Modeling the emergence of whisker direction maps in rat barrel cortex

Abstract

Based on measuring responses to rat whiskers as they are mechanically stimulated, one recent study suggests that barrel-related areas in layer 2/3 rat primary somatosensory cortex (S1) contain a pinwheel map of whisker motion directions. Because this map is reminiscent of topographic organization for visual direction in primary visual cortex (V1) of higher mammals, we asked whether the S1 pinwheels could be explained by an input-driven developmental process as is often suggested for V1. We developed a computational model to capture how whisker stimuli are conveyed to supragranular S1, and simulate lateral cortical interactions using an established self-organizing algorithm. Inputs to the model each represent the deflection of a subset of 25 whiskers as they are contacted by a moving stimulus object. The subset of deflected whiskers corresponds with the shape of the stimulus, and the deflection direction corresponds with the movement direction of the stimulus. If these two features of the inputs are correlated during the training of the model, a somatotopically aligned map of direction emerges for each whisker in S1. Predictions of the model that are immediately testable include (1) that somatotopic pinwheel maps of whisker direction exist in adult layer 2/3 barrel cortex for every large whisker on the rat's face, even peripheral whiskers; and (2) in the adult, neurons with similar directional tuning are interconnected by a network of horizontal connections, spanning distances of many whisker representations. We also propose specific experiments for testing the predictions of the model by manipulating patterns of whisker inputs experienced during early development. The results suggest that similar intracortical mechanisms guide the development of primate V1 and rat S1.

Figure 1. Maps in the rat whisker-barrel system.

A The whiskers are arranged on the snout of a 10 day old rat pup in an orderly grid pattern. B This pattern is reproduced in barrel clusters, revealed here in a tangential section in L4 barrel cortex stained for cytochrome oxidase, such that neurons in each cluster respond preferentially to stimulation of the whisker in the corresponding position in the whiskerpad. C Within a supra-barrel, a pinwheel map has been measured for the direction in which the corresponding whisker is deflected . The map is described as somatotopic because deflecting the principal whisker (PW) in the direction of an adjacent whisker on the snout selectively activates neurons in the PW's barrel that are closest to the adjacent whisker barrel. Reprinted and adapted by permission from Macmillan Publishers Ltd: Nature Neuroscience , copyright 2006; colors show the direction tuning of neurons in each location within a barrel, according to the color key in D. The black dots show positions of electrode penetrations, where multiple dots correspond to multiple-unit recordings. The white box in A outlines the base of the PW for the corresponding barrel outlined in B and whose supra-barrel is enlarged in C.

Figure 2. Model diagram and activity before any learning.

A 25 whiskers are arranged in a regular grid, where some are deflected (colored arrows) and some are not (dots). Deflected whiskers are those impinged by a wide stimulus (solid line) moving in the direction of the dashed line and unfilled arrow (). The stimulus is a half plane, which has moved almost half-way through the whisker field in this example. Deflected whiskers are those to the left of the plane. Impinged whiskers are deflected roughly in the direction of stimulus motion, but we apply normally distributed noise to each, with concentration parameter in the example. B The L4 sheet is divided into barrels (delineated by white), each containing 25 neurons with pre-assigned MEDs (pixel color) from around the circle, and located arbitrarily within the barrel. C L2/3 is divided into supra-barrels (2121 neurons in each), such that each neuron receives weighted projections from all L4 neurons in the corresponding barrel. Each L2/3 neuron also receives fixed excitatory lateral connections from itself and its 8 immediate neighbors (its lateral excitatory connection field). Each also receives inhibitory connections from all neurons that fall within a 44-barrel area (8484 neurons) centered on its location; the lateral inhibitory connection field for the neuron marked * is shown. The brightness indicates connection strengths from * to each neuron before training. D The example input is represented in L4 by activating neurons whose MEDs are similar to the direction of deflected whiskers. E Initially random activity in stimulated L2/3 supra-barrels migrates to the leading edge of the stimulus as lateral interactions settle for each of steps . All plots are normalized separately.

Figure 3. A somatotopically aligned map of whisker deflection direction emerges in each supra-barrel.

A Example map from one network trained on 5,000 input patterns in which whisker deflection directions are each concentrated towards the orientation of the stimulus (). Maps in each supra-barrel are a match to that measured by ref. in which neurons on the left of each supra-barrel, for example, prefer leftward deflections of the PW. Reprinted and adapted by permission from Macmillan Publishers Ltd: Nature Neuroscience , copyright 2006. Supra-barrels are delineated by white lines. B Mean direction preference for neurons at each cortical location, over the 20 networks in the same data set, showing that the organization is consistent across runs. C Plot of the long range lateral connection strengths, from the representative example neuron at the position marked by *, to the rest of the cortical map. Pixel brightness indicates lateral weight strength, and the color indicates the preferred deflection direction of each connected neuron. This neuron becomes most strongly connected to others, some located many supra-barrels away, that are tuned to similar directions of PW deflection.

Figure 4. Analysis of pinwheel quality and somatotopic alignment per supra-barrel in 20 model networks.

A At t = 5,000, direction maps in each supra-barrel were compared to the template pinwheel (inset) and classed as somatotopically correct pinwheels (the example map has a ‘pinwheelness’ score of 0.9), somatotopically inverted pinwheels (example score -0.9) or not pinwheels (score 0.2), as described in Results. When there is no correlation between the direction in which each whisker is stimulated during training (), pinwheel maps emerge in each supra-barrel, but they are equally likely to rotate clockwise or counter-clockwise. When such a correlation is present in the inputs (), the number of supra-barrels containing pinwheels that rotate in a somatotopically consistent way increases to a maximum of 76%. Surprisingly, perfectly correlated inputs () degrade pinwheel quality. B This behavior is reflected in a plot of absolute ‘pinwheelness’ scores, in which all but the scores for progress over training iterations (t = 0, 500, 1,000, 2,000, 3,000, 4,000 in progressive dashed lines) toward good scores at t = 5,000 (solid line). Scores are highest for , suggesting that networks trade a bias to maximize pinwheelness for one towards somatotopic alignment as is increased. C shows that pinwheels rotating in the correct direction become aligned to the somatotopic template, with a final circular standard deviation for .

Figure 5. Anisotropic inputs create anisotropic maps.

Values of were drawn from circular normal distributions with varying degrees of concentration (input anisotropy), towards a mean of . Results suggest that biased experience to a particular direction of stimulus will cause an over representation of that direction in the supra-barrels. Map anisotropy scores converge to 0.69 (out of a maximum of 1.0) when the networks are trained in a regime where half-plane stimuli always move in the same direction. B shows an example map from a network trained on input anisotropy 3.0, where pixel saturation indicates a lower direction selectivity for each neuron. Distorted pinwheel structures still form in many barrels, but the map is clearly dominated by neurons preferring deflection directions. C shows a similar map from a network trained on input anisotropy , wherein patches of non-selective neurons form on the right side of the left most supra-barrels where the leading edge of the stimulus is least likely to occur.

Figure 6. Model maps organized in control experiments and at .

A Whisker deflection directions are independent of one another. Example direction map from a representative network, which develops good pinwheels in each supra-barrel but no consistent global organization. B Removing global correlations. Example map measured from a network trained on 5,000 inputs wherein the location of the stimulated whiskers was randomly shuffled on each iteration (). C Direction map measured from one representative network trained on 5,000 inputs wherein the whiskers are deflected in the same combinations as in the normal case, but the mean direction in which they are deflected bears no relation to the stimulus direction implied by this combination (). In both controls, maps resemble V1 orientation or direction maps rather than rodent S1 maps, because they cover all directions continuously on the local scale but have no consistent global alignment. D When whisker deflection directions are perfectly correlated with the whisker combination (), the supra-barrel borders no longer affect the input correlations, and so the map groups similar directions together rather than developing independent pinwheels.

Figure 7. Predicting mappings for experimentally manipulated whisker inputs.

A Whisker trimming experiment. Whiskers in a chessboard configuration of the model barrels were deprived of whisker input. The plot shows the mean directional preference over 20 networks. Neurons in deprived supra-barrels have no opportunity to learn connections to particular L4 neurons. However, spared supra-barrels are still able to form reasonable somatotopic pinwheel maps. Thus the model does not predict any specific reorganization of spared portions of the map for the isolated whisker trimming case. B Anti-correlated whisker experiment. If a central whisker is consistently deflected in the direction opposite its neighbors, neurons in the central barrel should develop RFs for deflection directions opposite those suggested by their somatotopic location, forming a somatotopically inverted pinwheel in the corresponding supra-barrel. The mean preferred direction for neurons at each location is plotted (N = 20 different networks). This prediction could be tested by training rats on artificial stimuli in which the central whisker is deflected, for example, rostrally () whenever the more caudal whiskers are primarily deflected, during the critical period. Although difficult to perform, this experimental paradigm would be very useful for assessing the time course of map plasticity.