CELL DIVISION KINETICS IN THE SHOOT APICAL MERISTEM OF CERATOPTERIS THALICTROIDES BRONG. WITH SPECIAL REFERENCE TO THE APICAL CELL

The duration of mitosis and the cell cycle were determined for defined cell populations of the shoot apical meristem of Ceratopteris thalictroides Brong. by using the colchicine-induced metaphase accumulation technique. The results indicate that the apical cell is mitotically active and cycles at an apparently greater frequency than the cells of subjacent populations. Duration of mitosis was similar for all cells of the meristem. These results are correlated with mitotic indices of control apices, the geometry of the apex, and the mean number of cells in the meristem. Shoot apices from adult plants were examined to determine mitotic indices within the meristem; mitotic activity was again noted for the apical cell. These results contradict recent proposals that the pteridophyte apical cell serves as a unicellular quiescent center which lacks histogenic potential and offer experimental support for the classical concept of apical cell function in those fern shoot meristems which terminate in a single apical cell.     

An alternative stochastic model of generation of oligodendrocytes in cell culture

According to our previous model, oligodendrocyte – type 2 (O-2A) astrocyte progenitor cells become competent for differentiation in vitro after they complete a certain number of critical mitotic cycles. After attaining the competency to differentiate, progenitor cells divide with fixed probability p in subsequent cycles. The number of critical cycles is random; analysis of data suggests that it varies from zero to two. The present paper presents an alternative model in which there are no critical cycles, and the probability that a progenitor cell will divide again decreases gradually to a plateau value as the number of completed mitotic cycles increases. In particular all progenitor cells have the ability to differentiate from the time of plating. The Kiefer-Wolfowitz procedure is used to fit the new model to experimental data on the clonal growth of purified O-2A progenitor cells obtained from the optic nerves of 7 day old rats. The new model is shown to fit the experimental data well, indicating that it is not possible to determine whether critical cycles exist on the basis of these experimental data. In contrast to the fit of the previous model, which suggested that the addition of thyroid hormone increased the limiting probability of differentiation as the number of mitotic cycles increases, the fit of the new model suggests that the addition of thyroid hormone has almost no effect on the limiting probability of differentiation. Received: 6 March 2000 / Revised version: 18 September 2000 / Published online: 30 April 2001     

Growth Pattern and Movement of Epidermal Cells within Leaves of Asphodelus tenuifolius Cav.

The pattern of growth (velocity field) in the intercalary growthzones of monocotyledon leaves can be determined from patternsof cell number density (number per unit length of cell file)and leaf elongation rates using theory based on a cell numberconservation equation. The case where elongation rate is non-steadywhile the pattern of cell number density is steady is discussedand a method for extending calculations into the meristem usingobservations of numbers of mitotic cells is outlined. Applicationof these methods is illustrated using data for epidermal cellsin the first leaf of Asphodelus tenuifolius Cav. During earlyleaf development, leaf elongation rate increased exponentiallybut cell number density and mitotic number density were steady.Cells 0.1 mm from the base of the leaf when leaves were 3.2mm long took 8.3 d to move through the growth zone. In leavesthat were 4 d older, similar cells took 5.1 d to traverse thegrowth zone. Increases in the rates of leaf elongation and ofcell movement appeared to be associated mainly with increasesin total rates of cell production in the epidermal meristem. Asphodelus tenuifolius Cav., Asphodelus fistulosus L., velocity field, meristem, mitotic cell number density, extension-only zone     

Mathematical model for the effects of adhesion and mechanics on cell migration speed.

Migration of mammalian blood and tissue cells over adhesive surfaces is apparently mediated by specific reversible reactions between cell membrane adhesion receptors and complementary ligands attached to the substratum. Although in a number of systems these receptors and ligand molecules have been isolated and identified, a theory capable of predicting the effects of their properties on cell migration behavior currently does not exist. We present a simple mathematical model for elucidating the dependence of cell speed on adhesion-receptor/ligand binding and cell mechanical properties. Our model can be applied to propose answers to questions such as: does an optimal adhesiveness exist for cell movement? How might changes in receptor and ligand density and/or affinity affect the rate of migration? Can cell rheological properties influence movement speed? This model incorporates cytoskeletal force generation, cell polarization, and dynamic adhesion as requirements for persistent cell movement. A critical feature is the proposed existence of an asymmetry in some cell adhesion-receptor property, correlated with cell polarity. We consider two major alternative mechanisms underlying this asymmetry: (a) a spatial distribution of adhesion-receptor number due to polarized endocytic trafficking and (b) a spatial variation in adhesion-receptor/ligand bond strength. Applying a viscoelastic-solid model for cell mechanics allows us to represent one-dimensional locomotion with a system of differential equations describing cell deformation and displacement along with adhesion-receptor dynamics. In this paper, we solve these equations under the simplifying assumption that receptor dynamics are at a quasi-steady state relative to cell locomotion. Thus, our results are strictly valid for sufficiently slow cell movement, as typically observed for tissue cells such as fibroblasts. Numerical examples relevant to experimental systems are provided. Our results predict how cell speed might vary with intracellular contractile force, cell rheology, receptor/ligand kinetics, and receptor/ligand number densities. A biphasic dependence is shown to be possible with respect to some of the system parameters, with position of the maxima essentially governed by a balance between transmitted contractile force and adhesiveness. We demonstrate that predictions for the two alternative asymmetry mechanisms can be distinguished and could be experimentally tested using cell populations possessing different adhesion-receptor numbers.     

A mechanomolecular model for the movement of chromosomes during mitosis driven by a minimal kinetochore bicyclic cascade

During mitosis chromosomes use a complex network of dynamic microtubules to find the cell equator in preparation for division signals. The roles of cellular chemical signals in mechanisms driving mitotic chromosomal movements are not well understood. In this paper we propose a mathematical model of this process which incorporates a molecular scale model of kinetochore-microtubule interactions into a negative feedback loop between spindle forces and local kinetochore biochemical reactions. This system allows kinetochore biochemical reactions to control and coordinate chromosome movement thus providing a direct connection between mechanical signals and mitosis chemical species. Our feedback control model can recreate chromosome movement from prometaphase to anaphase in good agreement with experimental data.     

Intracellular spatial localization regulated by the microtubule network

The commonly recognized mechanisms for spatial regulation inside the cell are membrane-bounded compartmentalization and biochemical association with subcellular organelles. We use computational modeling to investigate another spatial regulation mechanism mediated by the microtubule network in the cell. Our results demonstrate that the mitotic spindle can impose strong sequestration and concentration effects on molecules with binding affinity for microtubules, especially dynein-directed cargoes. The model can recapitulate the essence of three experimental observations on distinct microtubule network morphologies: the sequestration of germ plasm components by the mitotic spindles in the Drosophila syncytial embryo, the asymmetric cell division initiated by the time delay in centrosome maturation in the Drosophila neuroblast, and the diffusional block between neighboring energids in the Drosophila syncytial embryo. Our model thus suggests that the cell cycle-dependent changes in the microtubule network are critical for achieving different spatial regulation effects. The microtubule network provides a spatially extensive docking platform for molecules and gives rise to a "structured cytoplasm", in contrast to a free and fluid environment.     

A stochastic model for adhesion-mediated cell random motility and haptotaxis

The active migration of blood and tissue cells is important in a number of physiological processes including inflammation, wound healing, embryogenesis, and tumor cell metastasis. These cells move by transmitting cytoplasmic force through membrane receptors which are bound specifically to adhesion ligands in the surrounding substratum. Recently, much research has focused on the influence of the composition of extracellular matrix and the distribution of its components on the speed and direction of cell migration. It is commonly believed that the magnitude of the adhesion influences cell speed and/or random turning behavior, whereas a gradient of adhesion may bias the net direction of the cell movement, a phenomenon known as haptotaxis. The mechanisms underlying these responses are presently not understood.A stochastic model is presented to provide a mechanistic understanding of how the magnitude and distribution of adhesion ligands in the substratum influence cell movement. The receptor-mediated cell migration is modeled as an interrelation of random processes on distinct time scales. Adhesion receptors undergo rapid binding and transport, resulting in a stochastic spatial distribution of bound receptors fluctuating about some mean distribution. This results in a fluctuating spatio-temporal pattern of forces on the cell, which in turn affects the speed and turning behavior on a longer time scale. The model equations are a system of nonlinear stochastic differential equations (SDE's) which govern the time evolution of the spatial distribution of bound and free receptors, and the orientation and position of the cell. These SDE's are integrated numerically to simulate the behavior of the model cell on both a uniform substratum, and on a gradient of adhesion ligand concentration.Furthermore, analysis of the governing SDE system and corresponding Fokker-Planck equation (FPE) yields analytical expressions for indices which characterize cell movement on multiple time scales in terms of cell cytomechanical, morphological, and receptor binding and transport parameters. For a uniform adhesion ligand concentration, this analysis provides expressions for traditional cell movement indices such as mean speed, directional persistence time, and random motility coefficient. In a small gradient of adhesion, a perturbation analysis of the FPE yields a constitutive cell flux expression which includes a drift term for haptotactic directional cell migration. The haptotactic drift contains terms identified as contributions from directional orientation bias (taxis).     

Dynamic instability of microtubules

Recent evidence shows that dynamic instability is the dominant mechanism for the assembly of pure tubulin in vitro and for the great majority of microtubules in the mitotic spindle and the interphase cytoplasmic microtubule complex. The basic concepts of this model provide a framework for future characterization of the molecular basis of spatial and temporal regulation of microtubule dynamics in the cell and the function of microtubule dynamics in motile processes such as chromosome movement.     

Mitotic indices of bone marrow cells and their correlative relationships in dogs]

It was shown that mitotic indices of erythroblasts, basophilic and polychromatophilic normoblasts, myeloblasts, promyelocytes and myelocytes decline depending on the degree of cell differentiation and are quantitatively expressed by the ratio 4:2:1. The feedback between the value of mitotic indices and the number of cells which is expressed by power dependence was identified.     

Partitioning of the Golgi Apparatus during Mitosis in Living HeLa Cells

The Golgi apparatus of HeLa cells was fluorescently tagged with a green fluorescent protein (GFP), localized by attachment to the NH₂-terminal retention signal of N-acetylglucosaminyltransferase I (NAGT I). The location was confirmed by immunogold and immunofluorescence microscopy using a variety of Golgi markers. The behavior of the fluorescent Golgi marker was observed in fixed and living mitotic cells using confocal microscopy. By metaphase, cells contained a constant number of Golgi fragments dispersed throughout the cytoplasm. Conventional and cryoimmunoelectron microscopy showed that the NAGT I–GFP chimera (NAGFP)-positive fragments were tubulo-vesicular mitotic Golgi clusters. Mitotic conversion of Golgi stacks into mitotic clusters had surprisingly little effect on the polarity of Golgi membrane markers at the level of fluorescence microscopy. In living cells, there was little self-directed movement of the clusters in the period from metaphase to early telophase. In late telophase, the Golgi ribbon began to be reformed by a dynamic process of congregation and tubulation of the newly inherited Golgi fragments. The accuracy of partitioning the NAGFP-tagged Golgi was found to exceed that expected for a stochastic partitioning process. The results provide direct evidence for mitotic clusters as the unit of partitioning and suggest that precise regulation of the number, position, and compartmentation of mitotic membranes is a critical feature for the ordered inheritance of the Golgi apparatus.     

Cellular proliferation during cicatrization of the skin of 7-day chick embryos cultured in vitro

A cell proliferation study during in vitro wound healing of dorsal thoraco-lumbar skin of 7-day chick embryos was performed by pulse labelling using a single isotope (tritiated thymidine). The unoperated (controls) and operated explants were incubated in the radioactive medium (1 microCi/ml tritiated thymidine) 1 h prior to fixation and where fixed 1 h (start control), 48, 72 and 96 h after the excision. Mean labelling and mitotic indices of the unwounded epidermis were, respectively, 18.22% and 2.66% at 7 days, and 7.03% and 0.88% at 11 days (7 days + 96 h). 72 h after the excision, the labelling and mitotic indices of wounded epidermis increased, on average, respectively to 212,5% and 220% with respect to those of the controls, in the proximal zones near the inner edge on the wound. The labelling and mitotic indices in the dermis were, respectively, 27.95% and 3.63% at 7 days and 7.65% and 1.30% at 11 days. 72 h after the excision, the labelling and mitotic indices of the operated dermis increased, on average, respectively to 220% and 130% with respect to those of the controls in the centre and the proximal zones of the wound. The increase of the labelling index of the operated integument persisted for a maximum of 24 h, between 48 to 72 hours after the excision.     

Mammalian spindle orientation and position respond to changes in cell shape in a dynein-dependent fashion

In animal cells, positioning of the mitotic spindle is crucial for defining the plane of cytokinesis and the size ratio of daughter cells. We have characterized this phenomenon in a rat epithelial cell line using microscopy, micromanipulation, and microinjection. Unmanipulated cells position the mitotic spindle near their geometric center, with the spindle axis lying roughly parallel to the long axis of the cell. Spindles that were initially misoriented underwent directed rotation and caused a delay in anaphase onset. To gain further insight into this process, we gently deformed cells with a blunted glass needle to change the spatial relationship between the cortex and spindle. This manipulation induced spindle movement or rotation in metaphase and/or anaphase, until the spindle reached a proper position relative to the deformed shape. Spindle positioning was inhibited by either treatment with low doses of nocodazole or microinjection of antibodies against dynein, apparently due to the disruption of the organization of dynein and/or astral microtubules. Our results suggest that mitotic cells continuously monitor and maintain the position of the spindle relative to the cortex. This process is likely driven by interactions among astral microtubules, the motor protein dynein, and the cell cortex and may constitute part of a mitotic checkpoint mechanism.     

Sex- and Age-Related Temporal Variations in Intestinal-Epithelium Proliferation in the Suckling Mouse

Intestinal-crypt enterocytes are a cell population undergoing constant renewal in the mouse. Both adult and 28 d old animals have been shown to exhibit circadian rhythms in cell proliferative indices, but there are only scant data on the 24 h mitotic activity in the small and large intestine of younger mice. The present studies were thus undertaken in order to characterize the proliferative pattern of enterocytes in the duodenum and colon of 7 and 14 d old males and females of the C3H/S strain. Animals of each sex and from each age group were sacrificed every 4 h during a 24 h span, with each animal receiving an injection of colchicine 4 h before sacrifice. Samples of duodenum and colon were removed and processed for hematoxylin–eosin staining. Twenty longitudinally sectioned crypts within each sample were analyzed, and the mitotic indices of both cell populations from each animal were estimated. The arithmetic mean±SEM for each experimental group were then calculated and the statistical significance of differences between the means assessed by ANOVA and Student t-tests. We observed a greater daily mitotic activity in the duodenum than the colon, and moreover enterocytic proliferation in both those regions was greater in 14 than 7 d old animals. Twenty-four hour variations in mitotic activity occurred in all the experimental groups and tissues except for the large intestine of 7 d old females. Finally, the temporal profile of epithelium proliferation in the suckling mouse varied with age, sex, and site of the intestine studied.     

Instantaneous evaluation of mammalian cell culture growth rates through analysis of the mitotic index

Since a culture increases in cell number when dividing cells separate into two newborn cells, the fraction of mitotic cells in a growing cell population directly reflects the overall growth behavior of a cell culture. To rapidly assess the effects of growth conditions on the fraction of mitotic cells we have employed an antibody specific for the phosphorylated form of histone H3 for the identification of mitotic cells using flow cytometry. The phosphorylation of histone H3 closely correlates with the chromosomal condensation that accompanies the onset of mitosis, and, therefore, it represents a convenient marker for dividing cells. We have optimized the protocol for the staining of mitotic cells for both Chinese hamster ovary and hybridoma cell cultures. Fluorescence micrographs taken of stained cells show that cells in the various stages of mitosis can be detected based on the morphological characteristics of the chromosomes. The variation in the mitotic cell fraction has been determined throughout the batch growth phases of cultures under different growth conditions. The dynamics of the mitotic index show that balanced growth was never truly reached and that the growth rate is in fact quite variable for these cultures since large variations in the mitotic index are observed. In addition, a large increase in the fraction of mitotic cells just prior to the exponential growth phase for all cultures indicates that they are partially synchronized at the exit from the lag phase. According to a two-staged, age structured population balance model, the mitotic index is directly proportional to the growth rate of a culture. The proportionality constant for this case is shown to be the time required for cells to progress through mitosis. This time is believed to be constant for a particular cell line, as shown by experimental data. Thus, growth rates can be determined solely by measurement of the fraction of cells in mitosis. The mitotic index measurements were then used to calculate the growth in cell number of the cultures, and these simulations accurately reflect observed cell counts. Other simulations also show that changes in cell growth can be predicted before they are reflected in the cell count data. This technique can be used as a sensitive indicator of cell growth and could be useful as a process monitoring technique and for developing better feeding strategies for animal cell cultures.     

Sex- and age-related temporal variations in intestinal-epithelium proliferation in the suckling mouse

Intestinal-crypt enterocytes are a cell population undergoing constant renewal in the mouse. Both adult and 28 d old animals have been shown to exhibit circadian rhythms in cell proliferative indices, but there are only scant data on the 24 h mitotic activity in the small and large intestine of younger mice. The present studies were thus undertaken in order to characterize the proliferative pattern of enterocytes in the duodenum and colon of 7 and 14 d old males and females of the C3H/S strain. Animals of each sex and from each age group were sacrificed every 4 h during a 24 h span, with each animal receiving an injection of colchicine 4 h before sacrifice. Samples of duodenum and colon were removed and processed for hematoxylin-eosin staining. Twenty longitudinally sectioned crypts within each sample were analyzed, and the mitotic indices of both cell populations from each animal were estimated. The arithmetic mean±SEM for each experimental group were then calculated and the statistical significance of differences between the means assessed by ANOVA and Student t-tests. We observed a greater daily mitotic activity in the duodenum than the colon, and moreover enterocytic proliferation in both those regions was greater in 14 than 7 d old animals. Twenty-four hour variations in mitotic activity occurred in all the experimental groups and tissues except for the large intestine of 7 d old females. Finally, the temporal profile of epithelium proliferation in the suckling mouse varied with age, sex, and site of the intestine studied.     

A Stochastic Model For Cell Populations With Circadian Rhythms

A mathematical model for cell kinetics, based on a random walk, is developed. the model allows variations with time of the rates of passage of proliferating cells through the four phases of the mitotic cycle. Circadian variations in the mitotic and labelling indices of the Syrian hamster cheek pouch epithelium have previously been observed, and the random walk model has been used to simulate this phenomenon. Assuming that all basal cells are proliferative and that these cells leave the basal layer randomly throughout the mitotic cycle to become differentiated cells, it was found that the experimentally observed circadian rhythms of the mitotic and labelling indices could be reproduced in the model by postulating a circadian rhythm in the rate of passage of cells through the G₁ and S phases only. Moreover, the growth activity of cells in both the G₁ and S phases appears to reach a peak during the dark hours of the light-dark cycle, and to fall off rapidly in the early hours of daylight. the postulate of Møller, Larsen & Faber (1974) that injection of the animals with tritiated thymidine causes a shortening of the G₂ phase duration has been qualitatively confirmed by using the random walk model to simulate the FLM and MI curves after injection with tritiated thymidine.     

Progressive sheet-to-tubule transformation is a general mechanism for endoplasmic reticulum partitioning in dividing mammalian cells

The endoplasmic reticulum (ER) is both structurally and functionally complex, consisting of a dynamic network of interconnected sheets and tubules. To achieve a more comprehensive view of ER organization in interphase and mitotic cells and to address a discrepancy in the field (i.e., whether ER sheets persist, or are transformed to tubules, during mitosis), we analyzed the ER in four different mammalian cell lines using live-cell imaging, high-resolution electron microscopy, and three dimensional electron microscopy. In interphase cells, we found great variation in network organization and sheet structures among different cell lines. In mitotic cells, we show that the ER undergoes both spatial reorganization and structural transformation of sheets toward more fenestrated and tubular forms. However, the extent of spatial reorganization and sheet-to-tubule transformation varies among cell lines. Fenestration and tubulation of the ER correlates with a reduced number of membrane-bound ribosomes.     

The effect of single and of multiple doses of prednisolone tertiary butyl acetate on cell population kinetics in the small bowel mucosa of the rat.

The effect of single and of multiple doses of prednisolone upon cell population kinetics in the rat jejunal crypt was investigated, using autoradiography and stathmokinetic techniques with vincristine. Single injections of prednisolone (2.5 mg/kg body weight) induced a depression both flash thymidine labelling and mitotic indices; this change was shown to be due to a decreased cell production rate. Recovery of these proliferative indices occurred over seven days after injection; measurement of crypt size parameters showed a transient decrease in crypt population. Multiple daily injections of prednisolone (1 mg/kg body weight) produced a more sustained decrease in labelling and mitotic indices, which lasted as long as injections were continued (7 days); stathmokinetic techniques showed decreases in cell production rates, and the crypt population was also depressed throughout this period. It is concluded that prednisolone depresses cell proliferative rates in rat jejunal mucosa.     

Computational Models Reveal a Passive Mechanism for Cell Migration in the Crypt

Cell migration in the intestinal crypt is essential for the regular renewal of the epithelium, and the continued upward movement of cells is a key characteristic of healthy crypt dynamics. However, the driving force behind this migration is unknown. Possibilities include mitotic pressure, active movement driven by motility cues, or negative pressure arising from cell loss at the crypt collar. It is possible that a combination of factors together coordinate migration. Here, three different computational models are used to provide insight into the mechanisms that underpin cell movement in the crypt, by examining the consequence of eliminating cell division on cell movement. Computational simulations agree with existing experimental results, confirming that migration can continue in the absence of mitosis. Importantly, however, simulations allow us to infer mechanisms that are sufficient to generate cell movement, which is not possible through experimental observation alone. The results produced by the three models agree and suggest that cell loss due to apoptosis and extrusion at the crypt collar relieves cell compression below, allowing cells to expand and move upwards. This finding suggests that future experiments should focus on the role of apoptosis and cell extrusion in controlling cell migration in the crypt.     

The mathematical modelling of cell kinetics in corneal epithelial wound healing

This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a computer modelling framework. We begin by briefly showing that previous models, used in the study of corneal epithelial wound healing speeds, are inadequate for the study of cell kinetics. We proceed to formulate a new modelling framework more suited to such a study. This framework is simulated in its simplest form, and the results from this motivate a new realisation of the modelling framework, including a caricature of age structuring. Finally, a model with a simple representation of juxtacrine signalling is considered. The final model captures many, though not all, of the trends of the experimental data. This paper thus lays a foundation for the modelling of the cell kinetics of corneal epithelial wound healing, and yields valuable insight regarding the important mechanisms a model should consider in order to reproduce the observed experimental trends.