Computational modeling of orientation tuning dynamics in monkey primary visual cortex

Stimulus Feature-Specific Information Flow Along the Columnar Cortical Microcircuit Revealed by Multivariate Laminar Spiking Analysis

Most of the mammalian neocortex is comprised of a highly similar anatomical structure, consisting of a granular cell layer between superficial and deep layers. Even so, different cortical areas process different information. Taken together, this suggests that cortex features a canonical functional microcircuit that supports region-specific information processing. For example, the primate primary visual cortex (V1) combines the two eyes' signals, extracts stimulus orientation, and integrates contextual information such as visual stimulation history. These processes co-occur during the same laminar stimulation sequence that is triggered by the onset of visual stimuli. Yet, we still know little regarding the laminar processing differences that are specific to each of these types of stimulus information. Univariate analysis techniques have provided great insight by examining one electrode at a time or by studying average responses across multiple electrodes. Here we focus on multivariate statistics to examine response patterns across electrodes instead. Specifically, we applied multivariate pattern analysis (MVPA) to linear multielectrode array recordings of laminar spiking responses to decode information regarding the eye-of-origin, stimulus orientation, and stimulus repetition. MVPA differs from conventional univariate approaches in that it examines patterns of neural activity across simultaneously recorded electrode sites. We were curious whether this added dimensionality could reveal neural processes on the population level that are challenging to detect when measuring brain activity without the context of neighboring recording sites. We found that eye-of-origin information was decodable for the entire duration of stimulus presentation, but diminished in the deepest layers of V1. Conversely, orientation information was transient and equally pronounced along all layers. More importantly, using time-resolved MVPA, we were able to evaluate laminar response properties beyond those yielded by univariate analyses. Specifically, we performed a time generalization analysis by training a classifier at one point of the neural response and testing its performance throughout the remaining period of stimulation. Using this technique, we demonstrate repeating (reverberating) patterns of neural activity that have not previously been observed using standard univariate approaches.

A cortical locus for anisotropic overlay suppression of stimuli presented at fixation

Human contrast sensitivity for narrowband Gabor targets is suppressed when superimposed on narrowband masks of the same spatial frequency and orientation (referred to as overlay suppression), with suppression being broadly tuned to orientation and spatial frequency. Numerous behavioral and neurophysiological experiments have suggested that overlay suppression originates from the initial lateral geniculate nucleus (LGN) inputs to V1, which is consistent with the broad tuning typically reported for overlay suppression. However, recent reports have shown narrowly tuned anisotropic overlay suppression when narrowband targets are masked by broadband noise. Consequently, researchers have argued for an additional form of overlay suppression that involves cortical contrast gain control processes. The current study sought to further explore this notion behaviorally using narrowband and broadband masks, along with a computational neural simulation of the hypothesized underlying gain control processes in cortex. Additionally, we employed transcranial direct current stimulation (tDCS) in order to test whether cortical processes are involved in driving narrowly tuned anisotropic suppression. The behavioral results yielded anisotropic overlay suppression for both broadband and narrowband masks and could be replicated with our computational neural simulation of anisotropic gain control. Further, the anisotropic form of overlay suppression could be directly modulated by tDCS, which would not be expected if the suppression was primarily subcortical in origin. Altogether, the results of the current study provide further evidence in support of an additional overlay suppression process that originates in cortex and show that this form of suppression is also observable with narrowband masks.

A review of the mechanisms by which attentional feedback shapes visual selectivity

The glut of information available for the brain to process at any given moment necessitates an efficient attentional system that can 'pick and choose' what information receives prioritized processing. A growing body of work, spanning numerous methodologies and species, reveals that one powerful way in which attending to an item separates the wheat from the chaff is by altering a basic response property in the brain: neuronal selectivity. Selectivity is a cornerstone response property, largely dictating our ability to represent and interact with the environment. Although it is likely that selectivity is altered throughout many brain areas, here we focus on how directing attention to an item affects selectivity in the visual system, where this response property is generally more well characterized. First, we review the neural architecture supporting selectivity, and then discuss the various changes that could occur in selectivity for an attended item. In a survey of the literature, spanning neurophysiology, neuroimaging and psychophysics, we reveal that there is general convergence regarding the manner with which selectivity is shaped by attentional feedback. In a nutshell, the literature suggests that the type of changes in selectivity that manifest appears to depend on the type of attention being deployed: whereas directing spatial attention towards an item only alters spatial selectivity, directing feature-based attention can alter the selectivity of attended features.

Gamma frequency feedback inhibition accounts for key aspects of orientation selectivity in V1

There is now strong evidence that gamma frequency oscillations occur during the engagement of cortical regions. These oscillations involve gamma frequency feedback inhibition. Thus, understanding the properties of this form of inhibition is critical to understanding how excitation and inhibition interact to determine which cells fire and, more generally, how cortex performs computations. In previous work, we argued that gamma frequency inhibition performs a type of winner-take-all computation that obeys simple rules: 1) cells fire if their excitation is within E% of the cell with maximum excitation; 2) E%max is determined by the delay of feedback inhibition and the membrane time constant. This framework was previously applied to the best-studied cortical computation, orientation selectivity of cells in V1. Measurements show that orientation tuning is insensitive to illumination contrast. We showed that this finding can be simply explained by the E%max model. Recently, a new property of orientation selectivity has been discovered: orientation tuning varies with the phase of the gamma oscillation. Here, we show that this too can be simply explained by the E%max model. These successes suggest that simple rules underlie the selection of which cells fire in cortical networks.

Orientation enhancement in early visual processing can explain time course of brightness contrast and White's illusion

Dynamics of orientation tuning in V1 indicates that computational model of V1 should not only comprise of bank of static spatially oriented filters but also include the contribution for dynamical response facilitation or suppression along orientation. Time evolution of orientation response in V1 can emerge due to time- dependent excitation and lateral inhibition in the orientation domain. Lateral inhibition in the orientation domain suggests that Ernst Mach's proposition can be applied for the enhancement of initial orientation distribution that is generated due to interaction of visual stimulus with spatially oriented filters and subcortical temporal filter. Oriented spatial filtering that appears much early (<70 ms) in the sequence of visual information processing can account for many of the brightness illusions observed at steady state. It is therefore expected that time evolution of orientation response might be reflecting in the brightness percept over time. Our numerical study suggests that only spatio-temporal filtering at early phase can explain experimentally observed temporal dynamics of brightness contrast illusion. But, enhancement of orientation response at early phase of visual processing is the key mechanism that can guide visual system to predict the brightness by "Max-rule" or "Winner Takes All" (WTA) estimation and thus producing White's illusions at any exposure.

Theoretical analysis of reverse-time correlation for idealized orientation tuning dynamics

A theoretical analysis is presented of a reverse-time correlation method used in experimentally investigating orientation tuning dynamics of neurons in the primary visual cortex. An exact mathematical characterization of the method is developed, and its connection with the Volterra-Wiener nonlinear systems theory is described. Various mathematical consequences and possible physiological implications of this analysis are illustrated using exactly solvable idealized models of orientation tuning.

Neural bases of stereopsis across visual field of the alert macaque monkey

Left and right retinal images of an object seen by the 2 eyes can occupy slightly disparate horizontal and/or vertical locations. The role of horizontal disparity (HD) in stereoscopic vision is well established, but the functional contribution of vertical disparity (VD) remains unclear. Various psychophysical studies have shown that HD and VD are used differently by the visual system depending on their location in the visual field, whether near the center of gaze or more peripheral. We show this horizontal/vertical distinction at the cellular level in monkey primary visual cortex (area V1). The range of VD encoding is reduced in central but not in the peripheral representation of the visual field. Moreover, neurons respond selectively to particular combinations of both types of disparities depending on the coded orientation as predicted by the disparity energy model. The preferred orientations of neurons near the fovea present a vertical bias that is well suited for stereopsis based on HD selectivity alone. In the periphery, instead, preferred orientations are radially biased, which allows a peripheral detector to convey the same depth signal based on either HD or VD. Such an organization has functional implications in both the perceptual and oculomotor domains.

Dynamic shape synthesis in posterior inferotemporal cortex

How does the brain synthesize low-level neural signals for simple shape parts into coherent representations of complete objects? Here, we present evidence for a dynamic process of object part integration in macaque posterior inferotemporal cortex (IT). Immediately after stimulus onset, neural responses carried information about individual object parts (simple contour fragments) only. Subsequently, information about specific multipart configurations emerged, building gradually over the course of approximately 60 ms, producing a sparser and more explicit representation of object shape. We show that this gradual transformation can be explained by a recurrent network process that effectively compares parts signals across neurons to generate inferences about multipart shape configurations.

Encoding and decoding target locations with waves in the turtle visual cortex

Visual stimuli elicit waves of activity that propagate across the visual cortex of turtles. An earlier study showed that these waves encode information about the positions of stimuli in visual space. This paper addresses the question of how this information can be decoded from the waves. Windowing techniques were used to temporally localize information contained in the wave. Sliding encoding windows were used to represent waves of activity as low dimensional temporal strands in an appropriate space. Expanding detection window (EDW) or sliding detection window (SDW) techniques were combined with statistical hypothesis testing to discriminate input stimuli. Detection based on an EDW was more reliable than detection based on a SDW. Detection performance improved at a very early stage of the cortical response as the length of the detection window is increased. The property of intrinsic noise was explicitly considered. Assuming that the noise is colored provided a more reliable estimate than did the assumption of a white noise in the cortical output.

Bottom-up and top-down dynamics in visual cortex

A key emergent property of the primary visual cortex (V1) is the orientation selectivity of its neurons. Recent experiments demonstrate remarkable bottom-up and top-down plasticity in orientation networks of the adult cortex. The basis for such dynamics is the mechanism by which orientation tuning is created and maintained, by integration of thalamocortical and intracortical inputs. Intracellular measurements of excitatory and inhibitory synaptic conductances reveal that excitation and inhibition balance each other at all locations in the cortex. This balance is particularly critical at pinwheel centers of the orientation map, where neurons receive intracortical input from a wide diversity of local orientations. The orientation tuning of neurons in adult V1 changes systematically after short-term exposure to one stimulus orientation. Such reversible physiological shifts in tuning parallel the orientation tilt aftereffect observed psychophysically. Neurons at or near pinwheel centers show pronounced changes in orientation preference after adaptation with an oriented stimulus, while neurons in iso-orientation domains show minimal changes. Neurons in V1 of alert, behaving monkeys also exhibit short-term orientation plasticity after very brief adaptation with an oriented stimulus, on the time scale of visual fixation. Adaptation with stimuli that are orthogonal to a neuron's preferred orientation does not alter the preferred orientation but sharpens orientation tuning. Thus, successive fixation on dissimilar image patches, as happens during natural vision, combined with mechanisms of rapid cortical plasticity, actually improves orientation discrimination. Finally, natural vision involves judgements about where to look next, based on an internal model of the visual world. Experiments in behaving monkeys in which information about future stimulus locations can be acquired in one set of trials but not in another demonstrate that V1 neurons signal the acquisition of internal representations. Such Bayesian updating of responses based on statistical learning is fundamental for higher level vision, for deriving inferences about the structure of the visual world, and for the regulation of eye movements.

An embedded network approach for scale-up of fluctuation-driven systems with preservation of spike information

To address computational "scale-up" issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information and, thus, cannot be used to investigate, e.g., cortical mechanisms that are encoded through detailed spike-timing statistics. To retain high-order statistical information of spikes, we develop a hybrid theoretical framework that embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We use a newly developed kinetic theory for the description of the coarse-grained background, in combination with a Poisson spike reconstruction procedure to ensure that our method applies to the fluctuation-driven regime as well as to the mean-driven regime. This embedded-network approach is verified to be dynamically accurate and numerically efficient. As an example, we use this embedded representation to construct "reverse-time correlations" as spiked-triggered averages in a ring model of orientation-tuning dynamics.

Neural Mechanisms for the Robust Representation of Junctions

Junctions provide important cues in various perceptual tasks, such as the determination of occlusion relationships for figure-ground separation, transparency perception, and object recognition, among others. In computer vision, junctions are used in a number of tasks, like point matching for image tracking or correspondence analysis. We propose a biologically motivated approach to junction representation in which junctions are implicitly characterized by high activity for multiple orientations within a cortical hypercolumn. A local measure of circular variance is suggested to extract junction points from this distributed representation. Initial orientation measurements are often fragmented and noisy. A coherent contour representation can be generated by a model of V1 utilizing mechanisms of collinear long-range integration and recurrent interaction. In the model, local oriented contrast estimates that are consistent within a more global context are enhanced while inconsistent activities are suppressed. In a series of computational experiments, we compare junction detection based on the new recurrent model with a feedforward model of complex cells. We show that localization accuracy and positive correctness in the detection of generic junction configurations such as L- and T-junctions is improved by the recurrent long-range interaction. Further, receiver operating characteristics analysis is used to evaluate the detection performance on both synthetic and camera images, showing the superior performance of the new approach. Overall, we propose that nonlocal interactions implemented by known mechanisms within V1 play an important role in detecting higher-order features such as corners and junctions.

Synchronization Phenomena in Pulse-Coupled Networks Driven by Spike-Train Inputs

We present a pulse-coupled network (PCN) of spiking oscillators (SOCs) which can be implemented as a simple electrical circuit. The SOC has a periodic reset level that can realize rich dynamics represented by chaotic spike-trains. Applying a spike-train input, the PCN can exhibit the following interesting phenomena. 1) Each SOC synchronizes with a part of the input without overlapping, i.e., the input is decomposed. 2) Some SOCs synchronize with a part of the input with overlapping, i.e., the input is decomposed and the SOCs are clustered. The PCN has multiple synchronization phenomena and exhibits one of them depending on the initial state. We clarify the numbers of the synchronization phenomena and the parameter regions in which these phenomena can be observed. Also stability of the synchronization phenomena is clarified. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

Visual cortex neurons of monkeys and cats: temporal dynamics of the spatial frequency response function

We measured the responses of striate cortex neurons as a function of spatial frequency on a fine time scale, over the course of an interval that is comparable to the duration of a single fixation (200 ms). Stationary gratings were flashed on for 200 ms and then off for 300 ms; the responses were analyzed at sequential 1-ms intervals. We found that 1) the preferred spatial frequency shifts through time from low frequencies to high frequencies, 2) the latency of the response increases as a function of spatial frequency, and 3) the poststimulus time histograms (PSTHs) are relatively shape-invariant across spatial frequency. The dynamic shifts in preferred spatial frequency appear to be a simple consequence of the latency shifts and the transient nature of the PSTH. The effects of these dynamic shifts on the coding of spatial frequency information are examined within the context of several different temporal integration strategies, and pattern-detection performance is determined as a function of the interval of integration, following response onset. The findings are considered within the context of related investigations as well as a number of functional issues: motion selectivity in depth, "coarse-to-fine" processing, direction selectivity, latency as a code for stimulus attributes, and behavioral response latency. Finally, we demonstrate that the results are qualitatively consistent with a simple feedforward model, similar to the one originally proposed in 1962 by Hubel and Wiesel, that incorporates measured differences in the response latencies and the receptive field sizes of different lateral geniculate nucleus inputs.

Separation of spatio-temporal receptive fields into sums of gaussian components

Visual cortical simple cells have been experimentally shown to reveal non-trivial spatio-temporal orientation tuning functions comprising different phases of specifically tuned enhanced and suppressed activity. A recently developed analytical method based on nonlinear neural field models suggests that such space-time responses should be approximately separable into a sum of temporally amplitude modulated Gaussian spatial components. In the present work, we investigate this possibility by means of numerical fits of sums of Gaussians to response functions observed in experiments and computer simulations. Because the theory relates each single component to a particular connectivity kernel between the underlying cell classes shaping the response, the relative contribution of feedforward and cortex-intrinsical excitatory and inhibitory feedback mechanisms to single cell tuning can be approached and quantified in experimental data.

Orientation tuning and synchronization in the hypercolumn model

The orientation selectivity in the firing rate of neurons is one of the most well-known properties of neurons in the primary visual cortex. To understand the dynamical mechanism of the orientation tuning, we introduce a biologically plausible network for a hypercolumn and investigate dynamical responses of its columnar activities. Numerical simulations show that the spike activities between excitatory cells in the same column exhibit strong synchronization and sharp orientation selectivity. The tuning curves for the synchronized activities also show orientation selectivity similar to those for the firing rate. The comparison between the two tuning curves for the firing rate and the synchronized activities suggests that the orientation selectivity is strongly correlated with the synchronized activities. We find from the analysis of columnar activities that the orientation selectivity depends strongly upon the inhibitory coupling strength and the synchronization upon the excitatory coupling strength. In particular, we find that at appropriate coupling parameters both sharp orientation selectivity and maximal synchronization can be achieved. This suggests the importance of the balance between the excitatory coupling and the inhibitory coupling in the primary visual cortex for visual information processing.

Spatiotemporal tuning of motor cortical neurons for hand position and velocity

A pursuit-tracking task (PTT) and multielectrode recordings were used to investigate the spatiotemporal encoding of hand position and velocity in primate primary motor cortex (MI). Continuous tracking of a randomly moving visual stimulus provided a broad sample of velocity and position space, reduced statistical dependencies between kinematic variables, and minimized the nonstationarities that are found in typical "step-tracking" tasks. These statistical features permitted the application of signal-processing and information-theoretic tools for the analysis of neural encoding. The multielectrode method allowed for the comparison of tuning functions among simultaneously recorded cells. During tracking, MI neurons showed heterogeneity of position and velocity coding, with markedly different temporal dynamics for each. Velocity-tuned neurons were approximately sinusoidally tuned for direction, with linear speed scaling; other cells showed sinusoidal tuning for position, with linear scaling by distance. Velocity encoding led behavior by about 100 ms for most cells, whereas position tuning was more broadly distributed, with leads and lags suggestive of both feedforward and feedback coding. Individual cells encoded velocity and position weakly, with comparable amounts of information about each. Linear regression methods confirmed that random, 2-D hand trajectories can be reconstructed from the firing of small ensembles of randomly selected neurons (3-19 cells) within the MI arm area. These findings demonstrate that MI carries information about evolving hand trajectory during visually guided pursuit tracking, including information about arm position both during and after its specification. However, the reconstruction methods used here capture only the low-frequency components of movement during the PTT. Hand motion signals appear to be represented as a distributed code in which diverse information about position and velocity is available within small regions of MI.

Dynamics of orientation tuning in macaque V1: the role of global and tuned suppression

The temporal development of neural selectivity to physical attributes of a visual stimulus, such as its orientation and spatial frequency, can provide important clues about mechanisms of cortical tuning. We measured the dynamics of orientation tuning in macaque primary visual cortex (V1) and found several dynamical features in the data: changes in global enhancement and suppression, narrowing of orientation bandwidth, small but significant shifts in preferred orientation, and "Mexican-hat" tuning curves. The dynamics data were analyzed with a model that sums two fixed, tuned components (enhancement and suppression) and one global (untuned) component. The analysis suggests that there is early global enhancement followed by global and tuned suppression. Tuned suppression accounts for the dynamical reduction of orientation bandwidth and for the generation of Mexican-hat tuning profiles. Our findings imply that global and tuned suppression are important factors that determine the selectivity and dynamics of V1 responses to orientation.

Role of afferent activity in the development of cortical specification

The surgical cross-modal rewiring paradigm is an experimental method for examining the physiological and anatomical consequences of exposing developing cortical subregions to specific types of patterned sensory inputs. Data from these experiments provide strong inferences about the role of extrinsic (subcortical) cortical inputs in shaping the local cortical networks that organize and process sensory information. Behavioral results from this work also suggest that such activity (and activity in general) is a profound organizer of cerebral connectivity. We discuss one future direction of these studies: the implication that extrinsic inputs regulate developmental genes that are responsible for refining the connectivity within local circuits, and a strategy to discover and characterize such genes.

Dynamic approximation of spatiotemporal receptive fields in nonlinear neural field models

This article presents an approximation method to reduce the spatiotemporal behavior of localized activation peaks (also called "bumps") in non-linear neural field equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simplified analysis of steady-state receptive fields and their stability, as well as spatiotemporal point spread functions and dynamic tuning properties. A lowest-order approximation for peak amplitudes alone shows that much of the well-studied behavior of small neural systems (e.g., the Wilson-Cowan oscillator) should carry over to localized solutions in neural fields. Full spatiotemporal response profiles can further be reconstructed from this low-dimensional approximation. The method is applied to two standard neural field models: a one-layer model with difference-of-gaussians connectivity kernel and a two-layer excitatory-inhibitory network. Similar models have been previously employed in numerical studies addressing orientation tuning of cortical simple cells. Explicit formulas for tuning properties, instabilities, and oscillation frequencies are given, and exemplary spatiotemporal response functions, reconstructed from the low-dimensional approximation, are compared with full network simulations.

Dynamics of spatial frequency tuning in macaque V1

Spatial frequency tuning in the lateral geniculate nucleus of the thalamus (LGN) and primary visual cortex (V1) differ substantially. LGN responses are largely low-pass in spatial frequency, whereas the majority of V1 neurons have bandpass characteristics. To study this transformation in spatial selectivity, we measured the dynamics of spatial frequency tuning using a reverse correlation technique. We find that a large proportion of V1 cells show inseparable responses in spatial frequency and time. In several cases, tuning becomes more selective over the course of the response, and the preferred spatial frequency shifts from low to higher frequencies. Many responses also show suppression at low spatial frequencies, which correlates with the increases in response selectivity and the shifts of preferred spatial frequency. These results indicate that suppression plays an important role in the generation of bandpass selectivity in V1.

Coarse-grained reduction and analysis of a network model of cortical response: I. Drifting grating stimuli

We present a reduction of a large-scale network model of visual cortex developed by McLaughlin, Shapley, Shelley, and Wielaard. The reduction is from many integrate-and-fire neurons to a spatially coarse-grained system for firing rates of neuronal subpopulations. It accounts explicitly for spatially varying architecture, ordered cortical maps (such as orientation preference) that vary regularly across the cortical layer, and disordered cortical maps (such as spatial phase preference or stochastic input conductances) that may vary widely from cortical neuron to cortical neuron. The result of the reduction is a set of nonlinear spatiotemporal integral equations for "phase-averaged" firing rates of neuronal subpopulations across the model cortex, derived asymptotically from the full model without the addition of any extra phenomological constants. This reduced system is used to study the response of the model to drifting grating stimuli-where it is shown to be useful for numerical investigations that reproduce, at far less computational cost, the salient features of the point-neuron network and for analytical investigations that unveil cortical mechanisms behind the responses observed in the simulations of the large-scale computational model. For example, the reduced equations clearly show (1) phase averaging as the source of the time-invariance of cortico-cortical conductances, (2) the mechanisms in the model for higher firing rates and better orientation selectivity of simple cells which are near pinwheel centers, (3) the effects of the length-scales of cortico-cortical coupling, and (4) the role of noise in improving the contrast invariance of orientation selectivity.

An amplitude equation approach to contextual effects in visual cortex

A mathematical theory of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the anisotropic nature of long-range lateral connections. Each hypercolumn is modeled as a ring of interacting excitatory and inhibitory neural populations with orientation preferences over the range 0 to 180 degrees. Analytical methods from bifurcation theory are used to derive nonlinear equations for the amplitude and phase of the population tuning curves in which the effective lateral interactions are linear in the amplitudes. These amplitude equations describe how mutual interactions between hypercolumns via lateral connections modify the response of each hypercolumn to modulated inputs from the lateral geniculate nucleus; such interactions form the basis of contextual effects. The coupled ring model is shown to reproduce a number of orientation-dependent and contrast-dependent features observed in center-surround experiments. A major prediction of the model is that the anisotropy in lateral connections results in a nonuniform modulatory effect of the surround that is correlated with the orientation of the center.

Suppression of neural responses to nonoptimal stimuli correlates with tuning selectivity in macaque V1

Neural responses in primary visual cortex (area V1) are selective for the orientation and spatial frequency of luminance-modulated sinusoidal gratings. Selectivity could arise from enhancement of the cell's response by preferred stimuli, suppression by nonoptimal stimuli, or both. Here, we report that the majority of V1 neurons do not only elevate their activity in response to preferred stimuli, but their firing rates are also suppressed by nonoptimal stimuli. The magnitude of suppression is similar to that of enhancement. There is a tendency for net response suppression to peak at orientations near orthogonal to the optimal for the cell, but cases where suppression peaks at oblique orientations are observed as well. Interestingly, selectivity and suppression correlate in V1: orientation and spatial frequency selectivity are higher for neurons that are suppressed by nonoptimal stimuli than for cells that are not. This finding is consistent with the idea that suppression plays an important role in the generation of sharp cortical selectivity. We show that nonlinear suppression is required to account for the data. However, the precise structure of the neural circuitry generating the suppressive signal remains unresolved. Our results are consistent with both feedback and (nonlinear) feed-forward inhibition.

Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks

To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of Delta(t) = 0.5 x 10(-3) seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10(-5) seconds or 10(-9) seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

A neuronal network model of macaque primary visual cortex (V1): orientation selectivity and dynamics in the input layer 4Calpha

In this paper, we offer an explanation for how selectivity for orientation could be produced by a model with circuitry that is based on the anatomy of V1 cortex. It is a network model of layer 4Calpha in macaque primary visual cortex (area V1). The model consists of a large number of integrate-and-fire conductance-based point neurons, both excitatory and inhibitory, which represent dynamics in a small patch of 4Calpha-1 mm(2) in lateral area-which contains four orientation hypercolumns. The physiological properties and coupling architectures of the model are derived from experimental data for layer 4Calpha of macaque. Convergent feed-forward input from many neurons of the lateral geniculate nucleus sets up an orientation preference, in a pinwheel pattern with an orientation preference singularity in the center of the pattern. Recurrent cortical connections cause the network to sharpen its selectivity. The pattern of local lateral connections is taken as isotropic, with the spatial range of monosynaptic excitation exceeding that of inhibition. The model (i) obtains sharpening, diversity in selectivity, and dynamics of orientation selectivity, each in qualitative agreement with experiment; and (ii) predicts more sharpening near orientation preference singularities.