Visual cortex: Looking into a Klein bottle

AbstractArguments based on mathematical topology may help in understanding the organization of topographic maps in the cerebral cortex

Retinal Wave Behavior through Activity- Dependent Refractory Periods

In the developing mammalian visual system, spontaneous retinal ganglion cell (RGC) activity contributes to and drives several aspects of visual system organization. This spontaneous activity takes the form of spreading patches of synchronized bursting that slowly advance across portions of the retina. These patches are non-repeating and tile the retina in minutes. Several transmitter systems are known to be involved, but the basic mechanism underlying wave production is still not well-understood. We present a model for retinal waves that focuses on acetylcholine mediated waves but whose principles are adaptable to other developmental stages. Its assumptions are that a) spontaneous depolarizations of amacrine cells drive wave activity; b) amacrine cells are locally connected, and c) cells receiving more input during their depolarization are subsequently less responsive and have longer periods between spontaneous depolarizations. The resulting model produces waves with non-repeating borders and randomly distributed initiation points. The wave generation mechanism appears to be chaotic and does not require neural noise to produce this wave behavior. Variations in parameter settings allow the model to produce waves that are similar in size, frequency, and velocity to those observed in several species. Our results suggest that retinal wave behavior results from activity-dependent refractory periods and that the average velocity of retinal waves depends on the duration a cell is excitatory: longer periods of excitation result in slower waves. In contrast to previous studies, we find that a single layer of cells is sufficient for wave generation. The principles described here are very general and may be adaptable to the description of spontaneous wave activity in other areas of the nervous system

Visual cortex maps are optimized for uniform coverage

articles Mammalian primary visual cortex contains a single continuous representation of retinotopic visual space, on which orderly, periodic maps of several different visual stimulus properties are superimposed. These properties include ocular dominance and preferred orientation [1][2] These maps are often structurally related. For example, in macaque monkey These findings are consistent with earlier suggestions 4 that visual cortex maps develop according to a combination of continuity and completeness constraints, which act in opposition. The continuity constraint specifies that neighboring cortical locations should have similar receptive field properties, whereas the completeness constraint ensures that all combinations of the parameters represented in individual maps are distributed uniformly over visual space. A quantitative measure of completeness, known as coverage uniformity, or c′, has been devised 16 . It is calculated in the following way: for a given combination of features (for example, some unique combination of orientation, spatial frequency, eye and retinal location), the total neural response, A, in the cortex is calculated, taking into account the spatial structure of the maps of these properties, and the receptive field tuning widths of individual cortical units. Uniform coverage means that A should be independent of the specific feature combination chosen. It is convenient to define c′ as the standard deviation of A divided by its mean, taken over some representative set of stimuli. This makes it a dimensionless measure of 'noise' in the cortical representation of a particular feature space. If c′ = 0, coverage is completely uniform; larger values correspond to an increasingly noisy representation: for example, if c′ = 1, the standard deviation of the signal across the feature space is equal to the mean. The hypothesis that cortical maps are organized so as to optimize (that is, minimize) c′ was tested here by systematically perturbing the spatial relationships between maps of orientation, ocular dominance and spatial frequency obtained simultaneously in area 17 of the cat 13 to see whether c′ is at a local minimum. Two different methods were used to do this, both of which left continuity in the individual maps unchanged. In the first, the spatial relationships were altered by various combinations of flips (mirror inversions) about either the horizontal or vertical axes and/or 180°rotation (equivalent to a mirror inversion about one axis followed by a mirror inversion about the other). For three rectangular maps, there are a total of 16 transformations that disturb the point-to-point relationships between the maps in a unique way. (Note that some combinations of flips are equivalent: for example, flipping two of the maps about the vertical axis is equivalent to flipping just the third one.) The second method examined the possibility that map structure is close to a local optimum for coverage uniformity. To test this, a single map was displaced sideways by a given number of pixels relative to the other two, which remained fixed relative to each other. Coverage was then calculated for the region common to all three maps. This was done separately for each of the ocular dominance, spatial frequency and orientation maps, for a range of Cat visual cortex contains a topographic map of visual space, plus superimposed, spatially periodic maps of ocular dominance, spatial frequency and orientation. It is hypothesized that the layout of these maps is determined by two constraints: continuity or smooth mapping of stimulus properties across the cortical surface, and coverage uniformity or uniform representation of combinations of map features over visual space. Here we use a quantitative measure of coverage uniformity (c') to test the hypothesis that cortical maps are optimized for coverage. When we perturbed the spatial relationships between ocular dominance, spatial frequency and orientation maps obtained in single regions of cortex, we found that cortical maps are at a local minimum for c'. This suggests that coverage optimization is an important organizing principle governing cortical map development

A Multi-Component Model of the Developing Retinocollicular Pathway Incorporating Axonal and Synaptic Growth

During development, neurons extend axons to different brain areas and produce stereotypical patterns of connections. The mechanisms underlying this process have been intensively studied in the visual system, where retinal neurons form retinotopic maps in the thalamus and superior colliculus. The mechanisms active in map formation include molecular guidance cues, trophic factor release, spontaneous neural activity, spike-timing dependent plasticity (STDP), synapse creation and retraction, and axon growth, branching and retraction. To investigate how these mechanisms interact, a multi-component model of the developing retinocollicular pathway was produced based on phenomenological approximations of each of these mechanisms. Core assumptions of the model were that the probabilities of axonal branching and synaptic growth are highest where the combined influences of chemoaffinity and trophic factor cues are highest, and that activity-dependent release of trophic factors acts to stabilize synapses. Based on these behaviors, model axons produced morphologically realistic growth patterns and projected to retinotopically correct locations in the colliculus. Findings of the model include that STDP, gradient detection by axonal growth cones and lateral connectivity among collicular neurons were not necessary for refinement, and that the instructive cues for axonal growth appear to be mediated first by molecular guidance and then by neural activity. Although complex, the model appears to be insensitive to variations in how the component developmental mechanisms are implemented. Activity, molecular guidance and the growth and retraction of axons and synapses are common features of neural development, and the findings of this study may have relevance beyond organization in the retinocollicular pathway

Modeling development in retinal afferents: retinotopy, segregation, and ephrinA/EphA mutants.

During neural development, neurons extend axons to target areas of the brain. Through processes of growth, branching and retraction these axons establish stereotypic patterns of connectivity. In the visual system, these patterns include retinotopic organization and the segregation of individual axons onto different subsets of target neurons based on the eye of origin (ocular dominance) or receptive field type (ON or OFF). Characteristic disruptions to these patterns occur when neural activity or guidance molecule expression is perturbed. In this paper we present a model that explains how these developmental patterns might emerge as a result of the coordinated growth and retraction of individual axons and synapses responding to position-specific markers, trophic factors and spontaneous neural activity. This model derives from one presented earlier (Godfrey et al., 2009) but which is here extended to account for a wider range of phenomena than previously described. These include ocular dominance and ON-OFF segregation and the results of altered ephrinA and EphA guidance molecule expression. The model takes into account molecular guidance factors, realistic patterns of spontaneous retinal wave activity, trophic molecules, homeostatic mechanisms, axon branching and retraction rules and intra-axonal signaling mechanisms that contribute to the survival of nearby synapses on an axon. We show that, collectively, these mechanisms can account for a wider range of phenomena than previous models of retino-tectal development