Response sub-additivity and variability quenching in visual cortex

Sub-additivity and variability are ubiquitous response motifs in the primary visual cortex (V1). Response sub-additivity enables the construction of useful interpretations of the visual environment, whereas response variability indicates the factors that limit the precision with which the brain can do this. There is increasing evidence that experimental manipulations that elicit response sub-additivity often also quench response variability. Here, we provide an overview of these phenomena and suggest that they may have common origins. We discuss empirical findings and recent model-based insights into the functional operations, computational objectives and circuit mechanisms underlying V1 activity. These different modelling approaches all predict that response sub-additivity and variability quenching often co-occur. The phenomenology of these two response motifs, as well as many of the insights obtained about them in V1, generalize to other cortical areas. Thus, the connection between response sub-additivity and variability quenching may be a canonical motif across the cortex.

Primate neocortex performs balanced sensory amplification

The sensory cortex amplifies relevant features of external stimuli. This sensitivity and selectivity arise through the transformation of inputs by cortical circuitry. We characterize the circuit mechanisms and dynamics of cortical amplification by making large-scale simultaneous measurements of single cells in awake primates and testing computational models. By comparing network activity in both driven and spontaneous states with models, we identify the circuit as operating in a regime of non-normal balanced amplification. Incoming inputs are strongly but transiently amplified by strong recurrent feedback from the disruption of excitatory-inhibitory balance in the network. Strong inhibition rapidly quenches responses, thereby permitting the tracking of time-varying stimuli.

Mammals Achieve Common Neural Coverage of Visual Scenes Using Distinct Sampling Behaviors

Most vertebrates use head and eye movements to quickly change gaze orientation and sample different portions of the environment with periods of stable fixation. Visual information must be integrated across fixations to construct a complete perspective of the visual environment. In concert with this sampling strategy, neurons adapt to unchanging input to conserve energy and ensure that only novel information from each fixation is processed. We demonstrate how adaptation recovery times and saccade properties interact and thus shape spatiotemporal tradeoffs observed in the motor and visual systems of mice, cats, marmosets, macaques, and humans. These tradeoffs predict that in order to achieve similar visual coverage over time, animals with smaller receptive field sizes require faster saccade rates. Indeed, we find comparable sampling of the visual environment by neuronal populations across mammals when integrating measurements of saccadic behavior with receptive field sizes and V1 neuronal density. We propose that these mammals share a common statistically driven strategy of maintaining coverage of their visual environment over time calibrated to their respective visual system characteristics.

Interactions between saccades and smooth pursuit eye movements in marmosets

Animals use a combination of eye movements to track moving objects. These different eye movements need to be coordinated for successful tracking, requiring interactions between the systems involved. Here, we study the interaction between the saccadic and smooth pursuit eye movement systems in marmosets. Using a single target pursuit task, we show that saccades cause an enhancement in pursuit following a saccade. Using a two-target pursuit task, we show that this enhancement in pursuit is selective towards the motion of the target selected by the saccade, irrespective of any biases in pursuit prior to the saccade. These experiments highlight the similarities in the functioning of saccadic and smooth pursuit eye movement systems across primates.

SIGNIFICANCE STATEMENT

We study the coordination between the smooth-pursuit and saccadic eye movement systems in marmosets using single and multiple object motions. We find that saccade to a target increases pursuit velocity towards the target. If multiple objects are visible, saccade choice makes pursuit more selective towards the saccade target. Our results show that coordination between different eye movement systems to successfully track moving objects is similar between marmosets and primates.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≃ 4 - 9 m V 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≅ 4-9mV 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Mammals achieve common neural coverage of visual scenes using distinct sampling behaviors

Most vertebrates use head and eye movements to quickly change gaze orientation and sample different portions of the environment with periods of stable fixation. Visual information must be integrated across several fixations to construct a more complete perspective of the visual environment. In concert with this sampling strategy, neurons adapt to unchanging input to conserve energy and ensure that only novel information from each fixation is processed. We demonstrate how adaptation recovery times and saccade properties interact, and thus shape spatiotemporal tradeoffs observed in the motor and visual systems of different species. These tradeoffs predict that in order to achieve similar visual coverage over time, animals with smaller receptive field sizes require faster saccade rates. Indeed, we find comparable sampling of the visual environment by neuronal populations across mammals when integrating measurements of saccadic behavior with receptive field sizes and V1 neuronal density. We propose that these mammals share a common statistically driven strategy of maintaining coverage of their visual environment over time calibrated to their respective visual system characteristics.

Ocular following eye movements in marmosets follow complex motion trajectories

Ocular following eye movements help stabilize images on the retina and offer a window to study motion interpretation by visual circuits. We use these ocular following eye movements to study motion integration behavior in the marmosets. We characterize ocular following responses in the marmosets using different moving stimuli such as dot patterns, gratings, and plaids. The marmosets can accurately track motion along different directions and exhibit spatial frequency and speed sensitivity that closely matches the sensitivity reported in neurons from their motion selective area MT. Marmosets are also able to track the integrated motion of plaids, with tracking direction consistent with intersection of constraints model of motion integration. Marmoset ocular following responses are similar to responses in macaques and humans with certain species-specific differences in peak sensitivities. Such motion sensitive eye movement behavior in combination with direct access to cortical circuitry makes the marmoset model well suited to study the neural basis of motion integration.Significance statementOcular following is a reflexive eye tracking behavior in response to large visual field motion. It reflects the properties of underlying motion sensing circuits. One of the primary motion sensing areas in primates is area MT. In the primate species of marmosets, this and other cortical areas are easily accessible due to their lissencephalic brain. We demonstrate ocular following behavior in the marmosets for simple and complex motion trajectories and describe its characteristics. We then use ocular following to distinguish between different motion integration models. Our results show the utility of ocular following to study the neural basis for motion sensing in marmosets.

On the Rotations of the Cranial Spheres

We integrate information from multiple sensory modalities and from ongoing plans to construct a perception of the world. In this issue of Neuron, Bouvier et al. (2020) and Guitchounts et al. (2020) examine the detailed circuitry that supports a flexible integration of head and visual signals in rodent primary visual cortex.

Interocular velocity cues elicit vergence eye movements in mice

We stabilize the dynamic visual world on our retina by moving our eyes in response to motion signals. Coordinated movements between the two eyes are characterized as version when both eyes move in the same direction and vergence when the two eyes move in opposite directions. Vergence eye movements are necessary to track objects in three dimensions. In primates they can be elicited by intraocular differences in either spatial signals (disparity) or velocity, requiring the integration of left and right eye inputs. Whether mice are capable of similar behaviors is not known. To address this issue, we measured vergence eye movements in mice using a stereoscopic stimulus known to elicit vergence eye movements in primates. We found that mice also exhibit vergence eye movements, although at a low gain and that the primary driver of these vergence eye movements is interocular motion. Spatial disparity cues alone are ineffective. We also found that the vergence eye movements we observed in mice were robust to silencing visual cortex and to manipulations that disrupt the normal development of binocularity in visual cortex. A sublinear combination of motor commands driven by monocular signals is sufficient to account for our results.NEW & NOTEWORTHY The visual system integrates signals from the left and right eye to generate a representation of the world in depth. The binocular integration of signals may be observed from the coordinated vergence eye movements elicited by object motion in depth. We explored the circuits and signals responsible for these vergence eye movements in rodent and find these vergence eye movements are generated by a comparison of the motion and not spatial visual signals.

Voltage-Gated Intrinsic Conductances Shape the Input-Output Relationship of Cortical Neurons in Behaving Primate V1

Neurons are input-output (I/O) devices-they receive synaptic inputs from other neurons, integrate those inputs with their intrinsic properties, and generate action potentials as outputs. To understand this fundamental process, we studied the interaction between synaptic inputs and intrinsic properties using whole-cell recordings from V1 neurons of awake, fixating macaque monkeys. Our measurements during spontaneous activity and visual stimulation reveal an intrinsic voltage-gated conductance that profoundly alters the integrative properties and visual responses of cortical neurons. This voltage-gated conductance increases neuronal gain and selectivity with subthreshold depolarization and linearizes the relationship between synaptic input and neural output. This intrinsic conductance is found in layer 2/3 V1 neurons of awake macaques, anesthetized mice, and acute brain slices. These results demonstrate that intrinsic conductances play an essential role in shaping the I/O relationship of cortical neurons and must be taken into account in future models of cortical computations.

Natural image and receptive field statistics predict saccade sizes

Humans and other primates sample the visual environment using saccadic eye movements that shift a high-resolution fovea toward regions of interest to create a clear perception of a scene across fixations. Many mammals, however, like mice, lack a fovea, which raises the question of why they make saccades. Here we describe and test the hypothesis that saccades are matched to natural scene statistics and to the receptive field sizes and adaptive properties of neural populations. Specifically, we determined the minimum amplitude of saccades in natural scenes necessary to provide uncorrelated inputs to model neural populations. This analysis predicts the distributions of observed saccade sizes during passive viewing for nonhuman primates, cats, and mice. Furthermore, disrupting the development of receptive field properties by monocular deprivation changed saccade sizes consistent with this hypothesis. Therefore, natural-scene statistics and the neural representation of natural images appear to be critical factors guiding saccadic eye movements.

Emergent Orientation Selectivity from Random Networks in Mouse Visual Cortex

The connectivity principles underlying the emergence of orientation selectivity in primary visual cortex (V1) of mammals lacking an orientation map (such as rodents and lagomorphs) are poorly understood. We present a computational model in which random connectivity gives rise to orientation selectivity that matches experimental observations. The model predicts that mouse V1 neurons should exhibit intricate receptive fields in the two-dimensional frequency domain, causing a shift in orientation preferences with spatial frequency. We find evidence for these features in mouse V1 using calcium imaging and intracellular whole-cell recordings.

Mechanisms of Orientation Selectivity in the Primary Visual Cortex

The mechanisms underlying the emergence of orientation selectivity in the visual cortex have been, and continue to be, the subjects of intense scrutiny. Orientation selectivity reflects a dramatic change in the representation of the visual world: Whereas afferent thalamic neurons are generally orientation insensitive, neurons in the primary visual cortex (V1) are extremely sensitive to stimulus orientation. This profound change in the receptive field structure along the visual pathway has positioned V1 as a model system for studying the circuitry that underlies neural computations across the neocortex. The neocortex is characterized anatomically by the relative uniformity of its circuitry despite its role in processing distinct signals from region to region. A combination of physiological, anatomical, and theoretical studies has shed some light on the circuitry components necessary for generating orientation selectivity in V1. This targeted effort has led to critical insights, as well as controversies, concerning how neural circuits in the neocortex perform computations.

Orientation selectivity in the visual cortex of the nine-banded armadillo

Orientation selectivity in primary visual cortex (V1) has been proposed to reflect a canonical computation performed by the neocortical circuitry. Although orientation selectivity has been reported in all mammals examined to date, the degree of selectivity and the functional organization of selectivity vary across mammalian clades. The differences in degree of orientation selectivity are large, from reports in marsupials that only a small subset of neurons are selective to studies in carnivores, in which it is rare to find a neuron lacking selectivity. Furthermore, the functional organization in cortex varies in that the primate and carnivore V1 is characterized by an organization in which nearby neurons share orientation preference while other mammals such as rodents and lagomorphs either lack or have only extremely weak clustering. To gain insight into the evolutionary emergence of orientation selectivity, we examined the nine-banded armadillo, a species within the early placental clade Xenarthra. Here we use a combination of neuroimaging, histological, and electrophysiological methods to identify the retinofugal pathways, locate V1, and for the first time examine the functional properties of V1 neurons in the armadillo (Dasypus novemcinctus) V1. Individual neurons were strongly sensitive to the orientation and often the direction of drifting gratings. We uncovered a wide range of orientation preferences but found a bias for horizontal gratings. The presence of strong orientation selectivity in armadillos suggests that the circuitry responsible for this computation is common to all placental mammals.NEW & NOTEWORTHY The current study shows that armadillo primary visual cortex (V1) neurons share the signature properties of V1 neurons of primates, carnivorans, and rodents. Furthermore, these neurons exhibit a degree of selectivity for stimulus orientation and motion direction similar to that found in primate V1. Our findings in armadillo visual cortex suggest that the functional properties of V1 neurons emerged early in the mammalian lineage, near the time of the divergence of marsupials.

Functional characterization and spatial clustering of visual cortical neurons in the predatory grasshopper mouse Onychomys arenicola

Mammalian neocortical circuits are functionally organized such that the selectivity of individual neurons systematically shifts across the cortical surface, forming a continuous map. Maps of the sensory space exist in cortex, such as retinotopic maps in the visual system or tonotopic maps in the auditory system, but other functional response properties also may be similarly organized. For example, many carnivores and primates possess a map for orientation selectivity in primary visual cortex (V1), whereas mice, rabbits, and the gray squirrel lack orientation maps. In this report we show that a carnivorous rodent with predatory behaviors, the grasshopper mouse (Onychomys arenicola), lacks a canonical columnar organization of orientation preference in V1; however, neighboring neurons within 50 μm exhibit related tuning preference. Using a combination of two-photon microscopy and extracellular electrophysiology, we demonstrate that the functional organization of visual cortical neurons in the grasshopper mouse is largely the same as in the C57/BL6 laboratory mouse. We also find similarity in the selectivity for stimulus orientation, direction, and spatial frequency. Our results suggest that the properties of V1 neurons across rodent species are largely conserved.NEW & NOTEWORTHY Carnivores and primates possess a map for orientation selectivity in primary visual cortex (V1), whereas rodents and lagomorphs lack this organization. We examine, for the first time, V1 of a wild carnivorous rodent with predatory behaviors, the grasshopper mouse (Onychomys arenicola). We demonstrate the cellular organization of V1 in the grasshopper mouse is largely the same as the C57/BL6 laboratory mouse, suggesting that V1 neuron properties across rodent species are largely conserved.

Functional characterization of spikelet activity in the primary visual cortex

KEY POINTS

In vivo whole-cell patch-clamp recordings in cat visual cortex revealed small deflections in the membrane potential of neurons, termed spikelets. Spikelet statistics and functional properties suggest these deflections originate from a single, nearby cell. Spikelets shared a number sensory selectivities with the principal neuron including orientation selectivity, receptive field location and eye preference. Principal neurons and spikelets did not, however, generally share preferences for depth (binocular disparity). Cross-correlation of spikelet activity and membrane potential revealed direct effects on the membrane potential of some principal neurons, suggesting that these cells were synaptically coupled or received common input from the cortical network. Other spikelet-neuron pairs revealed indirect effects, likely to be the result of correlated network events.

ABSTRACT

Intracellular recordings in the neocortex reveal not only the membrane potential of neurons, but small unipolar or bipolar deflections that are termed spikelets. Spikelets have been proposed to originate from various sources, including active dendritic mechanisms, gap junctions and extracellular signals. Here we examined the functional characteristics of spikelets measured in neurons from cat primary visual cortex in vivo. Spiking statistics and our functional characterization of spikelet activity indicate that spikelets originate from a separate, nearby cell. Spikelet kinetics and lack of a direct effect on spikelet activity from hyperpolarizing current injection suggest they do not arise from electrical coupling to the principal neuron being recorded. Spikelets exhibited matched orientation tuning preference and ocular dominance to the principal neuron. In contrast, binocular disparity preferences of spikelets and the principal neuron were unrelated. Finally, we examined the impact of spikelets on the principal neuron's membrane potential; we did observe some records for which spikelets were correlated with the membrane potential of the principal neuron, suggesting that these neurons were synaptically coupled or received common input from the cortical network.

Local Integration Accounts for Weak Selectivity of Mouse Neocortical Parvalbumin Interneurons

Dissecting the functional roles of excitatory and inhibitory neurons in cortical circuits is a fundamental goal in neuroscience. Of particular interest are their roles in emergent cortical computations such as binocular integration in primary visual cortex (V1). We measured the binocular response selectivity of genetically defined subpopulations of excitatory and inhibitory neurons. Parvalbumin (PV+) interneurons received strong inputs from both eyes but lacked selectivity for binocular disparity. Because broad selectivity could result from heterogeneous synaptic input from neighboring neurons, we examined how individual PV+ interneuron selectivity compared to that of the local neuronal network, which is primarily composed of excitatory neurons. PV+ neurons showed functional similarity to neighboring neuronal populations over spatial distances resembling measurements of synaptic connectivity. On the other hand, excitatory neurons expressing CaMKIIα displayed no such functional similarity with the neighboring population. Our findings suggest that broad selectivity of PV+ interneurons results from nonspecific integration within local networks. VIDEO ABSTRACT.

Motion dependence of smooth pursuit eye movements in the marmoset

Smooth pursuit eye movements stabilize slow-moving objects on the retina by matching eye velocity with target velocity. Two critical components are required to generate smooth pursuit: first, because it is a voluntary eye movement, the subject must select a target to pursue to engage the tracking system; and second, generating smooth pursuit requires a moving stimulus. We examined whether this behavior also exists in the common marmoset, a New World primate that is increasingly attracting attention as a genetic model for mental disease and systems neuroscience. We measured smooth pursuit in two marmosets, previously trained to perform fixation tasks, using the standard Rashbass step-ramp pursuit paradigm. We first measured the aspects of visual motion that drive pursuit eye movements. Smooth eye movements were in the same direction as target motion, indicating that pursuit was driven by target movement rather than by displacement. Both the open-loop acceleration and closed-loop eye velocity exhibited a linear relationship with target velocity for slow-moving targets, but this relationship declined for higher speeds. We next examined whether marmoset pursuit eye movements depend on an active engagement of the pursuit system by measuring smooth eye movements evoked by small perturbations of motion from fixation or during pursuit. Pursuit eye movements were much larger during pursuit than from fixation, indicating that pursuit is actively gated. Several practical advantages of the marmoset brain, including the accessibility of the middle temporal (MT) area and frontal eye fields at the cortical surface, merit its utilization for studying pursuit movements.

Mouse vision as a gateway for understanding how experience shapes neural circuits

Genetic programs controlling ontogeny drive many of the essential connectivity patterns within the brain. Yet it is activity, derived from the experience of interacting with the world, that sculpts the precise circuitry of the central nervous system. Such experience-dependent plasticity has been observed throughout the brain but has been most extensively studied in the neocortex. A prime example of this refinement of neural circuitry is found in primary visual cortex (V1), where functional connectivity changes have been observed both during development and in adulthood. The mouse visual system has become a predominant model for investigating the principles that underlie experience-dependent plasticity, given the general conservation of visual neural circuitry across mammals as well as the powerful tools and techniques recently developed for use in rodent. The genetic tractability of mice has permitted the identification of signaling pathways that translate experience-driven activity patterns into changes in circuitry. Further, the accessibility of visual cortex has allowed neural activity to be manipulated with optogenetics and observed with genetically-encoded calcium sensors. Consequently, mouse visual cortex has become one of the dominant platforms to study experience-dependent plasticity.

Binocular integration and disparity selectivity in mouse primary visual cortex

Signals from the two eyes are first integrated in primary visual cortex (V1). In many mammals, this binocular integration is an important first step in the development of stereopsis, the perception of depth from disparity. Neurons in the binocular zone of mouse V1 receive inputs from both eyes, but it is unclear how that binocular information is integrated and whether this integration has a function similar to that found in other mammals. Using extracellular recordings, we demonstrate that mouse V1 neurons are tuned for binocular disparities, or spatial differences, between the inputs from each eye, thus extracting signals potentially useful for estimating depth. The disparities encoded by mouse V1 are significantly larger than those encoded by cat and primate. Interestingly, these larger disparities correspond to distances that are likely to be ecologically relevant in natural viewing, given the stereo-geometry of the mouse visual system. Across mammalian species, it appears that binocular integration is a common cortical computation used to extract information relevant for estimating depth. As such, it is a prime example of how the integration of multiple sensory signals is used to generate accurate estimates of properties in our environment.

A spontaneous state of weakly correlated synaptic excitation and inhibition in visual cortex

Cortical spontaneous activity reflects an animal's behavioral state and affects neural responses to sensory stimuli. The correlation between excitatory and inhibitory synaptic input to single neurons is a key parameter in models of cortical circuitry. Recent measurements demonstrated highly correlated synaptic excitation and inhibition during spontaneous "up-and-down" states, during which excitation accounted for approximately 80% of inhibitory variance (Shu et al., 2003; Haider et al., 2006). Here we report in vivo whole-cell estimates of the correlation between excitation and inhibition in the rat visual cortex under pentobarbital anesthesia, during which up-and-down states are absent. Excitation and inhibition are weakly correlated, relative to the up-and-down state: excitation accounts for less than 40% of inhibitory variance. Although these correlations are lower than when the circuit cycles between up-and-down states, both behaviors may arise from the same circuitry. Our observations provide evidence that different correlational patterns of excitation and inhibition underlie different cortical states.

Mechanisms of neuronal computation in mammalian visual cortex

Orientation selectivity in the primary visual cortex (V1) is a receptive field property that is at once simple enough to make it amenable to experimental and theoretical approaches and yet complex enough to represent a significant transformation in the representation of the visual image. As a result, V1 has become an area of choice for studying cortical computation and its underlying mechanisms. Here we consider the receptive field properties of the simple cells in cat V1--the cells that receive direct input from thalamic relay cells--and explore how these properties, many of which are highly nonlinear, arise. We have found that many receptive field properties of V1 simple cells fall directly out of Hubel and Wiesel's feedforward model when the model incorporates realistic neuronal and synaptic mechanisms, including threshold, synaptic depression, response variability, and the membrane time constant.

The accuracy of membrane potential reconstruction based on spiking receptive fields

A common technique used to study the response selectivity of neurons is to measure the relationship between sensory stimulation and action potential responses. Action potentials, however, are only indirectly related to the synaptic inputs that determine the underlying, subthreshold, response selectivity. We present a method to predict membrane potential, the measurable result of the convergence of synaptic inputs, based on spike rate alone and then test its utility by comparing predictions to actual membrane potential recordings from simple cells in primary visual cortex. Using a noise stimulus, we found that spike rate receptive fields were in precise correspondence with membrane potential receptive fields (R(2) = 0.74). On average, spike rate alone could predict 44% of membrane potential fluctuations to dynamic noise stimuli, demonstrating the utility of this method to extract estimates of subthreshold responses. We also found that the nonlinear relationship between membrane potential and spike rate could also be extracted from spike rate data alone by comparing predictions from the noise stimulus with the actual spike rate. Our analysis reveals that linear receptive field models extracted from noise stimuli accurately reflect the underlying membrane potential selectivity and thus represent a method to generate estimates of the underlying average membrane potential from spike rate data alone.

Spatial organization of repetition rate processing in cat anterior auditory field

Auditory cortex updates incoming information on a segment by segment basis for human speech and animal communication. Measuring repetition rate transfer functions (RRTFs) captures temporal responses to repetitive sounds. In this study, we used repetitive click trains to describe the spatial distribution of RRTF responses in cat anterior auditory field (AAF) and to discern potential variations in local temporal processing capacity. A majority of RRTF filters are band-pass. Temporal parameters estimated from RRTFs and corrected for characteristic frequency or latency dependencies are non-homogeneously distributed across AAF. Unlike the shallow global gradient observed in spectral receptive field parameters, transitions from loci with high to low temporal parameters are steep. Quantitative spatial analysis suggests non-uniform, circumscribed local organization for temporal pattern processing superimposed on global organization for spectral processing in cat AAF.

Mechanisms of direction selectivity in cat primary visual cortex as revealed by visual adaptation

In contrast to neurons of the lateral geniculate nucleus (LGN), neurons in the primary visual cortex (V1) are selective for the direction of visual motion. Cortical direction selectivity could emerge from the spatiotemporal configuration of inputs from thalamic cells, from intracortical inhibitory interactions, or from a combination of thalamic and intracortical interactions. To distinguish between these possibilities, we studied the effect of adaptation (prolonged visual stimulation) on the direction selectivity of intracellularly recorded cortical neurons. It is known that adaptation selectively reduces the responses of cortical neurons, while largely sparing the afferent LGN input. Adaptation can therefore be used as a tool to dissect the relative contribution of afferent and intracortical interactions to the generation of direction selectivity. In both simple and complex cells, adaptation caused a hyperpolarization of the resting membrane potential (-2.5 mV, simple cells, -0.95 mV complex cells). In simple cells, adaptation in either direction only slightly reduced the visually evoked depolarization; this reduction was similar for preferred and null directions. In complex cells, adaptation strongly reduced visual responses in a direction-dependent manner: the reduction was largest when the stimulus direction matched that of the adapting motion. As a result, adaptation caused changes in the direction selectivity of complex cells: direction selectivity was reduced after preferred direction adaptation and increased after null direction adaptation. Because adaptation in the null direction enhanced direction selectivity rather than reduced it, it seems unlikely that inhibition from the null direction is the primary mechanism for creating direction selectivity.

Encoding of temporal information by timing, rate, and place in cat auditory cortex

A central goal in auditory neuroscience is to understand the neural coding of species-specific communication and human speech sounds. Low-rate repetitive sounds are elemental features of communication sounds, and core auditory cortical regions have been implicated in processing these information-bearing elements. Repetitive sounds could be encoded by at least three neural response properties: 1) the event-locked spike-timing precision, 2) the mean firing rate, and 3) the interspike interval (ISI). To determine how well these response aspects capture information about the repetition rate stimulus, we measured local group responses of cortical neurons in cat anterior auditory field (AAF) to click trains and calculated their mutual information based on these different codes. ISIs of the multiunit responses carried substantially higher information about low repetition rates than either spike-timing precision or firing rate. Combining firing rate and ISI codes was synergistic and captured modestly more repetition information. Spatial distribution analyses showed distinct local clustering properties for each encoding scheme for repetition information indicative of a place code. Diversity in local processing emphasis and distribution of different repetition rate codes across AAF may give rise to concurrent feed-forward processing streams that contribute differently to higher-order sound analysis.

Inhibition, spike threshold, and stimulus selectivity in primary visual cortex

Ever since Hubel and Wiesel described orientation selectivity in the visual cortex, the question of how precise selectivity emerges has been marked by considerable debate. There are essentially two views of how selectivity arises. Feed-forward models rely entirely on the organization of thalamocortical inputs. Feedback models rely on lateral inhibition to refine selectivity relative to a weak bias provided by thalamocortical inputs. The debate is driven by two divergent lines of evidence. On the one hand, many response properties appear to require lateral inhibition, including precise orientation and direction selectivity and crossorientation suppression. On the other hand, intracellular recordings have failed to find consistent evidence for lateral inhibition. Here we demonstrate a resolution to this paradox. Feed-forward models incorporating the intrinsic nonlinear properties of cortical neurons and feed-forward circuits (i.e., spike threshold, contrast saturation, and spike-rate rectification) can account for properties that have previously appeared to require lateral inhibition.

The emergence of contrast-invariant orientation tuning in simple cells of cat visual cortex

Simple cells in primary visual cortex exhibit contrast-invariant orientation tuning, in seeming contradiction to feed-forward models that rely on lateral geniculate nucleus (LGN) input alone. Contrast invariance has therefore been thought to depend on the presence of intracortical lateral inhibition. In vivo intracellular recordings instead suggest that contrast invariance can be explained by three properties of the excitatory pathway. (1) Depolarizations evoked by orthogonal stimuli are determined by the amount of excitation a cell receives from the LGN, relative to the excitation it receives from other cortical cells. (2) Depolarizations evoked by preferred stimuli saturate at lower contrasts than the spike output of LGN relay cells. (3) Visual stimuli evoke contrast-dependent changes in trial-to-trial variability, which lead to contrast-dependent changes in the relationship between membrane potential and spike rate. Thus, high-contrast, orthogonally oriented stimuli that evoke significant depolarizations evoke few spikes. Together these mechanisms, without lateral inhibition, can account for contrast-invariant stimulus selectivity.

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.

Mechanisms underlying cross-orientation suppression in cat visual cortex

In simple cells of the cat primary visual cortex, null-oriented stimuli, which by themselves evoke no response, can completely suppress the spiking response to optimally oriented stimuli. This cross-orientation suppression has been interpreted as evidence for cross-orientation inhibition: synaptic inhibition among cortical cells with different preferred orientations. In intracellular recordings from simple cells, however, we found that cross-oriented stimuli suppressed, rather than enhanced, synaptic inhibition and, at the same time, suppressed synaptic excitation. Much of the suppression of excitation could be accounted for by the behavior of geniculate relay cells: contrast saturation and rectification in relay cell responses, when applied to a linear feed-forward model, predicted cross-orientation suppression of the modulation (F1) component of excitation evoked in simple cells. In addition, we found that the suppression of the spike output of simple cells was almost twice the suppression of their synaptic inputs. Thus, cross-orientation suppression, like orientation selectivity, is strongly amplified by threshold.

Direction selectivity of excitation and inhibition in simple cells of the cat primary visual cortex

Direction selectivity in simple cells of primary visual cortex, defined from their spike responses, cannot be predicted using linear models. It has been suggested that the shunting inhibition evoked by visual stimulation is responsible for the nonlinear component of direction selectivity. Cortical inhibition would suppress a neuron's firing when stimuli move in the nonpreferred direction, but would allow responses to stimuli in the preferred direction. Models of direction selectivity based solely on input from the lateral geniculate nucleus, however, propose that the nonlinear response is caused by spike threshold. By extracting excitatory and inhibitory components of synaptic inputs from intracellular records obtained in vivo, we demonstrate that excitation and inhibition are tuned for the same direction, but differ in relative timing. Further, membrane potential responses combine in a linear fashion. Spike threshold, however, quantitatively accounts for the nonlinear component of direction selectivity, amplifying the direction selectivity of spike output relative to that of synaptic inputs.

Comparison of the spatial limits on direction selectivity in visual areas MT and V1

We recorded responses to apparent motion from directionally selective neurons in primary visual cortex (V1) of anesthetized monkeys and middle temporal area (MT) of awake monkeys. Apparent motion consisted of multiple stationary stimulus flashes presented in sequence, characterized by their temporal separation (delta t) and spatial separation (delta x). Stimuli were 8 degrees square patterns of 100% correlated random dots that moved at apparent speeds of 16 or 32 degrees/s. For both V1 and MT, the difference between the response to the preferred and null directions declined with increasing flash separation. For each neuron, we estimated the maximum flash separation for which directionally selective responses were observed. For the range of speeds we used, delta x provided a better description of the limitation on directional responses than did delta t. When comparing MT and V1 neurons of similar preferred speed, there was no difference in the maximum delta x between our samples from the two areas. In both V1 and MT, the great majority of neurons had maximal values of delta x in the 0.25-1 degrees range. Mean values were almost identical between the two areas. For most neurons, larger flash separations led to both weaker responses to the preferred direction and increased responses to the opposite direction. The former mechanism was slightly more dominant in MT and the latter slightly more dominant in V1. We conclude that V1 and MT neurons lose direction selectivity for similar values of delta x, supporting the hypothesis that basic direction selectivity in MT is inherited from V1, at least over the range of stimulus speeds represented by both areas.

The contribution of spike threshold to the dichotomy of cortical simple and complex cells

The existence of two classes of cells, simple and complex, discovered by Hubel and Wiesel in 1962, is one of the fundamental features of cat primary visual cortex. A quantitative measure used to distinguish simple and complex cells is the ratio between modulated and unmodulated components of spike responses to drifting gratings, an index that forms a bimodal distribution. We have found that the modulation ratio, when derived from the subthreshold membrane potential instead of from spike rate, is unimodally distributed, but highly skewed. The distribution of the modulation ratio as derived from spike rate can, in turn, be predicted quantitatively by the nonlinear properties of spike threshold applied to the skewed distribution of the subthreshold modulation ratio. Threshold also increases the spatial segregation of ON and OFF regions of the receptive field, a defining attribute of simple cells. The distinction between simple and complex cells is therefore enhanced by threshold, much like the selectivity for stimulus features such as orientation and direction. In this case, however, a continuous distribution in the spatial organization of synaptic inputs is transformed into two distinct classes of cells.

Modular Functional Organization of Cat Anterior Auditory Field

Two tonotopic areas, the primary auditory cortex (AI) and the anterior auditory field (AAF), are the primary cortical fields in the cat auditory system. They receive largely independent, concurrent thalamocortical projections from the different thalamic divisions despite their hierarchical equivalency. The parallel streams of thalamic inputs to AAF and AI suggest that AAF neurons may differ from AI neurons in physiological properties. Although a modular functional organization in cat AI has been well documented, little is known about the internal organization of AAF beyond tonotopy. We studied how basic receptive field parameters (RFPs) are spatially organized in AAF with single- and multiunit recording techniques. A distorted tonotopicity with an underrepresentation in midfrequencies (1 and 5 kHz) and an overrepresentation in the high-frequency range was found. Spectral bandwidth (Q-values) and response threshold were significantly correlated with characteristic frequency (CF). To understand whether AAF has a modular organization of RFPs, CF dependencies were eliminated by a nonparametric, local regression model, and the residuals (difference between the model and observed values) were evaluated. In a given isofrequency domain, clusters of low or high residual RFP values were interleaved for threshold, spectral bandwidth, and latency, suggesting a modular organization. However, RFP modules in AAF were not expressed as robustly as in AI. A comparison of RFPs between AAF and AI shows that AAF neurons were more broadly tuned and had shorter latencies than AI neurons. These physiological field differences are consistent with anatomical evidence of largely independent, concurrent thalamocortical projections in AI and AAF, which strongly suggest field-specific processing.

Estimating target speed from the population response in visual area MT

To guide behavior, perceptual and motor systems must estimate properties of the sensory environment from the responses of populations of cortical neurons. In the domain of visual motion, estimates of target speed are derived from the responses of motion-sensitive neurons in the middle temporal (MT) area of the extrastriate visual cortex and are used to drive smooth pursuit eye movements and perceptual judgments of speed. We have asked how these behavioral systems estimate target speed from the population response in area MT. We found that increasing the spatial frequency of a sine wave grating caused decreases in the target speed estimated by both pursuit and perception and commensurate changes in the identity of the active neurons in area MT. Decreasing the contrast of a sine wave grating caused decreases in the target speed estimated by both pursuit and perception, while altering only the response amplitude of MT neurons and not the identity of the active neurons. Applying a modified vector-averaging computation to the population response measured in area MT allowed us to predict the effects of both spatial frequency and contrast on speed estimation for both perception and pursuit. The modification biased the speed estimation toward low target speeds when responses across the population of neurons were small.

The neural representation of speed in macaque area MT/V5

Tuning for speed is one key feature of motion-selective neurons in the middle temporal visual area of the macaque cortex (MT, or V5). The present paper asks whether speed is coded in a way that is invariant to the shape of the moving stimulus, and if so, how. When tested with single sine-wave gratings of different spatial and temporal frequencies, MT neurons show a continuum in the degree to which preferred speed depends on spatial frequency. There is some dependence in 75% of MT neurons, and the other 25% maintain speed tuning despite changes in spatial frequency. When tested with stimuli constructed by adding two superimposed sine-wave gratings, the preferred speed of MT neurons becomes less dependent on spatial frequency. Analysis of these responses reveals a speed-tuning nonlinearity that selectively enhances the responses of the neuron when multiple spatial frequencies are present and moving at the same speed. Consistent with the presence of the nonlinearity, MT neurons show speed tuning that is close to form-invariant when the moving stimuli comprise square-wave gratings, which contain multiple spatial frequencies moving at the same speed. We conclude that the neural circuitry in and before MT makes no explicit attempt to render MT neurons speed-tuned for sine-wave gratings, which do not occur in natural scenes. Instead, MT neurons derive form-invariant speed tuning in a way that takes advantage of the multiple spatial frequencies that comprise moving objects in natural scenes.

Directional anisotropies reveal a functional segregation of visual motion processing for perception and action

Human exhibits an anisotropy in direction perception: discrimination is superior when motion is around horizontal or vertical rather than diagonal axes. In contrast to the consistent directional anisotropy in perception, we found only small idiosyncratic anisotropies in smooth pursuit eye movements, a motor action requiring accurate discrimination of visual motion direction. Both pursuit and perceptual direction discrimination rely on signals from the middle temporal visual area (MT), yet analysis of multiple measures of MT neuronal responses in the macaque failed to provide evidence of a directional anisotropy. We conclude that MT represents different motion directions uniformly, and subsequent processing creates a directional anisotropy in pathways unique to perception. Our data support the hypothesis that, at least for visual motion, perception and action are guided by inputs from separate sensory streams. The directional anisotropy of perception appears to originate after the two streams have segregated and downstream from area MT.

A new mechanism for neuronal gain control (or how the gain in brains has mainly been explained)

One of the more prosaic but necessary features of almost any information processing system is gain control. All such systems must have some way to adjust the relationship between input, which can vary dramatically depending on changes in the environment, and output, which is almost always required to remain within a limited range of amplitudes. While the volume control on a radio or the brightness control on a computer monitor are not the most exciting or highly touted features, imagine such devices without these forms of gain control. Many an engineer can attest to the large effort required to design automatic gain controls in telephones, cameras, and radio transmitters.

Constraints on the source of short-term motion adaptation in macaque area MT. I. the role of input and intrinsic mechanisms

Neurons in area MT, a motion-sensitive area of extrastriate cortex, respond to a step of target velocity with a transient-sustained firing pattern. The transition from a high initial firing rate to a lower sustained rate occurs over a time course of 20-80 ms and is considered a form of short-term adaptation. The present paper asks whether adaptation is due to input-specific mechanisms such as short-term synaptic depression or if it results from intrinsic cellular mechanisms such as spike-rate adaptation. We assessed the contribution of input-specific mechanisms by using a condition/test paradigm to measure the spatial scale of adaptation. Conditioning and test stimuli were placed within MT receptive fields but were spatially segregated so that the two stimuli would activate different populations of inputs from the primary visual cortex (V1). Conditioning motion at one visual location caused a reduction of the transient firing to subsequent test motion at a second location. The adaptation field, estimated as the region of visual space where conditioning motion caused adaptation, was always larger than the MT receptive field. Use of the same stimulus configuration while recording from direction-selective neurons in V1 failed to demonstrate either adaptation or the transient-sustained response pattern that is the signature of short-term adaptation in MT. We conclude that the shift from transient to sustained firing in MT cells does not result from an input-specific mechanism applied to inputs from V1 because it operates over a wider range of the visual field than is covered by receptive fields of V1 neurons. We used a direct analysis of MT neuron spike trains for many repetitions of the same motion stimulus to assess the contribution to adaptation of intrinsic cellular mechanisms related to spiking. On a trial-by-trial basis, there was no correlation between number of spikes in the transient interval and the interval immediately after the transient period. This is opposite the prediction that there should be a correlation if spikes cause adaptation directly. Further, the transient was suppressed or extinguished, not delayed, in trials in which the neuron emitted zero spikes during the interval that showed a transient in average firing rate. We conclude that the transition from transient to sustained firing in neurons in area MT is caused by mechanisms that are neither input-specific nor controlled by the spiking of the adapting neuron. We propose that the short-term adaptation observed in area MT emerges from the intracortical circuit within MT.

Constraints on the source of short-term motion adaptation in macaque area MT. II. tuning of neural circuit mechanisms

Neurons in area MT, a motion-sensitive area of extrastriate cortex, respond to a step of target velocity with a transient-sustained firing pattern. The transition from a high initial firing rate to a lower sustained rate occurs over a time course of 20-80 ms and is considered a form of short-term adaptation. In the present paper, we compared the tuning of the adaptation to the neuron's tuning to direction and speed. The tuning of adaptation was measured with a condition/test paradigm in which a testing motion of the preferred direction and speed of the neuron under study was preceded by a conditioning motion: the direction and speed of the conditioning motion were varied systematically. The response to the test motion depended strongly on the direction of the conditioning motion. It was suppressed in almost all neurons by conditioning motion in the same direction and could be either suppressed or enhanced by conditioning motion in the opposite direction. Even in neurons that showed suppression for target motion in the nonpreferred direction, the adaptation and response direction tuning were the same. The speed tuning of adaptation was linked much less tightly to the speed tuning of the response of the neuron under study. For just more than 50% of neurons, the preferred speed of adaptation was more than 1 log unit different from the preferred response speed. Many neurons responded best when slow motions were followed by faster motions (acceleration) or vice versa (deceleration), suggesting that MT neurons may encode information about the change of target velocity over time. Finally, adaptation by conditioning motions of different directions, but not different speeds, altered the latency of the response to the test motion. The adaptation of latency recovered with shorter intervals between the conditioning and test motions than did the adaptation of response size, suggesting that latency and amplitude adaptation are mediated by separate mechanisms. Taken together with the companion paper, our data suggest that short-term motion adaptation in MT is a consequence of the neural circuit in MT and is not mediated by either input-specific mechanisms or intrinsic mechanisms related to the spiking of individual neurons. The circuit responsible for adaptation is tuned for both speed and direction and has the same direction tuning as the circuit responsible for the initial response of MT neurons.

Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning

We study a recently proposed "correlation-based," push-pull model of the circuitry of layer 4 of cat visual cortex. This model was previously shown to explain the contrast-invariance of cortical orientation tuning. Here we show that it can simultaneously account for several contrast-dependent (c-d) "nonlinearities" in cortical responses. These include an advance with increasing contrast in the temporal phase of response to a sinusoidally modulated stimulus; a change in shape of the temporal frequency tuning curve, so that higher temporal frequencies may give little or no response at low contrast but reasonable responses at high contrast; and contrast saturation that occurs at lower contrasts in cortex than in the lateral geniculate nucleus (LGN). In the context of the model circuit, these properties arise from a mixture of nonlinear cellular and synaptic mechanisms: short-term synaptic depression, spike-rate adaptation, contrast-induced changes in cellular conductance, and the nonzero spike threshold. The former three mechanisms are sufficient to explain the experimentally observed increase in c-d phase advance in cortex relative to LGN. The c-d changes in temporal frequency tuning arise as a threshold effect: voltage modulations in response to higher-frequency inputs are only slightly above threshold at lower contrast, but become robustly suprathreshold at higher contrast. The other three nonlinear mechanisms also play a crucial role in this result, allowing contrast dependence of temporal frequency tuning to coexist with contrast-invariance of orientation tuning. Contrast saturation, and the observation that responses to stimuli of increasing temporal frequency saturate at increasingly high contrasts, can be induced both by the model's push-pull inhibition and by synaptic depression. Previous proposals explained these nonlinear response properties by assuming contrast-invariant orientation tuning as a starting point, and adding normalization by shunting inhibition derived equally from cells of all preferred orientations. The present proposal simultaneously explains both contrast-invariant orientation tuning and these contrast-dependent nonlinearities and requires only processing that is local in orientation, in agreement with intracellular measurements.

Reconstruction of target speed for the guidance of pursuit eye movements

We studied how object speed is reconstructed from the responses of motion-selective cells for the generation of a behavior that is tightly linked to the speed of visual motion. In theory, the speed of an object could be estimated either from the speed tuning of the active population of motion-selective cells or from the rate of displacement of activation across the cortical map of visual space. We measured the pursuit eye movements evoked by stimuli containing two conflicting motion components: a local component designed to excite motion-selective cells with a particular speed tuning and a displacement component designed to excite cells with a sequence of spatial receptive fields. Pursuit eye movements were driven primarily by the local-motion component and were affected to only a small degree by the rate of target displacement across visual space. Extracellular single-unit recordings using the same stimuli revealed that the responses of cells in the middle temporal visual area (MT) depended primarily on the local-motion component but were influenced by the displacement component to the same degree as were pursuit eye movements. We conclude that the initiation of pursuit is consistent with a reconstruction of target speed based on the speed tuning of the active population of MT cells.

Contrast-invariant orientation tuning in cat visual cortex: thalamocortical input tuning and correlation-based intracortical connectivity

The origin of orientation selectivity in visual cortical responses is a central problem for understanding cerebral cortical circuitry. In cats, many experiments suggest that orientation selectivity arises from the arrangement of lateral geniculate nucleus (LGN) afferents to layer 4 simple cells. However, this explanation is not sufficient to account for the contrast invariance of orientation tuning. To understand contrast invariance, we first characterize the input to cat simple cells generated by the oriented arrangement of LGN afferents. We demonstrate that it has two components: a spatial-phase-specific component (i.e., one that depends on receptive field spatial phase), which is tuned for orientation, and a phase-nonspecific component, which is untuned. Both components grow with contrast. Second, we show that a correlation-based intracortical circuit, in which connectivity between cell pairs is determined by the correlation of their LGN inputs, is sufficient to achieve well tuned, contrast-invariant orientation tuning. This circuit generates both spatially opponent, "antiphase" inhibition ("push-pull"), and spatially matched, "same-phase" excitation. The inhibition, if sufficiently strong, suppresses the untuned input component and sharpens responses to the tuned component at all contrasts. The excitation amplifies tuned responses. This circuit agrees with experimental evidence showing spatial opponency between, and similar orientation tuning of, the excitatory and inhibitory inputs received by a simple cell. Orientation tuning is primarily input driven, accounting for the observed invariance of tuning width after removal of intracortical synaptic input, as well as for the dependence of orientation tuning on stimulus spatial frequency. The model differs from previous push-pull models in requiring dominant rather than balanced inhibition and in predicting that a population of layer 4 inhibitory neurons should respond in a contrast-dependent manner to stimuli of all orientations, although their tuning width may be similar to that of excitatory neurons. The model demonstrates that fundamental response properties of cortical layer 4 can be explained by circuitry expected to develop under correlation-based rules of synaptic plasticity, and shows how such circuitry allows the cortex to distinguish stimulus intensity from stimulus form.