 Hz depending on the current state of adaptation. Complex naturalistic experiments have also further proven the robustness of the model to perform in real-world scenario. The model showed great correlation to the biological photoreceptors with an r ² value exceeding 0.83. Our model could act as an excellent platform for future experiments that could be carried out in scenarios where in vivo intracellular recording from biological photoreceptors would be impractical or impossible, or as a front-end for an artificial imaging system.