Using a stem cell and progeny model to illustrate the relationship between cell cycle times of in vivo human tumour cell tissue populations, in vitro primary cultures and the cell lines derived from them

There is increasing evidence that the growth of human tumours is driven by a small proportion of tumour stem cells with self-renewal properties. Multiplication of these cells leads to loss of self-renewal and after division for a finite number of times the cells undergo programmed cell death. Cell cycle times of human cancers have been measured in vivo and shown to vary in the range from two days to several weeks, depending on the individual. Cells cultured directly from tumours removed at surgery initially grow at a rate comparable to the in vivo rate but continued culture leads to the generation of cell lines that have shorter cycle times (1–3 days). It has been postulated that the more rapidly growing sub-population exhibits some of the properties of tumour stem cells and are the precursors of a slower growing sub-population that comprise the bulk of the tumour. We have previously developed a mathematical model to describe the behaviour of cell lines and we extend this model here to describe the behaviour of a system with two cell populations with different kinetic characteristics and a precursor–product relationship. The aim is to provide a framework for understanding the behaviour of cancer tissue that is sustained by a minor population of proliferating stem cells.     

Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel

Most anti-cancer drugs in use today exert their effects by inducing a programmed cell death mechanism. This process, termed apoptosis, is accompanied by degradation of the DNA and produces cells with a range of DNA contents. We have previously developed a phase transition mathematical model to describe the mammalian cell division cycle in terms of cell cycle phases and the transition rates between these phases. We now extend this model here to incorporate a transition to a programmed cell death phase whereby cellular DNA is progressively degraded with time. We have utilised the technique of flow cytometry to analyse the behaviour of a melanoma cell line (NZM13) that was exposed to paclitaxel, a drug used frequently in the treatment of cancer. The flow cytometry profiles included a complex mixture of living cells whose DNA content was increasing with time and dying cells whose DNA content was decreasing with time. Application of the mathematical model enabled estimation of the rate constant for entry of mitotic cells into apoptosis (0.035 per hour) and the duration of the period of DNA degradation (51 hours). These results provide a dynamic model of the action of an anticancer drug that can be extended to improve the clinical outcome in individual cancer patients.Revised version: 9 October 2003     

Modelling cell population growth with applications to cancer therapy in human tumour cell lines

In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis (cell death) from mitosis phase (Modelling cell death in human tumour cell lines exposed to anticancer drug paclitaxel, J. Math. Biol. 2004, in press). This enabled us to compare our model to flow cytometric data of a melanoma cell line where the anticancer drug, paclitaxel, had been added. The model gives a dynamic picture of the effects of paclitaxel on the cell cycle. We hope to use the model to describe the effects of other cancer therapies on a number of different cell lines.     

A microRNA network regulates proliferative timing and extracellular matrix synthesis during cellular quiescence in fibroblasts

Background

Although quiescence (reversible cell cycle arrest) is a key part in the life history and fate of many mammalian cell types, the mechanisms of gene regulation in quiescent cells are poorly understood. We sought to clarify the role of microRNAs as regulators of the cellular functions of quiescent human fibroblasts.

Results

Using microarrays, we discovered that the expression of the majority of profiled microRNAs differed between proliferating and quiescent fibroblasts. Fibroblasts induced into quiescence by contact inhibition or serum starvation had similar microRNA profiles, indicating common changes induced by distinct quiescence signals. By analyzing the gene expression patterns of microRNA target genes with quiescence, we discovered a strong regulatory function for miR-29, which is downregulated with quiescence. Using microarrays and immunoblotting, we confirmed that miR-29 targets genes encoding collagen and other extracellular matrix proteins and that those target genes are induced in quiescence. In addition, overexpression of miR-29 resulted in more rapid cell cycle re-entry from quiescence. We also found that let-7 and miR-125 were upregulated in quiescent cells. Overexpression of either one alone resulted in slower cell cycle re-entry from quiescence, while the combination of both together slowed cell cycle re-entry even further.

Conclusions

microRNAs regulate key aspects of fibroblast quiescence including the proliferative state of the cells as well as their gene expression profiles, in particular, the induction of extracellular matrix proteins in quiescent fibroblasts.     

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.     

Combining Gompertzian growth and cell population dynamics

A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: Phi(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically found and derive Phi(N). The Gyllenberg-Webb transition functions are shown to be characteristically related through Phi(N). Effectively, this leads to a hybrid model for which we find the explicit analytical solutions for proliferating and quiescent cell populations, and the relations among model parameters. Several classes of solutions are examined. Our model predicts that the number of proliferating cells may increase along with the total number of cells, but the proliferating fraction appears to be a continuously decreasing function. The net transition rate of cells is shown to retain direction from the proliferating into the quiescent compartment. The death rate parameter for quiescent cell population is shown to be a factor in determining the proliferation level for a particular Gompertz growth curve.     

Nitric oxide is involved in establishing the balance between cell cycle progression and cell death in the developing neural tube

Endogenous nitric oxide (NO) has recently been shown to affect cell cycle progression in the neural tube (NT) of the chick embryo. High NO levels trigger entry into S phase basally, while low NO levels facilitate mitosis apically. Here, we further explore the involvement of NO in determining cell numbers in the chick NT. In addition to the effect of short-term (6 h) NOS inhibition, we have observed a concomitant decrease in programmed cell death (PCD). Paradoxically, long-term (12 h) NOS inhibition caused an increase in PCD to compensate for the high proliferation rate under these conditions. Long-term treatment with a NO donor caused a decrease in S phase and increased PCD. The effects produced by the NO donor could be alleviated by folic acid that facilitated entry into S phase and prevented PCD. The effects produced by NOS inhibition (12 h) could be overcome by an embryo extract, used as a source of extracellular survival factors that enhanced proliferation and prevented PCD. Taken together, these data demonstrate that changing endogenous NO levels affect the balance between cell proliferation and PCD in NT of the developing chick embryo.     

TRP channels in cell survival and cell death in normal and transformed cells

TRP channels form a superfamily of channel proteins exhibiting versatile regulatory characteristics with many channels participating in the regulation of Ca²⁺ homeostasis and influencing the cell fate. Multitude of evidence is emerging that the colocalization of TRP channels with Ca²⁺-sensing elements of specific regulatory pathways leading to either proliferation or apoptosis is what makes these channels participate in cell fate regulation and, in turn, determines the final effect of Ca²⁺ entry via the particular channel. This review focuses on the aspects of TRP channel localization and function that affect the balance between cell survival and death and how various dysregulations of these channels may lead to perturbed balance and onset of cancer.     

Linking cell division to cell growth in a spatiotemporal model of the cell cycle

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.     

Cell quiescence correlates with enhanced glioblastoma cell invasion and cytotoxic resistance

Glioblastoma (GBM) tumor cells exhibit drug resistance and are highly infiltrative. GBM stem cells (GSCs), which have low proliferative capacity are thought to be one of the sources of resistant cells which result in relapse/recurrence. However, the molecular mechanisms regulating quiescent-specific tumor cell biology are not well understood. Using human GBM cell lines and patient-derived GBM cells, Oregon Green dye retention was used to identify and isolate the slow-cycling, quiescent-like cell subpopulation from the more proliferative cells in culture. Sensitivity of cell subpopulations to temozolomide and radiation, as well as the migration and invasive potential were measured. Differential expression analysis following RNAseq identified genes enriched in the quiescent cell subpopulation. Orthotopic transplantation of cells into mice was used to compare the in vivo malignancy and invasive capacity of the cells. Proliferative quiescence correlated with better TMZ resistance and enhanced cell invasion, in vitro and in vivo. RNAseq expression analysis identified genes involved in the regulation cell invasion/migration and a three-gene signature, TGFBI, IGFBP3, CHI3L1, overexpressed in quiescent cells which correlates with poor GBM patient survival.     

Analysis of resonance chemotherapy in leukemia treatment via multi-staged population balance models

An age-structured population balance model that explicitly models cell cycle phases is developed to investigate the effects of cell cycle specific (CCS) drugs. In particular, the benefits of timing CCS drug treatments in resonance chemotherapy are predicted and measured directly in vitro before evaluating likely in vivo scenarios. The phase transition rates are measured in vitro for the HL60 leukemia cell line and are used to predict the transient phase dynamics after exposure to the S phase specific drug, camptothecin. The phase oscillations predicted by the model are observed experimentally and the timing of a second camptothecin pulse is shown to significantly alter the overall treatment effectiveness. To explore the feasibility of designing resonance chemotherapeutic treatments to preferentially eliminate one cell type over another, Jurkat and HL60 leukemia cells are exposed to the same dual-pulse camptothecin treatment regimen. With the model framework validated for simplified cases, the model is used to extrapolate the effectiveness of resonance chemotherapy considering in vivo effects such as quiescence, drug metabolism, drug properties, and transport considerations that were not included in the in vitro experiments. While resonance chemotherapy is intuitive and looks promising in vitro, when in vivo considerations are included in the model, the phenomenon is dampened and the window of applicability becomes narrower.     

The cell cycle and development: redundant roles of cell cycle regulators

The existence of families of cell cycle regulators reflects the need by a developing organism to precisely control proliferation of its cells and also suggests that family members may play redundant roles. Recent advances have shown redundancy to be a theme in development.     

Modelling the movement of interacting cell populations

Mathematical modelling of cell movement has traditionally focussed on a single population of cells, often moving in response to various chemical and environmental cues. In this paper, we consider models for movement in two or more interacting cell populations. We begin by discussing intuitive ideas underlying the extension of models for a single-cell population to two interacting populations. We then consider more formal model development using transition probability methods, and we discuss how the same equations can be obtained as the limiting form of a velocity-jump process. We illustrate the models we have developed via two examples. The first of these is a generic model for competing cell populations, and the second concerns aggregation in cell populations moving in response to chemical gradients.     

Pancreatic small cells: analysis of quiescence, long-term maintenance and insulin expression in vitro

We have previously identified a novel population of small cells in human and canine pancreas characterized by immature morphology, quiescence, and a glucose-responsive insulin secretion. Based on their immature phenotype and predominant presence in small islets, we have hypothesized that small cells serve as islet progenitors. This hypothesis remains untested, however, due to persistent quiescence and scarcity of small cells in vitro. We have recently developed a culture medium that allowed for modest small cell proliferation. In this study we characterized the expression of genes potentially involved in small cell growth regulation by Q-RT-PCR. Our results suggest that quiescence of small cells correlates with up-regulation of Cdk inhibitors p27(Kip1), p16(INK4a) and p21(CIP1), PTEN, Hep27 and Foxo1a and with down-regulation of c-Myc and the receptors for EGF, FGF2 and HGF. The exit from quiescence correlates with activation of EGFR expression and down-regulation of p27(Kip1) and p16(INK4a). We also report here that small cells can be maintained in long-term non-adherent cultures preserving insulin and glucagon production for up to 208 days. Therefore, expansion of small cells in vitro may have a significant potential for the treatment of diabetes. This study is an important step in understanding the mechanisms involved in small cell growth regulation, which is required to fully evaluate their functional potential.     

Programmed cell death in fission yeast

Recently a metacaspase, encoded by YCA1, has been implicated in a primitive form of apoptosis or programmed cell death in yeast. Previously it had been shown that over-expression of mammalian pro-apoptotic proteins can induce cell death in yeast, but the mechanism of how cell death occurred was not clearly established. More recently, it has been shown that DNA or oxidative damage, or other cell cycle blocks, can result in cell death that mimics apoptosis in higher cells. Also, in fission yeast deletion of genes required for triacylglycerol synthesis leads to cell death and expression of apoptotic markers. A metacaspase sharing greater than 40% identity to budding yeast Yca1 has been identified in fission yeast, however, its role in programmed cell death is not yet known. Analysis of the genetic pathways that influence cell death in yeast may provide insights into the mechanisms of apoptosis in all eukaryotic organisms.     

Timing the changes of cyclin E cell content in G1 in exponentially growing cells

We present a method for measuring the content of immunocytochemically detected proteins in individual cells progressing through G(1) phase and its application in the analysis of cyclin E levels. The sequence of G(1) events is tracked under unaltered cycling conditions, in a cell line in the phase of balanced growth in vitro, to avoid the pitfalls of synchronization. Cells were pulse-labeled with BrdUrd and analyzed sequentially by multiparameter flow cytometry, focusing on the subpopulation of labeled cells progressively entering G(1). We use the time-from-birth ("age") of individual cells to track their position inside G(1). Using the average content of cyclin E in the whole population of G(1) cells as the internal reference for each sample, we analyzed the time course of the frequency histograms of cyclin E content within BrdUrd-labeled G(1) cells by exploiting the properties of the age distributions of asynchronous populations. This way we could calculate the average cyclin E content of cells in each age cohort. Cyclin E values were low until age 3 h, after which they rose gradually, reaching six times the value of newborn cells at the end of G(1).     

Expression and roles of Cl- channel ClC-5 in cell cycles of myeloid cells

This study investigated the effect of exogenous nitric oxide (NO) on endothelial glucocorticoid receptor (GR) function. The NO donor diethylenetriamine NONOate (DETA, 50-500microM) caused concentration dependent nuclear localization of transfected chimeric green fluorescent protein GFP-GR and elevated expression of secreted alkaline phosphatase (SEAP) from a glucocorticoid response element (GRE) promoter construct in bovine aortic endothelial cells. Other weaker NO donors (S-nitroso-N-acetylpenicillamine and spermine NONOate) failed to induce GFP-GR nuclear localization, but all the NO donors activated GRE-SEAP expression, a response unaffected by the antioxidant N-acetyl-L-cysteine. Overall, exogenous NO from high concentration donors can directly activate GR, suggesting a potential feedback mechanism for NO to regulate endothelial inducible nitric oxide synthase (iNOS) expression.     

Antagonic activities of Trypanosoma cruzi metacaspases affect the balance between cell proliferation, death and differentiation

Metacaspases are distant relatives of animal caspases present in plants, fungi and protozoa. At variance with caspases, metacaspases exhibit stringent specificity for basic amino-acid residues and are absolutely dependent on millimolar concentrations of calcium. In the protozoan parasite Trypanosoma cruzi, metacaspases have been suggested to be involved in an apoptosis-like phenomenon upon exposure of the parasite to fresh human serum (FHS). Nuclear relocalization of metacaspases was observed after FHS treatment and overexpression of metacaspase-5 led to enhanced sensitivity to this stimulus. Here we report some biochemical properties of T. cruzi metacaspases. Performing fluorescent-activated cell sorting (FACS) analysis of epimastigotes inducibly overexpressing metacaspase-3, we demonstrate a role for this metacaspase in cell cycle progression, protection of epimastigotes from naturally occurring cell death and differentiation to infective metacyclic trypomastigotes. We also show that regulation of metacaspase-3 activity is important for cell cycle completion inside the mammalian host. On the other hand, inducible overexpression of metacaspase-5 lacking its C-terminal domain caused an apoptotic-like response. These results suggest that the two T. cruzi metacaspases could play an important role in the life cycle and bring to light the close relationship between cell division, death and differentiation in this ancient unicellular eukaryote.     

Understanding the relationship between cell death and tissue shrinkage via a stochastic agent-based model

Cell death, a process which can occur both naturally and in response to insult, is both a complex and diverse phenomenon. Under some circumstances, dying cells actively contract and cause their neighbors to rearrange and maintain tissue integrity. Under other circumstances, dying cells leave behind gaps, which results in tissue separation. A better understanding of how the cellular scale features of cell death manifest on the population scale has implications ranging from morphogenesis to tumor response to treatment. However, the mechanistic relationship between cell death and population scale shrinkage is not well understood, and computational methods for studying these relationships are not well established. Here we propose a mechanically robust agent-based cell model designed to capture the implications of cell death on the population scale. In our agent-based model, algorithmic rules applied on the cellular level emerge on the population scale where their effects are quantified. To better quantify model uncertainty and parameter interactions, we implement a recently developed technique for conducting a variance-based sensitivity analysis on the stochastic model. From this analysis and subsequent investigation, we find that cellular scale shrinkage has the largest influence of all model parameters tested, and that by adjusting cellular scale shrinkage population shrinkage varies widely even across simulations which contain the same fraction of dying cells. We anticipate that the methods and results presented here are a starting point for significant future investigation toward quantifying the implications of different mechanisms of cell death on population and tissue scale behavior.