Download Spatial regularity among retinal neurons

Revised June 2002
To be published in 2003
Contribution to
‘The Visual Neurosciences’
eds. L.M. Chalupa and J.S. Werner
MIT Press
Author’s interim layout
Spatial regularity among retinal neurons
Jeremy E. Cook
Department of Anatomy and Developmental Biology, University College London,
Gower Street, London WC1E 6BT, UK
Short title:
Spatial regularity among retinal neurons
Corresponding author:
Jeremy E. Cook, Department of Anatomy and Developmental Biology,
University College London, Gower St., London WC1E 6BT, UK.
Tel: (44) 20 7679 3374; Fax: (44) 20 7679 7349; E-mail: [email protected]
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1. Introduction: patterns and tiles
In this chapter, we ‘zoom out’ from the study of individual retinal neurons and circuits to a
consideration of how these individuals are organized across the retinal surface. In particular, we focus
on an almost universal tendency for these neurons to lie in regular patterns. Although regularity can
be a consequence of uniform size and tight packing, it also occurs among neurons that are widely
spaced. In either case, it fulfils a behavioral requirement that each class of functional circuits should
sample the visual scene systematically and completely, so that vital features (such as prey and
predators) do not go undetected.
Regular arrays of retinal neurons often extend dendrites in a competitive, territorial manner
that minimizes the overlap of their dendritic fields and causes them to tesselate, ‘tiling’ the retina like
the individual pieces (Latin: tesserae) of a ceramic mosaic. By convention, regular arrays of neuronal
somata are often called ‘neuronal mosaics’ even if precise dendritic tiling has not been shown
directly, and the term ‘mosaic’ is used in this sense throughout the chapter. It is important to be aware
that geneticists and developmental biologists exploit the analogy of the tiled mosaic in another way,
using it to describe mixtures or clusters of cells with distinct histories or genotypes and emphasizing
the potential for abrupt contrasts at the boundaries of adjacent tesserae; these two senses of ‘mosaic’
may confront each other uneasily in studies of retinal developmental genetics.
Neuronal mosaics are informative in many different ways. The following sections briefly
review their implications for the function of the mature retina and the elucidation of its many
neuronal types, consider what they can tell us about retinal development and evolution, summarize
the methods used for their quantitation, and look ahead to questions that remain.
2. Retinal mosaics and visual function
As discussed in Chapter [##], the retina is organized in a way that allows each part of the image to be
analyzed by many local circuits, working in parallel to assess different aspects of brightness, contrast,
color and movement. These analyses demand different degrees of spatial resolution, so neurons with
different functions are repeated across the retina at different intervals. Neurons that report fine detail
are always small and closely spaced, whereas neurons that report movement, or the widespread
changes in luminosity that may herald a predator, are often large and broadly spaced. In general, the
spacings of overlapping circuits with distinct functions vary independently, and their mosaics are also
spatially independent, so the retina as a whole cannot be accurately described as modular even though
there are modular aspects to its function and to its development (Reichenbach & Robinson 1995;
Rockhill et al. 2000). In this respect the retina resembles the visual cortex, where functional maps are
also overlaid in a flexible way that is repetitive but not strictly modular (Swindale 1998).
The significance of the density and geometry of the sampling array is discussed in detail in
Chapter [##]. Here, we note only that the considerable contrasts of interval and scale between the
functional types are made more extreme by regional variations in species that have a visual streak,
area centralis, macula or fovea. Neurons may conserve their branching patterns during retinal growth,
but they cannot grow uniformly in all dimensions (allometrically) because growth that maintained a
linear scaling relationship between dendritic diameter and length would change their physiological
properties (Bloomfield & Hitchcock 1991). Thus, functionally homologous neurons may look very
different in different regions of the same eye and in eyes of differing size even before genuine
interspecies variation is taken into account (Fig. 1).
Given this complex, multiparametric relationship between neuronal spacing and visual
function, there are two distinct ways in which studying the spatial regularities of neurons can help us
understand how the retina does its job. One is by helping us to decide how much spatial resolution a
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Fig. 1 Variation of mosaic spacing and scale across species.
The graph shows how the spacing of the alpha-a ganglion cell
mosaic varies with eye size (represented as retinal radius) in eight
species of teleost fish, four of them at more than one stage of
growth. The small alpha-a cell is from an adult zebrafish Danio rerio
(marked Dr on the graph); the large one is from the sculpin Bero
elegans (Be), to the same scale. Bar = 100 µm. For further details,
see Cook (1998). © 1998 Plenum Publishing Corporation. Reprinted
by permission.
particular analytical function demands in a particular retinal
region of a particular species at a particular stage in its
growth. Simple cell counts can give us partial answers to such
questions, but neuronal arrays give higher resolutions when
they are regular than when they are not, and some techniques
for measuring spatial regularity have the potential to provide
more accurate density estimates than simple counting alone.
The other, and perhaps more interesting, way is by helping us
to draw up a catalogue of the different neuronal types in the
retina and their functional roles, which is the subject of the
next section.
3. What retinal mosaics tell us about neuronal types
It is hard to discover anything interesting by pooling data from heterogeneous neuronal populations,
so a thoughtful neuroscientist must put a high value on understanding the diversity of functionally
distinct neuronal types in the system under scrutiny. In the retina, mosaics have contributed greatly to
this, not only practically but also by helping to clarify the very concept of a neuronal type. This is a
surprisingly slippery concept to grasp. At one extreme, neurons vary in so many details that (as with
snowflakes) one can argue that no two individuals are ever identical. At the other extreme, the retina
is viewed simplistically by some as containing only five basic kinds of neuron (photoreceptors,
horizontal cells, bipolar cells, amacrine/interplexiform cells, and ganglion cells). The term ‘class’ can
usefully be applied to these most basic divisions; however, within each class, neurons can be further
divided into subclasses, types, subtypes or variants, although there is no consensus yet on the
terminology for such a hierarchy (Cook 1998). Vaney and Hughes (1990) estimated that there could
be as many as 70 functionally distinct neuronal types in a given retina, and subsequent studies have
already confirmed an inventory of about 55 morphologically distinct neuronal types in mammals
(Masland 2001).
3.1 Between-type and within-type variation
In attempting to get a grip on neuronal diversity, it is vital to find ways of distinguishing between two
radically different forms of variation that neurons – indeed all cells in complex organisms – display.
One is the categorical, hierarchical kind that is assumed to underlie cell-fate decisions during
development, where transcriptional mechanisms force cells to choose between predefined pathways,
and positive feedback loops drive those choices to completion. Rowe and Stone (1980) described this,
the kind of variation that distinguishes a cone from a ganglion cell or a red-sensitive cone from a
blue-sensitive cone, as ‘between-type’ variation. The other kind is the continuous variation of size,
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shape and functional properties that we see in the phenotypes of all living things, which Rowe and
Stone (1980) termed ‘within-type’ variation. Much of this may be stochastic and inherently
unpredictable, but some is correlated with external factors that have predictive power. A classic
example is the correlation between the sizes of alpha and beta ganglion cells and their retinal
eccentricities in the cat, which first allowed Boycott and Wässle (1974) to distinguish the two
populations even though the largest (most peripheral) beta cells overlap in size with the smallest
(most central) alpha cells.
In these terms, the task of identifying neuronal types equates to the task of working out which
aspects of neuronal diversity are between-type variation and which are within-type variation. At first
sight, this redefinition may seem unhelpful, even pedantic, because at the level of individual neurons
a distinction may simply not be available. When we measure a character such as cell size across a
mixed population, we often find that the overall distribution is unimodal even though the averages for
the component types may be distinct. Unless a major source of within-type variation can be ‘factored
out’ (as for the cat ganglion cells just described) it is impossible to assign an individual neuron to a
type on this basis, even provisionally. Rodieck and Brening (1983) argued that the problem can be
tackled only by examining many variables at once. In their view, variables of shape, stratification,
receptive field, conduction velocity, transmitter content, projection target and so forth should be
viewed as defining a multidimensional ‘virtual space’ within which every objectively defined
neuronal type (‘natural type’) would be represented as a discrete cluster of points, separable in at least
one dimension from every other cluster. Their argument was helpful in clarifying the problem, and
their approach to solving it remains the ideal approach, but it is so labour-intensive that practical
applications are rare (for an exception, see Kock et al. 1989).
This is where mosaics show their value. The more we can discover about the within-type
variation in a population of neurons, the easier it becomes to isolate between-type differences. The
discovery of a regular array of neurons with complete retinal coverage gives us access to a
presumptive ‘natural’ type laid out for inspection (Fig. 2A).
Presented with such an array, we can hypothesize that the
variation we see among its members is within-type variation.
Then, by noting which features show the most within-type
variation over the population, we can avoid relying on these
features when attempting to assign individual neurons to
specific types.
Fig. 2 Sporadic variation within a mosaic-forming
neuronal type.
These A-type horizontal cells in a cat retina have been immunostained for calbindin. Most of them (A) lie at the border of the outer
plexiform and inner nuclear layers, but others (B) are misplaced
into the ganglion cell layer, where in different circumstances they
could be mistaken for biplexiform ganglion cells. Bar = 100 µm. For
further details, see Wässle et al. (2000). Unpublished photographs
reproduced by kind permission of Prof. Heinz Wässle.
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3.2 Mosaics as guides to within-type variation
The first observations of mosaics were made serendipitously, when particular populations drew
attention to themselves by having an unusual reaction to staining and/or being in an unusual retinal
plane (Stell & Witkovsky 1973; Wässle & Riemann 1978). Observers had little difficulty in deciding
which neurons belonged to the mosaics they described because the property that drew their attention,
often combined with clear evidence of dendritic tesselation, left the issue in no doubt. The concept of
a ‘natural type’ was implicit in the very existence of such a mosaic.
Studies of these ‘self-evident’ mosaics have led to some valuable and durable conclusions.
One, as we have seen, is that absolute soma size is poorly correlated with neuronal type. A second is
that patterns of dendritic stratification tend to be strongly conserved within a mosaic-forming
neuronal type, to the extent that otherwise-similar neurons with distinct stratification patterns almost
always form spatially independent mosaics (Cook 1998). A third conclusion, refuting earlier
assumptions, is that somatic stratification is only weakly correlated with neuronal type. Individual
cells sometimes have their somata ‘misplaced’ into the wrong layer even though they meet the other
criteria for membership of a type and their dendrites tesselate with those of their neighbors (Fig. 2B).
These ‘misplaced’ cells can even include cells that belong to so-called ‘displaced’ types but are not
actually displaced (amacrine cells: Wässle et al. 1987; ganglion cells: Cook & Noden 1998). Indeed,
in some cases there is no ‘right’ or ‘wrong’ layer for the somata of a mosaic-forming population and
they appear to be arbitrarily distributed in depth (Fig. 3). These conclusions exposed serious flaws in
traditional morphological classification schemes for retinal neurons.
A further interesting conclusion was reached by blending in some later observations. Chalupa and his
colleagues (White & Chalupa 1991) found that the alpha ganglion cell mosaics of the cat (both outerand inner-stratified) contained a subset of cells with somatostatin-like immunoreactivity, confined
largely to the inferior (ventral) half of the retina and absent from the region where the density of alpha
cells peaks. It has been widely assumed that a neuron’s expression of neurotransmitter or
neuromodulator genes directly reflects its function, with the result that transmitter content has often
been used as the basis for an arbitrary classification. However, in these studies of a uniform
population, the archetypal mosaic of the mammalian inner retina, this neurochemical marker picked
out some individuals and not others.
While highly reproducible anomalies are known to occur within some natural types (Masland
et al. 1993), and there may be scope for genuine functional differences among mosaic members
(Cook 1998), this example demonstrates that neurochemical phenotypes are no more intrinsically
reliable than morphological phenotypes as guides to neuronal taxonomy. It has long been understood
in fields outside neuroscience that gene expression can sometimes be non-functional; that eukaryotic
cells must often tolerate uncontrolled expression because of constraints imposed by combinatorial
gene regulation. Bowers (1994) has summarized the evidence for neuroscientists, and all authors (and
reviewers) of papers in which neurochemical observations are taken as evidence of neuronal types
should read that summary.
3.3 Exposing hidden mosaics and types
In the outer retina, I have already noted (Section 3.1) that the high regularity of neuronal mosaics may
sometimes allow the identity of a neuron to be confirmed directly by its position. In the less regular
world of the inner retina there is no possibility of this direct approach, but mosaics can help with
neuronal identification in less direct ways.
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Fig. 3 Continuous variation within a mosaic-forming neuronal
type.
Two partially overlapping, alpha-a (outer-stratified) ganglion cells
from the cichlid fish Oreochromis spilurus are seen in profile below,
one with its soma in the ganglion cell layer (GCL) and one with its
soma in the inner nuclear layer (INL). The complete mosaic is
shown above, with iconic symbols representing different degrees of
soma displacement. The somatic part of each symbol marks the
actual location. The mosaic is highly regular but the distribution of
soma depths is arbitrary and sporadic. Bar = 1 mm for retina; 100
µm for cell profiles. For further details, see Cook and Becker
(1991). © 1991 Wiley-Liss, Inc. Reprinted by permission.
For example, in a preparation where most of the relevant neurons are visible, one can learn much
about the type-specific characteristics of an unfamiliar mixed set of neurons merely by attempting to
assign them to mosaics. The trick is to start by defining arbitrary cell-type criteria that are based on all
the observable differences between neurons that make up clusters or clumps. Clustered neurons with
overlapping dendrites are likely to belong to different mosaics, so any features that consistently
distinguish between cluster members are prime candidates for between-type variation. These
provisional cell-type criteria may need to be adjusted arbitrarily, by trial and error, until a regular,
self-consistent set of mosaics emerges. However, their objectivity can then be established by testing
the same criteria on new specimens. It was this iterative approach that made it possible to understand
an atypical and confusing set of large retinal ganglion cell types in a tree frog (Shamim et al. 1999).
Even by such methods, not all functionally distinct types can be distinguished directly by
shape or size. Direction-selective ganglion cells provide good examples of such types, and of others
ways to expose their hidden order. In the rabbit retina, bistratified ON-OFF direction-selective
ganglion cells occur at a much higher spatial density than would seem necessary for uniform retinal
coverage; and they also appear to be randomly distributed. Their high coverage is explained by the
fact that they actually comprise distinct functional types with different preferred directions of motion,
overlaid as a ‘polymosaic’ of overlapping arrays. Even when the distinct types are functionally
identified and compared, they remain morphologically indistinguishable. In this case, the key to
visualizing them is the intracellular injection of a tracer that passes through gap junctions, selectively
coupling cells of the same type. Tracer-coupling shows that they do in fact form regular, independent,
beautifully tesselated mosaics (Vaney 1994a; Amthor & Oyster 1995). This technique is also useful
for revealing the detailed mosaic organization of types that are already morphologically distinguishable (Ammermüller et al. 1993) and for revealing gap-junctional connections between the separate
mosaics of different neuronal types (review: Vaney 1994b; Xin & Bloomfield 1997; Mills 1999).
A separate category of direction-selective ganglion cells, again comprising distinct types with
different preferred directions of motion, projects to the accessory optic system. As before, these cells
appear almost random in their arrangement when taken together. However, spatial correlogram
analysis has been applied to distribution data from a frog, a reptile, a bird and a mammal to show that
these evolutionarily-conserved cells possess exactly the kind of cryptic order that is predicted for a
‘polymosaic’ of overlaid arrays (Cook & Podugolnikova 2001). Since these apparent exceptions have
both turned out to prove the rule, it seems likely that all neurons that integrate signals across their
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dendritic fields (rather than processing them only locally within the dendrites) may form regular
mosaics (DeVries & Baylor 1997; Rockhill et al. 2000). This being so, the combination of high
coverage with low apparent regularity should always trigger a search for hidden mosaics and multiple
functional types.
4. What retinal mosaics tell us about development
Studies of spatial regularity have provided many insights into retinal development. However, our
present state of knowledge, accumulated piecemeal from studies of several model systems, fails to
point to a unifying mechanism that could underlie all mosaic patterns. On the contrary, there seem to
be three separate ways in which mosaics can be established in the retina, with evidence that they may
act in combination, in different developmental contexts.
4.1 Inductive interactions and molecular markers
The interlaced and often highly regular mosaics of retinal photoreceptors are an obvious target for
developmental studies. In fish in particular, the cone mosaic is often geometrically exact and consists
of regularly repeated ‘modules’ (Engström 1963), which has led to speculative comparisons with the
near-crystalline patterning of the compound eyes of insects. In the eye of a fly, cell fate is known to be
determined by a cascade of inductive interactions, mostly between immediate neighbors. The first
photoreceptors of the fly (R8 cells) are formed by a multi-step process of lateral inhibition within an
initially featureless bed of dividing cells, and act as reference-points for the construction of each
ommatidial facet of the eye. This process spreads across the eye in a visible travelling wave, the
morphogenetic furrow, which marks a progression of inductive and responsive competence in which
the signalling protein Hedgehog plays an important self-regulating role and each cohort of
differentiating cells acts as a spatial template for the next (for a summary of the molecular
interactions see Baonza et al. 2001). A travelling wave may be needed to allow a globally coherent
pattern to emerge from interactions that involve only immediate neighbors; and, indeed, when
different eye regions in a mutant fly start the process independently, pattern coherence is lost
(Heberlein & Moses 1995).
In the retinas of vertebrates, built to an entirely different structural plan, there is no known
equivalent to the morphogenetic furrow. Nevertheless, some of the primary inductive mechanisms are
known to have been conserved, and a self-regulating travelling wave of expression of the orthologous
gene Sonic hedgehog has recently been shown to sweep through the zebrafish retina in the first
differentiated neurons, the retinal ganglion cells (Neumann and Nüsslein-Volhard 2000).
In the fish retina, the earliest regular patterns that can be seen by conventional histology
comprise either regular rows of morphologically identical single cones or alternating rows of double
and single cones (Fig. 4), and in some species these rows are eventually transformed into a modular
‘square’ mosaic (Engström 1963; Shand et al. 1999). As morphological distinctions between the
photoreceptor types are slow to develop, studies of their earliest relationships require them to be
identified in another way, usually by their content of photopigment (opsin) mRNA. Raymond and
colleagues have shown that the first opsin to be expressed in the embryonic eye-cup of the goldfish is
distributed in a predictable pattern, beginning at the nasal margin of the ventral fissure and spreading
around the retina in a circular or spiral path. The cells producing this first opsin sometimes form
regular rows at the leading edge of the wave (Raymond et al. 1995; Stenkamp et al. 1996). Further, in
the zebrafish, an additional wave of Sonic hedgehog expression precedes this wave of photoreceptor
differentiation and seems to be necessary for it (Stenkamp et al. 2000).
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Fig. 4 Quasi-crystalline cone lattice patterns in salmonid fish.
Tangential sections through the cone ellipsoids show a typical
square mosaic without corner cones (A) and a row mosaic (B).
Where both forms coexist within one retina, the row pattern
occupies younger, more peripheral regions. DC = double cone; S =
single cone. Bar = 50 µm for microphotographs. For further details,
see Beaudet et al. (1997). © 1997 Wiley-Liss, Inc. Reprinted by
permission.
While the potential parallels with the fly’s eye are clear, it is not yet possible to say whether the fish
has a direct equivalent to the fly’s pre-patterned array of R8 cells, defining ‘modules’ in the cone
mosaic. One reason is that this first opsin is actually found in rod photoreceptors, which are not
regularly patterned in the adult retina and not required for the formation of a normal cone mosaic
(Wan & Stenkamp 2000). Another reason is that we still know very little about the long period of
cone differentiation that precedes the expression of cone opsins, and next to nothing about the initial
spatial relationships of the cells that will develop into the different cone types over this long period
(Cook & Chalupa 2000). However, studies of retinal regeneration after physical wounding or
chemical lesioning show that the densest regenerated populations, where opportunities for inductive
interaction are greatest, are also typically the most orderly (Stenkamp et al. 2001), so we may
speculate that local relationships are important.
Computer-modeling studies (Tohya et al. 1999) confirm that regular mosaics of four different
cell types can emerge from ‘cellular-automaton’ rules of differentiation that involve purely local
interactions and are applied to initially random arrangements. Different rules converge on the same
simple patterns, precisely matching those observed in real fish, and these rules operate most
efficiently when they act at an advancing wavefront (like the fly’s furrow or the marginal zone of a
growing fish retina) rather than across a large area at once. Whether the biological interactions that
underlie the formation of real cone mosaics will turn out to be anything like the assumptions of such
models remains to be seen. However, the approach is adaptable: a more recent alternative model is
able to create appropriate patterns based on the assumption that the cone mosaics arise by secondary
cell rearrangements among pre-determined cone types that differ in their adhesion properties
(Mochizuki 2002).
Mammals also have cone mosaics, and those of Old World monkeys such as the macaque
have been studied intensively. However, tools for probing opsins are not as precise in mammals as in
fish, and the individual cone mosaics are not as precise either (Engström 1963; Roorda & Williams
1999). Blue-sensitive cones, which comprise about 10% of the cone population and form regular
mosaics in macaques and humans, are present in all mammalian orders (although not all species) but
do not always form regular mosaics (Chapter [##]). Red- and green-sensitive cones are derived from
an ancestral type that seems not to form a regular mosaic in any placental mammal (Ahnelt & Kolb
2000), and recent spectrophotometric studies show that they are intermingled in the human fovea as
irregular clumps and clusters (Roorda & Williams 1999). Other investigations into the origins of
mammalian cone patterning were summarized by Cook and Chalupa (2000).
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4.2 Lateral movements of developing neurons
A second way to generate a regular mosaic would be to create a random array of fate-determined
neuroblasts and then move them to regularize the spacing of each distinct type. Rockhill et al. (2000)
noted that such an approach might reduce the aliasing effects that would be expected if successive
wavefronts of differentiation laid down overlapping patterns at different scales, and there is now
convincing evidence that mosaic-forming neurons do move within the retinal plane in development.
An ingenious method for demonstrating such movements relies on the random and
irreversible inactivation of one of the two X-chromosomes in every cell of a female mammalian
embryo. This property has been used to generate transgenic mouse embryos whose eye-cups contain a
‘pepper-and-salt’ distribution of multipotential precursor cells, half with an active lacZ marker gene
and half without (Reese et al. 1999). The lacZ-active cells go on to generate beta-galactosidasepositive, blue-reacting clones of retinal cells, while their neighbors form white, non-reacting clones.
Within both white and blue clones, about 85% of all cells maintain strict radial alignment. However,
cones, horizontal cells, ganglion cells and at least one type of amacrine cell, which make up the
remaining 15%, are commonly tangentially displaced into clonally unrelated columns (Fig. 5) – so
commonly, indeed, that it would seem that lateral movement is the universal rule. This displacement
occurs late, and in many cases after birth. Its extent is limited to some ten or twenty soma diameters
but this could be enough to explain the emergence of mosaics (Reese et al. 1999). Similar evidence of
cell dispersal in chick retinas had earlier been interpreted as arising from the migration of precursors,
rather than differentiated neurons (Fekete et al. 1994). The same neuronal types were involved,
however, and the same explanation now seems likely to apply (review: Reese & Galli-Resta 2002).
This evidence that the neurons of all the major mosaic-forming classes move laterally during
development does not, of course, prove that their movement establishes their mosaics. In many cases
this further logical step is hard to take because there is no way to identify a future member of a
particular mosaic until that mosaic is complete. However, the cholinergic amacrine cells of rodents
bind antibodies to the transcription factor Islet-1 (Galli-Resta et al. 1997) and two cholinergic
markers (Galli-Resta 2000) while they are still migrating radially to form two independent mosaics in
the inner nuclear layer and the ganglion cell layer. During their migration, they show no spatial order
beyond a minimal spacing imposed by their occasional physical contact; but by the time they reach
the boundary between the inner nuclear layer and the ganglion cell layer they show a more regular
pattern with a minimal spacing several times the soma diameter. Remarkably, their regularity is then
maintained throughout a period of five days during which up to 30% more cells of the same type enter
each array. In order to achieve this, existing cells must move sideways to accommodate the
newcomers (Galli-Resta et al. 1997).
Fig. 5 Evidence for the tangential migration of developing
neurons.
In this wholemounted retina from an adult chimeric mouse, the
blue [dark] patches are columns of lacZ-active cells, derived
from a transgenic embryonic stem cell that was injected into the
blastocyst. Two individual lacZ-active horizontal cells
(arrowheads) have migrated laterally from these columns. They
are both immunopositive for calbindin, like the other, lacZinactive members of the horizontal cell mosaic. Bar = 50 µm.
For further details, see Reese et al. (1999). © 1999 European
Neuroscience Association. Reprinted by permission.
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Fig. 6 Minimal-spacing rules as a basis for neuronal
mosaic generation.
The dots in these figures represent young cholinergic
amacrine cells in a rat retina, during the period of mosaic
formation, and the polygons represent their Voronoi
domains, constructed to include all points that are closer to
that dot than to any other (see section 6.3). The dots in (A)
represent the locations of actual Islet-1-positive amacrine
cells in a rectangular sampling region of the inner nuclear
layer. The dots in (B) represent the result of a computer
simulation in which points were positioned randomly by a
probabilistic minimal spacing rule, with the minimal spacing
set to 15 ± 2 µm (mean ± standard deviation). The
distributions are indistinguishable, not only to the eye but
also to Voronoi and Fast Fourier Transform analysis. For
further details see Galli-Resta et al. (1997).
© 1997 Society for Neuroscience. Reprinted by permission.
The mosaics that are seen in this situation can be simulated rather exactly (Fig. 6) by a simple
computational model in which the only constraint on cell positioning is a probabilistic limit on the
minimal spacing between cells (Ammermüller et al. 1993; Galli-Resta 1998). When neuronal density
is relatively high, as it is here (and also in the case of the blue-sensitive cones – but not the rods – of
the ground squirrel retina: Galli-Resta et al. 1999) this simple minimal-spacing rule is sufficient to
create a fairly regular mosaic. It seems that many, and perhaps all, retinal mosaics may reflect a
simple rule of this kind. Whenever spatial autocorrelograms have been computed for inner-retinal
neurons, their dominant feature has always been a central area of low density that represents a zone
around each cell from which others of the same type are excluded, and there has been no sign of
longer-range order that might suggest a more complex patterning rule. In fact, of all the cell types so
far studied in this way, only cones have shown evidence of long-range order (Curcio & Sloan 1992;
Cook & Noden 1998); and modeling studies show that the particular type of order they possess can be
created entirely by short-range interactions (Tohya et al. 1999).
In the case of cones, a minimal spacing is imposed by the requirements of efficient packing,
because cone inner segments contact their neighbors directly. It is less clear what might determine the
larger minimal spacings of inner-retinal neurons during development: for example, the minimal
spacing of rodent cholinergic amacrine cells is at least three times the soma diameter at this stage
(Galli-Resta et al. 1997). A diffusible repulsive or inhibitory signal seems unlikely in this model
because the exclusion radius around close pairs of such cells is no greater than that around single cells
(Galli-Resta 2000). An obvious alternative, that such cells might already be in direct contact with
their neighbors through transient, fine filopodial processes, is considered below, in the context of
dendritic development (section 4.4). Reese and Galli-Resta (2002) provide a more detailed review of
all these issues.
4.3 Effects of neuronal death on mosaic development
A third model of mosaic formation involves the selective death of neurons. This is unlikely to be a
universal mechanism of mosaic formation because mosaics are a major feature of the retina in all
vertebrate groups while in anamniotes the death of differentiated retinal neurons is thought to be rare
(Williams & Herrup 1988). Even so, the massive and widespread increase in programmed cell death
within the amniote (and particularly mammalian) radiation must at the very least have disrupted those
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mosaics that were previously formed by other mechanisms, and may have stimulated the emergence
of entirely new mosaic-forming mechanisms.
For example, the alpha and beta ganglion-cell mosaics of the domestic cat (together forming
half of the ganglion-cell population) are highly regular in the adult, yet 80% of all ganglion cells die
between embryonic day 28 and postnatal week six (Williams et al. 1986). How can these observations
be reconciled? The most obvious possibility is that programmed cell death, even while it is tending to
obliterate any pre-existing regularity, might be actively selecting survivors that will form regular
arrays. The limited evidence currently available is consistent with such a mechanism (Chalupa et al.
1998). Between postnatal day 12 and adulthood, the overall density of alpha cells in the central region
falls by about 20%. Over the same period, the incidence of opposite-sign pairs among nearestneighbor alpha cells rises from less than 60% (not much higher than when two random populations
are overlaid) to about 90% (matching the adult level of regularity). It is not yet known how this rise in
opposite-sign pairs is achieved, but postnatal intraocular injection of the sodium-channel blocker
tetrodotoxin reduces the regularity of the adult alpha mosaics without increasing their density
(Jeyarasasingam et al. 1998). This suggests that electrical activity affects the spatial selectivity of
alpha cell death without controlling its extent. Computer simulations confirm that the death of 20% of
the original cells could account for the observed increase in regularity, provided that neighbor-pairs of
the same sign were selectively targeted and that one from each pair died. However, there are many
questions about the role of cell death still to be answered, and it has been shown not to contribute to
the regularity of the cholinergic amacrine arrays of the rat (Galli-Resta 2000).
4.4 Mosaics, competition and the development of dendritic fields
Implicit in the concept of a mosaic is the property of dendritic tesselation, yet we know surprisingly
little about how the sizes and shapes of individual dendritic trees are controlled (review: Scott & Luo
2001). Most studies of dendritic growth have been directed towards ganglion cells. Their patterns of
dendritic growth have been shown to be determined competitively in many experiments involving the
elimination of other ganglion cells; and their dendritic rearrangement in such circumstances is
disrupted by tetrodotoxin and therefore apparently depends on electrical activity (Deplano et al.
1999). However, only a few studies have directly addressed the question of whether dendritic
competition is selective between members of a ganglion-cell type, as it must be if it has a role in
mosaic formation (Weber et al. 1998). Such a role, while it needs to be confirmed, would be
consistent with the observations that ganglion-cell types with different receptive-field sizes establish
similar levels of functional coverage (DeVries & Baylor 1997), that coverage is constant across
substantial intraretinal gradients of cell density (review: Weber et al. 1998) and that coverage tends to
be maintained when cell density is altered by normal or abnormal eye growth (Finlay & Snow 1998).
While competitive dendritic growth alone cannot account for the regularity of somatic
mosaics, a recent computational model (Eglen et al. 2000) has shown how cell-type-selective
dendritic interactions might provide a controlling mechanism for the lateral migration of somata that
was described above (section 4.2). In this model, differentiated neurons reposition themselves
constantly to minimize the overlap between their dendrites. Under some constraints (fixed dendritic
field sizes) their distributions have properties that converge with those created by minimal spacing
rules, where regularity increases with density up to a packing limit. Under other constraints (adaptive
dendritic field sizes) they resemble distributions that have been observed in older retinas, where
regularity and density are independent of each other (Eglen et al. 2002).
Models based on dendritic interaction may not seem relevant to the earliest stages of mosaic
formation, when neurons lack differentiated dendrites. However, similar interactions may be possible
even between immature cells because some immediately postmigratory neurons, for instance retinal
11
ganglion cells in the chick (Nishimura et al. 1979), are surrounded by a ‘halo’ of fine protoplasmic
processes that may reach out to more distant neighbors, as do the telodendria of immature S cones
(Xiao & Hendrickson 2000). Such processes also resemble the delicate, hard-to-visualize cytonemes
of invertebrates (review: Bryant 1999), which have been implicated in remote contact-mediated
signalling functions. Indeed, they may not differ greatly from the motile filopodia that later cover the
dendrites (review: Wong & Wong 2001). Thus, paradoxically, a model such as that of Eglen et al.
(2000) might be more relevant to the earliest stages of neuronal differentiation, when most neuronal
processes are transient, motile and unbranched, than to later stages, when a thicket of established
dendritic branches must seriously constrain neuronal movement.
In vitro time-lapse imaging techniques have recently revealed much that is new and interesting
about the short-term behavior of dendritic filopodia and growth cones and their molecular regulation
by extrinsic factors such as neurotransmitters, as well as intrinsic factors such as small GTPases
(Wong & Wong 2001). However, the growth and remodeling of ganglion cell dendrites is a long-term
process, not well suited to in vitro study, and the molecular bases of dendritic competition and the
cell-type-specific recognition that must underlie it are not yet known, even in outline (Sernagor et al.
2001; Chapter [##: Wong]).
In the fly Drosophila, a particular class of segmentally-repeated sensory neurons (MD cells)
shows type-specific tiling behavior that might more easily be studied directly, in living embryos. The
dendritic interactions of MD cells are abnormal in several mutants, disrupting tiling behavior and
normal competitive interactions across the midline. The defective gene in at least one of these
mutants, flamingo, has mammalian homologs and codes for a protocadherin that would appear to be a
good candidate for selective cell adhesion (Gao et al. 2000). If MD neurons are as good an
experimental model for selective dendritic competition as the initial studies suggest, dendritic
tesselation may yet join the large class of vertebrate developmental problems into which significant
insights have been gained from invertebrate models.
5. What retinal mosaics tell us about evolution
We have seen how mosaics help us to develop objective neuronal classifications, which are essential
for any useful comparisons between species. In addition, the spatial characteristics of each mosaic (its
regularity, density, gradients, coverage) are phenotypic characters in their own right that can be used
in identifying cross-species homologies. In these two ways, mosaics help us to understand how
neuronal types are inter-related and, ultimately, how they evolved.
5.1 Comparing neuronal types across species
The notion of a ‘natural type’ among neurons is closely analogous to the notion of a species among
organisms in its implications of self-similarity and isolation, while a neuronal class is analogous to a
genus. It is disturbing, therefore, that our understanding of most neuronal types remains firmly rooted
in an 18th century, Linnaean mode of thought that classifies cells only by morphological and
functional similarity, whereas the rest of biology long ago embraced the Darwinian view that it is
ancestry, not similarity, that acts as the key to unlock biological meaning. For a full understanding of
any part of the brain, we need to see neuronal classifications not only as hypotheses about the
boundaries of variation in neuronal structure and function in a single species, but also as hypotheses
about the evolutionary relationships between ‘natural types’ in different species and the
developmental programs that create them (Cook 1998). While comparative studies of cone mosaic
patterns go back more than half a century (review: Engström 1963), the scope for a broader
evolutionary view can be illustrated by a few of many possible questions to which there are, as yet, no
clear answers: Which of the recorded neuronal types in salamander, turtle, cat and monkey retinas
12
have common ancestors and so are homologous, rather than merely analogous? What developmental
mechanisms control the emergence of a new, mosaic-forming, neuronal type and enable it to show
self-recognition? Why do mammalian ganglion cell mosaics seem to come in inner- and outerstratified pairs? The last of these alone is addressed here.
5.2 Is the paired mosaic a mammalian invention?
The dominance of mammalian alpha and beta cells in early studies of mosaics, starting with those that
first showed the importance of dendritic stratification (review: Wässle & Boycott 1991), has created a
general impression that mosaic-forming neurons are typically organized into pairs of related
‘subtypes’ that differ only in their stratification and in giving opposite-sign physiological responses to
visual stimuli. In fact, such mosaic pairings seem to be unusual among vertebrates as a whole (Cook
1998) and their predominance in mammals may reflect the emergence of novel, late-acting
mechanisms of mosaic formation in response to neuronal death (see section 4.3).
However, the paired, monostratified alpha and beta mosaics of the cat are known to be derived
from multistratified precursor populations by dendritic remodeling (review: Chalupa et al. 1998).
When the definitive adult inner- and outer-stratified mosaics of a pair are overlaid and compared, they
show some degree of spatial inter-dependence (alpha cells: Jeyarasasingam et al. 1998; beta cells:
Zhan & Troy 2000), which is unusual among retinal mosaics in general, even those that are
synaptically coupled (Galli-Resta et al. 2000; Rockhill et al. 2000). Thus, it is plausible that some of
the order in these paired mosaics is created by a process that encourages neighboring multistratified
cells to remodel their dendrites into opposite-sign pairs, and that each complementary pair of mosaics
may have evolved by the developmental remolding of a single ancestral mosaic whose neurons
remained bistratified or multistratified throughout life. For example, both of the mammalian alpha
mosaics might be homologous to a single mosaic of prominently bistratified large ganglion cells
(alpha-ab cells: Fig. 7) that occurs in fish, frogs and reptiles (Cook 1998). To test such hypotheses,
we would need either to study the phenotypes of these cells in many more species, especially among
reptiles and primitive mammals, or to ‘hack’ directly into the transcriptional control code that defines
each neuronal type and seek homologies at that level. The second method should be quicker, once the
tools for it become available.
Fig. 7 A bistratified ganglion cell mosaic could be the
ancestor of the mammalian alpha mosaics.
The two strictly bistratified cells in (A) form part of a highly regular
mosaic in a gekkonid lizard. Only their inner trees are shown in plan
view here, but the cell on the left is also shown in profile view (B).
All non-mammalian species studied so far have a single, prominent
mosaic of large-bodied ganglion cells that are either bistratified or
predominantly inner-stratified. It is likely that these have a
mammalian homolog. As mammalian alpha cells are initially
multistratified, they are an obvious candidate for this role. Bar = 50
µm. For further details see Cook and Noden (1998). © 1998 S.
Karger AG, Basel. Reprinted by permission.
13
6. Methods for measuring mosaics
It is the limits of the dendritic field that determine a neuron’s receptive field (Chapter [##]) so,
ideally, the quantitation of mosaics would focus on dendrites. However, it is technically challenging
to define the individual limits of a large array of partially overlapping dendrites, so mainstream
methods of quantitation consider only soma location. The analysis can take several different forms,
according to its aims. There is no space here for a detailed discussion of each approach but the
references include such discussions.
6.1 Methods based on nearest-neighbor distance
The aim may simply be to establish the objective reality of the mosaic, a step made necessary by the
tendency of our own visual systems to perceive pattern in random distributions. The methods first
adopted for this task were based on the statistical distribution of the distance from each neuron to its
nearest neighbor of the same type (the nearest neighbor distance or NND: Wässle & Riemann 1978).
NND-based methods still underlie the most useful general tests of mosaic significance, but care is
needed in interpreting them because some tests overestimate the degree of regularity within a small,
irregular or elongated sample (Cook 1996). The commonest, easiest and most conservative test is
based on the conformity ratio (mean NND / standard deviation). The sampling distribution of this
ratio has now been tabulated for a wide range of sample sizes and shapes so that the significance of
an observed value can be found by looking it up on a chart (Cook 1996).
It is often useful to show that one mosaic is spatially (and so presumably functionally and
developmentally) independent of another. Historically, NND methods have been used for this, too,
the standard approach being to combine the two mosaics and attempt to show that the NND
distribution of the combined set is close to that expected for a random population. This approach is
seriously flawed, not only because its sensitivity depends on the orderliness of the individual mosaics
and their relative spacings, but also because the sum of two mosaics depends on their spatial
relationship within the sampling area (Cook 1996). Spatial correlograms, discussed in the next
section, offer a much more informative approach to issues of this kind.
6.2 Methods based on spatial correlation
A powerful technique for the assessment of spatial order is the spatial correlogram, introduced into
retinal studies by Rodieck (1991), which reveals coincidences and relationships in two-dimensional
space. To create a spatial correlogram, each neuron in an array is placed, in turn, at a central reference
point and the locations of all its neighbors are plotted around it. The accumulation of overlaid plots
reveals overall trends in neighbour-relationships. Auto-correlation of a single array with itself
explores its internal spatial relationships and can reveal local order, global order and some aspects of
array geometry, whereas cross-correlation of one array with another explores any spatial interactions
between the two. While the correlogram itself is primarily a tool for visualization, it can be used to
derive a quantitative measure known as the density recovery profile (DRP; Rodieck 1991), which is
basically a histogram of the mean neuronal density in a series of concentric rings around the
correlogram’s origin.
The autocorrelation-DRP of a large sample drawn from a random point distribution is
completely flat. By contrast, autocorrelation-DRPs from individual neuronal mosaics are never flat,
because each neuron is surrounded by a territory from which other neurons of the same type tend to
be excluded. This exclusion leads to a central ‘hole’ in the autocorrelogram and a deep ‘well’ in the
DRP. The size of the neighbor-depleted region can be used to derive an objective measure of the
minimal spacing within the array (the exclusion radius) and a measure of the regularity of the array
14
(the packing factor: Rodieck 1991). Autocorrelation-DRPs with partial-depth ‘wells’ may be seen
when the sample contains a mixture of spatially independent neuronal types (Cook & Podugolnikova
2001). Cross-correlograms derived from two distinct mosaics normally yield essentially flat DRPs,
demonstrating spatial independence, although short-range ‘steric hindrance’ between co-stratifying
neurons can cause minor central deviations. Where the cross-correlation-DRP shows a broad central
well like that of an autocorrelation-DRP, the most likely explanation is that the two ‘mosaics’ are
actually subsets of a single mosaic.
A major merit of spatial correlograms is their robustness in the face of imperfect sampling
procedures. Real neuronal mosaic-samples vary in spacing across the sample area and contain gaps
where individual neurons or clusters have failed to label or are damaged or obscured. Estimates of the
exclusion radius are remarkably resistant to this kind of undersampling, to the extent that the radius
of a regular mosaic may be correctly estimated when as few as 20% of the neurons actually present in
the sample area are included in the analysis (Fig. 8). In such a case, NND-based methods are virtually
useless (Cook 1996).
6.3 Methods based on Voronoi domain analysis
A method that is growing in popularity is the analysis of
Voronoi polygons, constructed around each cell in a mosaic
so as to include all points that are closer to that cell than to
any other (Curcio & Sloan 1992; Ammermüller et al. 1993;
Fig. 6). This approach is potentially more informative than
NND analysis in that it allows additional aspects of mosaic
geometry to be assessed (for example, the distribution of the
number of neighbors around each neuron) as well as the
typical spacing. At present the extra data is of limited use
because (as the method itself has been used to confirm)
nothing more than the establishment of a certain minimal
spacing between neurons may be needed to simulate all their
observable properties (Galli-Resta et al. 1999). With a tightly
packed, quasi-crystalline mosaic such as the human cone
mosaic, however, estimates of domain orientation and
neighbor number can be used to identify regional
discontinuities within the mosaic (Curcio & Sloan 1992).
The method has been discussed in more detail by Zhan and
Troy (2000).
Fig. 8. The exclusion radius is insensitive to undersampling.
The alpha-b (inner-stratified) mosaic of Oreochromis spilurus is
highly regular (A) and has a well defined minimal spacing, shown
clearly by the ‘well’ in the autocorrelation-DRP (B). This yields an
exclusion radius (Rodieck 1991) of 70 µm. When 80% of these
cells are deleted at random, simulating an incompletely sampled
mosaic in which only one cell in five is recorded, the mosaic (C)
now appears irregular to the untutored eye. However, the
autocorrelation-DRP, although ‘noisier’, is otherwise unchanged
(D) and the calculated exclusion radius is still 70 µm. For further
details see Cook (1996). © 1996 Cambridge University Press.
Reprinted by permission.
15
There is a risk, with this type of analysis, that users will interpret the several different
variables that can computed from a single dataset as though they were statistically independent, and
thus overestimate their significance. The full utility of this approach will be reached only when there
is consensus on a set of tests that can be applied without falling into this trap.
6.4 Other methods
Other methods have appeared at various times in the literature, although their advantages have not
always been clear enough to lead to wider uptake. For example, Galli-Resta et al. (1997) used a fast
Fourier transform method to confirm the close similarity between real mosaics of cholinergic
amacrine cells and simulated mosaics created by a minimal-spacing rule, and their paper provides a
useful set of direct comparisons between this and standard methods based on NND, spatial
correlograms and Voronoi analysis. Stenkamp et al. (2001) have recently used a form of quadrat
analysis to assess clustering, as an alternative to the NND-based dispersion index (review: Cook
1996) which is also capable of measuring the entire spectrum of order from regularity through
randomness to clustering.
7. Looking ahead
The 1980s saw a revival of interest in structural and functional diversity within the retina and the
birth (after a long but little-remarked gestation) of the important concept of a ‘natural’ neuronal type.
Concurrently, evidence was accumulating for spatial regularity as a common phenomenon among
retinal neurons. In the 1990s, these ideas became more firmly coupled as mosaics were found in a
wide range of species and used to address questions of functional diversity and cross-species
homology. Recent work suggests that the focus in the next few years will be on exploring the
mechanisms through which mosaics develop, whether at the level of cell fate determination, of cell
migration or of cell death. What, then, are the big questions that remain?
For the molecular developmental neurobiologist, the key questions must be how neurons
acquire their type-diversity and spatial patterning through the interplay of intercellular and
intracellular signalling pathways, and how these properties are created and maintained by
transcriptional control. These are questions that transcend the visual system and seem likely to be
answered first for the spinal cord (review: Lee & Pfaff 2001); but the diverse and well-defined
neuronal mosaics of the retina offer an excellent model in which to test the generality of the answers.
At the cell-biological level, the primary spatial patterning issue must be the molecular
mechanisms that are used by members of each mosaic-forming type to recognize each other reliably
within a crowd of other types while migrating to appropriate positions, staking-out territory and tiling
the retina with their dendritic trees. In this respect, the recent discovery of large families of molecules
with the potential to mediate highly selective adhesion, attraction and repulsion among neuronal
processes (Wu & Maniatis 1999; Yu & Bargmann 2001) is highly encouraging, as are recent technical
advances for studying living, growing neurons in their natural habitat (Lichtman & Fraser 2001). An
interesting secondary issue is the molecular control of type-specific dendritic branching patterns.
Factors such as branch density, branch angle and narrowness of stratification will strongly affect the
density of interdendritic contacts at the boundaries of neighboring dendritic fields (Lohmann & Wong
2001; Chapter [## Wong?]) and so may be related to type-specific variations in coverage factor,
precision of tesselation, and the contouring of physiological receptive fields. A third issue needing
exploration is the two-edged relationship between spatial regularity and cell death, discussed earlier,
while a fourth is the generality of spatial regularity among neurons elsewhere in the CNS, which has
hardly yet been touched upon (Stevens 1998).
16
Finally, the key issue for the evolutionary biologist must be to discover what these
conspicuous and fascinating patterns can tell us about how retinal neurons have evolved. During
which of the evolutionary transitions that shaped the major vertebrate lineages have mosaic-forming
neurons (and thus, closing the circle, their transcriptional control systems) undergone duplication or
‘speciation’ to create novel neuronal types with independent functions and tilings? What are the
genetic and/or epigenetic mechanisms of ‘adaptation’ that enable homologous neuronal types to vary
their regularity and spacing in response to divergent visual demands in related taxa of a single
lineage? Ahnelt and Kolb (2000) have begun to address these difficult questions in respect of
mammalian cones; but only when they can be answered for all the major neuronal classes and
vertebrate groups shall we be able to say that we understand the relationships between development,
structure and function in the retina.
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