A theoretical model of axon guidance by the Robo code

After crossing the midline, different populations of commissural axons in Drosophila target specific longitudinal pathways at different distances from the midline. It has recently been shown that this choice of lateral position is governed by the particular combination of Robo receptors expressed by these axons, presumably in response to a gradient of Slit released by the midline. Here we propose a simple theoretical model of this combinatorial coding scheme. The principal results of the model are that purely quantitative rather than qualitative differences between the different Robo receptors are sufficient to account for the effects observed following removal or ectopic expression of specific Robo receptors, and that the steepness of the Slit gradient in vivo must exceed a certain minimum for the results observed experimentally to be consistent

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

A unifying objective function for topographic mappings

Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the map that each particular case favors. These differences have important consequences for the practical application of topographic mapping methods

Are visual cortex maps optimized for coverage?

The elegant regularity of maps of variables such as ocular dominance, orientation, and spatial frequency in primary visual cortex has prompted many people to suggest that their structure could be explained by an optimization principle. Up to now, the standard way to test this hypothesis has been to generate artificial maps by optimizing a hypothesized objective function and then to compare these artificial maps with real maps using a variety of quantitative criteria. If the artificial maps are similar to the real maps, this provides some evidence that the real cortex may be optimizing a similar function to the one hypothesized. Recently, a more direct method has been proposed for testing whether real maps represent local optima of an objective function (Swindale, Shoham, Grinvald, Bonhoeffer, & Hilbener, 2000). In this approach, the value of the hypothesized function is calculated for a real map, and then the real map is perturbed in certain ways and the function recalculated. If each of these perturbations leads to a worsening of the function, it is tempting to conclude that the real map is quite likely to represent a local optimum of that function. In this article, we argue that such perturbation results provide only weak evidence in favor of the optimization hypothesis

The role of weight normalization in competitive learning

The effect of different kinds of weight normalization on the outcome of a simple competitive learning rule is analyzed. It is shown that there are important differences in the representation formed depending on whether the constraint is enforced by dividing each weight by the same amount (''divisive enforcement'') or subtracting a fixed amount from each weight (''subtractive enforcement''). For the divisive cases weight vectors spread out over the space so as to evenly represent ''typical'' inputs, whereas for the subtractive cases the weight vectors tend to the axes of the space, so as to represent ''extreme'' inputs. The consequences of these differences are examined

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

Elastic net model of ocular dominance - overall stripe pattern and monocular deprivation

The elastic net (Durbin and Willshaw 1987) can account for the development of both topography and ocular dominance in the mapping from the lateral geniculate nucleus to primary visual cortex (Goodhill and Willshaw 1990). Here it is further shown for this model that (1) the overall pattern of stripes produced is strongly influenced by the shape of the cortex: in particular, stripes with a global order similar to that seen biologically can be produced under appropriate conditions, and (2) the observed changes in stripe width associated with monocular deprivation are reproduced in the model

Adaptation is not required to explain the long-term response of axons to molecular gradients

It has been suggested that growth cones navigating through the developing nervous system might display adaptation, so that their response to gradient signals is conserved over wide variations in ligand concentration. Recently however, a new chemotaxis assay that allows the effect of gradient parameters on axonal trajectories to be finely varied has revealed a decline in gradient sensitivity on either side of an optimal concentration. We show that this behavior can be quantitatively reproduced with a computational model of axonal chemotaxis that does not employ explicit adaptation. Two crucial components of this model required to reproduce the observed sensitivity are spatial and temporal averaging. These can be interpreted as corresponding, respectively, to the spatial spread of signaling effects downstream from receptor binding, and to the finite time over which these signaling effects decay. For spatial averaging, the model predicts that an effective range of roughly one-third of the extent of the growth cone is optimal for detecting small gradient signals. For temporal decay, a timescale of about 3 minutes is required for the model to reproduce the experimentally observed sensitivity

Labyrinthine window rupture as a cause of acute sensorineural hearing loss

Labyrinthine window rupture (LWR) is one cause of acute sensorineural hearing loss and need for early exploration is clear for good improved hearing. Acute sensorineural hearing loss of 60 dB or more treated from May 2006 to May 2010 were retrospectively analyzed. There were 21 ears of severe deafness, 18 ears of profound deafness, and 10 ears of total deafness. All patients were examined with temporal bone CT. Space-occupying lesions around the labyrinthine windows were suggestive images of LWR. Thirty-five ears were operated for LWR while 14 ears of SHL received conservative treatments. Fifty-seven percent of LWR improved 30 dB or more after sealing of both labyrinthine windows. Of the 15 markedly recovered ears, 14 ears were operated within 2 weeks from the onset. Of the five cured ears, four ears were operated within a week from the onset. As for the hearing prognosis of SHL, 88% of severe and profound deafness improved 30 dB or more but total deafness did not improve more than 30 dB. Exclusion of LWR from SHL and early surgical intervention in LWR will bring about good hearing prognosis to both LWR and SHL

Autocatalytic Loop, Amplification and Diffusion: A Mathematical and Computational Model of Cell Polarization in Neural Chemotaxis

The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response