Influences on the global structure of cortical maps

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119-138, 2006).

Theoretical models of neural circuit development

Proper wiring up of the nervous system is critical to the development of organisms capable of complex and adaptable behaviors. Besides the many experimental advances in determining the cellular and molecular machinery that carries out this remarkable task precisely and robustly, theoretical approaches have also proven to be useful tools in analyzing this machinery. A quantitative understanding of these processes can allow us to make predictions, test hypotheses, and appraise established concepts in a new light. Three areas that have been fruitful in this regard are axon guidance, retinotectal mapping, and activity-dependent development. This chapter reviews some of the contributions made by mathematical modeling in these areas, illustrated by important examples of models in each section. For axon guidance, we discuss models of how growth cones respond to their environment, and how this environment can place constraints on growth cone behavior. Retinotectal mapping looks at computational models for how topography can be generated in populations of neurons based on molecular gradients and other mechanisms such as competition. In activity-dependent development, we discuss theoretical approaches largely based on Hebbian synaptic plasticity rules, and how they can generate maps in the visual cortex very similar to those seen in vivo. We show how theoretical approaches have substantially contributed to the advancement of developmental neuroscience, and discuss future directions for mathematical modeling in the field.

Natural scene statistics and the structure of orientation maps in the visual cortex

Visual activity after eye-opening influences feature map structure in primary visual cortex (V1). For instance, rearing cats in an environment of stripes of one orientation yields an over-representation of that orientation in V1. However, whether such changes also affect the higher-order statistics of orientation maps is unknown. A statistical bias of orientation maps in normally raised animals is that the probability of the angular difference in orientation preference between each pair of points in the cortex depends on the angle of the line joining those points relative to a fixed but arbitrary set of axes. Natural images show an analogous statistical bias; however, whether this drives the development of comparable structure in V1 is unknown. We examined these statistics for normal, stripe-reared and dark-reared cats, and found that the biases present were not consistently related to those present in the input, or to genetic relationships. We compared these results with two computational models of orientation map development, an analytical model and a Hebbian model. The analytical model failed to reproduce the experimentally observed statistics. In the Hebbian model, while orientation difference statistics could be strongly driven by the input, statistics similar to those seen in experimental maps arose only when symmetry breaking was allowed to occur spontaneously. These results suggest that these statistical biases of orientation maps arise primarily spontaneously, rather than being governed by either input statistics or genetic mechanisms.

A model for the thick, thin and pale stripe organization of primate V2

Models based on the idea of dimension reduction have been successful in describing the patterns of ocular dominance, spatial frequency and orientation preference found in primate V1. It is shown here that this approach can be extended to describe the organization of thick, thin and pale cytochrome oxidase stripes of primate V2 given an appropriately constructed stimulus space which includes a 3-valued variable which co-varies with color, orientation and disparity. The model successfully describes several aspects of V2 organization, including the fact that there are two pale stripes for each thick and thin stripe and the strong tendency for stripes to run perpendicular to the V1 border. In addition it predicts the presence of reversals in the direction of mapping of retinal eccentricity which should be more common in the pale stripes than elsewhere.

The effect of angioscotomas on map structure in primary visual cortex

When blood vessels occlude the photoreceptor layer in the retina, they cast shadows onto the photoreceptors, creating angioscotomas (regions of the visual field to which that eye is blind). Remarkably, Adams and Horton (2002) have recently shown that it is sometimes possible to observe representations of these angioscotomas anatomically in the primary visual cortices of squirrel monkeys. However, there is substantial variability in the degree and form of these representations. The source of this variability is difficult to determine experimentally, because experimental studies are unavoidably limited by small sample size. In addition, experimental studies cannot compare the map structure that would develop with and without an angioscotoma. Here, we investigate these phenomena computationally using feature-mapping models of visual cortical development, which are not subject to the same limitations. These models suggest that the primary source of variability in angioscotoma representation is the precise timing of the onset of visual experience relative to the time course of ocular dominance column segregation. Furthermore, the models predict that angioscotomas could compete for control of local column layout with other influences such as cortical shape but that they have a small effect on the structure of orientation preference maps.

On the origin of the functional architecture of the cortex

The basic structure of receptive fields and functional maps in primary visual cortex is established without exposure to normal sensory experience and before the onset of the critical period. How the brain wires these circuits in the early stages of development remains unknown. Possible explanations include activity-dependent mechanisms driven by spontaneous activity in the retina and thalamus, and molecular guidance orchestrating thalamo-cortical connections on a fine spatial scale. Here I propose an alternative hypothesis: the blueprint for receptive fields, feature maps, and their inter-relationships may reside in the layout of the retinal ganglion cell mosaics along with a simple statistical connectivity scheme dictating the wiring between thalamus and cortex. The model is shown to account for a number of experimental findings, including the relationship between retinotopy, orientation maps, spatial frequency maps and cytochrome oxidase patches. The theory's simplicity, explanatory and predictive power makes it a serious candidate for the origin of the functional architecture of primary visual cortex.

A Computational Model for the Development of Multiple Maps in Primary Visual Cortex

Primary visual cortex contains multiple maps of features of the visual scene, including visual field position, orientation, direction, ocular dominance and spatial frequency. The complex relationships between these maps provide clues to the strategies the cortex uses for representing and processing information. Here we simulate the combined development of all these map systems using a computational model, the elastic net. We show that this model robustly produces combined maps of these four variables that bear a close resemblance to experimental maps. In addition we show that the experimentally observed effects of monocular deprivation and single-orientation rearing can be reproduced in this model, and we make some testable predictions. These results provide strong support for the hypothesis that cortical representations attempt to optimize a trade-off between coverage and continuity.

Pattern formation and cortical maps

The response selectivities of neurons in adult primary sensory cortices depend on intricate patterns of synaptic connections; these selectivities are arranged over cortex in equally rich fashion. Characterising these patterns, and particularly the activity-dependence (and independence) of their developmental trajectories, has been a major task for experimental and theoretical neuroscience. Here, we describe and analyse a paradigmatic algorithm for activity-dependent development of the refinement and generation of neuronal selectivities, and relate it to some of the wealth of suggestions in the literature.

Binocular disparity can explain the orientation of ocular dominance stripes in primate primary visual area (V1)

In the primate primary visual area (V1), the ocular dominance pattern consists of alternating monocular stripes. Stripe orientation follows systematic trends preserved across several species. I propose that these trends result from minimizing the length of intra-cortical wiring needed to recombine information from the two eyes in order to achieve the perception of depth. I argue that the stripe orientation at any point of V1 should follow the direction of binocular disparity in the corresponding point of the visual field. The optimal pattern of stripes determined from this argument agrees with the ocular dominance pattern of macaque and Cebus monkeys. This theory predicts that for any point in the visual field the limits of depth perception are greatest in the direction along the ocular dominance stripes at that point.

Computational models of association cortex

Recent computational models, or mathematical realizations of neurobiological theories, are providing insights into the organization and workings of the association cortex. Such models concern the construction of cortical maps, the neural basis of cognitive functions such as visual perception, reward-motivated learning and some aspects of consciousness.