Learning receptive field properties of complex cells in V1

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally.     

Orientation-Cue Invariant Population Responses to Contrast-Modulated and Phase-Reversed Contour Stimuli in Macaque V1 and V2

Visual scenes can be readily decomposed into a variety of oriented components, the processing of which is vital for object segregation and recognition. In primate V1 and V2, most neurons have small spatio-temporal receptive fields responding selectively to oriented luminance contours (first order), while only a subgroup of neurons signal non-luminance defined contours (second order). So how is the orientation of second-order contours represented at the population level in macaque V1 and V2? Here we compared the population responses in macaque V1 and V2 to two types of second-order contour stimuli generated either by modulation of contrast or phase reversal with those to first-order contour stimuli. Using intrinsic signal optical imaging, we found that the orientation of second-order contour stimuli was represented invariantly in the orientation columns of both macaque V1 and V2. A physiologically constrained spatio-temporal energy model of V1 and V2 neuronal populations could reproduce all the recorded population responses. These findings suggest that, at the population level, the primate early visual system processes the orientation of second-order contours initially through a linear spatio-temporal filter mechanism. Our results of population responses to different second-order contour stimuli support the idea that the orientation maps in primate V1 and V2 can be described as a spatial-temporal energy map.     

Dimensional reduction of a V1 ring model with simple and complex cells

In this paper, we extend a framework for constructing low-dimensional dynamical systems models of mammalian primary visual cortex to a cortical network model that incorporates the full nonlinear effects of complex cells. The procedure consists of capturing the essential dynamics in a low-dimensional subspace using empirical methods, then recasting the equations in the reduced vector space. Previously, we considered visual cortical network models consisting of only simple cells with nearly linear responses to external stimuli. Here we show that fully nonlinear effects can be incorporated by examining the dimensional reduction of an idealized ring model of V1 with both simple and complex cells. We found it expedient to divide the subspace into four separate neuronal populations: excitatory simple, excitatory complex, inhibitory simple and inhibitory complex. In order to reproduce the fluctuation-driven dynamics in this reduced space, we incorporated (1) white noises with different intensities into individual neuronal populations, and (2) firing rate estimates to capture the probability of firing due to subthreshold fluctuations. With a more accurate, fitted connectivity, our modified dimensional reduced models can reproduce the firing rates, circular variances and modulation ratios observed in the original ring model.     

Spatial structure of complex cell receptive fields measured with natural images

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

Standing waves and traveling waves distinguish two circuits in visual cortex

The visual cortex represents stimuli through the activity of neuronal populations. We measured the evolution of this activity in space and time by imaging voltage-sensitive dyes in cat area V1. Contrast-reversing stimuli elicit responses that oscillate at twice the stimulus frequency, indicating that signals originate mostly in complex cells. These responses stand clear of the noise, whose amplitude decreases as 1/frequency, and yield high-resolution maps of orientation preference and retinotopy. We first show how these maps are combined to yield the responses to focal, oriented stimuli. We then study the evolution of the oscillating activity in space and time. In the orientation domain, it is a standing wave. In the spatial domain, it is a traveling wave propagating at 0.2-0.5 m/s. These different dynamics indicate a fundamental distinction in the circuits underlying selectivity for position and orientation, two key stimulus attributes.     

Neural Mechanisms of Cortical Motion Computation Based on a Neuromorphic Sensory System

The visual cortex analyzes motion information along hierarchically arranged visual areas that interact through bidirectional interconnections. This work suggests a bio-inspired visual model focusing on the interactions of the cortical areas in which a new mechanism of feedforward and feedback processing are introduced. The model uses a neuromorphic vision sensor (silicon retina) that simulates the spike-generation functionality of the biological retina. Our model takes into account two main model visual areas, namely V1 and MT, with different feature selectivities. The initial motion is estimated in model area V1 using spatiotemporal filters to locally detect the direction of motion. Here, we adapt the filtering scheme originally suggested by Adelson and Bergen to make it consistent with the spike representation of the DVS. The responses of area V1 are weighted and pooled by area MT cells which are selective to different velocities, i.e. direction and speed. Such feature selectivity is here derived from compositions of activities in the spatio-temporal domain and integrating over larger space-time regions (receptive fields). In order to account for the bidirectional coupling of cortical areas we match properties of the feature selectivity in both areas for feedback processing. For such linkage we integrate the responses over different speeds along a particular preferred direction. Normalization of activities is carried out over the spatial as well as the feature domains to balance the activities of individual neurons in model areas V1 and MT. Our model was tested using different stimuli that moved in different directions. The results reveal that the error margin between the estimated motion and synthetic ground truth is decreased in area MT comparing with the initial estimation of area V1. In addition, the modulated V1 cell activations shows an enhancement of the initial motion estimation that is steered by feedback signals from MT cells.     

A motion-dependent distortion of retinotopy in area V4

When one element in an apparent motion sequence differs in color from the others, it is perceived as shifted along the motion trajectory. We examined whether V4 neurons encode the physical or perceived location of this "flashed" element by recording neuronal responses while monkeys viewed these stimuli. The retinotopic locus of V4 activity evoked by the flashed element shifted along the motion trajectory. The magnitude of the shift is consistent with the perceptual shift in humans viewing identical stimuli. This retinotopic distortion depended on the presence of a flashed element but was observed for both color-selective and non-color-selective neurons. The distortion was undiminished when the flashed element terminated the sequence, a condition that reduced the perceptual shift in humans. These findings are consistent with a Bayesian model of localization in which perceived location is derived from position signals optimally integrated across visual areas.     

Computational models of visual neurons specialised in the detection of periodic and aperiodic oriented visual stimuli: bar and grating cells

Computational models of periodic- and aperiodic-pattern selective cells, also called grating and bar cells, respectively, are proposed. Grating cells are found in areas V1 and V2 of the visual cortex of monkeys and respond strongly to bar gratings of a given orientation and periodicity but very weakly or not at all to single bars. This non-linear behaviour, which is quite different from the spatial frequency filtering behaviour exhibited by the other types of orientation-selective neurons such as the simple cells, is incorporated in the proposed computational model by using an AND-type non-linearity to combine the responses of simple cells with symmetric receptive field profiles and opposite polarities. The functional behaviour of bar cells, which are found in the same areas of the visual cortex as grating cells, is less well explored and documented in the literature. In general, these cells respond to single bars and their responses decrease when further bars are added to form a periodic pattern. These properties of bar cells are implemented in a computational model in which the responses of bar cells are computed as thresholded differences of the responses of corresponding complex (or simple) cells and grating cells. Bar and grating cells seem to play complementary roles in resolving the ambiguity with which the responses of simple and complex cells represent oriented visual stimuli, in that bar cells are selective only for form information as present in contours and grating cells only respond to oriented texture information. The proposed model is capable of explaining the results of neurophysiological experiments as well as the psychophysical observation that the perception of texture and the perception of form are complementary processes. Received: 4 June 1996 / Accepted in revised form: 7 October 1996     

Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli

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

Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.     

Spatio-temporal organization of receptive fields of the cat striate cortex

The responses of cortical cells to gratings and bars were compared. The excitatory and inhibitory on-and off-zones of a simple cell are composed of on- and off-subfields of CGL. Any zone is formed by an opponent pair of subfields one of which gives an excitatory effect, the other — inhibitory. Such organization assumes the linear properties of a simple field. The deviations from linearity are due to spatial dis-placements of the subfields, heterogeneity of subfields, or the absence of one subfield in the opponent pair. Subfields may be both phasic and tonic, even in the same RF. Analysis of the most common type of a complex cell with modulated responses against unmodulated background shows that a mask eliminating stimulation of any half of the RF causes (according to the theory of filtres) increasing the bandwidth due to the increase or the appearance of responses to side low and high frequencies. The modulated components of the responses from both halves of the RF are out of phase. Analysis of this fact and the responses to thin bars suggests that a complex field is formed by linear and nonlinear subsystems converging onto output neuron. Other types of complex fields are organized by different combinations of subsystems. Limited in area by masking the RF responds to much higher spatial frequencies than the whole RF. The optimal frequency in two-dimensional spatial frequency characteristics of the RF does not change with orientation. Simple RFs and a part of complex RF calculate the amplitude and the phase of the stimulus, the other part of complex RFs (with unmodulated response) calculate only amplitude. Given all this, the RFs are grating filters of spatial frequency.     

Cortical sensitivity to visual features in natural scenes

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

Bayesian analysis of signaling networks governing embryonic stem cell fate decisions

MOTIVATION: Signaling events that direct mouse embryonic stem (ES) cell self-renewal and differentiation are complex and accordingly difficult to understand in an integrated manner. We address this problem by adapting a Bayesian network learning algorithm to model proteomic signaling data for ES cell fate responses to external cues. Using this model we were able to characterize the signaling pathway influences as quantitative, logic-circuit type interactions. Our experimental dataset includes measurements for 28 signaling protein phosphorylation states across 16 different factorial combinations of cytokine and matrix stimuli as reported previously. RESULTS: The Bayesian network modeling approach allows us to uncover previously reported signaling activities related to mouse ES cell self-renewal, such as the roles of LIF and STAT3 in maintaining undifferentiated ES cell populations. Furthermore, the network predicts novel influences such as between ERK phosphorylation and differentiation, or RAF phosphorylation and differentiated cell proliferation. Visualization of the influences detected by the Bayesian network provides intuition about the underlying physiology of the signaling pathways. We demonstrate that the Bayesian networks can capture the linear, nonlinear and multistate logic interactions that connect extracellular cues, intracellular signals and consequent cell functional responses.     

Shaping up the membrane: diacylglycerol coordinates spatial orientation of signaling

Diacylglycerol signals by binding and activating C1 domain-containing proteins expressed principally in neuronal and immune tissues. This restricted expression profile suggests that diacylglycerol-regulated signals are particularly relevant in cell-cell communication processes in which active endocytosis and exocytosis take place. Not surprisingly, various experimental approaches have demonstrated a crucial role for diacylglycerol effectors and metabolizing enzymes in the control of immune responses, neuron communication and phagocytosis. Current research delineates a scenario in which coordinated decoding of diacylglycerol signals is translated into complex biological responses such as neuronal plasticity, T cell development or cytolytic killing. Diacylglycerol functions reach maximal diversity in these highly specialized systems in which signal intensity directly regulates distinct biological outcomes. This review brings together the most recent studies, emphasizing the contribution of compartmentalized DAG metabolism to orientated signaling events.     

Latency of chromatic information in area V4

In the primate visual system, information about color is known to be carried in separate divisions of the retino-geniculo-cortical pathway. From the retina, responses of photoreceptors to short (S), medium (M), and long (L) wavelengths of light are processed in two different opponent pathways. Signals in the S-opponent pathway, or blue/yellow channel, have been found to lag behind signals in the L/M-opponent pathway, or red/green channel in primary visual area V1, and psychophysical studies have suggested similar perceptual delays. However, more recent psychophysical studies have found that perceptual differences are negligible with the proper controls, suggesting that information between the two channels is integrated at some stage of processing beyond V1. To study the timing of color signals further downstream in visual cortex, we examined the responses of neurons in area V4 to colored stimuli varying along the two cardinal axes of the equiluminant opponent color space. We used information theory to measure the mutual information between the stimuli presented and the neural responses in short time windows in order to estimate the latency of color information in area V4. We found that on average, despite the latency difference in V1, information about S-opponent signals arrives in V4 at the same time as information about L/M-opponent signals. This work indicates a convergence of signal timing among chromatic channels within extrastriate cortex.     

Motion detection, noise reduction, texture suppression, and contour enhancement by spatiotemporal Gabor filters with surround inhibition

We study the orientation and speed tuning properties of spatiotemporal three-dimensional (3D) Gabor and motion energy filters as models of time-dependent receptive fields of simple and complex cells in the primary visual cortex (V1). We augment the motion energy operator with surround suppression to model the inhibitory effect of stimuli outside the classical receptive field. We show that spatiotemporal integration and surround suppression lead to substantial noise reduction. We propose an effective and straightforward motion detection computation that uses the population code of a set of motion energy filters tuned to different velocities. We also show that surround inhibition leads to suppression of texture and thus improves the visibility of object contours and facilitates figure/ground segregation and the detection and recognition of objects.     

Computer modeling of mechanisms of the information processing in the olfactory bulb. II. Mechanisms of identification and short-term storage in the olfactory bulb: results of the computer experimentation

The results of experimentation with the computer model of the olfactory bulb are presented. The architecture and scenario of the work of the model were described previously. The dynamic character of the identification process and the mechanism of memorizing short-term of smell stimuli are described. During the identification, a self-adjustment of the olfactory bulb to incoming signals occurs. The self-modification of mitral and tufted cell synapses enhances responses of the cells; upon subsequent presentation of the stimulus, the olfactory bulb responds with a higher activity. The modeling confirmed the validity of the assumption that the functions of mitral and tufted cells are to identify the components of a complex smell and the image of the smell as the whole.     

Predictive Feedback Can Account for Biphasic Responses in the Lateral Geniculate Nucleus

Biphasic neural response properties, where the optimal stimulus for driving a neural response changes from one stimulus pattern to the opposite stimulus pattern over short periods of time, have been described in several visual areas, including lateral geniculate nucleus (LGN), primary visual cortex (V1), and middle temporal area (MT). We describe a hierarchical model of predictive coding and simulations that capture these temporal variations in neuronal response properties. We focus on the LGN-V1 circuit and find that after training on natural images the model exhibits the brain's LGN-V1 connectivity structure, in which the structure of V1 receptive fields is linked to the spatial alignment and properties of center-surround cells in the LGN. In addition, the spatio-temporal response profile of LGN model neurons is biphasic in structure, resembling the biphasic response structure of neurons in cat LGN. Moreover, the model displays a specific pattern of influence of feedback, where LGN receptive fields that are aligned over a simple cell receptive field zone of the same polarity decrease their responses while neurons of opposite polarity increase their responses with feedback. This phase-reversed pattern of influence was recently observed in neurophysiology. These results corroborate the idea that predictive feedback is a general coding strategy in the brain.     

Spike Inference from Calcium Imaging Using Sequential Monte Carlo Methods

As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies, the signals of interest—spike trains and/or time varying intracellular calcium concentrations—are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing sequential Monte Carlo methods (particle filters) based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing error bars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence (e.g., refractoriness) of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate temporal superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation maximization with only a very limited amount of data (e.g., ∼5-10 s or 5-40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.