Retinal Circuitry Crash Course

    As mentioned in the previous post, the retina is actually an outcropping of the Central Nervous System and as such it is composed of interconnected neurons. Retinal neurons perform complex operations on the visual signals that are transduced by photoreceptors. But why wouldn’t the retina simply send the information directly from the photoreceptors and let the brain process the signals? There are many reasons, however, the simplest and most straight forward answer is that there is a wiring bottleneck from eye to brain: There are ~ 6.4 million cone and 110-125 million rod photoreceptors in the human eye.\(^1\) If they were to all send axons to project to the brain, this would make the optic nerve prohibitively large and cause all sorts of problems. For example, the point of exit for the optic nerve from the eye creates a space, the optic disc, where there are no photoreceptors and therefore is a blind spot. We typically aren’t perceptually unaware of our blind spot. However, I you would like to convince yourself it exists, please check out this demo from Dr. Michael Bach’s Optical Illusions & Visual Phenonmena page.

    Evolutionary pressures to simultaneously increase visual acuity (more photoreceptors) while reducing the size of the optic disc (less axons) favor retinal preprocessing of visual information. The retina compresses the information from the photoreceptors by intermixing the signals with both vertical and horizontal connections across the layers of retinal circuitry. Vertical connectivity is made through layers of the retina from the photoreceptors \(\rightarrow\) bipolar cells \(\rightarrow\) Retinal Ganglion Cells (RGCs). RGCs in the Ganglion cell layer (see figure below) are the output cells of the retina; their axons project through the optic nerve and onwards to the brain. Horizontal connections are established in within layers to interconnect photoreceptors by the Amacrine cells and to interconnect bipolar cells with the Horizontal Cells. As a result, the signals of ~116-132 million photoreceptors are reduced to the output of approximately 1 million RGCs. That reduces the number of axons by two orders of magnitude!

Image credit

Parallel Pathways of Retinal Ganglion Cells

    It’s not just about signal compression, because the retina performs some complex transformations on the photoreceptor signals. For example, there are multiple classes of RGCs that, through distinct anatomy, morphology and connectivity within the retina, effectively carry distinct visual information across parallel pathways from the retina to the brain for further processing\(^2\). In the primate retina, the most numerous ganglion cell classes are the Magnocellular (M) and Parvocellular (P) RGCs. There are certainly many other RGC classes\(^3\), however, in this post we will focus on M & P RGCs as examples.

    There are many differences between M and P RGCs. Perhaps most the most notable are the differences in physiological responses between the two cells classes, where a physiological response refers to the neurons’ changes in electrical excitability due to an environmental stimulus. Parvocellular RGCs are commonly observed to have longer, or sustained responses that are preferential to red-green chromatic stimuli whereas Magnocellular RGCs typically have a shorter or ‘transient’ response that is preferential of achromatic (light-dark) luminance stimuli.\(^{4,5}\) This difference in response arises due to differences in patterns of connectivity and one way that this manifests is a difference in receptive field size. The receptive field of a RGC refers to the region of visual space where changes in visual stimuli will elicit a change, or physiological response from the cell.

    In the following code, we will explore a data set adapted from Cronin & Kaplan (1994) that demonstrates the differences in receptive field sizes for M and P RGCs.\(^7\) RGC receptive fields are described as having a center-surround structure: vertical connections from the bipolar layer form the center input which has an antagonistic relationship to the presumably horizontal connections that make up the surround. Here, Cronin and Kaplan measured the receptive field center sizes for M and P RGCs in the primate retina:

#load the data into the R environment
url <- 'https://raw.githubusercontent.com/SmilodonCub/DATA621/master/macaqueRGCs.csv'
Macaque_RGCs <- read_csv( url )
glimpse( Macaque_RGCs )

## Rows: 91
## Columns: 3
## $ Eccentricity <dbl> 3.525, 6.234, 6.531, 7.718, 8.386, 11.503, 11.800, 12.542…
## $ Radius       <dbl> 0.098, 0.093, 0.122, 0.105, 0.123, 0.113, 0.189, 0.141, 0…
## $ Class        <chr> "M", "M", "M", "M", "M", "M", "M", "M", "M", "M", "M", "M…

Let’s visualize the receptive field center sizes for M and P RGCs as a function of Eccentricity.
Eccentricity refers to how far from the center of vision the receptive field is located and is measure in degrees of visual angle.

#visualize with ggplot
ggplot( data = Macaque_RGCs, aes( x = Eccentricity, y = Radius, col = Class) ) +
  geom_point(alpha = 0.5, size = 3) +
  geom_smooth( method = 'lm' ) +
  theme_classic() +
  ggtitle('Receptive Field Center Size', subtitle = 'M & P center radius as a function of retinal eccentricity') +
  ylab( 'Center Radius (deg)' ) +
  xlab( 'Eccentricity (deg)' )

The figure above plots receptive field center radius for M and P RGCs. We can see a clear difference between the two distributions.
Here we visualize box plots of the Radius and Eccentricity distributions for both cells classes

p1 <- ggplot( data = Macaque_RGCs, aes( x = Class, y = Radius ) ) +
  geom_boxplot() +
  theme_classic() +
  ggtitle( 'Radius' ) +
  ylab( 'Radius (deg)' )

p2 <- ggplot( data = Macaque_RGCs, aes( x = Class, y = Eccentricity ) ) +
  geom_boxplot() +
  theme_classic() +
  ggtitle( 'Eccentricity' ) +
  ylab( 'Eccentricity (deg)' )

grid.arrange( p2, p1, ncol = 2 )

From the box plots above we observe:

• Eccentricity: While there is a tendency for M cells to be found further in the periphery, there is a lot of overlap for the two distributions.
  • Welch 2 sample t-test finds no significant difference
• Radius: There is relatively greater separation between the M & P receptive field radius distributions
  • Welch 2 sample t-test finds a strong significant difference between M & P Radius distributions

Next we will use a linear regression to further characterize the distinctions between the two cell classes.

Macaque_RGCs_d <- Macaque_RGCs %>%
  mutate( Mcells = Class == 'M' ) #add a dummy variable
RGC_lm<- lm( data = Macaque_RGCs_d, Radius ~ Mcells + Eccentricity )
summary( RGC_lm )

## 
## Call:
## lm(formula = Radius ~ Mcells + Eccentricity, data = Macaque_RGCs_d)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.054479 -0.016994 -0.002438  0.014722  0.118379 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.0241523  0.0049620   4.867 4.93e-06 ***
## McellsTRUE   0.0830616  0.0072133  11.515  < 2e-16 ***
## Eccentricity 0.0038181  0.0003339  11.435  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02636 on 88 degrees of freedom
## Multiple R-squared:  0.786,  Adjusted R-squared:  0.7811 
## F-statistic: 161.6 on 2 and 88 DF,  p-value: < 2.2e-16

plot( RGC_lm )

Performing a linear regression on the data yields a significant fit with an \(R^2\) value that explains ~78% of the variance in the data. We interpret the model coefficients as follows:

• With an increase in Radius of 1 deg, the eccentricity increases by ~0.004 deg for either cell class.
• P cells (Intercept) have estimated average Radius of 0.024deg
• M cells (McellsTRUE) have estimated average Radius of (0.024 + 0.083) deg

This linear regression suggests that the cell Class is an important and statistically significant factor in determining the radius of a receptive field at a given eccentricity. However, we can also see from the diagnostic plots that there are some systematic changes of residual variance as a function of fitted values. This is likely due to some non-linear behavior in observations that are measured further out in the periphery of the retina.

Conclusion

    The simple analysis above demonstrates that there are measurable significant differences between retinal ganglion cell classes of the retina. In future posts we will explore retinal circuitry in more depth to come to a better understanding about how visual signals are represented and carried form the eye to the brain.

References

1. NIH Facts and Figures Concerning the Human Retina
2. Wässle, H. (2004). Parallel processing in the mammalian retina. Nature Reviews Neuroscience, 5(10), 747-757.
3. Dacey, D. M., Peterson, B. B., Robinson, F. R., & Gamlin, P. D. (2003). Fireworks in the primate retina: in vitro photodynamics reveals diverse LGN-projecting ganglion cell types. Neuron, 37(1), 15-27.
4. Yeh, T., Lee, B. B., & Kremers, J. (1995). Temporal response of ganglion cells of the macaque retina to cone-specific modulation. JOSA A, 12(3), 456-464.
5. Lee, B. B., Pokorny, J., Smith, V. C., Martin, P. R., & Valbergt, A. (1990). Luminance and chromatic modulation sensitivity of macaque ganglion cells and human observers. JOSA A, 7(12), 2223-2236.
6. Lee, B. B. (1996). Receptive field structure in the primate retina. Vision research, 36(5), 631-644.
7. Croner, L. J., & Kaplan, E. (1995). Receptive fields of P and M ganglion cells across the primate retina. Vision research, 35(1), 7-24.