Retinotopy and orientation columns in the monkey: A new model

A model is presented in which orientation columns arise directly out of retinotopy. According to the model, iso-orientation lines are arrayed radially around nodal centers which correspond to cytochrome oxidase patches. The nodal centers form a square matrix superimposed upon the map of ocular dominance stripes. In the supragranular layers horizontal iso-orientation lines run down the centers of ocular dominance stripes, with vertical iso-orientation lines crossing perpendicularly. Diagonal orientations (45 degrees and 135 degrees) are represented as alternating iso-orientation zones at the centers of the interstices in the matrix (internodal centers). Preferred orientations in the infragranular layers are reversed with respect to the supragranular layers. The model is consistent with new data concerning ocularity and preferred orientation in systematic penetrations through striate cortex, and helps to explain some previously puzzling features of the relationship between ocular dominance columns, orientation columns and retinotopy.     

Statistics and geometry of orientation selectivity in primary visual cortex

Orientation maps are a prominent feature of the primary visual cortex of higher mammals. In macaques and cats, for example, preferred orientations of neurons are organized in a specific pattern, where cells with similar selectivity are clustered in iso-orientation domains. However, the map is not always continuous, and there are pinwheel-like singularities around which all orientations are arranged in an orderly fashion. Although subject of intense investigation for half a century now, it is still not entirely clear how these maps emerge and what function they might serve. Here, we suggest a new model of orientation selectivity that combines the geometry and statistics of clustered thalamocortical afferents to explain the emergence of orientation maps. We show that the model can generate spatial patterns of orientation selectivity closely resembling the maps found in cats or monkeys. Without any additional assumptions, we further show that the pattern of ocular dominance columns is inherently connected to the spatial pattern of orientation.     

Neuronal selectivity and local map structure in visual cortex

The organization of primary visual cortex (V1) into functional maps makes individual cells operate in a variety of contexts. For instance, some neurons lie in regions of fairly homogeneous orientation preference (iso-orientation domains), while others lie in regions with a variety of preferences (e.g., pinwheel centers). We asked whether this diversity in local map structure correlates with the degree of selectivity of spike responses. We used a combination of imaging and electrophysiology to reveal that neurons in regions of homogeneous orientation preference have much sharper tuning. Moreover, in both monkeys and cats, a common principle links the structure of the orientation map, on the spatial scale of dendritic integration, to the degree of selectivity of individual cells. We conclude that neural computation is not invariant across the cortical surface. This finding must factor into future theories of receptive field wiring and map development.     

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.     

Mapping of contextual modulation in the population response of primary visual cortex

We review the evidence of long-range contextual modulation in V1. Populations of neurons in V1 are activated by a wide variety of stimuli outside of their classical receptive fields (RF), well beyond their surround region. These effects generally involve extra-RF features with an orientation component. The population mapping of orientation preferences to the upper layers of V1 is well understood, as far as the classical RF properties are concerned, and involves organization into pinwheel-like structures. We introduce a novel hypothesis regarding the organization of V1’s contextual response. We show that RF and extra-RF orientation preferences are mapped in related ways. Orientation pinwheels are the foci of both types of features. The mapping of contextual features onto the orientation pinwheel has a form that recapitulates the organization of the visual field: an iso-orientation patch within the pinwheel also responds to extra-RF stimuli of the same orientation. We hypothesize that the same form of mapping applies to other stimulus properties that are mapped out in V1, such as colour and contrast selectivity. A specific consequence is that fovea-like properties will be mapped in a systematic way to orientation pinwheels. We review the evidence that cytochrome oxidase blobs comprise the foci of this contextual remapping for colour and low contrasts. Neurodynamics and motion in the visual field are argued to play an important role in the shaping and maintenance of this type of mapping in V1.     

Random Wiring,Ganglion Cell Mosaics,and the Functional Architecture of the Visual Cortex

The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1’s intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models.     

Cortical templates for the self-organization of orientation-specific d- and l-hypercolumns in monkeys and cats

Blasdel and Salama's sensory maps of orientation-selective edge detectors in the monkey striate cortex can be reduced to an idealized scheme in which orientation hypercolumns of the d- and l-type occur in alternating sequence (Fig. 1). This scheme resolves the apparent contradiction between linear and circular arrangements of successive edge directions in earlier accounts. The actual configuration of hypercolumns is in register with two possible templates for the self-organization of orientation selectivity: the isometric cytochrome oxidase blobs of the colour system, and the anisometric slabs of the ocular dominance system. The centers of the hypercolumns coincide with the blobs. Simulation of cortical self-organization shows this co-incidence even in the absence of template-specific interactions. However, blobs and slabs are symmetrical to these centers, and therefore no templates for the asymmetrical distribution of preferred orientation in the hypercolumns. The present simulation derives the pre-natal formation of an initial scheme from a hypothetical gradient of nervous activity. Post-natal formation, or maturation, of this scheme is achieved by visual experience. Simulation of corresponding interactions between simultaneously activated neurons illustrates both the gain in orientation selectivity (Figs. 2 and 3), and the optimization of farfield diversity and nearfield conformity (Figs. 4 and 5). The results are compatible with the actual distribution of blob-centered d- and l-hypercolumns, iso-orientation modules and orientation fractures in the monkey. A surprisingly similar distribution of blobless d- and l-hypercolumns is expected in the absence of the colour system. Applied to the apparently blobless cortex of the cat, the scheme explains the modulation of deoxyglucose uptake along the iso-orientation bands in a report of Löwel, Freeman, and Singer.     

Coverage and the design of striate cortex

Hubel and Wiesel (1977) suggested that ocular dominance and orientation columns in the macaque monkey striate cortex might be bands of uniform width that intersected orthogonally. They pointed out that if this were the case, there would be an equal allocation of cells of different orientation preference to each eye and to each point in visual space. However, orientation and ocular dominance columns have a more complex structural organization than is implied by this model: for example, iso-orientation domains do not intersect ocular dominance stripes at right angles and the two columnar systems have different periodicities. This raises the question as to how well the striate cortex manages to allocate equal numbers of neurons of different orientation preference to each eye and to each region of visual space, a factor referred to here as coverage. This paper defines a measure of uniformity of coverage, c, and investigates its dependence on several different parameters of columnar organisation. Calculations were done first using a simplified one-dimensional model of orientation and ocular dominance columns and were then repeated using more realistic two-dimensional models, generated with the algorithms described in the preceding paper (Swindale 1991). Factors investigated include the relative periodicities of the two columnar systems, the size of the cortical point image, the width of orientation tuning curves, whether columns are spatially anisotropic or not, and the role of the structural relationships between columns described by Blasdel and Salama (1986). The results demonstrate that coverage is most uniform when orientation hypercolumns are about half the size of ocular dominance hypercolumns. Coverage is most uneven when the hypercolumns are the same size, unless they are related in the way described by Blasdel and Salama, in which case coverage gets only slightly worse as the size ratio (ori/od) increases above 0.5. The minimum diameter of cortical point image that ensures reasonably uniform coverage is about twice the size of an ocular dominance hypercolumn i.e. about 1.5–2.0 mm.     

A model for the coordinated development of columnar systems in primate striate cortex

The existence of patchy regions in primate striate cortex in which orientation selectivity is reduced, and which lie in the centers of ocular dominance stripes is well established (Hubel and Livingstone 1981). Analysis of functional maps obtained with voltage sensitive dyes (Blasdel and Salama 1986) has suggested that regions where the spatial rate of change of orientation preference is high, tend to be aligned either along the centers of ocular dominance stripes, or to intersect stripe borders at right angles. In this paper I present results from a developmental model which show that a tendency for orientation selectivity to develop more slowly in the centers of ocular dominance stripes would lead to the observed relationships between the layout of ocular dominance and the map of orientation gradient. This occurs despite the fact that there is no direct connection between the measures of preferred orientation (from which the gradient map is derived) and orientation selectivity (which is independent of preferred orientation). I also show that in both the monkey and the model, orientation singularities have an irregular distribution, but tend to be concentrated in the centers of the ocular dominance stripes. The average density of singularities is about 3/ ², where is the period of the orientation columns. The results are based on an elaboration of previous models (Swindale 1980, 1982) which show how, given initially disordered starting conditions, lateral interactions that are short-range excitatory and long-range inhibitory can lead to the development of patterns of orientation or ocular dominance that resemble those found in monkey striate cortex. To explain the coordinated development of the two kinds of column, it is proposed that there is an additional tendency in development for the rate of increase in orientation selectivity to be reduced in the centers of emerging ocular dominance stripes. This might come about if a single factor modulates plasticity in each cell, or column of cells. Thus plasticity may be turned off first in regions in the centers of ocular dominance stripes where relatively extreme and therefore stable ocular dominance values are achieved early in development. Consequently it will be hard for cells in these columns to modify other properties such as orientation preference or selectivity.     

Periodic organisation of foldback sequences in Physarum polycephalum nuclear DNA.

Nuclear DNA from the slime mould Physarum polycephalum is shown to contain interspersed inverted repeat sequences, such that denatured fragments of DNA containing pairs of these sequences form intra-chain duplexes under appropriate conditions. The organisation and distribution of the nucleotide sequences responsible for the formation of foldback structures in Physarum DNA have been investigated using the electron microscope. The majority of foldback duplexes have sizes ranging up to 800 base pairs, and about 60-80% of DNA molecules 2.2 X 10(4) bases in length contain interspersed foldback elements. The size of individual foldback duplexes, and also the length of the intervening sequences which separate them, are non-random. The results can best be explained by a model in which separate foldback foci in Physarum DNA are spaced periodically at regular intervals. The regions containing foldback foci are thought to contain smaller, tandemly-arranged sequences of discrete sizes, in some cases related to other nucleotide sequences of a similar nature in the same locality in Physarum DNA.     

Sensitivity to corners in flow patterns

Flow patterns are two-dimensional orientation structures that arise from the projection of certain kinds of surface coverings (such as fur) onto images. Detecting orientation changes within them is an important task, since the changes often correspond to significant events such as corners, occluding edges, or surface creases. We model such patterns as random-dot Moiré patterns, and examine sensitivity to change in orientation within them. We show that the amount of structure available from which orientation and curvature can be estimated is critical, and introduce a path-length parameter to model it. For short path lengths many discontinuities are smoothed over, which has further implications for computational modeling of orientation selectivity.     

Periodically arranged interactions within the myosin filament backbone revealed by mechanical unzipping

Numerous types of biological motion are driven by myosin thick filaments. Although the exact structure of the filament backbone is not known, it has long been hypothesized that periodically arranged charged regions along the myosin tail are the main contributors to filament stability. Here we provide a direct experimental test of this model by mechanically pulling apart synthetic myosin thick filaments. We find that unzipping is accompanied by broad force peaks periodically spaced at 4-, 14- and 43-nm intervals. This spacing correlates with the repeat distance of highly charged regions along the myosin tail. Lowering ionic strength does not change force-peak periodicity but increases the forces necessary for unzipping. The force peaks are partially reversible, indicating that the interactions are rapidly re-established upon mechanical relaxation. Thus, the zipping together of myosin tails via consecutive formation of periodically spaced bonds may be the underlying mechanism of spontaneous thick filament formation.     

Matching the modules: cortical maps and long-range intrinsic connections in visual cortex during development.

Visual cortical neurons exhibit a high degree of response selectivity and are grouped into small columns according to their response preferences. The columns are located at regularly spaced intervals covering the whole cortical representation of the visual field with a modular system of feature-selective neurons. The selectivity of these cells and their modular arrangement is thought to emerge from interactions in the network of specific intracortical and thalamocortical connections. Understanding the ontogenesis of this complex structure and contributions of intrinsic and extrinsic, experience-dependent mechanisms during cortical development can provide new insights into the way the visual cortex processes information about the environment. Available data about the development of connections and response properties in the visual cortex suggest that maturation proceeds in two distinct steps. In the first phase, mechanisms inherent to the cortex establish a crude framework of interconnected neural modules which exhibit the basic but still immature traits of the adult state. Relevant mechanisms in this phase are assumed to consist of molecular cues and patterns of spontaneous neural activity in cortical and corticothalamic interconnections. In a second phase, the primordial layout becomes refined under the control of visual experience establishing a fine-tuned network of connections and mature response properties.     

The Detection of Orientation Continuity and Discontinuity by Cat V1 Neurons

The orientation tuning properties of the non-classical receptive field (nCRF or “surround”) relative to that of the classical receptive field (CRF or “center”) were tested for 119 neurons in the cat primary visual cortex (V1). The stimuli were concentric sinusoidal gratings generated on a computer screen with the center grating presented at an optimal orientation to stimulate the CRF and the surround grating with variable orientations stimulating the nCRF. Based on the presence or absence of surround suppression, measured by the suppression index at the optimal orientation of the cells, we subdivided the neurons into two categories: surround-suppressive (SS) cells and surround-non-suppressive (SN) cells. When stimulated with an optimally oriented grating centered at CRF, the SS cells showed increasing surround suppression when the stimulus grating was expanded beyond the boundary of the CRF, whereas for the SN cells, expanding the stimulus grating beyond the CRF caused no suppression of the center response. For the SS cells, strength of surround suppression was dependent on the relative orientation between CRF and nCRF: an iso-orientation grating over center and surround at the optimal orientation evoked strongest suppression and a surround grating orthogonal to the optimal center grating evoked the weakest or no suppression. By contrast, the SN cells showed slightly increased responses to an iso-orientation stimulus and weak suppression to orthogonal surround gratings. This iso-/orthogonal orientation selectivity between center and surround was analyzed in 22 SN and 97 SS cells, and for the two types of cells, the different center-surround orientation selectivity was dependent on the suppressive strength of the cells. We conclude that SN cells are suitable to detect orientation continuity or similarity between CRF and nCRF, whereas the SS cells are adapted to the detection of discontinuity or differences in orientation between CRF and nCRF.     

Pooling strategies in V1 can account for the functional and structural diversity across species

Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of orientation maps in higher mammals’ V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a theoretical model based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence in V1 of complex cells with or without that of orientation maps, as observed in distinct species of mammals. In particular, we observed that pooling in the feature space is directly related to the orientation map formation while pooling in the retinotopic space is responsible for the emergence of a complex cells population. Introducing different forms of pooling in a predictive model of early visual processing as implemented in SDPC can therefore be viewed as a theoretical framework that explains the diversity of structural and functional phenomena observed in V1.     

A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: II.

In Part I, cross-linking entropy (CLE) was proposed as a mechanism that limits the size of functional domains of RNA. To test this hypothesis, the theory is developed into an RNA secondary structure prediction filter which is applied to nearest-neighbor secondary structure (NNSS) algorithms that utilize a free energy (FE) minimization strategy. (The NNSS strategies are also referred to as the dynamic programming algorithm in the literature.) The cross-linking entropy for RNA is derived from a generalized Gaussian polymer chain model where the entropic contributions caused by the formation of base pairs (stacking) in RNA are analysed globally. Local entropic contributions are associated with the freezing out of degrees of freedom in the links. Both global and local entropic effects are strongly influenced by the persistence length. The cross-linking entropy provides a physical origin for the size of functional domains in long nucleic acid sequences and may go further to explain as to why the majority of the domain regions in typical sequences tend to be less than 600 nucleotides in length. In addition, improvements were observed in the "best guess" predictive capacity over NNSS prediction strategies. The thermodynamic distribution is more representative of the expected structures and is strongly governed by such physical parameters as the persistence length and the excluded volume. The CLE appears to generalize the tabulated penalties used in NNSS algorithms. The principal parameter influencing this entropy is the persistence length. The model is shown to accomodate a variable persistence length and is capable of describing the folding dynamics of RNA. A two-state kinetic model based on the CLE principle is used to help elucidate the folding kinetics of functional domains in the group I introns.     

Addition of side chain interactions to modified Lifson-Roig helix-coil theory: application to energetics of phenylalanine-methionine interactions.

We introduce here i, i + 3 and i, i + 4 side chain interactions into the modified Lifson-Roig helix-coil theory of Doig et al. (1994, Biochemistry 33:3396-3403). The helix/coil equilibrium is a function of initiation, propagation, capping, and side chain interaction parameters. If each of these parameters is known, the helix content of any isolated peptide can be predicted. The model considers every possible conformation of a peptide, is not limited to peptides with only a single helical segment, and has physically meaningful parameters. We apply the theory to measure the i, i + 4 interaction energies between Phe and Met side chains. Peptides with these residues spaced i, i + 4 are significantly more helical than controls where they are spaced i, i + 5. Application of the model yields delta G for the Phe-Met orientation to be -0.75 kcal.mol-1, whereas that for the Met-Phe orientation is -0.54 kcal.mol-1. These orientational preferences can be explained, in part, by rotamer preferences for the interacting side chains. We place Phe-Met i, i + 4 at the N-terminus, the C-terminus, and in the center of the host peptide. The model quantitatively predicts the observed helix contents using a single parameter for the side chain-side chain interaction energy. This result indicates that the model works well even when the interaction is at different locations in the helix.