Steel's potential doubling time and its estimation in cell populations affected by nonuniform cell loss

Spontaneous death of rat chloroleukaemia cells induced by an endogenous growth inhibitor

OBJECTIVES

When rat chloroleukaemia (CHL) cells are grown undisturbed in a confined space, a genomic long interspersed nuclear element (LINE) is transcriptionally activated at a relatively low population density, followed by the retrotransposition of LINE and population death. This death programme is fundamentally different from conventional cell death pathways.

MATERIALS AND METHODS

This work is essentially based on the re-analysis of relevant, old experimental data. Elemental analysis of a highly purified, long-stored inhibitor sample was performed. Genomic sequence searches were performed using the basic local alignment search tool (BLAST).

RESULTS

This death programme is initiated by an endogenous inhibitor secreted by CHL cells. The inhibitor is almost certainly identical to the pentapeptide pyroGlu-Glu-Asp-Cys-Lys, shown to be a cell line-specific inhibitor of normal granulocytic cells. The inhibitor is derived from a highly conserved short open reading frame in mammalian genomes.

CONCLUSIONS

Although spontaneous population death may be a biological oddity restricted to rat CHL cells, we suggest that this death programme is responsible for the eradication of cancer cells following treatment with an inhibitor administered exogenously.

Insulin Signaling in Insulin Resistance States and Cancer: A Modeling Analysis

Insulin resistance is the common denominator of several diseases including type 2 diabetes and cancer, and investigating the mechanisms responsible for insulin signaling impairment is of primary importance. A mathematical model of the insulin signaling network (ISN) is proposed and used to investigate the dose-response curves of components of this network. Experimental data of C2C12 myoblasts with phosphatase and tensin homologue (PTEN) suppressed and data of L6 myotubes with induced insulin resistance have been analyzed by the model. We focused particularly on single and double Akt phosphorylation and pointed out insulin signaling changes related to insulin resistance. Moreover, a new characterization of the upstream signaling of the mammalian target of rapamycin complex 2 (mTORC2) is presented. As it is widely recognized that ISN proteins have a crucial role also in cell proliferation and death, the ISN model was linked to a cell population model and applied to data of a cell line of acute myeloid leukemia treated with a mammalian target of rapamycin inhibitor with antitumor activity. The analysis revealed simple relationships among the concentrations of ISN proteins and the parameters of the cell population model that characterize cell cycle progression and cell death.

Modeling of non-small cell lung cancer volume changes during CT-based image guided radiotherapy: patterns observed and clinical implications

Background. To characterize the lung tumor volume response during conventional and hypofractionated radiotherapy (RT) based on diagnostic quality CT images prior to each treatment fraction. Methods. Out of 26 consecutive patients who had received CT-on-rails IGRT to the lung from 2004 to 2008, 18 were selected because they had lung lesions that could be easily distinguished. The time course of the tumor volume for each patient was individually analyzed using a computer program. Results. The model fits of group L (conventional fractionation) patients were very close to experimental data, with a median Δ% (average percent difference between data and fit) of 5.1% (range 3.5-10.2%). The fits obtained in group S (hypofractionation) patients were generally good, with a median Δ% of 7.2% (range 3.7-23.9%) for the best fitting model. Four types of tumor responses were observed-Type A: "high" kill and "slow" dying rate; Type B: "high" kill and "fast" dying rate; Type C: "low" kill and "slow" dying rate; and Type D: "low" kill and "fast" dying rate. Conclusions. The models used in this study performed well in fitting the available dataset. The models provided useful insights into the possible underlying mechanisms responsible for the RT tumor volume response.

Dynamic rendering of the heterogeneous cell response to anticancer treatments

The antiproliferative response to anticancer treatment is the result of concurrent responses in all cell cycle phases, extending over several cell generations, whose complexity is not captured by current methods. In the proposed experimental/computational approach, the contemporary use of time-lapse live cell microscopy and flow cytometric data supported the computer rendering of the proliferative process through the cell cycle and subsequent generations during/after treatment. The effects of treatments were modelled with modules describing the functional activity of the main pathways causing arrest, repair and cell death in each phase. A framework modelling environment was created, enabling us to apply different types of modules in each phase and test models at the complexity level justified by the available data. We challenged the method with time-course measures taken in parallel with flow cytometry and time-lapse live cell microscopy in X-ray-treated human ovarian cancer cells, spanning a wide range of doses. The most suitable model of the treatment, including the dose-response of each effect, was progressively built, combining modules with a rational strategy and fitting simultaneously all data of different doses and platforms. The final model gave for the first time the complete rendering in silico of the cycling process following X-ray exposure, providing separate and quantitative measures of the dose-dependence of G₁, S and G₂M checkpoint activities in subsequent generations, reconciling known effects of ionizing radiations and new insights in a unique scenario.

The antiproliferative response to anticancer treatment is the result of concurrent effects in all cell cycle phases, where molecular control pathways (checkpoints) are activated and cells may be arrested to repair DNA damage or killed if not able to succeed in the repair process. The complexity and inter-cell variability of these phenomena are not captured by the available methods, and the origin of the dose-dependence of the response remains elusive. In this work, we present an experimental-computational method that discloses and measures the individual responses of cell cycle controls in each phase and generation. We demonstrate that the method, exploiting jointly data sets obtained by flow cytometry and time-lapse in vivo imaging with a suitable experimental design, is able to achieve a full reconstruction in silico of the actual movement of cell cohorts following X-ray exposure, providing separate and quantitative measures of the dose-dependence of G₁, S and G₂M checkpoint activities in subsequent generations. Best fit parameters values are actual measures of the probability of activation of the specific pathways of arrest, repair or death within the cell population, linking the molecular scale to the “macroscopic” response, with full appreciation of its dynamics and inter-cell heterogeneity.

Modelling cell turnover in a complex tissue during development

The growth of organs results from proliferation within distinct cellular compartments. Organ development also involves transitions between cell types and variations in cell cycle duration as development progresses, and is regulated by a balance between entry into the compartment, proliferation of cells within the compartment, acquisition of quiescence and exit from that cell state via differentiation or death. While it is important to understand how environmental or genetic alterations can perturb such development, most approaches employed to date are descriptive rather than quantitative. This is because the identification and quantification of such parameters, while tractable in vitro, is challenging in the context of a complex tissue in vivo. Here we present a new framework for determining cell turnover in developing organs in vivo that combines cumulative cell-labelling and quantification of distinct cell-cycle phases without assuming homogeneity of behaviour within that compartment. A mathematical model is given that allows the calculation of cell cycle length in the context of a specific biological example and assesses the uncertainty of this calculation due to incomplete knowledge of cell cycle dynamics. This includes the development of a two population model to quantify possible heterogeneity of cell cycle length within a compartment and estimate the aggregate proliferation rate. These models are demonstrated on data collected from a progenitor cell compartment within the developing mouse kidney, the cap mesenchyme. This tissue was labelled by cumulative infusion, volumetrically quantified across time, and temporally analysed for the proportion of cells undergoing proliferation. By combining the cell cycle length predicted by the model with measurements of total cell population and mitotic rate, this approach facilitates the quantification of exit from this compartment without the need for a direct marker of that event. As a method specifically designed with assumptions appropriate to developing organs we believe this approach will be applicable to a range of developmental systems, facilitating estimations of cell cycle length and compartment behaviour that extend beyond simple comparisons of mitotic rates between normal and perturbed states.

Cell killing and resistance in pre-operative breast cancer chemotherapy

Background

Despite the recent development of technologies giving detailed images of tumours in vivo, direct or indirect ways to measure how many cells are actually killed by a treatment or are resistant to it are still beyond our reach.

Methods

We designed a simple model of tumour progression during treatment, based on descriptions of the key phenomena of proliferation, quiescence, cell killing and resistance, and giving as output the macroscopically measurable tumour volume and growth fraction. The model was applied to a database of the time course of volumes of breast cancer in patients undergoing pre-operative chemotherapy, for which the initial estimate of proliferating cells by the measure of the percentage of Ki67-positive cells was available.

Results

The analysis recognises different patterns of response to treatment. In one subgroup of patients the fitting implied drug resistance. In another subgroup there was a shift to higher sensitivity during the therapy. In the subgroup of patients where killing of cycling cells had the highest score, the drugs showed variable efficacy against quiescent cells.

Conclusion

The approach was feasible, providing items of information not otherwise available. Additional data, particularly sequential Ki67 measures, could be added to the system, potentially reducing uncertainty in estimates of parameter values.

A generalised age- and phase-structured model of human tumour cell populations both unperturbed and exposed to a range of cancer therapies

We develop a general mathematical model for a population of cells differentiated by their position within the cell division cycle. A system of partial differential equations governs the kinetics of cell densities in certain phases of the cell division cycle dependent on time t (hours) and an age-like variable tau (hours) describing the time since arrival in a particular phase of the cell division cycle. Transition rate functions control the transfer of cells between phases. We first obtain a theoretical solution on the infinite domain -infinity < t < infinity. We then assume that age distributions at time t=0 are known and write our solution in terms of these age distributions on t=0. In practice, of course, these age distributions are unknown. All is not lost, however, because a cell line before treatment usually lies in a state of asynchronous balanced growth where the proportion of cells in each phase of the cell cycle remain constant. We assume that an unperturbed cell line has four distinct phases and that the rate of transition between phases is constant within a short period of observation ('short' relative to the whole history of the tumour growth) and we show that under certain conditions, this is equivalent to exponential growth or decline. We can then gain expressions for the age distributions. So, in short, our approach is to assume that we have an unperturbed cell line on t </= 0, and then, at t=0 the cell line is exposed to cancer therapy. This corresponds to a change in the transition rate functions and perhaps incorporation of additional phases of the cell cycle. We discuss a number of these cancer therapies and applications of the model.

Estimating cell death in G2M using bivariate BrdUrd/DNA flow cytometry

BACKGROUND

In an accompanying paper (Asmuth et al.) it was found necessary to include cell death explicitly to estimate parameters of cell proliferation. The use of bivariate flow cytometry to estimate the phase durations and the doubling times of cells labeled with thymidine analogues is well established. However, these methods of analysis do not consider the possibility of cell death. This report demonstrates that estimating cell death in G(2)/M is possible.

METHODS

Mathematical models for the experimental quantities, the fraction of labeled undivided cells, the fraction of labeled divided cells, and the relative movement were developed. These models include the possibility that, of the cells with G(2)/M DNA content, only a certain fraction will divide, with the remainder dying after some time T(R). Simulation studies were conducted to test the possibility of using simple methods to estimate phase durations and cell death rates.

RESULTS

Cell death alters the estimates of phase transit times in a rather complex manner that depends on the lifetime of the doomed cells. However, it is still possible to obtain estimates of the phase durations of cells in S and G(2)/M and the death rates of cells in G(2)/M.

CONCLUSIONS

The methods presented herein provide a new way to characterize cell populations that includes cell death rates and common measurements of cell proliferation.