Biological variation in the sizes, shapes and locations of visual cortical areas in the mouse
Biological variation in the sizes, shapes and locations of visual cortical areas in the mouse
Jack WatersID 0 1
Eric Lee 0 1
Nathalie Gaudreault 0 1
Fiona Griffin 0 1
Jerome Lecoq 0 1
Cliff Slaughterbeck 0 1
David Sullivan 0 1
Colin Farrell 0 1
Jed Perkins 0 1
David Reid 0 1
David Feng 0 1
Nile Graddis 0 1
Marina Garrett 0 1
Yang Li 0 1
Fuhui Long 0 1
Chris Mochizuki 0 1
Kate Roll 0 1
Jun ZhuangID 0 1
Carol Thompson 0 1
0 Editor: Nicholas V. Swindale, University of British Columbia , CANADA
1 Allen Institute for Brain Science , Seattle, WA , United States of America
Visual cortex is organized into discrete sub-regions or areas that are arranged into a hierarchy and serves different functions in the processing of visual information. In retinotopic maps of mouse cortex, there appear to be substantial mouse-to-mouse differences in visual area location, size and shape. Here we quantify the biological variation in the size, shape and locations of 11 visual areas in the mouse, after separating biological variation and measurement noise. We find that there is biological variation in the locations and sizes of visual areas.
Data Availability Statement: All relevant data are
within the manuscript and its Supporting
Funding: We wish to thank the Allen Institute
founder, Paul G. Allen, for his vision,
encouragement and support. The funders had no
role in study design, data collection and analysis,
decision to publish, or preparation of the
Competing interests: The authors have declared
that no competing interests exist.
Mammalian neocortex is generally considered to be organized into discrete anatomically and
functionally defined sub-regions or areas. For example, a major portion of posterior cortex is
concerned primarily with vision and is divided into discrete visual areas, >20 areas in primates
] and ~15 in the mouse [
]. Visual areas are arranged into a hierarchy and serve different
functions in the processing of visual information [
] and yet the sizes and shapes of visual
areas appear to vary across individuals of a given species. In mice for example, maps of visual
cortex consist of a stereotyped collection of visual areas, in approximately the same relative
locations in each mouse, but the relative positions of areas and in their sizes and shapes appear
to differ substantially between mice. Such differences in the organization of cortex might affect
the processing of visual information across mice. How much variation is there in the locations,
sizes and shapes of cortical areas from mouse to mouse?
Only a few studies describe differences in the size, shape and locations of cortical areas
across a population of individuals. Differences have been described in the size and shape of
primary visual cortex in humans, macaques, cats, rats and mice, the consensus being that V1
differs in size more than in shape [
]. Necessarily, comparisons were across small numbers
(<25) of individuals and no attempt was made to determine whether the differences resulted
from differing organization of cortex across individuals (biological variation) or simply
measurement error (noise). Separating biological variation from measurement noise requires
statistical analysis of measurements from large numbers of animals. To our knowledge, nobody
has assessed biological variation (after separation from measurement noise) of any cortical
area in any species.
In our previous work, we noted that retinotopic maps of cortical visual areas differed
between mice [
], but did not quantify these differences or determine the relative
contributions of biological variation and measurement noise. Here we quantify the variability in size,
shape and locations of cortical visual areas in the mouse
Results and discussion
Retinotopic maps differ across mice (S1 Fig). The differences between maps presumably
include biological variation and inaccuracies, or measurement noise in the mapping process.
Under the assumption that the retinotopic map is invariant in an individual, repeated map
generation from a mouse will result in maps that differ only because of measurement noise.
This assumption provides a method to isolate biological variation, given maps from a large
enough collection of mice and two or more maps from each mouse. From such a data set, one
can estimate (1) the effects of measurement noise, by comparing retinotopic maps across
mapping sessions in each mouse, and (2) the combined effects of biological variability and
measurement noise, by comparing retinotopic maps across mice. A second assumption, that
measurement noise and biological variation are independent, permits the isolation of
biological variation by subtraction of the variance of the between-session comparisons from the
variance of the between-mouse comparisons. Implicitly, a third assumption is made: that there are
no additional sources of measurement noise when comparing maps across mice, relative to the
comparison across mapping sessions.
We generated retinotopic maps for 60 adult mice by intrinsic signal imaging [
mouse was imaged twice, 11?121 days apart (Fig 1A). As in our previous publication [
retinotopy was displayed using the visual field sign [
] and field sign maps were segmented into
retinotopically-defined cortical areas using a numerical routine [
]. Maps were aligned to
the 3D Allen Mouse Brain Reference Atlas, assisted by surface vasculature images acquired
during mapping (S2 Fig).
The mean sign map included 11 visual areas (Fig 1B; V1, RL, LM, AM, PM, P, RLL, AL,
LLA, MMA, MMP). Consistent with our previous paper [
], there was an almost continuous
ring of field sign positive regions around V1 and the lateral retinotopic border of V1 was
~300 ?m medial to the 3D Allen Mouse Brain Reference Atlas border (Fig 1C and 1D).
Biological variation in the locations of visual areas
To test for biological variation in the locations of visual areas, we compared maps across mice
and across imaging sessions. We reduced each map to a set of points, each point representing
the centroid of a field sign patch and made pairwise comparisons of maps. As a measure of the
difference between each pair of maps, we calculated the paired patch distance (ppd; S3 Fig).
From 60 mice, two imaging sessions per mouse, we made 60 pairwise comparisons across
sessions (one per mouse) and 59 60 = 3540 pairwise comparisons across mice. For each pair of
maps, we defined paired patch distance as the mean of the distances between corresponding
field sign patches:
paired patch distance ?
xj?2 ? ?yi
where, x and y are the coordinates of the centroid of each field sign patch in m-l and a-p axes,
subscripts i and j denote the two maps being compared,
n is the number of field sign patches in both maps
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Fig 1. Repeated retinotopic mapping of mouse cortical areas. (A) Workflow of the Allen Brain Observatory, including
implantation of a 5 mm diameter cranial window and retinotopic mapping at two time points, separated by 11?121 days.
(B) Mean field sign map from 60 mice, with borders and labels for the 11 visual areas studied here. (C) Borders of cortical
areas in the 3D Allen Mouse Brain Reference Atlas. Visual areas are labeled. (D) Mean sign map aligned to the 3D Allen
Mouse Brain Reference Atlas, with atlas borders in white. The color scale bar applies to all field sign maps throughout the
There was no correlation between the time between imaging sessions and
session-tosession ppd, consistent with maps being stable between imaging sessions (S1 Fig, panel B).
Mouse-to-mouse and session-to-session distributions were significantly different (p = 4.6 x
10?9, Mann-Whitney U test), with mouse-to-mouse differences being greater than
session-tosession differences. We conclude that there is biological variation in the retinotopic map.
For each pairwise comparison of maps, one map could be translated relative to the other, or
rotated, scaled or the relative locations of visual areas might differ. Any combination of these
four transformations might be the source of the observed biological variability. In addition,
inaccuracies in our alignment process might generate translation and rotation errors that
differ between mouse-to-mouse and session-to-session comparisons and therefore be
interpreted, erroneously, as biological variation. To separate differences in translation, rotation,
scale and shape (shape, in this context, is the relative locations of patches), we adopted
Procrustes superimposition, an analytical approach used to compare shapes in biological
]. The approach involves the sequential estimation and removal of translation,
rotation and scaling to leave differences in only the locations of patches.
Across maps, the centroid of V1 moved by up to 1 mm in m-l and a-p axes. As might be
expected, the distributions of mouse-to-mouse and session-to-session differences were
different for V1 centroid locations in both a-p and m-l axes (p = 9.0 x 10?6 and 5.1 x 10?12
respectively, Levene?s test, Fig 2A and 2B). As a measure of the scale of each retinotopic map we
calculated a statistic we call the ?centroid size? from the centroids of areas V1, RL and PM, all
three of which were in every field sign map. Centroid size is the square root of the summed
squared distances of each landmark from the centroid [
]. Mean centroid size was 1.46 mm,
with centroid sizes being approximately normally distributed about this mean, most within
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Fig 2. Location, scaling and rotation of maps. (A) Frequency histogram of V1 centroid positions for 3540 pairwise
mouse-to-mouse comparisons and 60 pairwise session-to-session comparisons. Distance is in the a-p axis with higher
numbers corresponding to more posterior locations. (B) Frequency histogram of V1 centroid positions for 3540
pairwise mouse-to-mouse comparisons and 60 pairwise session-to-session comparisons. Distance is in the m-l axis
with higher numbers corresponding to more medial locations. (C) Distribution of scale factors applied to maps, where
scale factor is calculated as the centroid size of the map divided by that derived from the mean field sign map. (D)
Frequency histogram of centroid size differences for 3540 pairwise mouse-to-mouse comparisons and 60 pairwise
session-to-session comparisons. (E) Distribution of rotations applied to maps during alignment. (F) Frequency
histogram of rotations for 3540 pairwise mouse-to-mouse comparisons and 60 pairwise session-to-session
comparisons. (G) Frequency histogram of inter-patch distances for 3540 pairwise mouse-to-mouse comparisons and
60 pairwise session-to-session comparisons, after elimination of translation, scale and rotation differences between
maps. Frequency is displayed as a fractional probability, the integral of each distribution being 1. Lines are lognormal
~20% of the mean (Fig 2C). The mouse-to-mouse distribution of centroid sizes was broader
than the session-to-session distribution (p = 0.0026, Levene?s test, Fig 2D), indicating that
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there was biological variation in the size of the visual map. Rotations were extremely small
(range -0.11 to 0.22 degrees, Fig 2E) and mouse-to-mouse and session-to-session differences
in rotation were similar (Fig 2F). We aligned maps, eliminating differences in location, scale
and rotation. Comparing across the population of maps, neither map shape nor the area of V1
displayed obvious dependence on the scaling applied to the map during alignment (S1 Fig,
panel D, E). After eliminating differences in location, scale and rotation, and re-tested for
biological variation, finding that a significant difference between the distributions remained
(p = 4.4 x 10?5, Mann-Whitney U test; Fig 2G). We conclude that there is biological variation
in the overall shape of the retinotopic map in the mouse, in other words, that the field sign
patches are in different locations in different mice.
We further quantified the differences in centroid location for each field sign patch, aiming
to calculate the biological variation in location for each patch. Our approach is similar to that
of Garrett et al. [
], but here we separate biological variation and measurement noise.
Mouseto-mouse differences in centroid location were greater than session-to-session differences for
all 11 patches and in both a-p and m-l axes (Fig 3A and 3B), permitting us to estimate
biological variation by subtraction of variances. For most patches, biological variation and
measurement noise were approximately equal contributors to mouse-to-mouse differences in the
visual area map (Fig 3B). The standard deviation of biological variation was ~200 ?m for many
patches or ~15% of the diameter of the mean patch (Fig 3C).
Size and shape of each field sign patch
When comparing retinotopic maps from different mice, there appears to be striking variation
in the sizes and shapes of most patches in the map (S1 Fig). We further explored biological
variation in the size and shape of each field sign patch, to determine whether there is biological
variation and to quantify it.
We began by comparing mouse-to-mouse and session-to-session differences in the area of
each field sign patch (Fig 4A). For 9 of 11 patches, the variance of the mouse-to-mouse
distribution was greater than the variance of the session-to-session differences. Fig 4B plots
biological variation for these 9 patches and measurements noise for all 11 patches. The distributions
were significantly different for V1, which was also the patch with the least biological variation
in size, with a standard deviation of 16%. Hence in 50% of mice, V1 is >11% smaller or larger
than average and in 5% of mice, V1 is >32% smaller or larger than average. For the other
patches, mouse-to-mouse distributions were not significantly different from session-to-session
differences (each p > 0.05/11, Levene?s test with Bonferroni correction) and we can be less
confident that there was biological variation in the sizes of the other patches, but the fact that
the variance of the mouse-to-mouse distribution was greater than the variance of the
sessionto-session differences for almost all the patches suggests that there?s biological variation in size
for many of them. Although measurement noise was the main source of variability in patch
size, biological variation was also substantial at 16?56% of the area of the mean patch (Fig 4C).
The mean standard deviation of biological variation across all patches was 32%. Hence in 50%
of mice, the mean patch is >22% smaller or larger than average and in 5% of mice, the mean
patch is >64% smaller or larger than average. There was no correlation between the area of V1
and the age (Fig 4D) or weight (Fig 4E) of the mouse and the areas and locations of patches
differed little with sex or Cre line (Fig 4G, S4 Fig). There was no correlation between the sizes of
patches across mice (p < 0.05/11, Spearman rank-order correlation), so the sizes of
neighboring patches are unrelated.
We investigated biological variation in the shapes of field sign patches using the Jaccard
index, defined as the area of intersection of two patches divided by the area of their union.
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Fig 3. Biological variation in the locations of field sign patches. (A) Frequency histograms illustrating
mouse-tomouse and session-to-session differences in centroid location for AM. Frequency is displayed as a normalized
probability, the integral of each distribution being 1. Lines are fits to a normal distribution. Below: same distributions
normalized to their peaks. (B) Standard deviations of biological variation and measurement noise for distributions of
differences in centroid location. (C) Standard deviation of the biological variation of centroid positions, in a-p and m-l
axes, expressed as a percentage of the maximum width of the mean of each patch.
Jaccard index ranges from 0 (no overlap) to 1 (identical shapes). We calculated differences
pairwise for mouse-to-mouse and for session-to-session comparisons, resulting in
mouse-tomouse and session-to-session distributions of the Jaccard index for each patch. The median
Jaccard indices of mouse-to-mouse and session-to-session distributions were similar for all
patches (Fig 5A) and there was no patch for which the means of the two distributions differed
significantly (each p > 0.05 / 11, Mann-Whitney U test with Bonferroni correction).
Consistent with this conclusion, plots of the cumulative mouse-to-mouse and session-to-session
differences were similar (V1 in Fig 5B), with no indication that mouse-to-mouse differences were
greater than session-to-session differences in patch shape. Hence we find no evidence for
biological variation in the shapes of visual areas, the apparent variability across mice resulting
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Fig 4. Biological variation in the sizes of field sign patches. (A) Histogram of mouse-to-mouse and
session-tosession differences in area of V1. Frequency is displayed as a fractional probability, the integral of each distribution
being 1. Lines are normal distributions. Right: same distributions normalized to their peaks. (B) Standard deviations of
biological variation and measurement noise for distributions of differences in area. (C) For each patch, standard
deviation of biological variation in patch area as a percentage of the area of the mean patch. (D) Area of V1 in the first
imaging session, as a function of postnatal age during the first imaging session. Line is a linear fit. (E) Area of V1 in the
first imaging session, as a function of weight during the first imaging session. Line is a linear fit. (F) Weights of mice at
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first imaging session, sorted by sex (left) and Cre line (right). Mean ? SEM. (G) V1 area in first imaging session, sorted
by sex (left) and Cre line (right). Mean ? SEM.
from measurement noise. This result makes a strong statement about the reliability of border
positions in maps based on intrinsic imaging. The reproducibility of these maps is poor, even
with extensive averaging, likely because the signal-to-noise ratio of intrinsic imaging is low.
One might interpret the resulting border positions as approximate. In contrast, border
locations mapped with GCaMP6 indicators, an approach which can offer a higher signal-to-noise
ratio than intrinsic imaging, can be accurate to within tens of micrometers [
We have assumed that biological variation is the only difference between mouse-to-mouse
and session-to-session comparisons. Might some other mouse-to-mouse difference have been
classified as biological variation? Alignment errors are a concern, but our results show no
evidence of such alignment effects and the resulting errors would likely affect the locations of
visual areas and have little effect on their sizes. Hence alignment errors are unlikely to account
for the observed biological variation in the sizes of visual areas. Mouse-to-mouse differences in
the segmentation of field sign patches, arising from differences in the signal-to-noise ratio of
the underlying images, might contribute to the biological variation in size of patches. We
expect the effect to be greater for peripheral patches (patch P, for example) than for V1 and
other patches near the core of the map.
In summary, we assessed biological variation in the sizes, shapes and locations of field sign
patches in visual cortex of the mouse. Our results provide no evidence for biological variation
Fig 5. Biological variation in the shapes of field sign patches. (A) Median of the distribution of the Jaccard Indices
for mouse-to-mouse and session-to-session comparisons, for each patch. (B) Cumulative differences in V1 for
mouseto-mouse and session-to-session pairwise comparisons.
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in the shapes of visual areas and evidence of only modest biological variation in location, but
the sizes of visual areas differed substantially between mice, with the area of the average region
varying ~2-fold across the population of mice. We were surprised by this result. We reasoned
that there is some minimum amount of cortical tissue required for each visual area to perform
its functions and likely sufficient, but not excess cortex is allocated to each visual area. If the
functions of each visual area are invariant across mice, it seems likely that the required volume
of cortex for each visual area is similar across mice. Hence our expectation was that there might
be variability in the locations and shapes of visual areas, but that size would be more
constrained. Our results are not consistent with this expectation, raising the possibility the roles of
visual areas in the processing of visual information is more flexible than we had appreciated.
Materials and methods
Retinotopic maps were generated from 60 mice of 7 genotypes: 20
Cux2-CreERT2;Camk2atTA;Ai93 mice, 5 Emx1-IRES-Cre;Camk2a-tTA;Ai93 mice, 1 Emx1-IRES-Cre;Camk2a-tTA;
Ai94 mouse, 7 Nr5a1-Cre;Camk2a-tTA;Ai93 mice, 10 Rbp4-Cre;Camk2a-tTA;Ai93 mice, 11
Rorb-IRES2-Cre;Camk2a-tTA;Ai93 mice and 6 Scnn1a-Tg3-Cre;Camk2a-tTA;Ai93 mice.
Mice were crosses of the following lines:
Emx1-IRES-Cre: B6.129S2-Emx1tm1(cre)Krj/J [
Scnn1a-Tg3-Cre  https://www.jax.org/strain/009613
CaMK2a-tTA: B6.Cg-Tg(Camk2a-tTA)1Mmay/DboJ [
Ai93: B6;129S6-Igs7tm93.1(tetO-GCaMP6f)Hze/J [
Ai94: B6.Cg-Igs7tm94.1(tetO-GCaMP6s)Hze/J [
Retinotopic mapping and identification of visual areas
All animal procedures were approved by the Institutional Animal Care and Use Committee of
the Allen Institute for Brain Science. Retinotopic maps were generated by intrinsic signal
imaging as part of the Allen Brain Observatory data product (http://observatory.brain-map.
org/visualcoding/) and imaging methods are described in the Allen Brain Observatory
10813483/VisualCoding_Overview.pdf). Retinotopic mapping was performed under
isoflurane anesthesia (1?1.4%, inhaled). Altitude and azimuth maps were converted to a field sign
map and the borders between areas were identified using code presented in our previous
]. Here we took the additional step of automating the identification of 11 visual areas.
The field sign is defined as the sine of the difference in angle between altitude and azimuth
gradients. Field sign was calculated pixelwise, yielding a field sign map. Visual areas appear on
the field sign map as regions of consistent field sign (positive or negative) and the field sign
passes through zero at borders between visual areas.
Alignment of maps
Maps were aligned across mice and imaging sessions. Images from the first imaging session
were aligned to the 3D Allen Mouse Brain Reference Atlas as described previously [
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534/Mouse_Common_Coordinate_Framework.pdf). The origin of the reference space is an
arbitrary point anterior, ventral and lateral (left) of the brain. The mean location of V1 was
9.14 mm posterior and 3.01 mm medial from the origin of the reference space. Images from
the second imaging session were aligned to the first session using the surface vasculature
images and a scale-invariant feature transform algorithm implemented in opencv.
Translation, scaling and rotation of maps
In Procrustean morphometrics, shape is what remains after the removal of differences in
translation, scale (or size) and rotation [
]. To compare the shapes of retinotopic maps, we
used a Procrustean approach, eliminating map-to-map differences in translation, scale and
rotation. We converted each map into a collection of centroids, one for each field sign patch.
We translated maps such that the centroid of V1 was at the origin. We normalized the size of
each map using the centroids of patches V1, RL and PM since these three patches were
identified in every map. These three centroids form a triangle and we scaled each map such that the
circumference of this triangle equaled one. Finally, we rotated each map about the origin (the
centroid of V1) to minimize the sum of distances between the centroids of corresponding
patches (RL in map 1 vs RL in map 2, LM vs LM, etc.).
Data sets and analysis code
We include two Jupyter notebooks with this manuscript. The ?data viewer? notebook provides
code to download and view the data sets. The ?analysis? notebook contains most of the plots
and analyses in the manuscript and some additional analyses.
S1 Fig. Field sign maps from 60 mice. (A) Field sign maps from the first imaging session for
each of 60 mice, to illustrate the mouse-to-mouse variability in field sign maps. (B) Plot of
paired patch distance (ppd) as a function of time between first and second imaging sessions.
Line: best linear fit, slope -0.08. (C) Histogram of the number of times each patch appeared in
retinotopic maps. Each patch could occur in a maximum of 60 maps (one for each of 60 mice)
for each of the first and second imaging sessions. The right column indicates the number of
mice in which the patch was visible in both imaging sessions. (D) Relationship between the
scale factor applied to each map and its shape. Shape was measured as the ppd of the map in
pairwise comparison with the mean sign map (from 60 mice). Each point represents one map
from session 1. (E) Relationship between the scale factor applied to each map and its relative
V1 area, where relative V1 area is V1 area in the map divided by the area of V1 in the mean
sign map. Each point represents one map from session 1.
S2 Fig. Schematic of analysis workflow. Schematic illustration of the sequence of steps in the
core of the analysis.
S3 Fig. Illustration of paired patch distance. (A) Field sign maps from two mice. For each
map, the postnatal age (in days) during imaging is provided. Comparison across mice (across
rows) describes the sum of biological variation and measurement noise. Comparison across
imaging sessions (down columns) describes measurement noise. The difference between the
two comparisons provides an estimate of biological variation. (B) Maps of centroid locations
for each field sign patch in mouse 1. Each centroid is colored to match the field sign of its
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parent field sign patch. (C) Comparison of two maps, with the distances between patches
illustrated with black lines. The paired patch distance (ppd) is the mean of these distances.
S4 Fig. Patch locations and surface areas, by Cre line. Centroid positions (a-p axis, left
column; m-l axis, central column) and surface area (right column) for each patch, sorted by Cre
line. No significant differences between Cre lines in any plot (ANOVA, p > 0.05).
S1 Codeipynb. Jupyter notebook with code to download and view data sets.
S2 Codehtml. HTML copy of notebook_data_viewer.ipynb.
S3 Codeipynb. Jupyter notebook containing analysis of data sets.
S4 Codehtml. HTML copy of notebook_analysis.ipynb.
We wish to thank the Allen Institute founder, Paul G. Allen, for his vision, encouragement and
Conceptualization: Jack Waters.
Data curation: Jack Waters.
Formal analysis: Jack Waters.
Investigation: Eric Lee, Nathalie Gaudreault, Fiona Griffin, Kate Roll.
Methodology: Cliff Slaughterbeck, David Sullivan, Colin Farrell, David Reid.
Software: Jack Waters, Jed Perkins, David Feng, Nile Graddis, Yang Li, Fuhui Long, Chris
Validation: Jack Waters.
Visualization: Jack Waters.
Writing ? original draft: Jack Waters.
Writing ? review & editing: Jack Waters, Eric Lee, Nathalie Gaudreault, Fiona Griffin, Jerome
Lecoq, Cliff Slaughterbeck, David Sullivan, Colin Farrell, Jed Perkins, David Reid, David
Feng, Nile Graddis, Marina Garrett, Yang Li, Fuhui Long, Chris Mochizuki, Kate Roll, Jun
Zhuang, Carol Thompson.
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