A dynamic simulation model of tissue growth and cell patterning

Cell-Based Modeling of Tissue Developing in the Scaffold Pores of Varying Cross-Sections

In this work, we present a mathematical model of cell growth in the pores of a perfusion bioreactor through which a nutrient solution is pumped. We have developed a 2-D vertex model that allows us to reproduce the microscopic dynamics of the microenvironment of cells and describe the occupation of the pore space with cells. In this model, each cell is represented by a polygon; the number of vertices and shapes may change over time. The model includes mitotic cell division and intercalation. We study the impact of two factors on cell growth. On the one hand, we consider a channel of variable cross-section, which models a scaffold with a porosity gradient. On the other hand, a cluster of cells grows under the influence of a nutrient solution flow, which establishes a non-uniform distribution of shear stresses in the pore space. We present the results of numerical simulation of the tissue growth in a wavy channel. The model allows us to obtain complete microscopic information that includes the dynamics of intracellular pressure, the local elastic energy, and the characteristics of cell populations. As we showed, in a functional-graded scaffold, the distribution of the shear stresses in the pore space has a complicated structure, which implies the possibility of controlling the growth zones by varying the pore geometry.

Simulations of sea urchin early development delineate the role of oriented cell division in the morula-to-blastula transition

The sea urchin morula to blastula transition has long been thought to require oriented cell divisions and blastomere adherence to the enveloping hyaline layer. In a computer simulation model, cell divisions constrained by a surface plane division rule are adequate to effect morphological transition. The hyaline membrane acts as an enhancer but is not essential. The model is consistent with the orientation of micromere divisions and the open blastulae of direct developing species. The surface plane division rule precedes overt epithelization of surface cells and acts to organize the developing epithelium. It is a universal feature of early metazoan development and simulations of non-echinoid cleavage patterns support its role throughout Metazoa. The surface plane division rule requires only local cues and cells need not reference global positional information or embryonic axes.

Local cell interactions and self-amplifying individual cell ingression drive amniote gastrulation

Gastrulation generates three layers of cells (ectoderm, mesoderm, endoderm) from a single sheet, while large scale cell movements occur across the entire embryo. In amniote (reptiles, birds, mammals) embryos, the deep layers arise by epithelial-to-mesenchymal transition (EMT) at a morphologically stable midline structure, the primitive streak (PS). We know very little about how these events are controlled or how the PS is maintained despite its continuously changing cellular composition. Using the chick, we show that isolated EMT events and ingression of individual cells start well before gastrulation. A Nodal-dependent ‘community effect’ then concentrates and amplifies EMT by positive feedback to form the PS as a zone of massive cell ingression. Computer simulations show that a combination of local cell interactions (EMT and cell intercalation) is sufficient to explain PS formation and the associated complex movements globally across a large epithelial sheet, without the need to invoke long-range signalling.

DOI:http://dx.doi.org/10.7554/eLife.01817.001

A key process during the development of an embryo involves a single layer of cells reorganizing into three ‘germ layers’: the ectoderm, which becomes the skin and nervous system; the mesoderm, which gives rise to the skeleton, muscles and the circulatory and urinogenital systems, and the endoderm, which gives rise to the lining of the gut and associated organs. The process of forming these three layers is known as gastrulation.

To date most experiments on gastrulation in vertebrates have been performed on frog embryos. However, the embryos of amniotes, the group of ‘higher’ vertebrates that comprises reptiles, birds and mammals, differ from those of frogs in a number of ways. Now Voiculescu et al. have used a combination of experimental and computational techniques to shed new light on gastrulation in chick embryos.

Just prior to gastrulation, the cells of the amniote embryo are arranged in a flat disk, one cell thick, called the epiblast. The cells of the epiblast then move to form the mesoderm and endoderm (in a process called epithelial-to-mesenchymal transition). These cell movements also lead to the formation of a structure called the primitive streak that establishes the left-right symmetry of the organism, and also defines the midline of the body.

Now Voiculescu et al. have shown that the epithelial-to-mesenchymal transition starts before the primitive streak appears, and that two main processes drive gastrulation. One involves cells inserting themselves between other cells at the midline of the epiblast, which causes a double whorl-like movement within the plane of the epiblast. At the same time small numbers of cells leave the epiblast, and as these cells accumulate under the epiblast, they initiate a positive feedback effect by which they encourage more cells to leave the epiblast. Voiculescu et al. found that this ‘community effect’ involves signalling by a protein called Nodal. This protein effectively amplifies the epithelial-to-mesenchymal transition and leads to the appearance of the primitive streak at the midline.

Using computational modelling, Voiculescu et al. argue that the movements of gastrulation can be explained entirely based on local interactions between cells, without the need for cells to send signals over long distances to guide cell movements, as had been generally believed.

DOI:http://dx.doi.org/10.7554/eLife.01817.002

NEW COMPUTATIONAL APPROACHES FOR BIOPHYSICAL HEAT TRANSFER IN TISSUE UNDER ULTRASONIC WAVES: THE VARIATIONAL ITERATION AND CHEBYSCHEV SPECTRAL SIMULATIONS

A mathematical and numerical study is presented for simulating temperature distribution in a two-dimensional tissue medium using Pennes bioheat transfer equation, when the tissue is subjected to ultrasonic waves. Following nondimensionalization of the governing partial differential equation, a novel variational iteration method (VIM) solution is developed. This excellent technique introduced by He [Variational iteration method — a kind of non-linear analytical technique: Some examples, Int J Non-Linear Mech.34:699–708, 1999] employs Lagrange multipliers which can be identified optimally via variational theory. The space and time distributions of temperature are studied and solutions visualized via Mathematica. The influence of thermal conductivity and relaxation time are also examined. Excellent stability and convergence characteristics of VIM are demonstrated. Validation is achieved with a Chebyschev spectral collocation method (CSCM). The present work demonstrates the excellent potential of this powerful semi-numerical method in nonlinear biological heat transfer and furthermore provides an alternative strategy to conventional finite element and finite difference computational simulations. The model finds applications in minimally-invasive spinal laser treatments, glaucoma therapy in ophthalmology and thermoradiotherapy for malignant tumors.

Transition from organogenesis to stem cell maintenance in the mouse adrenal cortex

Mice showing mosaic expression of an appropriate marker gene that is activated during development provide simple tools for investigating cell lineages. We used the mosaic β-galactosidase staining patterns in adrenal cortices of 21OH/ LacZ transgenic mice to study both organogenesis and maintenance of the adult tissue. Randomly orientated mosaic patterns present in embryonic day 14.5 (E14.5) adrenals changed progressively during the perinatal period from discrete spots, via patches and radial arrays, to radial stripes, which first emerged between postnatal days 0 and 7 (P0 and P7). The mosaic radial stripe pattern was fully established by P21 and remained unchanged throughout the adult period (8-52 weeks). The mouse adrenal gland grew continuously between E14.5 and P21, including the period during which stripes emerge. Ki67-positive, proliferative cells in the adrenal cortex were mainly localized to the outer cell layers between E18.5 and P3. By P10, cell proliferation had increased, and the proliferative region had expanded but was still mainly confined to the outer cortex. Correlation of changes in mosaic patterns in 21OH/LacZ adrenal cortices with the locations of adrenocortical cell proliferation suggest that the radial stripes arise by edge-biased growth during the perinatal period, even if they are maintained by stem cells in adults. The stability of the adult stripe pattern suggests that stem cell function is unchanged between 8 and 52 weeks.

Evaluation of methods for one-dimensional spatial analysis of two-dimensional patterns in mouse chimaeras

The relative extent of cell mixing in tissues of mouse chimaeras or mosaics can be studied by comparing the distributions of the two cell populations in the tissues. However, the mean patch size is misleading because it is affected by both the extent of cell mixing and the relative contributions of the two cell populations. Previous work suggested that effects attributable to differences in tissue composition among chimaeras can be factored out either by correcting the mean patch size or by using the median patch size for the minority cell population and restricting the analysis to grossly unbalanced chimaeras. In the present study, computer simulations of two-dimensional mosaic arrays of black and white squares (representing cells) were used to simulate chimaeric tissues. Random arrays simulated tissues with extensive cell mixing, arrays of cell clumps (representing coherent clones) simulated less mixed tissues, and striped arrays simulated tissues with elongated but fragmented descendent clones. The computer simulations predicted that (i) the median patch length (minority cell population) and the corrected mean patch length would both distinguish between random and clumped patterns and (ii) differences in the variation of the composition of two perpendicular series of one-dimensional transects would distinguished between stripes and randomly orientated patches. Both predictions were confirmed by analysis of histological sections of the retinal pigment epithelium from fetal and adult mouse chimaeras. This study demonstrates that two types of non-random two-dimensional variegated patterns (clumps and stripes) can be identified in chimaeras without two-dimensional reconstruction of serial sections.

At the biological modeling and simulation frontier

We provide a rationale for and describe examples of synthetic modeling and simulation (M&S) of biological systems. We explain how synthetic methods are distinct from familiar inductive methods. Synthetic M&S is a means to better understand the mechanisms that generate normal and disease-related phenomena observed in research, and how compounds of interest interact with them to alter phenomena. An objective is to build better, working hypotheses of plausible mechanisms. A synthetic model is an extant hypothesis: execution produces an observable mechanism and phenomena. Mobile objects representing compounds carry information enabling components to distinguish between them and react accordingly when different compounds are studied simultaneously. We argue that the familiar inductive approaches contribute to the general inefficiencies being experienced by pharmaceutical R&D, and that use of synthetic approaches accelerates and improves R&D decision-making and thus the drug development process. A reason is that synthetic models encourage and facilitate abductive scientific reasoning, a primary means of knowledge creation and creative cognition. When synthetic models are executed, we observe different aspects of knowledge in action from different perspectives. These models can be tuned to reflect differences in experimental conditions and individuals, making translational research more concrete while moving us closer to personalized medicine.

Computer simulation analysis of normal and abnormal development of the mammalian diaphragm

BACKGROUND

Congenital diaphragmatic hernia (CDH) is a birth defect with significant morbidity and mortality. Knowledge of diaphragm morphogenesis and the aberrations leading to CDH is limited. Although classical embryologists described the diaphragm as arising from the septum transversum, pleuroperitoneal folds (PPF), esophageal mesentery and body wall, animal studies suggest that the PPF is the major, if not sole, contributor to the muscular diaphragm. Recently, a posterior defect in the PPF has been identified when the teratogen nitrofen is used to induce CDH in fetal rodents. We describe use of a cell-based computer modeling system (Nudge++) to study diaphragm morphogenesis.

METHODS AND RESULTS

Key diaphragmatic structures were digitized from transverse serial sections of paraffin-embedded mouse embryos at embryonic days 11.5 and 13. Structure boundaries and simulated cells were combined in the Nudge++ software. Model cells were assigned putative behavioral programs, and these programs were progressively modified to produce a diaphragm consistent with the observed anatomy in rodents. Homology between our model and recent anatomical observations occurred under the following simulation conditions: (1) cell mitoses are restricted to the edge of growing tissue; (2) cells near the chest wall remain mitotically active; (3) mitotically active non-edge cells migrate toward the chest wall; and (4) movement direction depends on clonal differentiation between anterior and posterior PPF cells.

CONCLUSION

With the PPF as the sole source of mitotic cells, an early defect in the PPF evolves into a posteromedial diaphragm defect, similar to that of the rodent nitrofen CDH model. A posterolateral defect, as occurs in human CDH, would be more readily recreated by invoking other cellular contributions. Our results suggest that recent reports of PPF-dominated diaphragm morphogenesis in the rodent may not be strictly applicable to man. The ability to recreate a CDH defect using a combination of experimental data and testable hypotheses gives impetus to simulation modeling as an adjunct to experimental analysis of diaphragm morphogenesis.

Formation of the chick primitive streak as studied in computer simulations

We have used a computer simulation system to examine formation of the chick primitive streak and to test the proposal (Wei and Mikawa Development 127 (2000) 87) that oriented cell division could account for primitive streak elongation. We find that this proposal is inadequate to explain elongation of the streak. In contrast, a correctly patterned model streak can be generated if two putative mechanisms are operative. First, a subpopulation of precursor cells that is known to contribute to the streak is assigned a specific, but simple, movement pattern. Second, additional cells within the epiblast are allowed to incorporate into the streak based on near-neighbor relations. In this model, the streak is cast as a steady-state system with continuous recruitment of neighboring epiblast cells, egress of cells into deeper layers and an internal pattern of cell movement. The model accurately portrays elongation and maintenance of a robust streak, changes in the composition of the streak and defects in the streak after experimental manipulation.

A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate

We developed a three-dimensional (3D) cell model of a multicellular aggregate consisting of several polyhedral cells to investigate the deformation and rearrangement of cells under the influence of external forces. The polyhedral cells fill the space in the aggregate without gaps or overlaps, consist of contracting interfaces and maintain their volumes. The interfaces and volumes were expressed by 3D vertex coordinates. Vertex movements obey equations of motion that rearrange the cells to minimize total free energy, and undergo an elementary process that exchanges vertex pair connections when vertices approach each other. The total free energy includes the interface energy of cells and the compression or expansion energy of cells. Computer simulations provided the following results: An aggregate of cells becomes spherical to minimize individual cell surface areas; Polygonal interfaces of cells remain flat; Cells within the 3D cell aggregate can move and rearrange despite the absence of free space. We examined cell rearrangement to elucidate the viscoelastic properties of the aggregate, e.g. when an external force flattens a cell aggregate (e.g. under centrifugation) its component cells quickly flatten. Under a continuous external force, the cells slowly rearrange to recover their original shape although the cell aggregate remains flat. The deformation and rearrangement of individual cells is a two-step process with a time lag. Our results showed that morphological and viscoelastic properties of the cell aggregate with long relaxation time are based on component cells where minimization of interfacial energy of cells provides a motive force for cell movement.

Clonal analysis of patterns of growth, stem cell activity, and cell movement during the development and maintenance of the murine corneal epithelium

Patterns of growth and cell movement in the developing and adult corneal epithelium were investigated by analysing clonal patches of LacZ-expressing cells in chimeric and X-inactivation mosaic mice. It was found that cell proliferation throughout the basal corneal epithelium during embryogenesis and early postnatal life creates a disordered mosaic pattern of LacZ(+) clones that contrasts with patterns of proliferation and striping produced during the later embryonic stages of retinal pigmented epithelium development. The early mosaic pattern in the corneal epithelium is replaced in the first 12 postnatal weeks by an ordered pattern of radial stripes or sectors that reflects migration without mixing of the progeny of clones of limbal stem cells. In contrast to previous assumptions, it was found that maturation of the activity of limbal stem cells and the pattern of migration of their progeny are delayed for several weeks postnatally. No evidence was found for immigration of the progeny of stem cells until the 5th postnatal week. There are approximately 100 clones of limbal stem cells initially, and clones are lost during postnatal life. Our studies provide a new assay for limbal and corneal defects in mutant mice.

Modeling of mosaic patterns in chimeric liver and adrenal cortex: algorithmic organogenesis?

If organogenesis were a completely deterministic process, then the amount of information required to store the spatial position and fate of every cell in vertebrate organisms would be larger than the total information that could be contained in their genomes. This suggests that the instructions of developmental mechanisms involved in organogenesis, coded in DNA, must be at least in part procedural or algorithmically based. Chimeric mosaic patterns in rat livers have been shown to be isotropic and to have fractal profiles (D approximately 1.3) whereas adrenal gland mosaics show a less irregular radial pattern, with lower fractal dimension (D approximately 1.2) than in the liver. These findings suggested a possible model of parenchyma generation. We propose that during organogenesis in both liver and adrenal cortex, the same basic mechanism is directed to organ mass enlargement, whereas the differences observed in mosaic patterns between the organs could be due to the control of a single parameter, namely, a form of contact inhibition. Computer simulations in two dimensions returned comparable results in both the fractal dimension value of mosaic patches and appearance of the mosaic 'tissues', as observed histologically in chimeras. This suggests that position information and locomotion of cells would not be required to produce the mosaic pattern observed in chimeras.

The biological toolbox: a computer program for simulating basic biological and pathological processes

The program described here has been written to enable pathologists and biologists with almost no computer experience to design complex models of cell interactions. The program although simulating in only two dimensions allows the user to define the individual rules governing cell behaviour using a language called Cell Description Language, then simulates the multiple interactions between the cells to produce a dynamic visual interpretation representing tissue growth and differentiation. The program has been developed using the World Wide Web, thereby giving access to anyone with an Internet connection. The Web technology allows others to use our powerful computers to perform the complex calculations that are necessary and effectively eliminates the problems of modifying and compiling the program to run on more than one hardware platform. The changes that take place during the simulation are presented as a video using the MPEG video format; they may then be viewed on many different types of computers. The toolbox provides a novel approach to computer-based biological simulations and an excellent resource for teaching.

Computer simulation modelling and visualization of 3D architecture of biological tissues. Simulation of the evolution of normal, metaplastic and dysplastic states of the nasal epithelium

Recent technical improvements, such as 3D microscopy imaging, have shown the necessity of studying 3D biological tissue architecture during carcinogenesis. In the present paper a computer simulation model is developed allowing the visualization of the microscopic biological tissue architecture during the development of metaplastic and dysplastic lesions. The static part of the model allows the simulation of the normal, metaplastic and dysplastic architecture of an external epithelium. This model is associated to a knowledge base which contains only data on the nasal epithelium. The latter has been well studied by numerous authors and its lesional states are well known. An inference engine allows the initialization of the static model parameters. A statistical comparison between simulated epithelia and real epithelia is achieved by adjusting the parameter values during the simulation. The dynamic part of the model allows the simulation of a growth process on a 3D representation based on the static model. The main hypothesis is that nasal epithelium is submitted to a continuous transformation from normal to cancer through metaplasia and dysplasia. The evolution of each cell (represented by its nucleus) depends on its local environment and also on its heritage from its mother-cell. Simulation of tissue renewal of the nasal pseudostratified epithelium has been achieved. The evolution from normal to hyperplasia has been simulated. After modification of the cell cycle modelling, the simulation of the development of metaplastic foci has been obtained.

A computer graphic simulation of squamous epithelium

An epithelium maintains its integrity through the organized growth and orderly differentiation of a transient cell population derived from stem cells. This organization is dependent upon both physical mechanisms such as cell adhesion and attraction and the relationship between differentiation and cell division. The interactions between these processes are complex and difficult to conceptualize from a purely mathematical approach. We have therefore set out to develop a graphic model of an epithelium controlled by rules that can be modified. We have chosen to model epidermis, the most superficial part of skin, with cells differentiating from a stem cell population and being lost from the surface of the model. The model is novel not only in the rules that govern cell behaviour, but also because it does not require a predefined lattice to assign the position of cells. Each cell assumes a position depending upon the balance of adhesive and repulsive forces that it experiences. Chemical factors which affect the differentiation of individual cell types are assumed to be produced both by cells within the model and externally from the underlying connective tissue. These "chemical factors" diffuse through the model with a concentration that declines as an inverse square with distance from the source. The rules allow the model to grow from a single stem cell to reach a steady state. At steady state the pattern and clonal structure is strikingly similar to that seen in a range of normal epithelia. Furthermore, if part of the model is removed it is capable of regenerating itself without additional rules. The model allows the visualization of the effects of introducing new rules and modifying the interaction between chosen rules. This study demonstrates that a set of simple rules can be used to make a dynamic flexible model resembling skin.

Migration patterns of clonally related granule cells and their progenitors in the developing chick cerebellum

During cerebellar development, granule neurons and their progenitors undergo complex migrations. To define these migratory paths better, we used replication-incompetent retroviruses to label dividing cells early in cerebellar development. Clonally related granule cells were widely dispersed in both rostrocaudal and mediolateral planes; clones often spanned the midline. The data suggest that granule cell progenitors originate from the ventricular zone along the entire mediolateral extent of the caudal edge of the cerebellum. After reaching the cerebellar surface, progenitors move primarily rostrally and proliferate in the superficial external granule layer. Postmitotic granule cells then migrate long distances medially and laterally in the transverse plane in the deep external granule layer, where previously they had been thought simply to extend transverse processes.

Spatial patterns of cells in dividing epithelia

The spatial patterns of cell boundaries in a view of the apical surface of a dividing epithelium are explored by constructing a hypothetical cell pattern of an epithelium of dividing cells. The two elements specified in the hypothetical pattern are the orientation of division planes and the separation between the division planes in neighbouring cells. The orientations of division planes in one generation are all the same but are orthogonal to those in the preceding generation. The division-plane orientations follow in an orthogonal succession, as happens in early embryos. The division planes in neighbouring cells are offset. The contractions of division planes that would occur during cytokinesis distort existing boundaries creating various types of cell shapes. The patterns generated resemble cell patterns found in life. The hypothetical pattern is regenerative and shows how epithelial cell patterns where cells divide might arise. It has enabled the putative identification of sister cells and first cousins in the embryonic chick chorion.

Fractal geometry of mosaic pattern demonstrates liver regeneration is a self-similar process

Partial hepatectomy causes compensatory, nonneoplastic growth and regeneration in mammalian liver. Compensatory liver growth can be used to examine aspects of patterns of cell division in regenerating tissue. Chimeric animals provide markers of cell lineage which are independent of growth and can be used to follow cell division patterns. Previous experimental evidence suggests that compensatory liver growth is uniform, without focal centers of proliferation. In this study we have extended that observation to include genes important in regeneration and cell cycle control in order to establish that nascent growth centers are not present in regenerating liver. There is a uniform spatial distribution of expression of these genes which is not related to mosaic pattern in the chimeras. While these genes may help regulate hepatocyte proliferation they do not appear to regulate patch pattern in the chimeras. With this information confirming uniform growth it was possible to use fractal analysis to test various hypothesized patterns of regenerative growth in the liver. The results of this analysis indicate that mosaic pattern does not change substantially during the regenerative process. Patch area and perimeter (the area occupied by or perimeter around cells of like lineage) increase during compensatory liver growth in chimeric rats without alteration of the geometric complexity of patch boundaries (boundaries around cells of like lineage). These tissue findings are consistent with previously reported computer models of growth in which repetitive application of simple decisions assuming uniform growth created complex mosaic patterns. They support the notion that an iterating (repeating), self-similar (a pattern in which parts are representative of, but not identical to the whole) cell division program is sufficient for the regeneration of liver tissue following partial hepatectomy. Iterating, self-similar cell division programs are important because they suggest a way in which complex patterns (or morphogenesis) can be efficiently created from a small amount of stored information.

Contact response of cells can mediate morphogenetic pattern formation

Theories of morphogenetic pattern formation have included Turing's chemical prepatterns, mechanochemical interactions, cell sorting, and other mechanisms involving guided motion or signalling of cells. Many of these theories presuppose long-range cellular communication or other controls such as chemical concentration fields. However, the possibility that direct interactions between cells can lead to order and structure has not been seriously investigated in mathematical models. In this paper we consider this possibility, with emphasis on cells that reorient and align with each other when they come into contact. We show that such contact responses can account for the formation of multicellular patterns called parallel arrays. These patterns typically occur in tissue cultures of fibroblasts, and consist of clusters of cells sharing a common axis of orientation. Using predictions of a mathematical model and computer simulations of cell motion and interactions we show that contact responses alone, in the absence of other global controls, can promote the formation of these patterns. We suggest other situations in which patterns may result from direct cellular communication. Previous theories of morphogenesis are briefly reviewed and compared with this proposed mechanism.

Comparison of epidermal patch size in X-chromosome-linked mosaic and dizygotic chimeric mice

Mosaic animals can be made by aggregating embryonic tissues of distinguishable strains or they will occur spontaneously in eutherian mammals as a result of X-chromosome inactivation. Tissues of mosaic animals comprise aggregates of cells of similar lineage called 'patches'. The patch size of isolated epidermis from chimeras and X-chromosome-linked mosaics was compared in a quantitative fashion. Patch size was determined in the isolated epidermis of skin from aggregation chimeras between BALB/c and C3H/He strains of mice variant at the Gpi-1 locus and from the skin of X-chromosome-linked mosaic female BALB/c x C3H/He a mice heterozygous at the Pgk-1 locus. Patch size in this isolated tissue was not significantly different in these two types of mosaic animals. The results suggest that mechanisms in patch formation are primarily mechanical, dependent on cell division patterns.

Probabilistic division systems modeling the generation of mosaic fields

The explanation of mosaic pattern in chimeric organs analyzed by in situ methods requires modeling of specific hypotheses. The use of computer simulations to achieve this has led to the conclusion that finely variegated mixtures of cell lineage within chimeric tissues does not require extensive cell movement. Cell division models were used to determine the distribution of patch size as mosaic fields are generated. The results establish that these distributions are sensitive to the proportion of the two cell types which comprise the mosaic.

Positional variations in germinal cell growth in pigment-chimeric eyes of Xenopus: posterior half of the developing eye studied in genetic chimerae and in computer simulations

Growth of germinal cells at different angular positions within the posterior portion of the embryonic frog eye has been examined by orthotopically transplanting small groups of germinal cells from pigmented (stage 30-38) donor embryos into albino (stage 28-36) hosts and then serially photographing the polyclonal-cell progeny domain (typically a black sector) in the pigmented retinal epithelium of the living, growing eye. Far-ventral (6 o'clock) germinal cells formed a narrow sector along the ventral fissure, but ventral germinal cells at a position just posterior to the fissure (7 o'clock on a right eye) were seen to expand rapidly their angular territory on the germinal zone and formed huge sectors that widened toward the front of the older larval eye. Posterior (8, 9, and 10 o'clock) germinal cells were seen to shift their angular positions gradually toward dorsal and formed sectors that appeared to veer dorsalward nearing the front of the older eye. Dorsal (11 o'clock) germinal cells showed attenuative growth, forming sectors that narrowed approaching the front of the older eye. A simulation model of the growth dynamic was used to examine how expansive growth ventrally drives the positional variations in growth. When far-ventral germinal cells were programmed to retain the 6 o'clock position and ventral (7 o'clock) germinal cells were programmed to divide symmetrically at a high probability to produce two daughter germinal cells, not only were the observed ventral chimeric patterns simulated, but also simulated were the attenuative growth of dorsal transplants and the dorsal displacement and veering seen in the growth of posterior transplants.

Growth and development of the mouse retinal pigment epithelium. II. Cell patterning in experimental chimaeras and mosaics

The retinal pigment epithelium (PE), with pigmentation as a cell-autonomous marker, was analyzed in three types of mice: congenic pigmented----albino chimaeras, X-inactivation mosaics (Cattanach's translocation), and mosaics homozygous for the pink-eyed unstable mutation, which contain rare fully pigmented cells. In 10 chimaeric and 34 X-inactivation eyes, the proportionate mix in the right and left eyes of an individual animal was similar, the mix was approximately constant in all parts of a given eye, average patch size was larger toward the periphery of the PE, and peripheral patches tended to be elongated in the radial dimension. In all 44 whole mounts from pink-eyed unstable mutants, patches of 1-12 pigmented cells, each representing a single clone, were scattered throughout the PE; they tended to be larger with increasing distance from the optic nerve head. The collective data are consistent with significant cell mixing prior to specification of the two eye fields, during early organ-forming stages, and during later development of the PE. The tendency of peripheral patches to orient radially reflects the edge-biased pattern of cell proliferation in the PE. Cell mixing appears to be more prominent posteriorly in the PE sheet; growth proceeds anteriorly for more generations.

Growth and development of the mouse retinal pigment epithelium. I. Cell and tissue morphometrics and topography of mitotic activity

A computer-assisted morphometric and kinetic analysis of retinal pigment epithelium (PE) development was carried out in C57BL/6J and hybrid mice from Embryonic Day 13 (E13) to Postnatal Day 250 (P250). Total cell number rose from 14,000 at E15 at the rate of about 4000 cells/day to P1 and then at about 1500 cells/day to reach a stable level of 54,000 cells at P15. Compared to the 4-fold rise in cell number, PE area increased about 10-fold, in part through cell hypertrophy which continued beyond P15. Cell concentration increased with distance from the optic nerve head during development, but the gradient disappeared by P20 except for a consistent population of small cells around the optic nerve head and a late-appearing population of very large cells at the ora serrata. Binucleate cells constitute 2.1% of the PE cell population at P1 and 26% at P30, almost all of them located in the posterior 75% of the PE where they comprise 70% of the cell population at some radial positions. Mitotic cells, detected by fluorescent monoclonal antibody R3, are distributed across the entire PE at E13. As the eye grows the mitotic zone occupies a progressively smaller and more distal proportion of the increasing radius; by P5 only the region near the ora serrata is highly active, with some additional mitotic cells trailing into a broad central zone. From P7 to P15 nuclear divisions persist only centrally to generate the youngest uninucleate and binucleate cells. The mouse PE thus shows a pattern of edge-biased interstitial growth (in contrast to amphibians with strict edge growth).