Modeling and Inferring Cleavage Patterns in Proliferating Epithelia

The regulation of cleavage plane orientation is one of the key mechanisms driving epithelial morphogenesis. Still, many aspects of the relationship between local cleavage patterns and tissue-level properties remain poorly understood. Here we develop a topological model that simulates the dynamics of a 2D proliferating epithelium from generation to generation, enabling the exploration of a wide variety of biologically plausible cleavage patterns. We investigate a spectrum of models that incorporate the spatial impact of neighboring cells and the temporal influence of parent cells on the choice of cleavage plane. Our findings show that cleavage patterns generate “signature” equilibrium distributions of polygonal cell shapes. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from global observations of the distribution of cell shape. Applying these insights to the proliferating epithelia of five diverse organisms, we find that strong division symmetry and moderate neighbor/maternal influence are required to reproduce the predominance of hexagonal cells and low variability in cell shape seen empirically. Furthermore, we present two distinct cleavage pattern models, one stochastic and one deterministic, that can reproduce the empirical distribution of cell shapes. Although the proliferating epithelia of the five diverse organisms show a highly conserved cell shape distribution, there are multiple plausible cleavage patterns that can generate this distribution, and experimental evidence suggests that indeed plants and fruitflies use distinct division mechanisms.     

Mechanisms of regulating cell topology in proliferating epithelia: impact of division plane, mechanical forces, and cell memory

Regulation of cell growth and cell division has a fundamental role in tissue formation, organ development, and cancer progression. Remarkable similarities in the topological distributions were found in a variety of proliferating epithelia in both animals and plants. At the same time, there are species with significantly varied frequency of hexagonal cells. Moreover, local topology has been shown to be disturbed on the boundary between proliferating and quiescent cells, where cells have fewer sides than natural proliferating epithelia. The mechanisms of regulating these topological changes remain poorly understood. In this study, we use a mechanical model to examine the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells. We find that regardless of orientation of division plane, our model can reproduce the commonly observed topological distributions of cells in natural proliferating animal epithelia with the consideration of cell rearrangements. In addition, with different schemes of division plane, we are able to generate different frequency of hexagonal cells, which is consistent with experimental observations. In proliferating cells interfacing quiescent cells, our results show that differential proliferation alone is insufficient to reproduce the local changes in cell topology. Rather, increased tension on the boundary, in conjunction with differential proliferation, can reproduce the observed topological changes. We conclude that both division plane orientation and mechanical forces play important roles in cell topology in animal proliferating epithelia. Moreover, cell memory is also essential for generating specific topological distributions.     

Topological Progression in Proliferating Epithelia Is Driven by a Unique Variation in Polygon Distribution

Morphogenesis is consequence of lots of small coordinated variations that occur during development. In proliferating stages, tissue growth is coupled to changes in shape and organization. A number of studies have analyzed the topological properties of proliferating epithelia using the Drosophila wing disc as a model. These works are based in the existence of a fixed distribution of these epithelial cells according to their number of sides. Cell division, cell rearrangements or a combination of both mechanisms have been proposed to be responsible for this polygonal assembling. Here, we have used different system biology methods to compare images from two close proliferative stages that present high morphological similarity. This approach enables us to search for traces of epithelial organization. First, we show that geometrical and network characteristics of individual cells are mainly dependent on their number of sides. Second, we find a significant divergence between the distribution of polygons in epithelia from mid-third instar larva versus early prepupa. We show that this alteration propagates into changes in epithelial organization. Remarkably, only the variation in polygon distribution driven by morphogenesis leads to progression in epithelial organization. In addition, we identify the relevant features that characterize these rearrangements. Our results reveal signs of epithelial homogenization during the growing phase, before the planar cell polarity pathway leads to the hexagonal packing of the epithelium during pupal stages.     

Mitotic orientation in three dimensions determined from multiple projections.

The three-dimensional orientation of mitoses in mouse small intestinal crypts of Lieberkuhn was determined from multiple projections of the mitotic figures in whole mounts of isolated intestinal crypts. We found evidence of a significant orientational bias for mitoses whose daughter cells would be added along the long axis of the crypt, and thus conform to the maintenance of the cylindrical shape of the intestinal crypt. However, we also observed many mitoses whose progeny must be rearranged if the simple cylindrical shape of the intestinal crypt is to be maintained. Our results indicate that the ultimate behavior of progeny cells and hence of local tissue form may not strictly depend on the orientation of mitosis. The methods presented may also be used in the study of mitotic orientation in other tissues.     

Cadherin Adhesion Receptors Orient the Mitotic Spindle during Symmetric Cell Division in Mammalian Epithelia

Oriented cell division is a fundamental determinant of tissue organization. Simple epithelia divide symmetrically in the plane of the monolayer to preserve organ structure during epithelial morphogenesis and tissue turnover. For this to occur, mitotic spindles must be stringently oriented in the Z-axis, thereby establishing the perpendicular division plane between daughter cells. Spatial cues are thought to play important roles in spindle orientation, notably during asymmetric cell division. The molecular nature of the cortical cues that guide the spindle during symmetric cell division, however, is poorly understood. Here we show directly for the first time that cadherin adhesion receptors are required for planar spindle orientation in mammalian epithelia. Importantly, spindle orientation was disrupted without affecting tissue cohesion or epithelial polarity. This suggests that cadherin receptors can serve as cues for spindle orientation during symmetric cell division. We further show that disrupting cadherin function perturbed the cortical localization of APC, a microtubule-interacting protein that was required for planar spindle orientation. Together, these findings establish a novel morphogenetic function for cadherin adhesion receptors to guide spindle orientation during symmetric cell division.     

Modeling of Noisy Spindle Dynamics Reveals Separable Contributions to Achieving Correct Orientation

The mechanisms by which the mammalian mitotic spindle is guided to a predefined orientation through microtubule-cortex interactions have recently received considerable interest, but there has been no dynamic model that describes spindle movements toward the preferred axis in human cells. Here, we develop a dynamic model based on stochastic activity of cues anisotropically positioned around the cortex of the mitotic cell and we show that the mitotic spindle does not reach equilibrium before chromosome segregation. Our model successfully captures the characteristic experimental behavior of noisy spindle rotation dynamics in human epithelial cells, including a weak underlying bias in the direction of rotation, suppression of motion close to the alignment axis, and the effect of the aspect ratio of the interphase cell shape in defining the final alignment axis. We predict that the force exerted per cue has a value that minimizes the deviation of the spindle from the predefined axis. The model has allowed us to systematically explore the parameter space around experimentally relevant configurations, and predict the mechanistic function of a number of established regulators of spindle orientation, highlighting how physical modeling of a noisy system can lead to functional biological understanding. We provide key insights into measurable parameters in live cells that can help distinguish between mechanisms of microtubule and cortical-cue interactions that jointly control the final orientation of the spindle.     

Dlg1 controls planar spindle orientation in the neuroepithelium through direct interaction with LGN

Oriented cell divisions are necessary for the development of epithelial structures. Mitotic spindle orientation requires the precise localization of force generators at the cell cortex via the evolutionarily conserved LGN complex. However, polarity cues acting upstream of this complex in vivo in the vertebrate epithelia remain unknown. In this paper, we show that Dlg1 is localized at the basolateral cell cortex during mitosis and is necessary for planar spindle orientation in the chick neuroepithelium. Live imaging revealed that Dlg1 is required for directed spindle movements during metaphase. Mechanistically, we show that direct interaction between Dlg1 and LGN promotes cortical localization of the LGN complex. Furthermore, in human cells dividing on adhesive micropatterns, homogenously localized Dlg1 recruited LGN to the mitotic cortex and was also necessary for proper spindle orientation. We propose that Dlg1 acts primarily to recruit LGN to the cortex and that Dlg1 localization may additionally provide instructive cues for spindle orientation.     

Getting cells and tissues into shape

Cells of all shapes and sizes are able to calculate the location of their middles in order to divide into two during mitosis. Minc et?al. (2011) and Gibson et?al. (2011) now show that simple mechanical models accurately predict cleavage-plane positioning, and that geometrical interactions between neighboring cells are sufficient to generate ordered patterns of mitosis in growing epithelia.     

The Non-Proliferative Nature of Ascidian Folliculogenesis as a Model of Highly Ordered Cellular Topology Distinct from Proliferative Epithelia

Previous studies have addressed why and how mono‐stratified epithelia adopt a polygonal topology. One major additional, and yet unanswered question is how the frequency of different cell shapes is achieved and whether the same distribution applies between non-proliferative and proliferative epithelia. We compared different proliferative and non-proliferative epithelia from a range of organisms as well as Drosophila melanogaster mutants, deficient for apoptosis or hyperproliferative. We show that the distribution of cell shapes in non‐proliferative epithelia (follicular cells of five species of tunicates) is distinctly, and more stringently organized than proliferative ones (cultured epithelial cells and Drosophila melanogaster imaginal discs). The discrepancy is not supported by geometrical constraints (spherical versus flat monolayers), number of cells, or apoptosis events. We have developed a theoretical model of epithelial morphogenesis, based on the physics of divided media, that takes into account biological parameters such as cell‐cell contact adhesions and tensions, cell and tissue growth, and which reproduces the effects of proliferation by increasing the topological heterogeneity observed experimentally. We therefore present a model for the morphogenesis of epithelia where, in a proliferative context, an extended distribution of cell shapes (range of 4 to 10 neighbors per cell) contrasts with the narrower range of 5-7 neighbors per cell that characterizes non proliferative epithelia.     

Processes that occur before second cleavage determine third cleavage orientation in Xenopus

As in many organisms, the first three cleavage planes of Xenopus laevis eggs form in a well-described mutually orthogonal geometry. The factors dictating this simple pattern have not been unambiguously identified. Here, we describe experiments, using static magnetic fields as a novel approach to perturb normal cleavage geometry, that provide new insight into these factors. We show that a magnetic field applied during either or both of the first two cell cycles can induce the third cell cycle mitotic apparatus (MA) at metaphase and the third cleavage plane to align nearly perpendicular to their nominal orientations without changing cell shape. These results indicate that processes occurring during the first two cell cycles primarily dictate the third cleavage plane and mitotic apparatus orientation. We discuss how mechanisms that can align the MA after it has formed are likely to be of secondary importance in determining cleavage geometry in this system.     

Coupling mechanical deformations and planar cell polarity to create regular patterns in the zebrafish retina

The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina. Based on observations of the emergence of photoreceptor packing near the retinal margin, we propose a mathematical model in which ordered columns of cells form as a result of coupling between planar cell polarity (PCP) and anisotropic tissue-scale mechanical stresses. This model recapitulates many observed features of cone photoreceptor organization during retinal growth and regeneration. Consistent with the model's predictions, we report a planar-polarized distribution of Crumbs2a protein in cone photoreceptors in both unperturbed and regenerated tissue. We further show that the pattern perturbations predicted by the model to occur if the imposed stresses become isotropic closely resemble defects in the cone pattern in zebrafish lrp2 mutants, in which intraocular pressure is increased, resulting in altered mechanical stress and ocular enlargement. Evidence of interactions linking PCP, cell shape, and mechanical stresses has recently emerged in a number of systems, several of which show signs of columnar cell packing akin to that described here. Our results may hence have broader relevance for the organization of cells in epithelia. Whereas earlier models have allowed only for unidirectional influences between PCP and cell mechanics, the simple, phenomenological framework that we introduce here can encompass a broad range of bidirectional feedback interactions among planar polarity, shape, and stresses; our model thus represents a conceptual framework that can address many questions of importance to morphogenesis.     

Integrin signaling regulates spindle orientation in Drosophila to preserve the follicular-epithelium monolayer

Epithelia act as important physiological barriers and as structural components of tissues and organs. In the Drosophila ovary, follicle cells envelop the germline cysts to form a monolayer epithelium. During division, the orientation of the mitotic spindle in follicle cells is such that both daughter cells remain within the same plane, and the simple structure of the follicular epithelium is thus preserved. Here we show that integrins, heterodimeric transmembrane receptors that connect the extracellular matrix to the cell's cytoskeleton [1, 2], are required for maintaining the ovarian monolayer epithelium in Drosophila. Mosaic egg chambers containing integrin mutant follicle cells develop stratified epithelia at both poles. This stratification is due neither to abnormal cell proliferation nor to defects in the apical-basal polarity of the mutant cells. Instead, integrin function is required for the correct orientation of the mitotic apparatus both in mutant cells and in their immediately adjacent wild-type neighbors. We further demonstrate that integrin-mediated signaling, rather than adhesion, is sufficient for maintaining the integrity of the follicular epithelium. The above data show that integrins are necessary for preserving the simple organization of a specialized epithelium and link integrin-mediated signaling to the correct orientation of the mitotic spindle in this epithelial cell type.     

Expression of a nondegradable cyclin B1 affects plant development and leads to endomitosis by inhibiting the formation of a phragmoplast

In plants after the disassembly of mitotic spindle, a specific cytokinetic structure called the phragmoplast is built, and after cytokinesis, microtubules populate the cell cortex in an organized orientation that determines cell elongation and shape. Here, we show that impaired cyclin B1 degradation, resulting from a mutation within its destruction box, leads to an isodiametric shape of epidermal cells in leaves, stems, and roots and retarded growth of seedlings. Microtubules in these misshaped cells are grossly disorganized, focused around the nucleus, whereas they were entirely missing or abnormally organized along the cell cortex. A high percentage of cells expressing nondestructible cyclin B1 had doubled DNA content as a result of undergoing endomitosis. During anaphase the cytokinesis-specific syntaxin KNOLLE could still localize to the midplane of cell division, whereas NPK1-activating kinesin-like protein 1, a cytokinetic kinesin-related protein, was unable to do so, and instead of the formation of a phragmoplast, the midzone microtubules persisted between the separated nuclei, which eventually fused. In summary, our results show that the timely degradation of mitotic cyclins in plants is required for the reorganization of mitotic microtubules to the phragmoplast and for proper cytokinesis. Subsequently, the presence of nondegradable cyclin B1 leads to a failure in organizing properly the cortical microtubules that determine cell elongation and shape.     

Prenatal Organophosphates Exposure Alternates the Cleavage Plane Orientation of Apical Neural Progenitor in Developing Neocortex

Prenatal organophosphate exposure elicits long-term brain cytoarchitecture and cognitive function impairments, but the mechanism underlying the onset and development of neural progenitors remain largely unclear. Using precise positioned brain slices, we observed an alternated cleavage plane bias that emerged in the mitotic neural progenitors of embryonal neocortex with diazinion (DZN) and chlorpyrifos (CPF) pretreatment. In comparison with the control, DZN and CPF treatment induced decrease of vertical orientation, increase of oblique orientation, and increase of horizontal orientation. That is, the cleavage plane orientation bias had been rotated from vertical to horizontal after DZN and CPF treatment. Meanwhile, general morphology and mitotic index of the progenitors were unchanged. Acephate (ACP), another common organophosphate, had no significant effects on the cleavage plane orientation, cell morphology and mitotic index. These results represent direct evidence for the toxicity mechanism in onset multiplication of neural progenitors.     

Cellular responses to extracellular guidance cues

Extracellular guidance cues have a key role in orchestrating cell behaviour. They can take many forms, including soluble and cell‐bound ligands (proteins, lipids, peptides or small molecules) and insoluble matrix substrates, but to act as guidance cues, they must be presented to the cell in a spatially restricted manner. Cells that recognize such cues respond by activating intracellular signal transduction pathways in a spatially restricted manner and convert the extracellular information into intracellular polarity. Although extracellular cues influence a broad range of cell polarity decisions, such as mitotic spindle orientation during asymmetric cell division, or the establishment of apical–basal polarity in epithelia, this review will focus specifically on guidance cues that promote cell migration (chemotaxis), or localized cell shape changes (chemotropism).     

A computer model for reshaping of cells in epithelia due to in-plane deformation and annealing

Although cell reshaping is fundamental to the mechanics of epithelia, technical barriers have prevented the methods of mechanics from being used to investigate it. These barriers have recently been overcome by the cell-based finite element formulation of Chen and Brodland. Here, parameters to describe the fabric of an epithelium in terms of cell shape and orientation and cell edge density are defined. Then, rectangular "patches" of model epithelia having various initial fabric parameters are generated and are either allowed to anneal or are subjected to one of several patterns of in-plane deformation. The simulations show that cell reshaping lags the deformation history, that it is allayed by cell rearrangement and that it causes the epithelium as a whole to exhibit viscoelastic mechanical properties. Equations to describe changes in cell shape due to annealing and in-plane deformation are presented.     

Drosophila atypical protein kinase C associates with Bazooka and controls polarity of epithelia and neuroblasts

The establishment and maintenance of polarity is of fundamental importance for the function of epithelial and neuronal cells. In Drosophila, the multi-PDZ domain protein Bazooka (Baz) is required for establishment of apico-basal polarity in epithelia and in neuroblasts, the stem cells of the central nervous system. In the latter, Baz anchors Inscuteable in the apical cytocortex, which is essential for asymmetric localization of cell fate determinants and for proper orientation of the mitotic spindle. Here we show that Baz directly binds to the Drosophila atypical isoform of protein kinase C and that both proteins are mutually dependent on each other for correct apical localization. Loss-of-function mutants of the Drosophila atypical isoform of PKC show loss of apico-basal polarity, multilayering of epithelia, mislocalization of Inscuteable and abnormal spindle orientation in neuroblasts. Together, these data provide strong evidence for the existence of an evolutionary conserved mechanism that controls apico-basal polarity in epithelia and neuronal stem cells. This study is the first functional analysis of an atypical protein kinase C isoform using a loss-of-function allele in a genetically tractable organism.     

The Frizzled Planar Cell Polarity signaling pathway controls Drosophila wing topography

The Drosophila wing is a primary model system for studying the genetic control of epithelial Planar Cell Polarity (PCP). Each wing epithelial cell produces a distally pointing hair under the control of the Frizzled (Fz) PCP signaling pathway. Here, we show that Fz PCP signaling also controls the formation and orientation of ridges on the adult wing membrane. Ridge formation requires hexagonal cell packing, consistent with published data showing that Fz PCP signaling promotes hexagonal packing in developing wing epithelia. In contrast to hair polarity, ridge orientation differs across the wing and is primarily anteroposterior (A-P) in the anterior and proximodistal (P-D) in the posterior. We present evidence that A-P ridge specification is genetically distinct from P-D ridge organization and occurs later in wing development. We propose a two-phase model for PCP specification in the wing. P-D ridges are specified in an Early PCP Phase and both A-P ridges and distally pointing hairs in a Late PCP Phase. Our data suggest that isoforms of the Fz PCP pathway protein Prickle are differentially required for the two PCP Phases, with the Spiny-legs isoform primarily active in the Early PCP Phase and the Prickle isoform in the Late PCP Phase.     

A Computer Model for Reshaping of Cells in Epithelia Due to In-plane Deformation and Annealing

Although cell reshaping is fundamental to the mechanics of epithelia, technical barriers have prevented the methods of mechanics from being used to investigate it. These barriers have recently been overcome by the cell-based finite element formulation of Chen and Brodland. Here, parameters to describe the fabric of an epithelium in terms of cell shape and orientation and cell edge density are defined. Then, rectangular "patches" of model epithelia having various initial fabric parameters are generated and are either allowed to anneal or are subjected to one of several patterns of in-plane deformation. The simulations show that cell reshaping lags the deformation history, that it is allayed by cell rearrangement and that it causes the epithelium as a whole to exhibit viscoelastic mechanical properties. Equations to describe changes in cell shape due to annealing and in-plane deformation are presented.     

Small-World Communication of Residues and Significance for Protein Dynamics

It is not merely the position of residues that is critically important for a protein's function and stability, but also their interactions. We illustrate, by using a network construction on a set of 595 nonhomologous proteins, that regular packing is preserved in short-range interactions, but short average path lengths are achieved through some long-range contacts. Thus, lying between the two extremes of regularity and randomness, residues in folded proteins are distributed according to a “small-world” topology. Using this topology, we show that the core residues have the same local packing arrangements irrespective of protein size. Furthermore, we find that the average shortest path lengths are highly correlated with residue fluctuations, providing a link between the spatial arrangement of the residues and protein dynamics.