Calculation of the radiation-induced delay in cell division during a study of the induction of chromosome aberrations (the theoretical and experimental bases of the approach)

The possible influence of a radiation-induced delay of cell division on the yield of chromosome aberrations has been analyzed theoretically. The analysis is based on the assumption that the delay is caused by the damages that are realized in the mitosis as chromosome aberrations. It has been shown that the distributions of cells, that are registered by the number of chromosome aberrations, are a function of time of cell fixation and may substantially differ from actual disturbance. There is a correlation between the registered and actual disturbances which is determined by the kinetics of the first mitosis of nonirradiated cells and the degree of the radiation-induced division delay. Some qualitative sequels of the proposed model are in agreement with the experimental data.     

ON THE EXISTENCE OF A Go-PHASE IN THE CELL CYCLE

The model is based on the assumption that the cell cycle contains a G_o-phase which cells leave randomly with a constant probability per unit time, γ. After leaving the G_o-phase, the cells enter the C-phase which ends with cell division. The C-phase and its constituent phases, the‘true’G₁-phase, the S-phase, the G₂-phase and mitosis are assumed to have constant durations of T, T₁T_s, T₂ and T_m, respectively. For renewal tissue it is assumed that the probability per unit time of being lost from the population is a constant for all cells irrespective of their position in the cycle. The labelled mitosis curve and labelling index for continuous labelling are derived in terms of γ, T, and T_s. The model generates labelled mitosis curves which damp quickly and reach a constant value of twice the initial labelling index, if the mean duration of the G_o-phase is sufficiently long. It is shown that the predicted labelled mitosis and continuous labelling curves agree reasonably well with the experimental curves for the hamster cheek pouch if T has a value of about 60 hr. Data are presented for the rat dorsal epidermis which support the assumption that there is a constant probability per unit time of a cell being released from the Go-phase.     

Prediction of X-ray induced mitotic delay and recovery of G2 cells

A mathematical model is presented that predicts the delay of mitosis caused by X-irradiation of an asynchronous, exponentially growing cell culture (data of Schneiderman & Schneiderman, 1984). In the model, based on Gompertz kinetics, the driving function to generate the curves is a simple exponential decay expression. For the delayed mitotic progress curves, this function characterizes the distribution of the time required for cells to enter mitosis.     

Prediction of X-ray induced mitotic delay and recovery of G2 cells

Abstract. A mathematical model is presented that predicts the delay of mitosis caused by X-irradiation of an asynchronous, exponentially growing cell culture (data of Schneiderman & Schneiderman, 1984). In the model, based on Gompertz kinetics, the driving function to generate the curves is a simple exponential decay expression. For the delayed mitotic progress curves, this function characterizes the distribution of the time required for cells to enter mitosis.     

Cluster growth by mitosis

A stochastic mitosis growth model is introduced. The colony enlarge by random mitosis of a mother cell which is replaced by two daughter cells. Unlike growth models based on a grid, the present model is isotropic. Using simulation of colonies of 10,000 cells, it is found that the density is constant and the boundary is fractal.     

Regularities and irregularities in the cell cycle of the fission yeast,Schizosaccharomyces pombe (a review)

In an exponentially growing wild-type fission yeast culture a size control mechanism ensures that mitosis is executed only if the cells have reached a critical size. However, there is some scattering both in cell length at birth (BL) and in cycle time (CT). By computational simulations we show here that this scattering cannot be explained solely by asymmetric cell division, therefore we assume that nuclear division is a stochastic, asymmetric process as well. We introduce an appropriate stochastic variable into a mathematical model and prove that this assumption is suitable to describe the CT vs. BL graph in a wild-type fission yeast population. In a double mutant of fission yeast (namely wee1-50 cdc25 delta) this CT vs. BL plot is even more curious: cycle time splits into three different values resulting in three clusters in this coordinate system. We show here that it is possible to describe these quantized cycles by choosing the appropriate values of the key parameters of mitotic entry and exit and even more the clustered behavior may be simulated by applying a further stochastic parameter.     

A mathematical model of the mechanism of vertebrate somitic segmentation.

A mathematical model for the mechanism of periodic pattern formation in the process of somitogenesis is proposed. It is assumed that the metameric arrangement first appears before somite formation at the stage of transition of mesodermal cells into a polarized state. The model is based on the assumption that besides the mechanism of contact cell polarization there exists a mechanism of polarization suppression due to excretion of some chemical substance by polarized cells. Periodicity appears as a result of interaction of a kinematic wave of somitogenic cell determination with the cell cycles of mesodermal cells.     

Proliferation and differentiation sequence of osteoblast histogenesis under physiological conditions in rat periodontal ligament

To define the mechanism of osteoblast histogenesis, nuclear morphometry was utilized as a marker for precursor cell differentiation. One hour after 3H-thymidine injection, groups of 7-week-old rats were killed at hourly intervals over one complete 24-hr photoperiod (LD 12:12). S-phase and mitosis were assessed in autoradiographs of 3-micron sections of molar periodontal ligament (PDL) adjacent to a physiological bone-forming surface. Labeled nuclei were divided into four categories according to morphometry of nuclear size: A (40-79 micron3), B (80-119 micron3), C (120-169 micron3), and D (greater than or equal to 170 micron3) cells. C and D cells synthesize DNA during the light and divide in the following dark phase; the rhythm for A cells is the opposite. B cells demonstrated no preference and were subsequently determined to be nonosteogenic. Compared to A cells the S-phase photoperiod of C and D cells (combined) is approximately a one-to-one reciprocal relationship, suggesting two proliferating progenitors in series. Based on arrest points in the histogenesis sequence, five compartments are defined: 1) A cells, less differentiated, self-perpetuating precursors; 2) A' cells, committed osteoprogenitors; 3) C cells, G1 stage preosteoblasts; 4) D cells, G2 stage preosteoblasts; and 5) Ob cells, morphologically distinct osteoblasts. Minimal elapsed time for the A----A'----C----D----Ob sequence is about 60 hr (five alternating dark/light cycles). A stress/strain-mediated increase in nuclear volume (A'----C) is an important, rate-limiting step in osteoblast differentiation.     

Transition of the blastomere cell cycle from cell size-independent to size-dependent control at the midblastula stage in Xenopus laevis

Dissociated animal cap blastomeres of Xenopus laevis blastulae were cultured at a low Ca level (1 microM) from 9th to 18th cell cycle at 22 +/- 1 degrees C and observed by a time-lapse video recorder. Blastomeres cleaved unequally to increase variability in cell size as cell cycles progressed, but synchronously at a constant cell cycle time of about 30 min up to the 12th cleavage in diploid cells, and up to the 13th cleavage in haploid cells, regardless of their cell sizes. Thereafter, blastomeres cleaved asynchronously at varying cell cycle times in proportion to the inverse square of their radii. The transition from the cell size-independent to -dependent cell cycles occurred at the critical cell radius, 37.5 microm for the diploid and 27.9 microm for the haploid. While the protein synthesis inhibitor, cycloheximide (CHX) lengthened cell cycle times two- to six-fold, epidermal growth factor (EGF) had no significant effect on the cell cycle. CHX-treated blastomeres synchronously cleaved at a constant cell cycle time of 60 min up to the 12th cleavage. Thereafter, cell cycle times became variable in proportion to the inverse square of radii in the presence of CHX at 0.10-0.14 microg/ml, but to the inverse cube of radii at 0.18 microg/ml. The critical cell size of CHX-treated blastomeres for the transition from cell size-independent to -dependent cell cycles remained the same as that of untreated blastomeres. Frequency distributions of cell cycle times of synchronous cell cycles were monomodal with the peak at 30 min, except for CHX-treated blastomeres with the peak at 60 min. In contrast, frequency distributions of asynchronous cell cycles were polymodal with peaks at multiples of a unit time of 30-35 min. To explain these results, we propose that blastomere cytoplasm has 30-min cycles that repeatedly produce mitosis promoting factor (MPF) in a quantity proportional to the cell surface area. MPF is neutralized when it titrates a nuclear inhibitor present in a quantity proportional to the genome size, and sequestered in the nucleus. When the total amount of MPF produced exceeds the threshold required to titrate all of the inhibitor, mitosis is initiated.     

A novel model for studying Baculovirus infection process

In this paper, a new Ansatz for modelling the Baculovirus infection cycle is presented. The base of this model is the cell cycle distribution at the time of infection. It is possible to calculate the growth of the culture and the initiation of virus processing by considering cell cycle distribution. By taking into account the length of the viral genome and the polymerase activity, it is possible to calculate the virus production rate, which underlies a logistic growth. In the present work, a new hypothesis explaining the accelerated death rates of infected cells has been introduced. This assumption provides the possibilities of performing calculation without any fixed time intervals. The simulation was tested by comparing experimental data with the model prediction. Therefore, cell cycle distributions over the culture time and the growth behaviour of infected and non-infected insect cells were measured. A model, Baculovirus coding for GFP was employed for the present investigation, as it allows tracking the infection and determining the effectiveness of the infection, which is highly dependent on the cell density at the time of infection (TOI). Furthermore, the new model is is taken to simulate data gained from literature about virus release and adsorption. The new assumptions make the model more independent to fit into different cultivation systems.     

S-phase and M-phase timing are under independent circadian control in the dinoflagellate Lingulodinium

In many phytoplankton species, cell division (mitosis) usually occurs at defined times of day. This timing is also observed under constant conditions, indicating that it is regulated by a circadian clock rather than by a simple response to the light-dark cycle. For those algae with cell cycles longer than a day, the clock opens a window of opportunity for mitosis at a particular time of day through which cells in an appropriate phase of the cell cycle can pass. Although the timing of mitosis is generally studied due to ease of measurement, for some phytoplankton the timing of S-phase is also circadian. This thus raises the possibility that mitosis is not directly gated by the clock but occurs instead at a defined interval (a constant G2 length) following a circadian controlled S-phase. To determine if the clock exercises independent control over the timing of both S- and M-phase, we measured the timing of both S- and M-phase in cultures of the dinoflagellate Lingulodinium grown under a variety of different photoperiods. We interpret the phase angles of both rhythms, in particular those resulting in a change in the length of G2, as an indication that the clock independently regulates the timing of S-phase and mitosis.     

Estimation of spontaneous mutation rates

Spontaneous or randomly occurring mutations play a key role in cancer progression. Estimation of the mutation rate of cancer cells can provide useful information about the disease. To ascertain these mutation rates, we need mathematical models that describe the distribution of mutant cells. In this investigation, we develop a discrete time stochastic model for a mutational birth process. We assume that mutations occur concurrently with mitosis so that when a nonmutant parent cell splits into two progeny, one of these daughter cells could carry a mutation. We propose an estimator for the mutation rate and investigate its statistical properties via theory and simulations. A salient feature of this estimator is the ease with which it can be computed. The methods developed herein are applied to a human colorectal cancer cell line and compared to existing continuous time models.     

The problem of cell debris in pulse-cytophotometry: A probability theoretic model

The problem of cell debris in pulse-cytophotometry is considered on the basis of a probability-theoretic model and the results are compared with the model of a pure exponential function for the portions of the DNA fragments in the channels of the flow cyclometer, which is generally used in practice. The model is based on the assumption that the possible decomposition of the DNA content of a single cell into some parts as a consequence of the necessary preparation of the cell material for measurement can be interpreted as a Poisson point process. Therefore the number of divisions of the DNA content of a cell is assumed as a Poisson random variable. It follows a well-defined distribution function of the DNA content in the common population of intact cells and fragments depending on the apriori distribution before pretreatment. This distribution determines a theoretical histogram which can be compared with the measurements. The results corroborate the assumption of a pure exponential course for the portions of DNA fragments only in the area of very small DNA contents. For greater DNA contents there are differences between the pure exponential course and the model described here depending on the a priori distribution and on the intensity of the cell disintegration process. As a byproduct, an estimation of the fraction of disintegrated cells is obtained with respect to the fraction of fragments. A corresponding computer program was applied to a number of experimental histograms. The results have shown that the theory describes the measured histograms satisfactory in most cases.     

Differentiation in Leaf Epidermis of Chlorophytum comosum Baker

The distribution of guard mother-cell formation has been studiedin developing abaxial epidermis in the basal meristem of theleaf of Chlorophytum comosum. It is concluded that, as tissueis displaced from the base of the leaf by growth, it passesthrough a proliferative zone in which only proliferative mitosesoccur, and then passes a boundary into a formative zone in whichformative mitoses occur, giving rise to guard mother cells,and proliferative mitoses are absent. Further distally, formativemitoses die out and in the next zone (the guard-cell zone) theonly mitoses which occur are those by which the guard mothercells give rise to the guard cells. Most distally there is azone with no mitotic activity. The probability of a cell undergoinga formative mitosis is highest at the proximal boundary of theformative zone. It is consequently suggested that the fate ofa cell on entering the formative zone depends partly on itsposition in the mitotic cycle; cells nearest to mitosis at entryare the most likely to undergo a formative mitosis during theirpassage through the formative zone. Similarly, guard mothercells which fail to undergo mitosis may be those which weremost distant from mitosis on entry into the guard cell zone.These suggestions may explain some of the elements of patternpreviously found in the mature epidermis. Chlorophytum comosum Baker, spider plant, leaf epidermis, stomata, pattern, development, formative mitosis, proliferative mitosis     

Hypothesis: cyclical histogenesis is the basis of circannual timing

Circannual rhythms are innately timed long-term (tau ≈ 12 months) cycles of physiology and behavior, crucial for life in habitats ranging from the equator to the Poles. Here the authors propose that circannual rhythm generation depends on tissue-autonomous, reiterated cycles of cell division, functional differentiation, and cell death. They see the feedback control influencing localized stem cell niches as crucial to this cyclical histogenesis hypothesis. Analogous to multi-oscillator circadian organization, circannual rhythm generation occurs in multiple tissues with hypothalamic and pituitary sites serving as central pacemakers. Signals including day length, nutrition, and social factors can synchronize circannual rhythms through hormonal influences, notably via the thyroid and glucocorticoid axes, which have profound effects on histogenesis. The authors offer 4 arguments in support of this hypothesis: (1) Cyclical histogenesis is a prevalent process in seasonal remodeling of physiology. It operates over long time domains and exhibits tissue autonomy in its regulation. (2) Experiments in which selected peripheral endocrine signals are held constant indicate that circannual rhythms are not primarily the product of interacting hormonal feedback loops. (3) Hormones known to control cell proliferation, differentiation, and organogenesis profoundly affect circannual rhythm expression. (4) The convergence point between photoperiodic input pathways and circannual rhythm expression occurs in histogenic regions of the hypothalamus and pituitary. In this review, the authors discuss how testing this hypothesis will depend on the use of cellular/molecular tools and animal models borrowed from developmental biology and neural stem cell research.     

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.     

Co-cultivation of whole blood from male and female muntjacs and the cell proliferation kinetics in vitro

A mixed blood culture (MBC) of heparinized whole blood from male and female Indian muntjac has been done using the BrdU-Hoechst-sunlight-Giemsa method to study the cell-cycle kinetics in vitro. Blood lymphocytes of both male and female muntjacs show a much shorter cell cycle time, roughly, 10-12 h for the initial but only 8 h for the subsequent cycles. There is a significant difference in the rate of cell proliferation between male and female cells. The male blood cells constitute a majority of the 'slow'-dividing cells which reach a peak at the first cycle of mitosis at 40 h, whereas a similar peak of first cycle mitosis is reached by female cells at 32 h, indicating the occurrence of a high frequency of 'fast' dividing female cells as compared to those of males. This novel sex-based differential cell proliferation kinetics is observed both in mixed and separate cultures. This type of MBC method which is free of interculture variations can be reliably used for comparative studies where two genomes can be distinguished.     

A quantitative theory of liver regeneration in the rat. II: matching an improved mitotic inhibitor model to the data

A model of liver regeneration is put forward in which the rate of liver growth is controlled both by a liver-produced mitotic inhibitor and by the availability of parenchymal cells to enter the mitotic cycle. The model can be expressed as a pair of coupled differential equations, the first describing the dependance of inhibitor concentration on liver size and inhibitor decay and the second specifying the dependance of liver growth on inhibitor concentration and entry of cells into the mitotic cycle. The model is tested by comparing its solutions to the published data on mitotic indices following partial hepatectomy. For such a comparison, it is necessary to specify the cell-cycle time and the inhibitor dose-response function and half-life. If a negative exponential dose-response function, an inhibitor half-life of 11·4 h, and a cycle time of 18·25 h are postulated, the solutions match the data of Fabrikant (1968) who found that there were two waves of mitosis with a period of quiescence between them. The data of Grisham (1962), characterized by a single peak of mitosis, is matched by the theory using similar inhibitor properties but a shorter cell-cycle time (13·25 h); this causes the two peaks to overlap. In both cases, a better fit is obtained if the second cell cycle is longer than the first by 2–3 h. This suggests that cells enter a G₀ period after mitosis. A mechanism for littoral cell division, which occurs some 24 h after parenchymal cell division, is put forward in which the former cells depend on the enlargement of the latter for the stimulus to divide.     

Epidermal cell proliferation. II. A comprehensive mathematical model of cell proliferation and migration in the basal layer predicts some unusual properties of epidermal stem cells

The clustering of 3HTdR labelled cells in the epidermal basal layer and their changes with time have been modelled mathematically and cannot be adequately fitted by an earlier model of the cell kinetic organisation of the skin. A more refined model analysis was performed based on Monte Carlo computer simulations of cell layers which take cell division, cell aging and lateral as well as vertical cell migration into account. A large variety of hypothetical scenarios was tested to see if each could provide a fit to the clustering data. The analysis provides further support for the concept of a cell kinetic heterogeneity with a stem-transit-postmitotic differentiation scheme. In the best overall model scheme three transit divisions are predicted but unlike in the earlier model it is now postulated that postmitotic cells can be produced at all stages in the lineage rather than only at the end of the amplification scheme. Most important, the model predicts that stem cells and most of the transit cells differ in the way they process 3HTdR label. Grain dilution is an important mechanism to explain the fate of some labelled cells in the tissue, but on its own it can only consistently explain the data if the stem cells have a very low labelling index (LI less than or equal to 1%) which implies a very short biologically unreasonable S-phase. If a higher LI (longer S-phase) is assumed for the stem-cells other mechanisms must be predicted to explain the lack of large clusters and the increase in time of the singles. The selective segregation of chromosomes at mitosis is one such mechanism. However, on its own a large number of cells would have to behave in this way (i.e. both stem and T1 cells). If combined with other assumptions such as some grain dilution this selective segregation may be restricted only to stem cells. In addition the model allows cell production and migration rates to be estimated and the analysis can be related to the EPU-concept. Indeed the model itself would tend to automatically generate an EPU like structure. The model quantitatively reproduces LI, PLM, CL and clustering data.     

On the progenitor cell migration velocity

An attempt is presented to extract cell kinetic information from histomorphological features. It is applicable to rapidly proliferating tissues like the intestinal epithelium. Each replicating tissue has an origin where cells are formed and a periphery toward which cells migrate. The migration path along which they move is denominated as tissue radius on which all cell positions are mapped. Cell migration on the radius is associated with cell proliferation at tissue origin. Each mitosis there is associated with the displacement of all cells distal to it by one cell position. The more mitoses positioned between a cell and tissue origin, the greater its migration velocity. It is possible therefore to derive the cell migration velocity v(x) from the cumulative mitotic distribution on the radius, N(x). v(x) = N(x)/tm (tm = mitotic time). In this form v(x) represents also cell production at any point on the radius and may serve for the computation of other cell kinetic parameters like generation time. These arguments are illustrated on the rat incisor tooth inner enamel epithelium which has been studied in the normal and rapidly erupting tooth.