Responses Of Complex Cells Research Articles

What simple and complex cells compute

Visual neuroscientists seek to answer two related questions. First, what does the visual system do? Second, how does it do it? While an answer to the second question is a description based on anatomy and biophysics, an answer to the first question is a description of computations performed on images. Important steps in providing this description were made with the publication of two classical studies on primary visual cortex by Movshon et al. (1978a,b). These studies have not aged in their readability, and do not require an interpretive key to be enjoyed by the contemporary reader. As an introduction, however, this Perspectives article briefly reviews the state of the art at the time of their appearance, their main findings, and their influence on three decades of subsequent investigations.

'Simplification' of responses of complex cells in cat striate cortex: suppressive surrounds and 'feedback' inactivation.

In mammalian striate cortex (V1), two distinct functional classes of neurones, the so-called simple and complex cells, are routinely distinguished. They can be quantitatively differentiated from each other on the basis of the ratio between the phase-variant (F1) component and the mean firing rate (F0) of spike responses to luminance-modulated sinusoidal gratings (simple, F1/F0 > 1; complex, F1/F0 < 1). We investigated how recurrent cortico-cortical connections affect the spatial phase-variance of responses of V1 cells in the cat. F1/F0 ratios of the responses to optimally oriented drifting sine-wave gratings covering the classical receptive field (CRF) of single V1 cells were compared to those of: (1) responses to gratings covering the CRFs combined with gratings of different orientations presented to the 'silent' surrounds; and (2) responses to CRF stimulation during reversible inactivation of postero-temporal visual (PTV) cortex. For complex cells, the relative strength of the silent surround suppression on CRF-driven responses was positively correlated with the extent of increases in F1/F0 ratios. Inactivation of PTV cortex increased F1/F0 ratios of CRF-driven responses of complex cells only. Overall, activation of suppressive surrounds or inactivation of PTV 'converted' substantial proportions (50 and 30%, respectively) of complex cells into simple-like cells (F1/F0 > 1). Thus, the simple-complex distinction depends, at least partly, on information coming from the silent surrounds and/or feedback from 'higher-order' cortices. These results support the idea that simple and complex cells belong to the same basic cortical circuit and the spatial phase-variance of their responses depends on the relative strength of different synaptic inputs.

Tuning for spatiotemporal frequency and speed in directionally selective neurons of macaque striate cortex.

We recorded the responses of direction-selective simple and complex cells in the primary visual cortex (V1) of anesthetized, paralyzed macaque monkeys. When studied with sine-wave gratings, almost all simple cells in V1 had responses that were separable for spatial and temporal frequency: the preferred temporal frequency did not change and preferred speed decreased as a function of the spatial frequency of the grating. As in previous recordings from the middle temporal visual area (MT), approximately one-quarter of V1 complex cells had separable responses to spatial and temporal frequency, and one-quarter were "speed tuned" in the sense that preferred speed did not change as a function of spatial frequency. Half fell between these two extremes. Reducing the contrast of the gratings caused the population of V1 complex cells to become more separable in their tuning for spatial and temporal frequency. Contrast dependence is explained by the contrast gain of the neurons, which was relatively higher for gratings that were either both of high or both of low temporal and spatial frequency. For stimuli that comprised two spatially superimposed sine-wave gratings, the preferred speeds and tuning bandwidths of V1 neurons could be predicted from the sum of the responses to the component gratings presented alone, unlike neurons in MT that showed nonlinear interactions. We conclude that spatiotemporal modulation of contrast gain creates speed tuning from separable inputs in V1 complex cells. Speed tuning in MT could be primarily inherited from V1, but processing that occurs after V1 and possibly within MT computes selective combinations of speed-tuned signals of special relevance for downstream perceptual and motor mechanisms.

植物の病原菌感染応答に関する電子顕微鏡学的解析

When plants come into contact with fungal pathogens and their disease chemical stressors such as toxins and elicitors, they exhibit a variety of complex cell responses against the disease stress. Some plants induce a series of resistant reactions to the stress, eventually resulting in survival by overcoming it, while some submit to fungal infection because of failure to establish defense reactions. Electron microscopy is one of a number of powerful techniques that can analyze cell functions with pathological significance by observing the responses of the stressed plant cells. This article describes the results of ultrastructural analysis on both the mode of action of Alternaria and Stemphylium host-specific toxins (HSTs) produced from some saprophytic pathogens in respective host cells to evaluate the pathological roles of HSTs. In addition, the aggressive roles of pathogen penetration pegs, lignin-induced resistant responses, and the apoptosis-like cell death mechanism by pathogen infection are also reported. Ultrastructural studies of plant diseases had been performed vigorously and extensively in the 1970s and 1980s in Japan, but they declined in number and in the 1990s they came to a standstill. This tendency is common in every field of natural science. Unfortunately, experts in electron microscopy with diverse and skillful techniques are now less common due to their gradual retirement from employment. The cytological posts have been insured by genome workers. The decline of electron microscopy is attributed to the difficulty of electron microscopy techniques and the rise of molecular biology. Molecular biology is excellent in analyzing the gene functions of pathogen-stressed host cells or differentiated pathogens during pathogenesis and the tech-

Physics must join with biology in better assessing risk from low-dose irradiation

This review summarises the complex response of mammalian cells and tissues to low doses of ionising radiation. This thesis encompasses induction of DNA damage, and adaptive protection against both renewed damage and against propagation of damage from the basic level of biological organisation to the clinical expression of detriment. The induction of DNA damage at low radiation doses apparently is proportional to absorbed dose at the physical/chemical level. However, any propagation of such damage to higher levels of biological organisation inherently follows a sigmoid function. Moreover, low-dose-induced inhibition of damage propagation is not linear, but instead follows a dose-effect function typical for adaptive protection, after an initial rapid rise it disappears at doses higher than approximately 0.1-0.2 Gy to cells. The particular biological response duality at low radiation doses precludes the validity of the linear-no-threshold hypothesis in the attempt to relate absorbed dose to cancer. In fact, theory and observation support not only a lower cancer incidence than expected from the linear-no-threshold hypothesis, but also a reduction of spontaneously occurring cancer, a hormetic response, in the healthy individual.

Cortical sensitivity to visual features in natural scenes.

A central hypothesis concerning sensory processing is that the neuronal circuits are specifically adapted to represent natural stimuli efficiently. Here we show a novel effect in cortical coding of natural images. Using spike-triggered average or spike-triggered covariance analyses, we first identified the visual features selectively represented by each cortical neuron from its responses to natural images. We then measured the neuronal sensitivity to these features when they were present in either natural images or random stimuli. We found that in the responses of complex cells, but not of simple cells, the sensitivity was markedly higher for natural images than for random stimuli. Such elevated sensitivity leads to increased detectability of the visual features and thus an improved cortical representation of natural scenes. Interestingly, this effect is due not to the spatial power spectra of natural images, but to their phase regularities. These results point to a distinct visual-coding strategy that is mediated by contextual modulation of cortical responses tuned to the spatial-phase structure of natural scenes.

Differential Behavior of Simple and Complex Cells in Visual Cortex during a Brief IOP Elevation

To study and compare responses of different types of cortical neurons in the primary visual cortex in cats to grating stimuli before and during brief elevation of intraocular pressure (IOP). Single-unit electrophysiological recordings were performed in anesthetized and paralyzed cats. The IOP was elevated by injecting saline into the anterior chamber of the cat's eyes through a syringe needle. The IOP was elevated to a level at which the retinal perfusion pressure (arterial pressure minus IOP) was maintained at approximately 30 mmHg for a period of 4 minutes. The responses of simple and complex cells in the primary visual cortex to visually drifting sinusoidal gratings were measured before and during the elevation of IOP. The response amplitude of all the cortical cells in the primary visual cortex declined during a brief elevation of IOP. The decrease in the response of simple cells was always more significant than that of complex cells. The differential decrease between the two major types of cells was independent of the cell's receptive field location and cortical depth. There was a mild tendency for cells with higher preferred spatial frequencies to be more sensitive than those with lower frequencies. The preferred orientation and direction of most cortical cells remained roughly unchanged though their orientation and direction biases decreased. An increase in the animal's blood pressure, which returned the retinal perfusion pressure to a normal level, compensated for the decreased response induced by the elevation of IOP. The differential effects of a brief elevation of IOP on the response of simple and complex cells in the visual cortex are general and may originate from the retina through the lateral geniculate nucleus (LGN), where different effects of elevation of IOP are exerted on X- and Y-type retinal ganglion cells. The results may suggest differential behavior of neurons tin the parvo and magno pathways of the primate.

Spatiotemporal Elements of Macaque V1 Receptive Fields

Neurons in primary visual cortex (V1) are commonly classified as simple or complex based upon their sensitivity to the sign of stimulus contrast. The responses of both cell types can be described by a general model in which the outputs of a set of linear filters are nonlinearly combined. We estimated the model for a population of V1 neurons by analyzing the mean and covariance of the spatiotemporal distribution of random bar stimuli that were associated with spikes. This analysis reveals an unsuspected richness of neuronal computation within V1. Specifically, simple and complex cell responses are best described using more linear filters than the one or two found in standard models. Many filters revealed by the model contribute suppressive signals that appear to have a predominantly divisive influence on neuronal firing. Suppressive signals are especially potent in direction-selective cells, where they reduce responses to stimuli moving in the nonpreferred direction.

Spatial Structure of Complex Cell Receptive Fields Measured with Natural Images

Neuronal receptive fields (RFs) play crucial roles in visual processing. While the linear RFs of early neurons have been well studied, RFs of cortical complex cells are nonlinear and therefore difficult to characterize, especially in the context of natural stimuli. In this study, we used a nonlinear technique to compute the RFs of complex cells from their responses to natural images. We found that each RF is well described by a small number of subunits, which are oriented, localized, and bandpass. These subunits contribute to neuronal responses in a contrast-dependent, polarity-invariant manner, and they can largely predict the orientation and spatial frequency tuning of the cell. Although the RF structures measured with natural images were similar to those measured with random stimuli, natural images were more effective for driving complex cells, thus facilitating rapid identification of the subunits. The subunit RF model provides a useful basis for understanding cortical processing of natural stimuli.

Computing relative motion with complex cells

Contextual influences shape our perception of local visual stimuli. Relative-motion stimuli represent an important contextual influence, yet the mechanism subserving relative-motion computation remains largely unknown. In the present work, we investigated the responses of an established model for simple and complex cells to relative-motion stimuli. A straightforward mathematical analysis showed that relative-motion computation is inherent in the nonlinear transformation of the complex-cell model. Tuning to relative velocity is achieved by applying a temporal filter to the complex-cell response. The mathematical inference is supported by simulations that quantitatively reproduce measured complex-cell responses in both cat and monkey to a variety of relative-motion stimuli. Importantly, the posited mechanism for cortical computation of relative motion does not require an intermediate neural representation of local velocities and does not require lateral or feedback interactions within a network.

Image Representation by Complex Cell Responses

We present an analysis of the representation of images as the magnitudes of their transform with complex-valued Gabor wavelets. Such a representation is a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding, because it makes the representation insensitive to small local shifts. We show that if the images are band limited and of zero mean, then reconstruction from the magnitudes is unique up to the sign for almost all images.

Selectivity and sparseness in the responses of striate complex cells

Probability distributions of macaque complex cell responses to a large set of images were determined. Measures of selectivity were based on the overall shape of the response probability distribution, as quantified by either kurtosis or entropy. We call this non-parametric selectivity, in contrast to parametric selectivity, which measures tuning curve bandwidths. To examine how receptive field properties affected non-parametric selectivity, two models of complex cells were created. One was a standard Gabor energy model, and the other a slight variant constructed from a Gabor function and its Hilbert transform. Functionally, these models differed primarily in the size of their DC responses. The Hilbert model produced higher selectivities than the Gabor model, with the two models bracketing the data from above and below. Thus we see that tiny changes in the receptive field profiles can lead to major changes in selectivity. While selectivity looks at the response distribution of a single neuron across a set of stimuli, sparseness looks at the response distribution of a population of neurons to a single stimulus. In the model, we found that on average the sparseness of a population was equal to the selectivity of cells comprising that population, a property we call ergodicity. We raise the possibility that high sparseness is the result of distortions in the shape of response distributions caused by non-linear, information-losing transforms, unrelated to information theoretic issues of efficient coding.

Modeling the responses of V1 complex cells to natural temporal inputs

Modeling the responses of V1 complex cells to natural temporal inputs

A preference for phase-based disparity in a neuromorphic implementation of the binocular energy model.

The relative depth of objects causes small shifts in the left and right retinal positions of these objects, called binocular disparity. This letter describes an electronic implementation of a single binocularly tuned complex cell based on the binocular energy model, which has been proposed to model disparity-tuned complex cells in the mammalian primary visual cortex. Our system consists of two silicon retinas representing the left and right eyes, two silicon chips containing retinotopic arrays of spiking neurons with monocular Gabor-type spatial receptive fields, and logic circuits that combine the spike outputs to compute a disparity-selective complex cell response. The tuned disparity can be adjusted electronically by introducing either position or phase shifts between the monocular receptive field profiles. Mismatch between the monocular receptive field profiles caused by transistor mismatch can degrade the relative responses of neurons tuned to different disparities. In our system, the relative responses between neurons tuned by phase encoding are better matched than neurons tuned by position encoding. Our numerical sensitivity analysis indicates that the relative responses of phase-encoded neurons that are least sensitive to the receptive field parameters vary the most in our system. We conjecture that this robustness may be one reason for the existence of phase-encoded disparity-tuned neurons in biological neural systems.

Spike-triggered characterization of excitatory and suppressive stimulus dimensions in monkey V1

Neurons in primary visual cortex are commonly characterized using linear models, or simple extensions of linear models. Specifically, V1 simple cell responses are often characterized using a rectified linear receptive field, and complex cell responses are often described as the sum of squared responses of two linear subunits. We examined this class of model directly by applying spike-triggered covariance analysis to responses of monkey V1 neurons under binary white noise stimulation. The analysis extracts a low-dimensional subspace of the full stimulus space that is primarily responsible for generation of the neural response, including both excitatory and suppressive components. We found no fewer than two excitatory dimensions in simple cells, and as many as seven dimensions in complex cells. For all cells, we also found suppressive dimensions that were at least equal in number to the excitatory dimensions. These results suggest that extensions to standard models are required to fully describe the response properties of cells in V1.

Spike-triggered characterization of excitatory and suppressive stimulus dimensions in monkey V1

Neurons in primary visual cortex are commonly characterized using linear models, or simple extensions of linear models. Specifically, V1 simple cell responses are often characterized using a rectified linear receptive field, and complex cell responses are often described as the sum of squared responses of two linear subunits. We examined this class of model directly by applying spike-triggered covariance analysis to responses of monkey V1 neurons under binary white noise stimulation. The analysis extracts a low-dimensional subspace of the full stimulus space that is primarily responsible for generation of the neural response, including both excitatory and suppressive components. We found no fewer than two excitatory dimensions in simple cells, and as many as seven dimensions in complex cells. For all cells, we also found suppressive dimensions that were at least equal in number to the excitatory dimensions. These results suggest that extensions to standard models are required to fully describe the response properties of cells in V1.

Quadratic forms in natural images

Several studies have succeeded in correlating natural image statistics with receptive field properties of neurons in the primary visual cortex. If we determine the parameters of linear transformations that make their output values as independent as possible when input data are natural images, we obtain parameter values that correspond to simple cell characteristics. It was also proved that, by making output values as temporally coherent as possible, simple cell characteristics also emerge. However, complex cell properties have not been fully explained by previous studies of natural image statistics. In this study, we examine whether we could reproduce complex cell properties by determining the parameters of two-layer networks that make their outputs as independent and sparse as possible or as temporally coherent as possible. Input-output functions of two-layer networks correspond to quadratic forms and they form a class of functions that includes complex cell responses and many other functions. Therefore, we employed two-layer networks as a framework for discussing complex cell properties as in previous studies. By maximizing the independence and sparseness of output values of two-layer networks without considering the temporal structure of input images, squared responses of simple cells are obtained and complex cell properties are not reproduced. On the other hand, by maximizing the temporal coherence of output, we obtain complex cell properties among other kinds of input-output functions. In previous studies, the measure of temporal coherence was the squared difference between the responses to two consecutive input images. We obtain two-layer networks that minimize this measure and show that some of them exhibit properties of complex cells but not clearly. We propose the sparseness of difference between responses to two consecutive inputs as an alternative measure of temporal coherence. We formulate an algorithm to maximize the sparseness of difference and show that complex cell properties emerge more clearly.

Mechanical injury and repair of cells.

To concisely review the field of cell plasma membrane disruption (torn cell surface) and repair. Plasma membrane disruption is a common form of cell injury under physiologic conditions, after trauma, in certain muscular dystrophies, and during certain forms of clinical intervention. Rapid repair of a disruption is essential to cell survival and involves a complex and active cell response that includes membrane fusion and cytoskeletal activation. Tissues, such as cardiac and skeletal muscle, adapt to a disruption injury by hypertrophying. Cells adapt by increasing the efficiency of their resealing response. Plasma membrane disruption is an important cellular event in both health and disease. The disruption repair mechanism is now well understood at the cellular level, but much remains to be learned at the molecular level. Cell and tissue level adaptational responses to the disruption either prevent its further occurrence or facilitate future repairs. Therapeutically useful drugs might result if, using this accumulating knowledge, chemical agents can be developed that can enhance repair or adaptive responses.

Quadratic forms in natural images

Several studies have succeeded in correlating natural image statistics with receptive field properties of neurons in the primary visual cortex. If we determine the parameters of linear transformations that make their output values as independent as possible when input data are natural images, we obtain parameter values that correspond to simple cell characteristics. It was also proved that, by making output values as temporally coherent as possible, simple cell characteristics also emerge. However, complex cell properties have not been fully explained by previous studies of natural image statistics. In this study, we examine whether we could reproduce complex cell properties by determining the parameters of two-layer networks that make their outputs as independent and sparse as possible or as temporally coherent as possible. Input–output functions of two-layer networks correspond to quadratic forms and they form a class of functions that includes complex cell responses and many other functions. Therefore, we employed two-layer networks as a framework for discussing complex cell properties as in previous studies. By maximizing the independence and sparseness of output values of two-layer networks without considering the temporal structure of input images, squared responses of simple cells are obtained and complex cell properties are not reproduced. On the other hand, by maximizing the temporal coherence of output, we obtain complex cell properties among other kinds of input–output functions. In previous studies, the measure of temporal coherence was the squared difference between the responses to two consecutive input images. We obtain two-layer networks that minimize this measure and show that some of them exhibit properties of complex cells but not clearly. We propose the sparseness of difference between responses to two consecutive inputs as an alternative measure of temporal coherence. We formulate an algorithm to maximize the sparseness of difference and show that complex cell properties emerge more clearly.

Isolation of Relevant Visual Features from Random Stimuli for Cortical Complex Cells

A crucial step in understanding the function of a neural circuit in visual processing is to know what stimulus features are represented in the spiking activity of the neurons. For neurons with complex, nonlinear response properties, characterization of feature representation requires measurement of their responses to a large ensemble of visual stimuli and an analysis technique that allows identification of relevant features in the stimuli. In the present study, we recorded the responses of complex cells in the primary visual cortex of the cat to spatiotemporal random-bar stimuli and applied spike-triggered correlation analysis of the stimulus ensemble. For each complex cell, we were able to isolate a small number of relevant features from a large number of null features in the random-bar stimuli. Using these features as visual stimuli, we found that each relevant feature excited the neuron effectively in isolation and contributed to the response additively when combined with other features. In contrast, the null features evoked little or no response in isolation and divisively suppressed the responses to relevant features. Thus, for each cortical complex cell, visual inputs can be decomposed into two distinct types of features (relevant and null), and additive and divisive interactions between these features may constitute the basic operations in visual cortical processing.