A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.     

Temperature response of the cell cycle of Haplopappus gracilis in suspension culture and its significance to the G1 transition probability model

The effects of temperature on the cell cycle of Haplopappus gracilis suspension cultures were analysed by the fraction of labelled mitoses method. Sphase in these cultures shows a different temperature optimum as compared to optima derived for G₂ and mitosis. G₁ phase has a much lower Q₁₀ than the other cell cycle phases and shows no temperature optimum between 22 and 34° C. These results are discussed in relation to a transition probability model of the cell cycle proposed by Smith and Martin (Proc. Natl. Acad. Sci. USA 70, 1263–1267, 1973), in which each cell has a time independent probability of initiating the transition into another round of DNA replication and division. The implications of such a model for cell cycle analysis are discussed and a tentative model for a probabilistic transition trigger is advanced.Abbreviations FLM Fraction of labelled mitoses - T_B Total B-phase     

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

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

Methylmercury Effects On Cell Cycle Kinetics

Abstract. Methylmercury (MeHg) effects on cell cycle kinetics were investigated to help identify its mechanisms of action. Flow cytometric analysis of normal human fibroblasts grown in vitro in the presence of BrdU allowed quantitation of the proportion of cells in G₁, S, G₂ and the next G₁ phase. This technique provides a rapid and easily performed method of characterizing phase lengths and transition rates for the complete cell cycle. After first exposure to MeHg the cell cycle time was lengthened due to a prolonged G₁. At 3, μm MeHg the G₁ phase length was 25% longer than the control. the G₁/S transition rate was also decreased in a dose-related manner. Confluent cells exposed to MeHg and replated with MeHg respond in the same way as cells which have not been exposed to MeHg before replating. Cells exposed for long times to MeHg lost a detectable G₁ effect, and instead showed an increase in the G₂ percentage, which was directly related to MeHg concentration and length of exposure. After 8 days at 5 μM MeHg, 45% of the population was in G₂. the G₂ accumulation was reversible up to 3 days, but at 6 days the cells remained in G₂ when the MeHg was removed. Cell counts and viability indicated that there was not a selective loss of cells from the MeHg. MeHg has multiple effects on the cell cycle which include a lengthened G₁ and decreased transition probability after short term exposure of cycling cells, and a G₂ accumulation after a longer term exposure. There were no detectable S phase effects. It appears that mitosis (the G₂ accumulation) and probably synthesis of some macromolecules in G₁ (the lengthened G₁ and lowered transition probability) are particularly susceptible to MeHg.     

AN EXTENDED TRANSITION PROBABILITY MODEL OF THE VARIABILITY OF CELL GENERATION TIMES

The transition probability model of variability of cell generation times is extended so that the rate constant for the transition from the A-state to the B-phase of the cell cycle depends on time which a particular cell has already spent in the A-state. A specific time dependence of this rate constant is introduced. It is determined by the value of one constant which is then an additional parameter of the model. The corresponding cell population kinetics are calculated and compared to existing experimental evidence. The model accounts satisfactorily for the generation time distribution function and for the shortening of the G₁ phase of binucleate cells. The time dependence of the transition probability is related to the cell kinetics of an hypothetical cell constituent. A possible relationship is proposed between the chemical parameters within the cell and the parameters of the cell population kinetics.     

Density‐independent reproductive success of the hemiparasitic plant Striga hermonthica,despite positive and negative density‐dependent phases

The hemiparasite Striga hermonthica is a major constraint to smallholder farmer livelihoods and food security in sub‐Saharan Africa. A better understanding of its life‐cycle can help developing more effective management strategies. Here, we studied density dependence in S. hermonthica on Sorghum bicolor. We exposed two genotypes of S. bicolor that differed in the level of tolerance and resistance to S. hermonthica to a range of seed densities of the parasite. We evaluated multiple host and parasite performance parameters through periodic, destructive harvests and related these to the initial seed density using model selection. Initially, the probability for attachment was positively density‐dependent, suggesting facilitation of new infections. However, at host maturity, S. hermonthica infection probability showed strong negative density dependence, indicating severe competition, in particular in the early developmental stages. Although parasite shoot dry weight showed a strong negative density dependence at host maturity, flower production per parasite exhibited positive density dependence again, suggesting compensation. The two host genotypes had similar responses to increased parasite densities, indicating differences between the genotypes in tolerance but not resistance. Consequently, despite density dependence in life‐cycle components, the per capita reproductive output of S. hermonthica, R₀ (flowers seed^?1) was density‐independent. Apparently, management of the hemiparasite can neither benefit from a negatively density‐dependent bottleneck, nor from a positively density‐dependent Allee effect. The most promising suggestion to obtain S. hermonthica population decline (R₀ < 1) and long‐term control is to increase host shading by growing a vigorous, competitive crop.     

DIATOM MINERALIZATION OF SILICIC ACID. II. REGULATION OF Si (OH)4 TRANSPORT RATES DURING THE CELL CYCLE OF NAVICULA PELLICULOSA1

Synchronized populations of Navicula pelliculosa (Bréb.) Hilse show a 10-fold increase in Si(OH)₄ transport rate during traverse through the cell division cycle. The transport activity pattern is similar to a “peak enzyme.” Kinetic analysis showed there was a significant change in K_s values, indicating increased “affinity” for Si(OH)₄ as cells neared maximal uptake rates. However, the dramatic changes in transport rate at various cell cycle stages were also reflected by alterations in the V_max, values of the transport process, suggesting a change in the number of functional transport “sites” in the plasma membrane. Cells in the wall forming stage, arrested from further development by Si(OH)₄ deprivation, maintained high transport rates for as long as 7 h. The rates decreased rapidly if protein synthesis were blocked or if Si(OH)₄ was added, the latter allowing the cells to traverse the rest of the cycle. The half-life of the transport activity ranged from 1.0 to 2.2 h when protein synthesis was inhibited at various cell cycle stages and during the natural decline of activity late in the cycle. The transport system appears to be metabolically unstable as is typical for a “peak protein.” The rise in transport rate through the cell cycle did not depend on the presence of Si(OH)₄ in the medium; therefore, the transport system does not appear to be induced by its substrate. The rise in transport is also observed in L:D synchronized cells developing in the presence of Si(OH)₄; neither does the transport system appear to be derepressed. The transport rate was strongly cell cycle-stage dependent; the data appeared to fit the “dependent pathway” model proposed by Hart-well to explain oscillations in enzyme synthesis during the cell cycle.     

Influence of the existence of a resting state on the probability of cell division in culture

A cell cycle model developed by Smith and Martin is generalized to allow for the possibility that the duration of the B phase is not fixed. The B phase is the equivalent of the traditional S, G₂, and M phases of the cell cycle. The duration of the B phase is represented by a Gaussian probability distribution; the duration of the resting or A state which replaces the traditional G₁ phase is represented by a decaying exponential distribution. A doubling time distribution, termed the CEG distribution, is obtained by convolution of the A state and B phase distributions. Like the reciprocal normal, rate normal, and log normal distributions, it is a rounded unimodal peak that is skewed to the right. None of the three former distributions is associated with a cell cycle model that includes a resting state. However the CEG distribution, which is so associated, bears little resemblance to the delayed exponential distribution which results when the duration of the B phase is fixed and the duration of the A state is random. Consequently, it would be difficult to use the doubling time distribution to determine whether or not a resting state exists in a particular cell population.     

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.     

Size and age at sexual maturity of Atlantic argentine,Argentina silus: a critique

Synopsis A recent analysis of size and age at sexual maturity ofArgentina silus on the Scotian Shelf is invalid because field maturity stage data collected during the non-spawning, quiescent stage of the reproductive cycle were unreliable for distinguishing between immature and resting mature stages. Thus two-thirds of the data used must be discounted. Utilization of different length measurement criteria for different years, for which no correction is made, could introduce substantial error in length at maturity estimates based on the remaining data. Age data collections were restricted to one 12 month period and thus were inadequate to characterize age at maturity by 5 yr time periods as attempted in this analysis. No attempt is made in the analysis to determine whether available samples adequately represent the population with regard to maturity i.e. whether immature and mature fish of the same length had an equal probability of being sampled. It is demonstrated here that maturity ogives can differ greatly depending on assumptions made concerning the representativeness of samples. Many of the criticisms made are likely valid for a series of papers on maturity of Atlantic coast fishes by the same author.     

Regulation of the Cell Cycle by Protein Phosphatase 2A in Saccharomyces cerevisiae

Protein phosphatase 2A (PP2A) has long been implicated in cell cycle regulation in many different organisms. In the yeast Saccharomyces cerevisiae, PP2A controls cell cycle progression mainly through modulation of cyclin-dependent kinase (CDK) at the G₂/M transition. However, CDK does not appear to be a direct target of PP2A. PP2A affects CDK activity through its roles in checkpoint controls. Inactivation of PP2A downregulates CDK by activating the morphogenesis checkpoint and, consequently, delays mitotic entry. Defects in PP2A also compromise the spindle checkpoint and predispose the cell to an error-prone mitotic exit. In addition, PP2A is involved in controlling the G₁/S transition and cytokinesis. These findings suggest that PP2A functions in many stages of the cell cycle and its effect on cell cycle progression is pleiotropic.     

Changes in size and age at maturity in a population of kokanee Oncorhynchus nerka during a period of declining growth conditions

Trends in size distributions and age at maturity of spawning kokanee Oncorhynchus nerka during a 5 year period of declining growth conditions at Bucks Lake, California, U.S.A. were consistent with the hypothesis that reductions in growth rates in successive cohorts induce a shift to an older age at maturity. This forestalls decreases in size at maturity during a transitional period characterized by an increasing proportion of individuals that delay maturation. During the course of the study, kokanee first began declining in size at maturity, and then shifted from a 3 year to a 4 year egg to adult cycle. Individuals that spawned during their fourth year (age 3 years) were significantly larger, on average, than members of their cohort that spawned during their third year (age 2 years). This difference was greatest when age 2 year adults were smallest. The shift to an older age at maturity prevented a steady decline in size at maturity, even though age‐specific size was steadily declining over time. Size at maturity, however, began to decline again once the transition to a 4 year cycle was complete. In addition, there was a general trend of decreasing length‐specific mass. The data indicate that there is a range of growth trajectories over which delayed maturity can prevent a temporal pattern of decreasing size at maturity as growth rates decline.     

A NEW METHOD FOR THE ESTIMATION OF CELL CYCLE PHASES

A method is described, which is applicable to cell renewal systems with an anatomical structure in which all cell locations may be uniquely mapped. Its use is demonstrated on the rat incisor inner enamel epithelium, which forms a one cell thick column in the sagittally sectioned tooth. Cells born in the apical part of the column migrate toward the distal end of the tooth, where they mature. As the cells migrate along the column, they traverse the various cell cycle phases. The present study has been designed to estimate the probability of a cell being in a given phase; all cells touching the basement membrane were numbered, and the number of cells separating any two cells was taken as a measure of distance. Since generally all cells move in one direction (lateral cell migration may occur), it is possible to solve the problem with the aid of functions describing the renewal counting stochastic process in which cell distance serves as an independent variable. The method predicts labelled cell and mitotic rates which agree with those estimated in the usual way. It was then utilized to estimate the fraction of cells in G₂.     

The cancer‐related transcription factor Runx2 modulates cell proliferation in human osteosarcoma cell lines

Runx2 regulates osteogenic differentiation and bone formation, but also suppresses pre‐osteoblast proliferation by affecting cell cycle progression in the G₁ phase. The growth suppressive potential of Runx2 is normally inactivated in part by protein destabilization, which permits cell cycle progression beyond the G₁/S phase transition, and Runx2 is again up‐regulated after mitosis. Runx2 expression also correlates with metastasis and poor chemotherapy response in osteosarcoma. Here we show that six human osteosarcoma cell lines (SaOS, MG63, U2OS, HOS, G292, and 143B) have different growth rates, which is consistent with differences in the lengths of the cell cycle. Runx2 protein levels are cell cycle‐regulated with respect to the G₁/S phase transition in U2OS, HOS, G292, and 143B cells. In contrast, Runx2 protein levels are constitutively expressed during the cell cycle in SaOS and MG63 cells. Forced expression of Runx2 suppresses growth in all cell lines indicating that accumulation of Runx2 in excess of its pre‐established levels in a given cell type triggers one or more anti‐proliferative pathways in osteosarcoma cells. Thus, regulatory mechanisms controlling Runx2 expression in osteosarcoma cells must balance Runx2 protein levels to promote its putative oncogenic functions, while avoiding suppression of bone tumor growth. J. Cell. Physiol. 228: 714–723, 2013. © 2012 Wiley Periodicals, Inc.     

Phase-Specific Polypeptides and Poly(A) RNAs during the Cell Cycle in Synchronous Cultures of Catharanthus roseus Cells

This study shows an overall analysis of gene expression during the cell cycle in synchronous suspension cultures of Catharanthus roseus cells. First, the cellular cytoplasmic proteins were fractionated by two-dimensional gel electrophoresis and visualized by staining with silver. Seventeen polypeptides showed qualitative or quantitative changes during the cell cycle. Second, the rates of synthesis of cytoplasmic proteins were also investigated by autoradiography by labeling cells with [³⁵S]methionine at each phase of the cell cycle. The rates of synthesis of 13 polypeptides were found to vary during the cell cycle. The silverstained electrophoretic pattern of proteins in the G₂ phase in particular showed characteristic changes in levels of polypeptides, while the rates of synthesis of polypeptides synthesized during the G₂ phase did not show such phase-specific changes. This result suggests that posttranslational processing of polypeptides occurs during or prior to the G₂ phase. In the G₁ and S phases and during cytokinesis, several other polypeptides were specifically synthesized. Finally, the variation of mRNAs was analyzed from the autoradiograms of in vitro translation products of poly(A)⁺ RNA isolated at each phase. Three poly(A)⁺ RNAs increased in amount from the G₁ to the S phase and one poly (A)⁺ RNA increased preferentially from the G₂ phase to cytokinesis.     

Global asymptotic stability of the size distribution in probabilistic models of the cell cycle

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for _n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, _*(x). For the special case of the transition probability model, we display _*(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).     

Cell cycle-independent expression of immediate-early gene 3 results in G1 and G2 arrest in murine cytomegalovirus-infected cells

The infectious cycle of human cytomegalovirus (HCMV) is intricately linked to the host's cell cycle. Viral gene expression can be initiated only in G₀/G₁ phase. Once expressed, the immediate-early gene product IE2 prevents cellular DNA synthesis, arresting infected cells with a G₁ DNA content. This function is required for efficient viral replication in vitro. A prerequisite for addressing its in vivo relevance is the characterization of cell cycle-regulatory activities of CMV species for which animal models have been established. Here, we show that murine CMV (MCMV), like HCMV, has a strong antiproliferative capacity and arrests cells in G₁. Unexpectedly, and in contrast to HCMV, MCMV can also block cells that have passed through S phase by arresting them in G₂. Moreover, MCMV can also replicate in G₂ cells. This is made possible by the cell cycle-independent expression of MCMV immediate-early genes. Transfection experiments show that of several MCMV candidate genes, only immediate-early gene 3 (ie3), the homologue of HCMV IE2, exhibits cell cycle arrest activity. Accordingly, an MCMV ie3 deletion mutant has lost the ability to arrest cells in either G₁ or G₂. Thus, despite interspecies variations in the cell cycle dependence of viral gene expression, the central theme of HCMV IE2-induced cell cycle arrest is conserved in the murine counterpart, raising the possibility of studying its physiological relevance at the level of the whole organism.     

The potential for disruptive selection on growth rates across genetically influenced alternative reproductive tactics

A trade-off between survival to sexual maturity and mating success is common across alternative reproductive tactics (ARTs), and can lead to tactical disruptive selection on shared traits (i.e. positive selection gradient in one tactic, and negative selection gradient in another). We were interested in examining the theoretical possibility of tactical disruptive selection on intrinsic growth rate. The male ARTs in Xiphophorus multilineatus express two distinct life histories: “courters” optimize mating success by maturing later at larger size and coaxing females to mate, while “sneakers” optimize survival to sexual maturity by maturing earlier at a smaller size, using both coaxing and coercive mating behaviors. In addition to differences in mating behaviors, body length, body depth, and the pigment pattern vertical bars, courter males grow faster than sneaker males. We present a new hypothesis for differences in growth rates between genetically influenced ARTs. The “growth-maturity optimization” hypothesis suggests that ARTs with differences in the probability of surviving to sexual maturity may have different optimal growth rates, leading to tactical disruptive selection. We also present a simple model to suggest that when considering both a cost and benefit to faster growth, tactical disruptive selection on growth rates is theoretically possible. In our model, the value that determines when tactical disruptive selection on growth rate will occur is the increase in probability of survival to sexual maturity gained through faster growth multiplied by the cost of faster growth (reduced longevity). Finally, we present empirical evidence to support the prediction that faster growth has a cost in X. multilineatus: in a controlled laboratory setting, courter males that did not survive 1.2 years past sexual maturity grew faster as juveniles (14–70 days) than those that survived.