Epithelia are one of the basic building blocks from which animals sculpt complex tissues and organs during development 
. These sheets of cells are held together by specialized structures—notably apical junctional complexes, including adherens junctions—that allow cells to adhere tightly to their neighbors and ensure the epithelium's mechanical integrity 
. In most epithelia, individual cells of distinct identities are packed together in quasi-two-dimensional arrays of varying complexity. Despite the fundamental importance of epithelial organization for many biological functions, the biophysical mechanisms that control cell shape and position in epithelia—and in particular the development of regular, ordered epithelial cell packings—remain only partially understood.
In vertebrates, the neural retina exhibits a particularly high degree of epithelial organization, both in the radial direction, where it comprises multiple, stratified layers, and within layers, where the spatial distribution of each class of neuron within the epithelial plane has consistently been shown to be non-random 
. This planar order is especially pronounced in adult teleost fish, where the cone photoreceptor cells are arranged in a well-defined, periodic pattern—the cone mosaic—that shows strong heterotypic as well as homotypic correlations 
. The cone mosaic thus represents a rare vertebrate example of the precise regulation of cell fate and organization at the single cell level (more instances of which have been described in invertebrate systems 
Previous studies have characterized cone mosaic patterns primarily by observing regular spatial arrangements of various individual cone cell subtypes, identified morphologically and/or with specific cell markers 
. They have, in contrast, left largely unexplored the complementary question of how cone photoreceptors, together with rod photoreceptors and the apical processes of Müller glia, pack together and occupy space in the epithelial plane. Depending on the species, cone photoreceptors in teleost fish include several morphologically identifiable classes of single cones and double cones that express distinct visual pigments 
. For example, the zebrafish, Danio rerio
, has four spectral subtypes of cones designated red, green, blue, and ultraviolet (UV), respectively, based on the absorption maxima of their visual pigments 
. These cone photoreceptors are distributed in a repeating pattern that has been classically described as a row mosaic () 
Cone mosaics in the embryonic, larval, and adult zebrafish retina.
The zebrafish retina is a thin, hemispheric sheet that lines the back of the eye. This sheet continues to grow along with the rest of the fish throughout postembryonic larval and adult stages: the diameter of the eye at the end of embryonic development (~3 days post-fertilization [dpf]) is only ~0.2 mm, but several months later it can reach ~2 mm or more. From ~3 dpf onwards, retinal growth is accomplished by the addition of new cone cells at the rim of the retinal hemisphere, where the retinal and ciliary epithelia meet at a circumferential germinal zone of proliferative precursor cells () 
. Due to this particular mode of continuous growth, successive stages of development and cell differentiation are laid out spatially in concentric annuli in a single epithelium: the remnant of the embryonic and larval retina remains in the center of the retina of the adult fish, whereas the majority of the adult retina extending out to the periphery is more recently created tissue 
. The embryonic/larval remnant is easily distinguished in a flat-mounted preparation of the entire adult retina because neither the cones generated from the embryonic retinal primordium nor those added post-embryonically to the growing larval retina are arrayed in a regular, rectangular mosaic 
. Even though the growing retina adds annuli of new cones at the periphery from late embryonic stages onwards, only those born after the end of larval development, at ~3 weeks post-fertilization (wpf), form an ordered mosaic lattice. Thus, addition of successive annuli of cone photoreceptors at the retinal perimeter is not, by itself, sufficient to produce a crystalline cone mosaic.
The appearance of the ordered lattice of cone photoreceptors at ~3 wpf, on the other hand, does
coincide with the completion of significant developmental changes in ocular anatomy. These include the formation and maturation of the anterior segment—that is, the iris, the ciliary epithelium, and the annular ligament, a circular bracket of connective tissue that is thought to give structural support to the front of the eye and that roughly encircles the retinal germinal zone 
. The maturation of the anterior segment leads to the production of aqueous humor, a fluid secreted by the ciliary epithelium that fills the eyeball. The aqueous humor is maintained at a significant intraocular hydrostatic pressure (IOP) relative to the outside environment, and this pressure inflates and stretches the retinal epithelium 
. Similar mechanical stresses are known to affect epithelial cell packing in other contexts, but the potential relationship between these tissue-scale influences and the organization of the cone mosaic pattern has not been explored.
Another mechanism known to influence cell shape and packing in epithelia is planar cell polarity (PCP)—the organization of cellular properties along a preferred direction within the plane of an epithelium 
. Such polarization is increasingly recognized as a widespread and important feature of epithelial organization. PCP has not previously been studied in the vertebrate retina, but its molecular mechanisms have been worked out in considerable detail in certain Drosophila
model systems 
, and the same pathway appears to be conserved in some vertebrate systems 
. One of the major functions of PCP is to introduce anisotropic mechanical stresses in epithelial sheets through modulation of acto-myosin cortical contractility or cell-cell adhesion, leading to polarized cell shape changes and rearrangements 
; conversely, PCP can itself be affected by changes in cell shape and packing 
and by mechanical stress 
. Several mathematical models of PCP have been developed, ranging from the relatively molecularly detailed to the more schematic and phenomenological 
, and the consequences of polarized contractility and adhesion for cell movement have also been examined computationally 
. A mathematical model that can capture the full range of interactions between PCP and mechanical forces has, however, so far been lacking.
Here, we propose just such a model to explain the developmental mechanisms behind the emergence of the ordered cone mosaic in the adult zebrafish retina. We present the first systematic experimental characterization of the epithelial packing of cone and rod photoreceptors and Müller glia at the apical surface of the retina, and we describe both the evolution of packing order as new cells are generated during retinal growth and the defects in order that accompany photoreceptor regeneration and that occur in a mutant strain of zebrafish with elevated intraocular pressure. Based on our observations, we introduce a mathematical model in which anisotropic, tissue-scale mechanical stresses interact with intrinsic planar cell polarity (PCP) in cones to generate cell packing in a rectangular lattice with long-ranged order. We provide morphological observations to verify the existence of the postulated PCP and functional genetic data consistent with the predicted role of anisotropic mechanical stress in the generation of the rectangular cone lattice.