Development of spatiotemporal receptive fields of simple cells: I. Model formulation

A model for the development of spatiotemporal receptive fields of simple cells in the visual cortex is proposed. The model is based on the 1990 hypothesis of Saul and Humphrey that the convergence of four types of input onto a cortical cell, viz. non-lagged ON and OFF inputs and lagged ON and OFF inputs, underlies the spatial and temporal structure of the receptive fields. It therefore explains both orientation and direction selectivity of simple cells. The response properties of the four types of input are described by the product of linear spatial and temporal response functions. Extending the 1994 model of one of the authors (K.D. Miller), we describe the development of spatiotemporal receptive fields as a Hebbian learning process taking into account not only spatial but also temporal correlations between the different inputs. We derive the correlation functions that drive the development both for the period before and after eye-opening and demonstrate how the joint development of orientation and direction selectivity can be understood in the framework of correlation-based learning. Our investigation is split into two parts that are presented in two papers. In the first, the model for the response properties and for the development of direction-selective receptive fields is presented. In the second paper we present simulation results that are compared with experimental data, and also provide a first analysis of our model. Received: 18 June 1997 / Accepted: 16 September 1997     

A ring model for spatiotemporal properties of simple cells in the visual cortex

 A neural model is proposed for the spatiotemporal properties of simple cells in the visual cortex. In the model, several cortical cells are arranged on a ring, with mutual excitatory or inhibitory connections. The cells also receive excitatory inputs either from lagged and nonlagged cells of the lateral geniculate nucleus in one setting or from nonlagged cells in the other. Computer simulation shows that the cortical cells have spatiotemporally inseparable receptive fields in the former setting and separable fields in the latter; spatial profiles at a given time in the spatiotemporal fields are described with a Gabor function whose phase parameter varies regularly from 0 to 2π with rotation along the ring; the inseparable cells have directional selectivity as observed physiologically. Received: 13 November 1995 / Accepted in revised form: 1 July 1997     

Responses of recurrent nets of asymmetric ON and OFF cells

A neural field model of ON and OFF cells with all-to-all inhibitory feedback is investigated. External spatiotemporal stimuli drive the ON and OFF cells with, respectively, direct and inverted polarity. The dynamic differences between networks built of ON and OFF cells (“ON/OFF”) and those having only ON cells (“ON/ON”) are described for the general case where ON and OFF cells can have different spontaneous firing rates; this asymmetric case is generic. Neural responses to nonhomogeneous static and time-periodic inputs are analyzed in regimes close to and away from self-oscillation. Static stimuli can cause oscillatory behavior for certain asymmetry levels. Time-periodic stimuli expose dynamical differences between ON/OFF and ON/ON nets. Outside the stimulated region, we show that ON/OFF nets exhibit frequency doubling, while ON/ON nets cannot. On the other hand, ON/ON networks show antiphase responses between stimulated and unstimulated regions, an effect that does not rely on specific receptive field circuitry. An analysis of the resonance properties of both net types reveals that ON/OFF nets exhibit larger response amplitude. Numerical simulations of the neural field models agree with theoretical predictions for localized static and time-periodic forcing. This is also the case for simulations of a network of noisy integrate-and-fire neurons. We finally discuss the application of the model to the electrosensory system and to frequency-doubling effects in retina.     

Voltage-clamp measurement of visually-evoked conductances with whole-cell patch recordings in primary visual cortex

Whole cell patch recordings have been realized in the primary visual cortex of the anesthetized and paralyzed cat, in order to better characterize input resistance and time constant of visual cortical cells in vivo. Measurements of conductance changes evoked by visual stimulation were derived from voltage clamp recordings achieved in continuous mode at two or more different subtreshold holding potentials. They show that the magnitude of the conductance increase can reach up to 300% of the mean conductance at rest. The observation of similar changes for the preferred and antagonist responses, when flashing ON and OFF, a test stimulus in pure ON and OFF subfields supports the hypothesis of a role for shunting inhibition in the spatial organization of simple receptive fields.     

Organization of receptive fields of motion-senstitive neurons in the cat pulvinar

The distribution of 70 visually sensitive neurons in the cat pulvinar sensitive to motion in the receptive fields was studied. The experimental results showed that components with directional characteristics are present in the structure of these fields of both direction-selective and unselective neurons. In the receptive fields of direction-selective neurons the directional elements of the substructure have identical preferred directions, which coincide with the preferred directions of response to stimulus movement over the entire receptive field. The organization of receptive fields of direction-selective neurons of the visual association structure thus does not differ significantly from that of analogous fields of visual projection neurons. Directional elements of the receptive fields of direction-unselective neurons were found to have different preferred directions, thereby providing a basis for organization of the nondirectional response of the neuron to a stimulus moving across the entire receptive field.L. A. Orbeli Institute of Physiology, Academy of Sciences of the Armenian SSR, Erevan. Translated from Neirofiziologiya, Vol. 14, No. 4, pp. 339–346, July–August, 1982.     

Spontaneously emerging direction selectivity maps in visual cortex through STDP

It is still an open question as to whether, and how, direction-selective neuronal responses in primary visual cortex are generated by feedforward thalamocortical or recurrent intracortical connections, or a combination of both. Here we present an investigation that concentrates on and, only for the sake of simplicity, restricts itself to intracortical circuits, in particular, with respect to the developmental aspects of direction selectivity through spike-timing-dependent synaptic plasticity. We show that directional responses can emerge in a recurrent network model of visual cortex with spiking neurons that integrate inputs mainly from a particular direction, thus giving rise to an asymmetrically shaped receptive field. A moving stimulus that enters the receptive field from this (preferred) direction will activate a neuron most strongly because of the increased number and/or strength of inputs from this direction and since delayed isotropic inhibition will neither overlap with, nor cancel excitation, as would be the case for other stimulus directions. It is demonstrated how direction-selective responses result from spatial asymmetries in the distribution of synaptic contacts or weights of inputs delivered to a neuron by slowly conducting intracortical axonal delay lines. By means of spike-timing-dependent synaptic plasticity with an asymmetric learning window this kind of coupling asymmetry develops naturally in a recurrent network of stochastically spiking neurons in a scenario where the neurons are activated by unidirectionally moving bar stimuli and even when only intrinsic spontaneous activity drives the learning process. We also present simulation results to show the ability of this model to produce direction preference maps similar to experimental findings     

The role of cortical feedback in the generation of the temporal receptive field responses of lateral geniculate nucleus neurons: a computational modelling study

The influence of cortical feedback on thalamic visual responses has been a source of much discussion in recent years. In this study we examine the possible role of cortical feedback in shaping the spatiotemporal receptive field (STRF) responses of thalamocortical (TC) cells in the lateral geniculate nucleus (LGN) of the thalamus. A population-based computational model of the thalamocortical network is used to generate a representation of the STRF response of LGN TC cells within the corticothalamic feedback circuit. The cortical feedback is shown to have little influence on the spatial response properties of the STRF organization. However, the model suggests that cortical feedback may play a key role in modifying the experimentally observed biphasic temporal response property of the STRF, that is, the reversal over time of the polarity of ON and OFF responses of the centre and surround of the receptive field, in particular accounting for the experimentally observed mismatch between retinal cells and TC cells in respect of the magnitude of the second (rebound) phase of the temporal response. The model results also show that this mismatch may result from an anti-phase corticothalamic feedback mechanism.     

A minimal mechanistic model for temporal signal processing in the lateral geniculate nucleus

The receptive fields of cells in the lateral geniculate nucleus (LGN) are shaped by their diverse set of impinging inputs: feedforward synaptic inputs stemming from retina, and feedback inputs stemming from the visual cortex and the thalamic reticular nucleus. To probe the possible roles of these feedforward and feedback inputs in shaping the temporal receptive-field structure of LGN relay cells, we here present and investigate a minimal mechanistic firing-rate model tailored to elucidate their disparate features. The model for LGN relay ON cells includes feedforward excitation and inhibition (via interneurons) from retinal ON cells and excitatory and inhibitory (via thalamic reticular nucleus cells and interneurons) feedback from cortical ON and OFF cells. From a general firing-rate model formulated in terms of Volterra integral equations, we derive a single delay differential equation with absolute delay governing the dynamics of the system. A freely available and easy-to-use GUI-based MATLAB version of this minimal mechanistic LGN circuit model is provided. We particularly investigate the LGN relay-cell impulse response and find through thorough explorations of the model’s parameter space that both purely feedforward models and feedback models with feedforward excitation only, can account quantitatively for previously reported experimental results. We find, however, that the purely feedforward model predicts two impulse response measures, the time to first peak and the biphasic index (measuring the relative weight of the rebound phase) to be anticorrelated. In contrast, the models with feedback predict different correlations between these two measures. This suggests an experimental test assessing the relative importance of feedforward and feedback connections in shaping the impulse response of LGN relay cells.     

Development of feedforward receptive field structure of a simple cell and its contribution to the orientation selectivity: a modeling study

Recent experimental studies of hetero-synaptic interactions in various systems have shown the role of signaling in the plasticity, challenging the conventional understanding of Hebb's rule. It has also been found that activity plays a major role in plasticity, with neurotrophins acting as molecular signals translating activity into structural changes. Furthermore, role of synaptic efficacy in biasing the outcome of competition has also been revealed recently. Motivated by these experimental findings we present a model for the development of simple cell receptive field structure based on the competitive hetero-synaptic interactions for neurotrophins combined with cooperative hetero-synaptic interactions in the spatial domain. We find that with proper balance in competition and cooperation, the inputs from two populations (ON/OFF) of LGN cells segregate starting from the homogeneous state. We obtain segregated ON and OFF regions in simple cell receptive field. Our modeling study supports the experimental findings, suggesting the role of synaptic efficacy and the role of spatial signaling. We find that using this model we obtain simple cell RF, even for positively correlated activity of ON/OFF cells. We also compare different mechanism of finding the response of cortical cell and study their possible role in the sharpening of orientation selectivity. We find that degree of selectivity improvement in individual cells varies from case to case depending upon the structure of RF field and type of sharpening mechanism.     

Directional inhibition: a new slant on an old question

In this issue of Neuron, Priebe and Ferster describe the direction selectivity and spatiotemporal organization of excitatory and inhibitory inputs to direction-selective simple cells in cat visual cortex. Their most surprising finding is that inhibition shows the same preferred direction as excitation.     

Orientation and spatiotemporal tuning of cells in the primary visual cortex of an Australian marsupial,the wallaby<Emphasis Type="Italic"> Macropus eugenii</Emphasis>

The metatherians (marsupials) have been separated from eutherians (placentals) for approximately 135 million years. It might, therefore, be expected that significant independent evolution of the visual system has occurred. The present paper describes for the first time the orientation, direction and spatiotemporal tuning of neurons in the primary visual cortex of an Australian marsupial, the wallaby Macropus eugenii. The stimuli consisted of spatial sinusoidal gratings presented within apertures covering the classical receptive fields of the cells. The neurons can be classified as those with clear ON and OFF zones and those with less well-defined receptive field structures. Seventy-percent of the total cells encountered were strongly orientation selective (tuning functions at half height were less than 45 degrees ). The preferred orientations were evenly distributed throughout 360 degrees for cells with uniform receptive fields but biased towards the vertical and horizontal for cells with clear ON-OFF zones. Many neurons gave directional responses but only a small percentage of them (4%) showed motion opponent properties (i.e. they were excited by motion in one direction and actively inhibited by motion in the opposite direction). The median peak temporal tuning for cells with clear ON-OFF zones and those without were 3 Hz and 6 Hz, respectively. The most common peak spatial frequency tuning for the two groups were 2 cycles per degree and 0.5 cycles per degree, respectively. Spatiotemporal tuning was not always the same for preferred and antipreferred direction motion. In general, the physiology of the wallaby cortex was similar to well studied eutherian mammals suggesting either convergent evolution or a highly conserved architecture that stems from a common therian ancestor.     

Extended difference-of-Gaussians model incorporating cortical feedback for relay cells in the lateral geniculate nucleus of cat

A striking feature of the organization of the early visual pathway is the significant feedback from primary visual cortex to cells in the dorsal lateral geniculate nucleus (LGN). Despite numerous experimental and modeling studies, the functional role for this feedback remains elusive. We present a new firing-rate-based model for LGN relay cells in cat, explicitly accounting for thalamocortical loop effects. The established DOG model, here assumed to account for the spatial aspects of the feedforward processing of visual stimuli, is extended to incorporate the influence of thalamocortical loops including a full set of orientation-selective cortical cell populations. Assuming a phase-reversed push-pull arrangement of ON and OFF cortical feedback as seen experimentally, this extended DOG (eDOG) model exhibits linear firing properties despite non-linear firing characteristics of the corticothalamic cells. The spatiotemporal receptive field of the eDOG model has a simple algebraic structure in Fourier space, while the real-space receptive field, as well as responses to visual stimuli, are found by evaluation of an integral. As an example application we use the eDOG model to study effects of cortical feedback on responses to flashing circular spots and patch-grating stimuli and find that the eDOG model can qualitatively account for experimental findings.     

Emergence of spatiotemporal receptive fields and its application to motion detection

A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.     

Predicting Cortical Dark/Bright Asymmetries from Natural Image Statistics and Early Visual Transforms

The nervous system has evolved in an environment with structure and predictability. One of the ubiquitous principles of sensory systems is the creation of circuits that capitalize on this predictability. Previous work has identified predictable non-uniformities in the distributions of basic visual features in natural images that are relevant to the encoding tasks of the visual system. Here, we report that the well-established statistical distributions of visual features -- such as visual contrast, spatial scale, and depth -- differ between bright and dark image components. Following this analysis, we go on to trace how these differences in natural images translate into different patterns of cortical input that arise from the separate bright (ON) and dark (OFF) pathways originating in the retina. We use models of these early visual pathways to transform natural images into statistical patterns of cortical input. The models include the receptive fields and non-linear response properties of the magnocellular (M) and parvocellular (P) pathways, with their ON and OFF pathway divisions. The results indicate that there are regularities in visual cortical input beyond those that have previously been appreciated from the direct analysis of natural images. In particular, several dark/bright asymmetries provide a potential account for recently discovered asymmetries in how the brain processes visual features, such as violations of classic energy-type models. On the basis of our analysis, we expect that the dark/bright dichotomy in natural images plays a key role in the generation of both cortical and perceptual asymmetries.     

Cell-type specific dendritic contacts between retinal ganglion cells during development.

The extent of a neuron's dendritic field defines the region within which information is processed. The dendritic fields of functionally distinct ON and OFF center retinal ganglion cells (RGCs) form separate mosaics across the retina. Within each mosaic, neighboring dendritic fields overlap by a constant amount, sampling the visual field with the appropriate coverage. Contact-mediated lateral inhibition between neighboring RGCs has long been thought to regulate both the extent and overlap of dendritic fields during development. Here we show that dendro-dendritic contact exists between developing RGCs and occurs in a manner that would regulate the formation of ON and OFF mosaics separately. Dye-filled neighboring ON and OFF ferret alpha RGCs were reconstructed using multiphoton microscopy. At all neonatal ages examined, we observed dendro-dendritic contacts between RGCs of the same sign (ON/ON; OFF/OFF), but never between cells of opposite signs (ON/OFF). Terminal dendrites of one cell often touched a dendrite of its neighbor as they intersected. In some instances, the distal dendrite of one cell formed a fascicle with the proximal process of its neighbor. Alpha cells did not form contacts with neighboring beta cells of the same sign. Together, these observations suggest that dendro-dendritic contact between RGCs is cell-type specific. Dendritic contacts were observed even before the alpha cell arbors were completely stratified, suggesting that cell-cell recognition may take place early in their development. For each cell type, the relative overlap of dendritic fields was constant with age, despite a two-fold increase in field area. We suggest that dendro-dendritic contacts may be sites of intercellular signaling that could regulate local extension of dendrites to maintain the relative overlap of RGCs within a mosaic during development.     

‘Vector white noise’: a technique for mapping the motion receptive fields of direction-selective visual neurons

A technique is described and tested for mapping the sensitivities and preferred directions of motion at different locations within the receptive fields of direction-selective motion-detecting visual neurons. The procedure is to record the responses to a number of visual stimuli, each stimulus presentation consisting of a set of short, randomly-oriented, moving bars arranged in a square grid. Each bar moves perpendicularly to its long axis. The vector describing the sensitivity and preferred direction of motion at each grid location is obtained as a sum of the unit vectors defining the directions of motion of the bars in each of the stimuli at that location, weighted by the strengths of the corresponding responses. The resulting vector field specifies the optimum flow field for the neuron. The advantage of this technique over the conventional approach of probing the receptive field sequentially at each grid location is that the parallel nature of the stimulus is sensitive to nonlinear interactions (such as shunting inhibition for mutual facilitation) between different regions of the visual field. The technique is used to determine accurately the motion receptive fields of direction-selective motion detecting neurons in the optic lobes of insects. It is potentially applicable to motion-sensitive neurons with highly structured receptive fields, such as those in the optic tectum of the pigeon or in area MST of the monkey.     

Dark rearing alters the normal development of spatiotemporal response properties but not of contrast detection threshold in mouse retinal ganglion cells

The mouse visual system is immature when the eyes open two weeks after birth. As in other mammals, some of the maturation that occurs in the subsequent weeks is known to depend on visual experience. Development of the retina, which as the first stage of vision provides the visual information to the brain, also depends on light‐driven activity for proper development but has been less well studied than visual cortical development. The critical properties for retinal encoding of images include detection of contrast and responsiveness to the broad range of temporal stimulus frequencies present in natural stimuli. Here we show that contrast detection threshold and temporal frequency response characteristics of ON and OFF retinal ganglion cells (RGCs), which are poor at eye opening, subsequently undergo maturation, improving RGC performance. Further, we find that depriving mice of visual experience from before birth by rearing them in the dark causes ON and OFF RGCs to have smaller receptive field centers but does not affect their contrast detection threshold development. The modest developmental increase in temporal frequency responsiveness of RGCs in mice reared on a normal light cycle was inhibited by dark rearing only in ON but not OFF RGCs. Thus, these RGC response characteristics are in many ways unaffected by the experience‐dependent changes to synaptic and spontaneous activity known to occur in the mouse retina in the two weeks after eye opening, but specific differences are apparent in the ON vs. OFF RGC populations. © 2014 Wiley Periodicals, Inc. Develop Neurobiol 74: 692–706, 2014     

Analysis of synaptic inputs to on-off amacrine cells of the carp retina

To elucidate the synaptic transmission between bipolar cells and amacrine cells, the effect of polarization of a bipolar cell on an amacrine cell was examined by simultaneous intracellular recordings from both cells in the isolated carp retina. When either an ON or OFF bipolar cell was depolarized by an extrinsic current step, an ON-OFF amacrine cell was transiently depolarized at the onset of the current but no sustained polarization during the current was detected. The current hyperpolarizing the OFF bipolar cell also produced the transient depolarization of the amacrine cell at the termination of the current. These responses had a latency of approximately 10 ms. The amplitude of the current-evoked responses changed gradually with current intensity within the range used in these experiments. They were affected by polarization of the amacrine cell membrane; the amplitude of the current-evoked responses as well as the light-evoked responses was increased when the amacrine cell membrane was hyperpolarized, while the amplitude was decreased when the cell was depolarized. These results confirm directly that ON-OFF amacrine cells receive excitatory inputs from both ON and OFF bipolar cells: the ON transient is due to inputs from ON bipolar cells, and the OFF transient to inputs from OFF bipolar cells. The steady polarization of bipolar cells is converted into transient signals during the synaptic process.     

Characteristics of bipolar-bipolar coupling in the carp retina

ON and OFF bipolar cells were identified in the light-adapted carp retina by means of intracellular recording and Lucifer yellow dye injection. The receptive field centers, determined by measuring the response amplitudes obtained by centered spots of different diameters, were 0.3-1.0 mm for ON bipolar cells and 0.3-0.4 mm for OFF bipolar cells. These central receptive field values were much larger than the dendritic field diameters measured by histological methods. Simultaneous intracellular recordings were made from pairs of neighboring bipolar cells. Current of either polarity injected into one member of a bipolar cell pair elicited a sign-conserving, sustained potential change in the other bipolar cell. The coupling efficiency was nearly identical for both depolarizing and hyperpolarizing currents. The maximum separation of coupled bipolar cells was approximately 130 microns. This electrical coupling was reciprocal and summative, and it was observed in cell types of similar function and morphology. Dye coupling was observed in 4 out of 34 stained cells. These results strongly suggest that there is a spatial summation of signals at the level of bipolar cells, which makes their central receptive fields much larger than their dendritic fields.     

Can Retinal Ganglion Cell Dipoles Seed Iso-Orientation Domains in the Visual Cortex?

It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moiré-Interference between hexagonal ON/OFF RGC mosaics. While this Moiré-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.