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.     

A Modeling Study on How Cell Division Affects Properties of Epithelial Tissues Under Isotropic Growth

Cell proliferation affects both cellular geometry and topology in a growing tissue, and hence rules for cell division are key to understanding multicellular development. Epithelial cell layers have for long times been used to investigate how cell proliferation leads to tissue-scale properties, including organism-independent distributions of cell areas and number of neighbors. We use a cell-based two-dimensional tissue growth model including mechanics to investigate how different cell division rules result in different statistical properties of the cells at the tissue level. We focus on isotropic growth and division rules suggested for plant cells, and compare the models with data from the Arabidopsis shoot. We find that several division rules can lead to the correct distribution of number of neighbors, as seen in recent studies. In addition we find that when also geometrical properties are taken into account other constraints on the cell division rules result. We find that division rules acting in favor of equally sized and symmetrically shaped daughter cells can best describe the statistical tissue properties.     

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.     

The nature of cell division forces in epithelial monolayers

Epithelial cells undergo striking morphological changes during division to ensure proper segregation of genetic and cytoplasmic materials. These morphological changes occur despite dividing cells being mechanically restricted by neighboring cells, indicating the need for extracellular force generation. Beyond driving cell division itself, forces associated with division have been implicated in tissue-scale processes, including development, tissue growth, migration, and epidermal stratification. While forces generated by mitotic rounding are well understood, forces generated after rounding remain unknown. Here, we identify two distinct stages of division force generation that follow rounding: (1) Protrusive forces along the division axis that drive division elongation, and (2) outward forces that facilitate postdivision spreading. Cytokinetic ring contraction of the dividing cell, but not activity of neighboring cells, generates extracellular forces that propel division elongation and contribute to chromosome segregation. Forces from division elongation are observed in epithelia across many model organisms. Thus, division elongation forces represent a universal mechanism that powers cell division in confining epithelia.     

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.     

Cell cycle dynamics inferred from the static properties of cells in balanced growth

The duration of a morphological phase of the cell cycle is reflected in the steady state distribution of the sizes of cells in that phase. Relationships presented here provide a method for estimating the timing and variability of any cell cycle phase. It is shown that the mean size of cells initiating and finishing any phase can be estimated from (1) the frequency of cells exhibiting the distinguishing morphological or autoradiographic features of the phase; (2) the mean size of cells in the phase; and (3) their coefficient of variation. The calculations are based on a submodel of the Koch-Schaechter Growth Controlled Model which assumes that (i) the distribution of division sizes is Gaussian; (ii) there is no correlation in division sizes between successive generations; and (iii) every cell division gives rise to two daughter cells of equal size. The calculations should be useful for a wider range of models, however, because the extrapolation factors are not sensitive to the chosen model. Criteria are proposed to allow the user to check the method's applicability for any experimental case. The method also provides a more efficient test of the dependence of growth on cell size than does the Collins-Richmond method. This is because the method uses the mean and coefficient of variation of the size of the total population, in conjunction with those of the cells in a final phase of the cell cycle, to test potential growth laws. For Escherichia coli populations studied by electron microscopy, an exponential growth model provided much better agreement than did a linear growth model. The computer simulations were used to generate rules for three types of cell phases: those that end at cell division, those that start at cell division, and those totally contained within a single cell cycle. For the last type, additional criteria are proposed to establish if the phase is well enough contained for the formulae and graphs to be used. The most useful rule emerging from these computer studies is that the fraction of the cell cycle time occupied by a phase is the product of the frequency of the phase and the ratio of the mean size of cells in that phase to the mean size of all cells in the population. A further advantage of the techniques presented here is that they use the 'extant' distributions that were actually measured, and not hypothesized distributions nor the special distributions needed for Collins-Richmond method that can only be calculated from the observed distributions of dividing or newborn cells on the basis of an assumed growth law.     

Cell elongation and division probability during the Escherichia coli growth cycle.

A new method is presented for determining the growth rate and the probability of cell division (separation) during the cell cycle, using size distributions of cell populations grown under steady-state conditions. The method utilizes the cell life-length distribution, i.e., the probability that a cell will have any specific size during its life history. This method was used to analyze cell length distributions of six cultures of Escherichia coli, for which doubling times varied from 19 to 125 min. The results for each culture are in good agreement with a single model of growth and division kinetics: exponential elongation of cells during growth phase of the cycle, and normal distributions of length at birth and at division. The average value of the coefficient of variation was 13.5% for all strains and growth rates. These results, based upon 5,955 observations, support and extend earlier proposals that growth and division patterns of E. coli are similar at all growth rates and, in addition, identify the general growth pattern of these cells to be exponential.     

Cell survival and radiation induced chromosome aberrations

Summary Existing mathematical formulations to predict the frequency of radiation induced chromosome aberrations in 2nd post-irradiation division are based on the Poisson distribution [3, 4]. Meanwhile several studies have shown that intercellular distributions exist, deviating from Poisson. In the present study a modified model was developed which permits the application of empirical distributions. Transmission and survival parameters of aberrations can be iteratively computed. A general formula was derived for the calculation of cell survival from 1st to 2nd division.     

The size distribution of conspecific populations: the peoples of New Guinea

The size distribution of the language populations in New Guinea, which represent over 15% of the world's languages, is analysed using models analogous to the resource division models of species abundance distribution in ecological communities. A model distribution of resource segments reflecting population size is created by repeated selection of an existing resource segment and its division into two. We found that any dependency of the selection probability on the size of the segment generated negatively skewed abundance distributions after log transformation. Asymmetric segment division further exacerbated the negative skewness. Size-independent selection produced lognormal abundance distributions, irrespective of the segment division method. Size-dependent selection and asymmetric division were deemed reasonable assumptions since large language populations are more likely to generate isolates, which develop into new populations, than small ones, and these isolates are likely to be small relative to the progenitor population. A negatively skewed distribution of the log-transformed population sizes was therefore expected. However, the observed distributions were lognormal, scale invariant for areas containing between 100 and over 1000 language populations. The dynamics of language differentiation, as reflected by the models, may therefore be unimportant relative to the effect of variable growth rates among populations. All lognormal distributions from resource division models had a higher variance than the observed one, where half of the 1053 populations had between 350 and 3000 individuals. The possible mechanisms maintaining such a low variance around a modal population size of 1000 are discussed.     

A dynamic simulation model of tissue growth and cell patterning

The distributions of cells in tissues of experimental chimaeras and mosaics can serve as tests of mechanisms and rules by which single cells organize themselves into complex, multicellular structures during embryogenesis. We have devised a dynamic, computer simulation model of tissue growth and cell patterning which is directly applicable to the analysis of chimaeras and mosaics. In the model, schematized cells possess a small behavioral repertoire and simple rules for the carrying out of these behaviors. Populations of such cells evolve tissue patterns in real-time that are very similar to those seen in experimental animals. In particular, we have modeled the major pattern features seen in amphibian and mammalian eye chimaeras and mosaics. We have demonstrated that cell mixing can be a passive concomitant of interstitial cell division, a result which alleviates the need to postulate active cell mixing in such mammalian systems. We expect this approach to be a valuable addition to methods of pattern analysis in development.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Correlation between phosphatidylinositol degradation and cell division in embryonic chicken lens epithelia

Differentiation of embryonic chicken lens epithelial cells to form lens fibers is associated with a marked decrease in both the rate of phosphatidylinositol degradation and the rate of cell division. In cells of the central region of the lens epithelium, the rate of cell division also declines with developmental age. The present study measures phosphatidylinositol degradation in cultured explants of the central lens epithelium of chicken embryos of different ages to determine the extent of the correlation between phosphatidylinositol degradation and cell division in this tissue. The results show that the rate of phosphatidylinositol degradation also decreases during development and is proportional to the rate of cell division throughout the period from 6 to 19 days of development. Furthermore, stimulating cell division in central explants of lens epithelia of 19-day-old chicken embryos by culturing them in the presence of fetal calf serum produces a proportional increase in the rate of phosphatidylinositol degradation. These findings indicate that cell division and phosphatidylinositol degradation are tightly coupled in this tissue, and raise the possibility that phosphatidylinositol metabolism may regulate some aspect of the cell cycle.     

Myogenesis during holothurian intestinal regeneration

Echinoderms are well known as being able to regenerate body parts and thus provide excellent models for studying regenerative processes in adult organisms. We are interested in intestinal regeneration in the sea cucumber, Holothuria glaberrima, and focus here on the regeneration of intestinal muscle components. We have used immunohistochemical techniques to describe the formation of the intestinal muscle layers. Myoblasts are first observed within the regenerating structure, adjacent to the coelomic epithelia. Within a few days, these cells acquire muscle markers and form a single cell layer that underlies the epithelia. Animals injected with BrdU at various regeneration stages have been subsequently analyzed for the presence of muscle differentiation markers. BrdU-labeled muscle nuclei are observed in myocytes of 3-week regenerates, showing that these cells originate from proliferating precursors. The peak in muscle precursor proliferation appears to occur during the second week of regeneration. Therefore, new muscle cells in the regenerating intestine originate from precursors that have undergone cell division. Our results suggest that the precursor cells arise from the coelomic epithelia. We also provide a comparative view of muscle regeneration in an echinoderm, a topic of interest in view of the many recent studies of muscle regeneration in vertebrate species. This work was supported by NSF (IBN-0110692) and NIH-MBRS (S06GM08102). We also acknowledge partial support from NIH-RCMI (RRO-3641-01) and the University of Puerto Rico     

Cell proliferation and cell differentiation in tissue cultures of adult muco-cilliary epithelia.

Explants and monolayers from a variety of muco-ciliary epithelia were cultivated in vitro and the kinetics of their proliferation and differentiation described. New epithelial lining and epithelial-like monolayer sheets of cells formed in which the migration cells were all originally undifferentiated cycling stem cells. The divided and differentiated in ML growth into cell types characteristic of the tissue source: however, the control mechanisms which regulate cell division and cell differentiation in the tissues were lost outside the tissue framework. Cell division and cyto-differentiation in ML growths both in ciliated and in mucus-producing cells, were not always mutually exclusive.     

Growth factor regulation of the cell Cycle in developing and mature inner ear sensory epithelia

Growth factors and other extracellular signals regulate cell division in many tissues. Consequently, growth factors may have therapeutic uses to stimulate the production of replacement sensory hair cells in damaged human inner ears, thereby assisting in alleviating hearing loss and vestibular dysfunction. Assessment of the ability of growth factors to stimulate cell proliferation in inner ear sensory epithelia is at an early stage. This paper provides a brief account of what we know regarding growth factor regulation of cell proliferation in developing and mature inner ear sensory epithelia.     

How institutions shaped the last major evolutionary transition to large-scale human societies

What drove the transition from small-scale human societies centred on kinship and personal exchange, to large-scale societies comprising cooperation and division of labour among untold numbers of unrelated individuals? We propose that the unique human capacity to negotiate institutional rules that coordinate social actions was a key driver of this transition. By creating institutions, humans have been able to move from the default ‘Hobbesian’ rules of the ‘game of life’, determined by physical/environmental constraints, into self-created rules of social organization where cooperation can be individually advantageous even in large groups of unrelated individuals. Examples include rules of food sharing in hunter–gatherers, rules for the usage of irrigation systems in agriculturalists, property rights and systems for sharing reputation between mediaeval traders. Successful institutions create rules of interaction that are self-enforcing, providing direct benefits both to individuals that follow them, and to individuals that sanction rule breakers. Forming institutions requires shared intentionality, language and other cognitive abilities largely absent in other primates. We explain how cooperative breeding likely selected for these abilities early in the Homo lineage. This allowed anatomically modern humans to create institutions that transformed the self-reliance of our primate ancestors into the division of labour of large-scale human social organization.     

Isolation of third, fourth, and fifth instar larval midgut epithelia of the moth, Trichoplusia ni

A new tissue isolation technique was used to create intact midgut epithelial wholemounts from three Trichoplusia ni (Lepidoptera: Noctuidae) larval instars. The protease, dispase, removed the basal lamina and associated connective tissue and allowed for high resolution light microscopy of entire epithelia. Columnar, goblet, differentiating, and stem cells were characterized by double fluorescent labelling of f-actin and nuclei. A comparison of cell populations by digital image analysis revealed significant regional and temporal changes in the density and number of differentiating and stem cells. Growth of the midgut epithelium from third to fourth instar, and from fourth to fifth instar, was accomplished by both cell differentiation and cell division. Cell division however, was greatly reduced from fourth to fifth instar with a concomitant sharp decrease in the stem cell population.     

Auxin transport synchronizes the pattern of cell division in a tobacco cell line

The open morphogenesis of plants requires coordination of patterning by intercellular signals. The tobacco (Nicotiana tabacum cv Virginia Bright Italia) cell line VBI-0 provides a simple model system to study the role of intercellular communication in patterning. In this cell line, singular cells divide axially to produce linear cell files of distinct polarity. The trigger for this axial division is exogenous auxin. When frequency distributions of files are constructed over the number of cells per file during the exponential phase of the culture, even numbers are found to be frequent, whereas files consisting of uneven numbers of cells are rare. We can simulate these distributions with a mathematical model derived from nonlinear dynamics, which describes a chain of cell-division oscillators where elementary oscillators are coupled unidirectionally and where the number of oscillators is not conserved. The model predicts several nonintuitive properties of our experimental system. For instance, files consisting of six cells are more frequent than expected from a strictly binary division system. More centrally, the model predicts a polar transport of the coordinating signal. We therefore tested the patterns obtained after treatment with 1-N-naphthylphthalamic acid, an inhibitor of auxin efflux carriers. Using low concentrations of 1-N-naphthylphthalamic acid that leave cell division and axiality of division unaltered, we observe that the frequencies of files with even and uneven cell numbers are equalized. Our findings are discussed in the context of auxin transport as synchronizing signal in cell patterning.