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. 2013 Oct 2;33(40):15747-66.
doi: 10.1523/JNEUROSCI.1037-13.2013.

Mechanisms for stable, robust, and adaptive development of orientation maps in the primary visual cortex

Jean-Luc R Stevens  1 , Judith S Law, Ján Antolík, James A Bednar
Affiliations

Mechanisms for stable, robust, and adaptive development of orientation maps in the primary visual cortex

Jean-Luc R Stevens et al. J Neurosci. .

Abstract

Development of orientation maps in ferret and cat primary visual cortex (V1) has been shown to be stable, in that the earliest measurable maps are similar in form to the eventual adult map, robust, in that similar maps develop in both dark rearing and in a variety of normal visual environments, and yet adaptive, in that the final map pattern reflects the statistics of the specific visual environment. How can these three properties be reconciled? Using mechanistic models of the development of neural connectivity in V1, we show for the first time that realistic stable, robust, and adaptive map development can be achieved by including two low-level mechanisms originally motivated from single-neuron results. Specifically, contrast-gain control in the retinal ganglion cells and the lateral geniculate nucleus reduces variation in the presynaptic drive due to differences in input patterns, while homeostatic plasticity of V1 neuron excitability reduces the postsynaptic variability in firing rates. Together these two mechanisms, thought to be applicable across sensory systems in general, lead to biological maps that develop stably and robustly, yet adapt to the visual environment. The modeling results suggest that topographic map stability is a natural outcome of low-level processes of adaptation and normalization. The resulting model is more realistic, simpler, and far more robust, and is thus a good starting point for future studies of cortical map development.

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Figures

Figure 1.
Figure 1.
Stable development of orientation maps in ferret striate cortex. Orientation maps recorded in the primary visual cortex of one ferret (animal 1-3-3630) at the postnatal ages indicated are shown. In these polar maps, pixel color indicates orientation preference, and pixel brightness indicates the strength of orientation tuning. The selectivity of each map is normalized independently, making blood vessels visible at P31 (e.g., the blue streak in the top left corner), but not at P42, once orientation selectivity has developed. As the maps mature, iso-orientation domains become visible as colored regions that become more strongly responsive over time, without changing the overall map pattern. Data are reproduced from the study by Chapman et al. (1996).
Figure 2.
Figure 2.
Development of orientation maps measured by chronic optical imaging in ferrets. A, Recorded selectivity (red square markers) and stability values (blue round markers) for all eight ferrets, as a function of postnatal day [replotted data from the study by Chapman et al. (1996), their Figs. 4, 7]. Stability is quantified by the average difference in preference of each orientation map with the final map, as defined by Equation 1. A common selectivity and stability scale is used to allow comparison between ferrets. All values are in arbitrary normalized units, using the lowest recorded value as the zero reference point and the highest recorded value as the maximum (see Materials and Methods). B, The mean selectivity and stability across ferrets as a function of postnatal day, with the ±95% confidence intervals for each day indicated by the shaded area around the mean line. Selectivity and stability increase steadily and simultaneously over development so that once neurons are selective, they are organized into a map with the same form as the final measured map. These results show that selectivity does not precede increasing stability, indicating stable map development. C, As a reference for later modeling work, the final orientation preference map (without selectivity) for ferret 1-3-360 on day P42 (Fig. 1, rightmost plot) is shown. The map is organized into regularly repeating hypercolumns in all directions, as seen by the ringness in the Fourier power spectrum, plotted with the highest amplitude component in black. The center value is the DC component, and the midpoint of each edge represents half of the highest possible spatial frequency in the cardinal directions (i.e., the Nyquist frequency). This Fourier spectrum is used to calculate the average periodicity of the map, which is then plotted as a hypercolumn area Λ2, covering one period in the cardinal directions (white boxed area). Figure 3 illustrates how to use these calculations to determine whether a model map resembles this animal data.
Figure 3.
Figure 3.
Evaluating map quality as the deviation from π pinwheel density (ρ). A, High-quality, realistic, orientation preference and selectivity map with approximately π pinwheel density (3.146), from the final model to be discussed in this paper (GCAL). Corresponding preference-only map is shown in Ca. Pinwheel density is defined as the average number of pinwheels (white circles) per hypercolumn area (Λ2) indicated by the white boxed area (A, B). Pinwheels are identified at the intersection of the zero contours of the real and imaginary components in polar representation (white and black contours respectively). The periodicity of hypercolumns is estimated from the radius of the ring in the Fourier power spectrum (FFT) using the fitting method described in Kaschube et al. (2010). B, A lower-quality map generated from the first model introduced in this paper (L), which has visible discontinuities in OR preference seen in Cb. The greater pinwheel density (5.917) is due to a higher pinwheel count and a larger hypercolumn area due to more widely spaced orientation blobs. The histogram (FFT plot inset) indicates mean spectral power as a function of radius, the red line indicates the least-squares fit (Kaschube et al. 2010, their supporting online material, Eq. 7), and the blue arrow indicates the estimated peak spectral power radius (A, B). C, A selection of model maps ordered by pinwheel density with pinwheel count to hypercolumn area ratio, shown in parentheses. Lower-quality maps usually have higher estimated pinwheel counts and correspondingly higher pinwheel densities, with pinwheel counts so large for very poor maps as to be effectively undefined. D, Pinwheel density of three species (diamonds) and simulated maps (circles) as a function of hypercolumn size [data replotted from the study by Kaschube et al. (2010)]. Horizontal lines indicate median values of each cluster with the medians of high quality model maps also clustered around π. E, Normalized, heavily tailed gamma distribution used to transform pinwheel density into a suitable metric on a unit interval with values for maps a, b, and c.
Figure 4.
Figure 4.
General model architecture. The four models discussed in this paper consist of two-dimensional arrays of computational units representing local groups of neurons at each visual processing stage. Connections to one unit in each sheet are shown with afferent connections in yellow and lateral connections in red. The V1 region shown here covers ∼4 × 4 mm of ferret cortex, matching the cortical area represented by all the simulated orientation map plots in this paper. V1 units receive lateral excitatory (small circle) and lateral inhibitory (large circle) connections from nearby V1 units, leading to the “bubbles” of activity seen on the V1 sheet. V1 units receive afferent input from sheets representing the ON and OFF channels, representing the action of retinal ganglion cells and the lateral geniculate nucleus, which in turn receive input from the retinal photoreceptors. The difference-of-Gaussian afferent connections from the photoreceptors to the ON and OFF units form a local receptive field on the retina, and cause ON-center units to respond to light areas surrounded by dark, and OFF-center units to dark areas surrounded by light. Neighboring neurons in the ON and OFF sheets have different but overlapping receptive fields. Input to the retinal photoreceptors can be any type of patterned image, such as the small natural image patch shown here. The GCL and GCAL models have additional lateral inhibitory connections within the ON and OFF sheets, but otherwise all four models discussed share identical initial weight profiles, spatial extents, and projection strengths.
Figure 5.
Figure 5.
Model L develops maps, but is not stable. A, Model development at six different iteration time points for a single simulation. Self-organization was driven by two elongated Gaussian patterns at 25% contrast per iteration, with an example inset into the plot for iteration 0. Polar orientation maps from the beginning of development to the final map at iteration 20,000 are shown. Each unit is color coded according to orientation preference, as shown by the color key. The brightness and saturation of the color indicates the strength of orientation tuning of the afferent connections, and each panel corresponds to ∼4 × 4 mm of visual cortex (a 1.0 × 1.0 area in sheet coordinates). B, Afferent connections from the ON sheet to V1 are shown for an arbitrary set of V1 units throughout development. Initially random connections are strengthened and weakened by Hebbian learning, forming orientation-selective receptive fields, but the map patterns change significantly over time. These results, while an improvement over existing models that have additional, biologically implausible mechanisms for reducing stability to improve their final map organization, represent a baseline for the results of the later models (AL, GCL, and GCAL). The behavior of L is analyzed further in Figure 6, and the last map shown corresponds to Figure 6E.
Figure 6.
Figure 6.
Model L: basic model has relatively poor stability, map quality, and robustness to contrast. A, B, The transfer functions from photoreceptor activity to LGN activity (A) and from LGN activity to V1 afferent response (B). Both transfer functions have unit slope, and V1 units have a fixed threshold of θ = 0.2. C, The mean map stability (green), selectivity (red), and map quality (blue) as a function of contrast, across 10 simulations with randomized input sequences. Shaded areas indicate ±95% confidence intervals. For low-contrast inputs, neurons are not activated, and thus no learning occurs (point D); at slightly higher contrasts neurons have higher stability and selectivity (point E), but at the highest contrasts (point F) neurons are very unstable. Neurons have a relatively high selectivity and stability in a small range of contrasts for which the model has been tuned (contrasts 15–30%). D–F, Organization of model L at the end of development (iteration 20,000) at 10% (D), 25% (E), and 100% (F) contrast. Polar orientation preference maps with estimated pinwheel positions, along with sample inputs (inset) and afferent connection fields (CFs) from the ON sheet to V1 neurons for an arbitrary selection of model neurons (evenly spaced along the vertical midline of the map), are shown. The corresponding two-dimensional FFTs are shown, with 1D the spectral power histogram (green), function fit (red), and estimated peak position (blue arrow) used to estimate the hypercolumn distance (white scale bar). These values determine the value of the map metric, which is fairly poor even for the best L maps due to the large number of pinwheels identified. On the right, the stability and selectivity are plotted as a function of simulation time for that contrast, showing the average across all 10 random seeds with the ±95% confidence intervals. D, For low-contrast inputs (contrast 10%) orientation maps do not develop, yielding nominally high stability values that are meaningless because the selectivity remains low. E, Maps are well ordered, and development is somewhat stable, within the “tuned” range of contrasts (contrast 25%, as in Fig. 5). F, Orientation maps for high-contrast patterns (100% contrast) are highly disorganized, with sharp boundaries between hypercolumns and a non-ring-shaped FFT. Afferent connections are highly orientation-selective imprints of the elongated Gaussians presented to the photoreceptor sheet, and map development is highly unstable, indicated by an early rise in selectivity without a corresponding increase in stability. Note that the final value of each stability plot will always be 1.0; the final map compared with itself has a stability index of unity. Overall, although L develops maps, it fails to be robust to contrast, develops relatively poor quality maps, and is not very stable compared to the ferret data.
Figure 7.
Figure 7.
Model AL: adding homeostatic threshold adaptation improves selectivity, stability, and map quality across all contrasts. All plotting conventions (colors, symbols, and scale bars) are as in Figure 6. A, The transfer function from photoreceptor activity to LGN activity remains unchanged. B, Each V1 unit now possesses an independent adaptive threshold θ that is automatically adjusted to maintain a fixed target activity. C, Maps are more stable across contrast, with higher selectivities at high contrast than the L model. Map quality is relatively high throughout, with a drop at high contrasts. D, The AL model can respond and self-organize at lower contrasts by lowering the adaptive threshold of V1 units. E, AL self-organizes into higher-quality maps than L at identical contrasts, though stability has suffered compared to D. F, Adaptation greatly improves the map quality relative to the L model at high contrasts. However, the map still suffers from sharp boundaries due to highly selective connection fields (CFs) that are imprints of the elongated Gaussians presented to the photoreceptor layer, and the FFT becomes non-ring-shaped at high contrast. Stability is also very poor (with selectivity achieved long before stability), because the afferent weights continually reorganize at high contrasts. Thus, homeostatic adaptation offers significant benefits over the L model, but is not sufficiently robust or stable to account for the animal data.
Figure 8.
Figure 8.
Model GCL: adding contrast-gain control independently improves stability and map quality. All plotting conventions (colors, symbols, and scale bars) are as in Figure 6. A, Contrast-gain control in the ON/OFF sheets results in a nonlinear transfer function, compressing unbounded photoreceptor inputs into a bounded range of LGN activities. B, V1 units share the same fixed threshold as those in the L model. C, Map quality is improved across all contrasts and map stability no longer degrades as contrast increases. Selectivity remains both high and stable with increasing contrast. D, At the low-contrast point, GCAL can just begin to self-organize as contrast-gain control boosts enough of the afferent signal over the fixed V1 threshold for some Hebbian learning to occur. E, GCL self-organizes into higher quality maps than L at the same 25% contrast level. Unlike the AL model, some small areas of the map fail to self-organize properly, resulting in regions of low selectivity and clusters of pinwheels. F, For high (100%) contrast inputs, map quality remains consistently high, connection fields (CFs) remain well formed, the map remains smooth and the FFT is appropriately ring shaped. However, small areas of the map fail to self-organize or develop selectivity, as shown by the noisy connection field. Overall, gain control supports robust and stable map development across contrasts, but some neurons are left behind as the others develop, and cannot reach threshold, leading to unevenly organized maps.
Figure 9.
Figure 9.
Model GCAL: combining homeostatic adaptation with gain control yields high-quality, selective, stable maps at all contrasts. All plotting conventions (colors, symbols, and scale bars) are as in Figure 6. A, The contrast-gain control mechanism introduced in GCL is retained. B, V1 units now have the same adaptive threshold (θ) as in the AL model. C, Map quality metric indicates that all GCAL maps have very close to π pinwheel density for all simulated orientation maps (also see Fig. 3D), with high stability and selectivity across all contrasts. D–F, Maps are properly self-organized at all contrasts, with ring-shaped FFTs. At high contrast, GCAL remains smooth and does not suffer from low-selectivity pinwheel clusters or noisy connection fields (CFs) due to the introduction of the homeostatic threshold. Stability increases alongside selectivity, indicating highly stable map development. The GCAL model robustly generates high-selectivity, highly stable, high-quality maps.
Figure 10.
Figure 10.
Stable map development before and after eye opening. A, Polar orientation maps recorded using chronic optical imaging at different ages in one ferret [Fig. 1A, ferret 1-3-3630; reprinted from the study by Chapman et al. (1996)]. Scale bar, 2 mm. B, Simulated GCAL polar orientation maps. Noisy disk patterns drive the map development until 6000 iterations, after which natural images are presented to the model retina. A, B, Both the ferret and model map have a ring-shaped FFT (inset in the final map plot of each). C, Afferent connections from the ON sheet to V1 are shown for an arbitrary set of model V1 units throughout development, to illustrate how neurons become more selective over time. D, Orientation stability indices (Eq. 1) across development for the ferret from A, replotted from Figure 2B for comparison. E, SI for the simulation shown in B. As selectivity develops in both the ferret and GCAL, the map smoothly increases in stability, indicating a highly stable process of development. Stability can also be seen by tracking individual features of the orientation map across time, again for the ferret and for GCAL. These results show that the mechanisms in GCAL are sufficient to account for the observed levels of stability in ferret map development.
Figure 11.
Figure 11.
Experimental and GCAL model orientation maps developed in orientation-biased environments. A, Orientation map measured in a normally reared kitten at postnatal day 84 and orientation histogram. The color and brightness indicate the preferred orientation and the orientation magnitude, respectively. The color code for preferred orientations is shown to the side. Scale bars: 2 mm. B, Orientation map measured in a kitten at postnatal day 42 after 13 d of goggle rearing with vertical lines. Orientation histogram now shows a strong bias toward vertical orientations. Reprinted from Tanaka et al. (2009). C, Orientation preference maps during development from a GCAL simulation driven by noisy disk patterns until 6000 iterations, after which natural images that have been anisotropically blurred vertically are presented to the model retinal photoreceptors. D, Histograms show an expansion of yellow (vertically preferring) regions in the orientation after eye opening, reflecting the statistics of the natural image input and reproducing the results observed in biological map development.
Figure 12.
Figure 12.
GCAL model: contrast-invariant orientation tuning. Example orientation tuning curves for three representative model neurons, measured at the indicated contrasts. Orientation tuning width remains constant despite changes in contrast (except for small deviations at the lowest contrasts), as confirmed by the normalized tuning curves (inset).
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