CiteULike: bayesian's nonlinear

Cortical pyramidal cells as non-linear oscillators: experiment and spike-generation theory.

JC Brumberg — 2008-02-15T16:23:11-00:00

Brain Res, Vol. 1171 (26 September 2007), pp. 122-137.

Cortical neurons are capable of generating trains of action potentials in response to current injections. These discharges can take different forms, e.g., repetitive firing that adapts during the period of current injection or bursting behaviors. We have used a combined experimental and computational approach to characterize the dynamics leading to action potential responses in single neurons. Specifically we investigated the origin of complex firing patterns in response to sinusoidal current injections. Using a reduced model, the theta-neuron, alongside recordings from cortical pyramidal cells we show that both real and simulated neurons show phase-locking to sine wave stimuli up to a critical frequency, above which period skipping and 1-to-x phase-locking occurs. The locking behavior follows a complex "devil's staircase" phenomena, where locked modes are interleaved with irregular firing. We further show that the critical frequency depends on the time scale of spike generation and on the level of spike frequency adaptation. These results suggest that phase-locking of neuronal responses to complex input patterns can be explained by basic properties of the spike-generating machinery.

Cooperative Nonlinearities in Auditory Cortical Neurons

Craig Atencio — 2008-06-26T11:18:50-00:00

Neuron, Vol. 58, No. 6. (26 June 2008), pp. 956-966.

Summary Cortical receptive fields represent the signal preferences of sensory neurons. Receptive fields are thought to provide a representation of sensory experience from which the cerebral cortex may make interpretations. While it is essential to determine a neuron's receptive field, it remains unclear which features of the acoustic environment are specifically represented by neurons in the primary auditory cortex (AI). We characterized cat AI spectrotemporal receptive fields (STRFs) by finding both the spike-triggered average (STA) and stimulus dimensions that maximized the mutual information between response and stimulus. We derived a nonlinearity relating spiking to stimulus projection onto two maximally informative dimensions (MIDs). The STA was highly correlated with the first MID. Generally, the nonlinearity for the first MID was asymmetric and often monotonic in shape, while the second MID nonlinearity was symmetric and nonmonotonic. The joint nonlinearity for both MIDs revealed that most first and second MIDs were synergistic and thus should be considered conjointly. The difference between the nonlinearities suggests different possible roles for the MIDs in auditory processing.

Processing of Natural Temporal Stimuli by Macaque Retinal Ganglion Cells

JH van Hateren — 2008-06-10T12:16:38-00:00

J. Neurosci., Vol. 22, No. 22. (15 November 2002), pp. 9945-9960.

This study quantifies the performance of primate retinal ganglion cells in response to natural stimuli. Stimuli were confined to the temporal and chromatic domains and were derived from two contrasting environments, one typically northern European and the other a flower show. The performance of the cells was evaluated by investigating variability of cell responses to repeated stimulus presentations and by comparing measured to model responses. Both analyses yielded a quantity called the coherence rate (in bits per second), which is related to the information rate. Magnocellular (MC) cells yielded coherence rates of up to 100 bits/sec, rates of parvocellular (PC) cells were much lower, and short wavelength (S)-cone-driven ganglion cells yielded intermediate rates. The modeling approach showed that for MC cells, coherence rates were generated almost exclusively by the luminance content of the stimulus. Coherence rates of PC cells were also dominated by achromatic content. This is a consequence of the stimulus structure; luminance varied much more in the natural environment than chromaticity. Only approximately one-sixth of the coherence rate of the PC cells derived from chromatic content, and it was dominated by frequencies below 10 Hz. S-cone-driven ganglion cells also yielded coherence rates dominated by low frequencies. Below 2-3 Hz, PC cell signals contained more power than those of MC cells. Response variation between individual ganglion cells of a particular class was analyzed by constructing generic cells, the properties of which may be relevant for performance higher in the visual system. The approach used here helps define retinal modules useful for studies of higher visual processing of natural stimuli.

Information theoretical evaluation of parametric models of gain control in blowfly photoreceptor cells

JH van Hateren — 2008-06-10T12:15:54-00:00

Vision Research, Vol. 41, No. 14. (June 2001), pp. 1851-1865.

Models are developed and evaluated that are able to describe the response of blowfly photoreceptor cells to natural time series of intensities. Evaluation of the models is performed using an information theoretical technique that evaluates the performance of the models in terms of a coherence function and a derived coherence rate (in bit/s). Performance is gauged against a maximum expected coherence rate determined from the repeatability of the response to the same stimulus. The best model performs close to this maximum performance, and consists of a cascade of two divisive feedback loops followed by a static nonlinearity. The first feedback loop is fast, effectively compressing fast and large transients in the stimulus. The second feedback loop also contains slow components, and is responsible for slow adaptation in the photoreceptor in response to large steps in intensity. Any remaining peaks that would drive the photoreceptor out of its dynamic range are handled by the final compressive nonlinearity.

Functional Mechanisms Shaping Lateral Geniculate Responses to Artificial and Natural Stimuli

Valerio Mante — 2008-05-26T08:21:46-00:00

Neuron, Vol. 58, No. 4. (22 May 2008), pp. 625-638.

Summary Functional models of the early visual system should predict responses not only to simple artificial stimuli but also to sequences of complex natural scenes. An ideal testbed for such models is the lateral geniculate nucleus (LGN). Mechanisms shaping LGN responses include the linear receptive field and two fast adaptation processes, sensitive to luminance and contrast. We propose a compact functional model for these mechanisms that operates on sequences of arbitrary images. With the same parameters that fit the firing rate responses to simple stimuli, it predicts the bulk of the firing rate responses to complex stimuli, including natural scenes. Further improvements could result by adding a spiking mechanism, possibly one capable of bursts, but not by adding mechanisms of slow adaptation. We conclude that up to the LGN the responses to natural scenes can be largely explained through insights gained with simple artificial stimuli.

On the Importance of Static Nonlinearity in Estimating Spatiotemporal Neural Filters With Natural Stimuli

Tatyana Sharpee — 2008-05-14T11:38:09-00:00

J Neurophysiol, Vol. 99, No. 5. (1 May 2008), pp. 2496-2509.

Understanding neural responses with natural stimuli has increasingly become an essential part of characterizing neural coding. Neural responses are commonly characterized by a linear-nonlinear (LN) model, in which the output of a linear filter applied to the stimulus is transformed by a static nonlinearity to determine neural response. To estimate the linear filter in the LN model, studies of responses to natural stimuli commonly use methods that are unbiased only for a linear model (in which there is no static nonlinearity): spike-triggered averages with correction for stimulus power spectrum, with or without regularization. Although these methods work well for artificial stimuli, such as Gaussian white noise, we show here that they estimate neural filters of LN models from responses to natural stimuli much more poorly. We studied simple cells in cat primary visual cortex. We demonstrate that the filters computed by directly taking the nonlinearity into account have better predictive power and depend less on the stimulus than those computed under the linear model. With noise stimuli, filters computed using the linear and LN models were similar, as predicted theoretically. With natural stimuli, filters of the two models can differ profoundly. Noise and natural stimulus filters differed significantly in spatial properties, but these differences were exaggerated when filters were computed using the linear rather than the LN model. Although regularization of filters computed under the linear model improved their predictive power, it also led to systematic distortions of their spatial frequency profiles, especially at low spatial and temporal frequencies. 10.1152/jn.01397.2007

A Canonical Neural Circuit for Cortical Nonlinear Operations.

Minjoon Kouh — 2008-02-24T01:26:44-00:00

Neural Comput (6 February 2008)

A few distinct cortical operations have been postulated over the past few years, suggested by experimental data on nonlinear neural response across different areas in the cortex. Among these, the energy model proposes the summation of quadrature pairs following a squaring nonlinearity in order to explain phase invariance of complex V1 cells. The divisive normalization model assumes a gain-controlling, divisive inhibition to explain sigmoid-like response profiles within a pool of neurons. A gaussian-like operation hypothesizes a bell-shaped response tuned to a specific, optimal pattern of activation of the presynaptic inputs. A max-like operation assumes the selection and transmission of the most active response among a set of neural inputs. We propose that these distinct neural operations can be computed by the same canonical circuitry, involving divisive normalization and polynomial nonlinearities, for different parameter values within the circuit. Hence, this canonical circuit may provide a unifying framework for several circuit models, such as the divisive normalization and the energy models. As a case in point, we consider a feedforward hierarchical model of the ventral pathway of the primate visual cortex, which is built on a combination of the gaussian-like and max-like operations. We show that when the two operations are approximated by the circuit proposed here, the model is capable of generating selective and invariant neural responses and performing object recognition, in good agreement with neurophysiological data.

Homeostatic Matching and Nonlinear Amplification at Identified Central Synapses

Hokto Kazama — 2008-05-08T12:45:44-00:00

Neuron, Vol. 58, No. 3. (8 May 2008), pp. 401-413.

Summary Here we describe the properties of a synapse in the Drosophila antennal lobe and show how they can explain certain sensory computations in this brain region. The synapse between olfactory receptor neurons (ORNs) and projection neurons (PNs) is very strong, reflecting a large number of release sites and high release probability. This is likely one reason why weak ORN odor responses are amplified in PNs. Furthermore, the amplitude of unitary synaptic currents in a PN is matched to the size of its dendritic arbor. This matching may compensate for a lower input resistance of larger dendrites to produce uniform depolarization across PN types. Consistent with this idea, a genetic manipulation that lowers input resistance increases unitary synaptic currents. Finally, strong stimuli produce short-term depression at this synapse. This helps explain why PN odor responses are transient, and why strong ORN odor responses are not amplified as powerfully as weak responses.

Spectrotemporal Processing Differences between Auditory Cortical Fast-Spiking and Regular-Spiking Neurons

Craig Atencio — 2008-04-10T09:36:19-00:00

J. Neurosci., Vol. 28, No. 15. (9 April 2008), pp. 3897-3910.

Excitatory pyramidal neurons and inhibitory interneurons constitute the main elements of cortical circuitry and have distinctive morphologic and electrophysiological properties. Here, we differentiate them by analyzing the time course of their action potentials (APs) and characterizing their receptive field properties in auditory cortex. Pyramidal neurons have longer APs and discharge as regular-spiking units (RSUs), whereas basket and chandelier cells, which are inhibitory interneurons, have shorter APs and are fast-spiking units (FSUs). To compare these neuronal classes, we stimulated cat primary auditory cortex neurons with a dynamic moving ripple stimulus and constructed single-unit spectrotemporal receptive fields (STRFs) and their associated nonlinearities. FSUs had shorter latencies, broader spectral tuning, greater stimulus specificity, and higher temporal precision than RSUs. The STRF structure of FSUs was more separable, suggesting more independence between spectral and temporal processing regimens. The nonlinearities associated with the two cell classes were indicative of higher feature selectivity for FSUs. These global functional differences between RSUs and FSUs suggest fundamental distinctions between putative excitatory and inhibitory interneurons that shape auditory cortical processing. 10.1523/JNEUROSCI.5366-07.2008

Inferring input nonlinearities in neural encoding models

Misha Ahrens — 2008-03-23T16:19:17-00:00

Network: Computation in Neural Systems, Vol. 19, No. 1. (2008), pp. 35-67.

We describe a class of models that predict how the instantaneous firing rate of a neuron depends on a dynamic stimulus. The models utilize a learnt pointwise nonlinear transform of the stimulus, followed by a linear filter that acts on the sequence of transformed inputs. In one case, the nonlinear transform is the same at all filter lag-times. Thus, this “input nonlinearity” converts the initial numerical representation of stimulus value to a new representation that provides optimal input to the subsequent linear model. We describe algorithms that estimate both the input nonlinearity and the linear weights simultaneously; and present techniques to regularise and quantify uncertainty in the estimates. In a second approach, the model is generalized to allow a different nonlinear transform of the stimulus value at each lag-time. Although more general, this model is algorithmically more straightforward to fit. However, it has many more degrees of freedom than the first approach, thus requiring more data for accurate estimation. We test the feasibility of these methods on synthetic data, and on responses from a neuron in rodent barrel cortex. The models are shown to predict responses to novel data accurately, and to recover several important neuronal response properties.

Nonlinear Integration of Binocular Optic Flow by DNOVS2, A Descending Neuron of the Fly

Adrian Wertz — 2008-03-19T17:49:09-00:00

J. Neurosci., Vol. 28, No. 12. (19 March 2008), pp. 3131-3140.

For visual orientation and course stabilization, flies rely heavily on the optic flow perceived by the animal during flight. The processing of optic flow is performed in motion-sensitive tangential cells of the lobula plate, which are well described with respect to their visual response properties and the connectivity among them. However, little is known about the postsynaptic descending neurons, which convey motion information to the motor circuits in the thoracic ganglion. Here we investigate the physiology and connectivity of an identified premotor descending neuron, called DNOVS2 (for descending neuron of the ocellar and vertical system). We find that DNOVS2 is tuned in a supralinear way to rotation around the longitudinal body axis. Experiments involving stimulation of the ipsilateral and the contralateral eye indicate that ipsilateral computation of motion information is modified nonlinearly by motion information from the contralateral eye. Performing double recordings of DNOVS2 and lobula plate tangential cells, we find that DNOVS2 is connected ipsilaterally to a subset of vertical-sensitive cells. From the contralateral eye, DNOVS2 receives input most likely from V2, a heterolateral spiking neuron. This specific neural circuit is sufficient for the tuning of DNOVS2, making it probably an important element in optomotor roll movements of the head and body around the fly's longitudinal axis. 10.1523/JNEUROSCI.5460-07.2008

Nonlinearities and Contextual Influences in Auditory Cortical Responses Modeled with Multilinear Spectrotemporal Methods

Misha Ahrens — 2008-02-21T09:23:33-00:00

Journal of Neuroscience, Vol. 28, No. 8. (20 February 2008), pp. 1929-1942.

The relationship between a sound and its neural representation in the auditory cortex remains elusive. Simple measures such as the frequency response area or frequency tuning curve provide little insight into the function of the auditory cortex in complex sound environments. Spectrotemporal receptive field (STRF) models, despite their descriptive potential, perform poorly when used to predict auditory cortical responses, showing that nonlinear features of cortical response functions, which are not captured by STRFs, are functionally important. We introduce a new approach to the description of auditory cortical responses, using multilinear modeling methods. These descriptions simultaneously account for several nonlinearities in the stimulusresponse functions of auditory cortical neurons, including adaptation, spectral interactions, and nonlinear sensitivity to sound level. The models reveal multiple inseparabilities in cortical processing of time lag, frequency, and sound level, and suggest functional mechanisms by which auditory cortical neurons are sensitive to stimulus context. By explicitly modeling these contextual influences, the models are able to predict auditory cortical responses more accurately than are STRF models. In addition, they can explain some forms of stimulus dependence in STRFs that were previously poorly understood. 10.1523/JNEUROSCI.3377-07.2008

Contrast Sensitivity Is Enhanced by Expansive Nonlinear Processing in the Lateral Geniculate Nucleus

Thang Duong — 2008-01-15T12:30:48-00:00

J Neurophysiol, Vol. 99, No. 1. (1 January 2008), pp. 367-372.

The firing rates of neurons in the central visual pathway vary with stimulus strength, but not necessarily in a linear manner. In the contrast domain, the neural response function for cells in the primary visual cortex is characterized by expansive and compressive nonlinearities at low and high contrasts, respectively. A compressive nonlinearity at high contrast is also found for early visual pathway neurons in the lateral geniculate nucleus (LGN). This mechanism affects processing in the visual cortex. A fundamentally related issue is the possibility of an expansive nonlinearity at low contrast in LGN. To examine this possibility, we have obtained contrastresponse data for a population of LGN neurons. We find for most cells that the best-fit function requires an expansive component. Additionally, we have measured the responses of LGN neurons to m-sequence white noise and examined the static relationship between a linear prediction and actual spike rate. We find that this static relationship is well fit by an expansive nonlinear power law with average exponent of 1.58. These results demonstrate that neurons in early visual pathways exhibit expansive nonlinear responses at low contrasts. Although this thalamic expansive nonlinearity has been largely ignored in models of early visual processing, it may have important consequences because it potentially affects the interpretation of a variety of visual functions. 10.1152/jn.00873.2007

Natural scene statistics and nonlinear neural interactions between frequency-selective mechanisms.

C Zetzsche — 2006-03-04T21:32:19-00:00

Biosystems, Vol. 79, No. 1-3. (r 2005), pp. 143-149.

Linear filtering is a basic concept in neural models of early sensory information processing. In particular the visual system has been described to perform a wavelet-like multi-channel decomposition by a set of independent spatial-frequency selective filter mechanisms. Here we suggest that this principle of linear filtering deserves a critical re-evaluation. We propose that an optimal adaptation to natural scene statistics would require AND-like nonlinear interactions between the frequency-selective filter channels. We describe how this hypothesis can be tested by predicted violations of the principle of linearity that should be observable if cortical neurons would actually implement the proposed nonlinearities. We further explain why these effects might have been easily overlooked in earlier tests of the linearity of neurons in primary visual cortex.

The Consequences of Response Nonlinearities for Interpretation of Spectrotemporal Receptive Fields

Bjorn Christianson — 2008-01-09T18:25:44-00:00

J. Neurosci., Vol. 28, No. 2. (9 January 2008), pp. 446-455.

Neurons in the central auditory system are often described by the spectrotemporal receptive field (STRF), conventionally defined as the best linear fit between the spectrogram of a sound and the spike rate it evokes. An STRF is often assumed to provide an estimate of the receptive field of a neuron, i.e., the spectral and temporal range of stimuli that affect the response. However, when the true stimulusresponse function is nonlinear, the STRF will be stimulus dependent, and changes in the stimulus properties can alter estimates of the sign and spectrotemporal extent of receptive field components. We demonstrate analytically and in simulations that, even when uncorrelated stimuli are used, interactions between simple neuronal nonlinearities and higher-order structure in the stimulus can produce STRFs that show contributions from timefrequency combinations to which the neuron is actually insensitive. Only when spectrotemporally independent stimuli are used does the STRF reliably indicate features of the underlying receptive field, and even then it provides only a conservative estimate. One consequence of these observations, illustrated using natural stimuli, is that a stimulus-induced change in an STRF could arise from a consistent but nonlinear neuronal response to stimulus ensembles with differing higher-order dependencies. Thus, although the responses of higher auditory neurons may well involve adaptation to the statistics of different stimulus ensembles, stimulus dependence of STRFs alone, or indeed of any overly constrained stimulusresponse mapping, cannot demonstrate the nature or magnitude of such effects. 10.1523/JNEUROSCI.1775-07.2007

Spike train encoding by regular-spiking cells of the visual cortex

M Carandini — 2007-08-08T15:07:22-00:00

J Neurophysiol, Vol. 76, No. 5. (1 November 1996), pp. 3425-3441.

The role of spiking nonlinearity in contrast gain control and information transmission

Yuguo Yu — 2007-08-08T14:24:39-00:00

Vision Research, Vol. 45, No. 5. (March 2005), pp. 583-592.

Threshold and saturation are two nonlinear features common to almost all spiking neurons. How these nonlinearities affect the performance gain of the transfer function and coding properties of the neurons has attracted much attention. Here, we deduce basic analytical relationships among these nonlinearities (threshold and saturation), performance gain and information transmission in neurons. We found that performance gain and information transmission can be maximized by input signals with optimal variance. The threshold and saturation inside the model determines the gain tuning property and maximum coding capacity. This framework provides an understanding of some basic design principles underlying information processing systems that can be adjusted to match the statistics of signals in the environment. This study also isolates the exact contributions of the nonlinearities on the contrast adaptation phenomena observed in real visual neurons.

Effects of stimulus spectral contrast on receptive fields of dorsal cochlear nucleus neurons

Lina Reiss — 2007-08-06T13:05:07-00:00

J Neurophysiol (1 August 2007), 01239.2006.

Neurons in the dorsal cochlear nucleus (DCN) exhibit strong nonlinearities in spectral processing. Low-order models that transform the stimulus spectrum into discharge rate using a combination of 1st- and 2nd-order weighting of the spectrum (quadratic models) usually fail to predict responses to novel stimuli for principal neurons in the DCN, even though they work well in ventral cochlear nucleus (Yu and Young 2000). Here we investigate the effects of spectral contrast on the performance of such models. Typically, the models fail for stimuli with natural-sound-like spectral contrasts (~12-dB), but have good prediction performance at small (3-dB) contrasts. The weights also typically increase substantially in amplitude at smaller spectral contrast. These changes in weight size with contrast are partly inherited from similar effects seen in auditory nerve fibers, but there must be additional effects from inhibitory circuits in the DCN. These results provide insight into the reasons for the poor performance of spectro-temporal receptive field (STRF) models in predicting responses of auditory neurons. Because the general shapes of the weights do not change between low and high contrast, they also suggest that STRFs may capture meaningful properties of neural receptive fields, even though they do not do well at predicting responses. 10.1152/jn.01239.2006

Processing of Modulated Sounds in the Zebra Finch Auditory Midbrain: Responses to Noise, Frequency Sweeps, and Sinusoidal Amplitude Modulations

Sarah Woolley — 2007-07-07T16:52:11-00:00

J Neurophysiol, Vol. 94, No. 2. (1 August 2005), pp. 1143-1157.

The avian auditory midbrain nucleus, the mesencephalicus lateralis, dorsalis (MLd), is the first auditory processing stage in which multiple parallel inputs converge, and it provides the input to the auditory thalamus. We studied the responses of single MLd neurons to four types of modulated sounds: 1) white noise; 2) band-limited noise; 3) frequency modulated (FM) sweeps, and 4) sinusoidally amplitude-modulated tones (SAM) in adult male zebra finches. Responses were compared with the responses of the same neurons to pure tones in terms of temporal response patterns, thresholds, characteristic frequencies, frequency tuning bandwidths, tuning sharpness, and spike rate/intensity relationships. Most neurons responded well to noise. More than one-half of the neurons responded selectively to particular portions of the noise, suggesting that, unlike forebrain neurons, many MLd neurons can encode specific acoustic components of highly modulated sounds such as noise. Selectivity for FM sweep direction was found in only 13% of cells that responded to sweeps. Those cells also showed asymmetric tuning curves, suggesting that asymmetric inhibition plays a role in FM directional selectivity. Responses to SAM showed that MLd neurons code temporal modulation rates using both spike rate and synchronization. Nearly all cells showed low-pass or band-pass filtering properties for SAM. Best modulation frequencies matched the temporal modulations in zebra finch song. Results suggest that auditory midbrain neurons are well suited for encoding a wide range of complex sounds with a high degree of temporal accuracy rather than selectively responding to only some sounds. 10.1152/jn.01064.2004

Cochlear tuning in the gerbil: a comparison of responses to sinusoidal amplitude modulation and difference tone stimuli.

KR Henry — 2007-07-07T16:51:48-00:00

Audiology, Vol. 37, No. 5. (t 1998), pp. 262-277.

Vocalizations often have periodic variations of their acoustic waveform envelope. Two simultaneously presented frequencies have an envelope fluctuation with a frequency equal to their difference tone (DT = F2-F1). Sinusoidal amplitude modulation (SAM) of a carrier frequency also produces an envelope fluctuation. Electrical ensemble responses to DT and SAM stimuli were recorded from the gerbil's round window. The predominant frequency of the response to the DT stimuli is F2-F1; to the SAM stimuli, it is the modulation frequency. Both responses are spectrally, temporally, and dynamically non-linear. Forward masking of a low-frequency DT response produced a tuning curve (TC) with a tip at the high-stimulus frequency. Forward masker TCs of a low-frequency SAM ensemble response had tips at the high frequency of the carrier. Tip thresholds and sharpness of tuning of DT and SAM TCs are quite similar, with cochlear neurons having high characteristic frequencies providing sharply tuned information about low frequency acoustic envelope periodicities.

Dynamic amplitude coding in the auditory cortex of awake rhesus macaques

Brian Malone — 2007-07-07T12:52:52-00:00

J Neurophysiol, Vol. 98, No. 3. (5 July 2007), pp. 1451-1474.

In many animals, the information most important for processing communication sounds, including speech, consists of temporal envelope cues below approximately 20 Hz. Physiological studies, however, typically emphasize upper limits of modulation encoding. Responses to sinusoidal amplitude modulation (SAM) are generally summarized by modulation transfer functions (MTFs), which emphasize tuning to modulation frequency rather than representations of instantaneous stimulus amplitude. Unfortunately, MTFs fail to capture important but nonlinear aspects of amplitude coding in the central auditory system. We focus on an alternative data representation, the modulation period histogram (MPH), which depicts the spike train folded on the modulation period of the SAM stimulus. At low modulation frequencies, the fluctuations of stimulus amplitude in dB are robustly encoded by the cycle-by-cycle response dynamics evident in the MPH. We demonstrate that all of the parameters that define a SAM stimulus - carrier frequency, carrier level, modulation frequency, and modulation depth - are reflected in the shape of cortical MPHs. In many neurons that are nonmonotonically tuned for sound amplitude, the representation of modulation frequency is typically sacrificed in order to preserve the mapping between the instantaneous discharge rate and the instantaneous stimulus amplitude, resulting in two response modes per modulation cycle. This behavior, as well as the relatively poor tuning of cortical MTFs, suggests that auditory cortical neurons are not well suited for operating as a "modulation filterbank." Instead, our results suggest that below 20 Hz, the processing of modulated signals is better described as envelope shape discrimination rather than modulation frequency extraction. 10.1152/jn.01203.2006

A Dynamic Nonlinearity and Spatial Phase Specificity in Macaque V1 Neurons

Patrick Williams — 2007-05-23T17:16:46-00:00

J. Neurosci., Vol. 27, No. 21. (23 May 2007), pp. 5706-5718.

While studying the visual response dynamics of neurons in the macaque primary visual cortex (V1), we found a nonlinearity of temporal response that influences the visual functions of V1 neurons. Simple cells were recorded in all layers of V1; the nonlinearity was strongest in neurons located in layer 2/3. We recorded the spike responses to optimal sinusoidal gratings that were displayed for 100 ms, a temporal step response. The step responses were measured at many spatial phases of the grating stimulus. To judge whether simple cell behavior was consistent with linear temporal integration, the decay of the 100 ms step response at the preferred spatial phase was used to predict the step response at the opposite spatial phase. Responses in layers 4B and 4C were mostly consistent with a linear-plus-static-nonlinearity cascade model. However, this was not true in layer 2/3 where most cells had little or no step responses at the opposite spatial phase. Many layer 2/3 cells had transient preferred-phase responses but did not respond at the offset of the opposite-phase stimuli, indicating a dynamic nonlinearity. A different stimulus sequence, rapidly presented random sinusoids, also produced the same effect, with layer 2/3 simple cells exhibiting elevated spike rates in response to stimuli at one spatial phase but not 180degrees away. The presence of a dynamic nonlinearity in the responses of V1 simple cells indicates that first-order analyses often capture only a fraction of neuronal behavior. The visual implication of our results is that simple cells in layer 2/3 are spatial phase-sensitive detectors that respond to contrast boundaries of one sign but not the opposite. 10.1523/JNEUROSCI.4743-06.2007

A method of nonlinear analysis in the frequency domain.

J Victor — 2006-10-16T15:07:22-00:00

Biophys J, Vol. 29, No. 3. (March 1980), pp. 459-483.

A method is developed for the analysis of nonlinear biological systems based on an input temporal signal that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grafting, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.