Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.

Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). The competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data. Additional models including a theory based on distant cytotoxic log-kill effects were unable to fit the data. The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration. Cancer Res; 77(18); 5183-93. ©2017 AACR.

Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation.

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development, cancer dormancy, and immunotherapies. In fact, early immunotherapy failures were partly due to a lack in understanding of the nonlinear growth dynamics these competing immune actions may cause. To study this biological phenomenon theoretically, we construct a minimally parameterized framework that incorporates all aspects of the immune response. We combine the effects of all immune cell types, general principles of self-limited logistic growth, and the physical process of inflammation into one quantitative setting. Simulations suggest that while there are pro-tumor or antitumor immunogenic responses characterized by larger or smaller final tumor volumes, respectively, each response involves an initial period where tumor growth is stimulated beyond that of growth without an immune response. The mathematical description is non-identifiable which allows an ensemble of parameter sets to capture inherent biological variability in tumor growth that can significantly alter tumor-immune dynamics and thus treatment success rates. The ability of this model to predict non-intuitive yet clinically observed patterns of immunomodulated tumor growth suggests that it may provide a means to help classify patient response dynamics to aid identification of appropriate treatments exploiting immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.

Radiation-Induced Reprogramming of Pre-Senescent Mammary Epithelial Cells Enriches Putative CD44(+)/CD24(-/low) Stem Cell Phenotype.

The enrichment of putative CD44(+)/CD24(-/low) breast stem cell populations following exposure to ionizing radiation (IR) has been ascribed to their inherent radioresistance and an elevated frequency of symmetric division during repopulation. However, recent studies demonstrating radiation-induced phenotypic reprogramming (the transition of non-CD44(+)/CD24(-/low) cells into the CD44(+)/CD24(-/low) phenotype) as a potential mechanism of CD44(+)/CD24(-/low) cell enrichment have raised the question of whether a higher survival and increased self-renewal of existing CD44(+)/CD24(-/low) cells or induced reprogramming is an additional mode of enrichment. To investigate this question, we combined a cellular automata model with in vitro experimental data using both MCF-10A non-tumorigenic human mammary epithelial cells and MCF-7 breast cancer cells, with the goal of identifying the mechanistic basis of CD44(+)/CD24(-/low) stem cell enrichment in the context of radiation-induced cellular senescence. Quantitative modeling revealed that incomplete phenotypic reprogramming of pre-senescent non-stem cells (reprogramming whereby the CD44(+)/CD24(-/low) phenotype is conveyed, along with the short-term proliferation capacity of the original cell) could be an additional mode of enriching the CD44(+)/CD24(-/low) subpopulation. Furthermore, stem cell enrichment in MCF-7 cells occurs both at lower doses and earlier time points, and has longer persistence, than that observed in MCF-10A cells, suggesting that phenotypic plasticity appears to be less regulated in breast cancer cells. Taken together, these results suggest that reprogramming of pre-senescent non-stem cells may play a significant role in both cancer and non-tumorigenic mammary epithelial populations following exposure to IR, a finding with important implications for both radiation therapy and radiation carcinogenesis.

Evaluating biomarkers to model cancer risk post cosmic ray exposure.

Robust predictive models are essential to manage the risk of radiation-induced carcinogenesis. Chronic exposure to cosmic rays in the context of the complex deep space environment may place astronauts at high cancer risk. To estimate this risk, it is critical to understand how radiation-induced cellular stress impacts cell fate decisions and how this in turn alters the risk of carcinogenesis. Exposure to the heavy ion component of cosmic rays triggers a multitude of cellular changes, depending on the rate of exposure, the type of damage incurred and individual susceptibility. Heterogeneity in dose, dose rate, radiation quality, energy and particle flux contribute to the complexity of risk assessment. To unravel the impact of each of these factors, it is critical to identify sensitive biomarkers that can serve as inputs for robust modeling of individual risk of cancer or other long-term health consequences of exposure. Limitations in sensitivity of biomarkers to dose and dose rate, and the complexity of longitudinal monitoring, are some of the factors that increase uncertainties in the output from risk prediction models. Here, we critically evaluate candidate early and late biomarkers of radiation exposure and discuss their usefulness in predicting cell fate decisions. Some of the biomarkers we have reviewed include complex clustered DNA damage, persistent DNA repair foci, reactive oxygen species, chromosome aberrations and inflammation. Other biomarkers discussed, often assayed for at longer points post exposure, include mutations, chromosome aberrations, reactive oxygen species and telomere length changes. We discuss the relationship of biomarkers to different potential cell fates, including proliferation, apoptosis, senescence, and loss of stemness, which can propagate genomic instability and alter tissue composition and the underlying mRNA signatures that contribute to cell fate decisions. Our goal is to highlight factors that are important in choosing biomarkers and to evaluate the potential for biomarkers to inform models of post exposure cancer risk. Because cellular stress response pathways to space radiation and environmental carcinogens share common nodes, biomarker-driven risk models may be broadly applicable for estimating risks for other carcinogens.

Tumor-host signaling interaction reveals a systemic, age-dependent splenic immune influence on tumor development.

The concept of age-dependent host control of cancer development raises the natural question of how these effects manifest across the host tissue/organ types with which a tumor interacts, one important component of which is the aging immune system. To investigate this, changes in the spleen, an immune nexus in the mouse, was examined for its age-dependent interactive influence on the carcinogenesis process. The model is the C57BL/6 male mice (adolescent, young adult, middle-aged, and old or 68, 143, 551 and 736 days old respectively) with and without a syngeneic murine tumor implant. Through global transcriptome analysis, immune-related functions were found to be key regulators in the spleen associated with tumor progression as a function of age with CD2, CD3ε, CCL19, and CCL5 being the key molecules involved. Surprisingly, other than CCL5, all key factors and immune-related functions were not active in spleens from non-tumor bearing old mice. Our findings of age-dependent tumor-spleen signaling interaction suggest the existence of a global role of the aging host in carcinogenesis. Suggested is a new avenue for therapeutic improvement that capitalizes on the pervasive role of host aging in dictating the course of this disease.

Proton irradiation impacts age-driven modulations of cancer progression influenced by immune system transcriptome modifications from splenic tissue.

Age plays a crucial role in the interplay between tumor and host, with additional impact due to irradiation. Proton irradiation of tumors induces biological modulations including inhibition of angiogenic and immune factors critical to 'hallmark' processes impacting tumor development. Proton irradiation has also provided promising results for proton therapy in cancer due to targeting advantages. Additionally, protons may contribute to the carcinogenesis risk from space travel (due to the high proportion of high-energy protons in space radiation). Through a systems biology approach, we investigated how host tissue (i.e. splenic tissue) of tumor-bearing mice was altered with age, with or without whole-body proton exposure. Transcriptome analysis was performed on splenic tissue from adolescent (68-day) versus old (736-day) C57BL/6 male mice injected with Lewis lung carcinoma cells with or without three fractionations of 0.5 Gy (1-GeV) proton irradiation. Global transcriptome analysis indicated that proton irradiation of adolescent hosts caused significant signaling changes within splenic tissues that support carcinogenesis within the mice, as compared with older subjects. Increases in cell cycling and immunosuppression in irradiated adolescent hosts with CDK2, MCM7, CD74 and RUVBL2 indicated these were the key genes involved in the regulatory changes in the host environment response (i.e. the spleen). Collectively, these results suggest that a significant biological component of proton irradiation is modulated by host age through promotion of carcinogenesis in adolescence and resistance to immunosuppression, carcinogenesis and genetic perturbation associated with advancing age.

Host age is a systemic regulator of gene expression impacting cancer progression.

Aging is the major determinant of cancer incidence, which, in turn, is likely dictated in large part by processes that influence the progression of early subclinical (occult) cancers. However, there is little understanding of how aging informs changes in aggregate host signaling that favor cancer progression. In this study, we provide direct evidence that aging can serve as an organizing axis to define cancer progression-modulating processes. As a model system to explore this concept, we employed adolescent (68 days), young adult (143 days), middle-aged (551 days), and old (736 days) C57BL/6 mice as syngeneic hosts for engraftment of Lewis lung cancer to identify signaling and functional processes varying with host age. Older hosts exhibited dysregulated angiogenesis, metabolism, and apoptosis, all of which are associated with cancer progression. TGFß1, a central player in these systemic processes, was downregulated consistently in older hosts. Our findings directly supported the conclusion of a strong host age dependence in determining the host tumor control dynamic. Furthermore, our results offer initial mechanism-based insights into how aging modulates tumor progression in ways that may be actionable for therapy or prevention.

Evolution and phenotypic selection of cancer stem cells.

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change, and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cells(CSC), as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits, including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of non-stem cancer cells(CC) that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The sub-population of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

Therapeutic implications from sensitivity analysis of tumor angiogenesis models.

Anti-angiogenic cancer treatments induce tumor starvation and regression by targeting the tumor vasculature that delivers oxygen and nutrients. Mathematical models prove valuable tools to study the proof-of-concept, efficacy and underlying mechanisms of such treatment approaches. The effects of parameter value uncertainties for two models of tumor development under angiogenic signaling and anti-angiogenic treatment are studied. Data fitting is performed to compare predictions of both models and to obtain nominal parameter values for sensitivity analysis. Sensitivity analysis reveals that the success of different cancer treatments depends on tumor size and tumor intrinsic parameters. In particular, we show that tumors with ample vascular support can be successfully targeted with conventional cytotoxic treatments. On the other hand, tumors with curtailed vascular support are not limited by their growth rate and therefore interruption of neovascularization emerges as the most promising treatment target.

Capturing the Driving Role of Tumor-Host Crosstalk in a Dynamical Model of Tumor Growth.

In 1999, Hahnfeldt et al. proposed a mathematical model for tumor growth as dictated by reciprocal communications between tumor and its associated vasculature, introducing the idea that a tumor is supported by a dynamic, rather than a static, carrying capacity. In this original paper, the carrying capacity was equated with the variable tumor vascular support resulting from the net effect of tumor-derived angiogenesis stimulators and inhibitors. This dynamic carrying capacity model was further abstracted and developed in our recent publication to depict the more general situation where there is an interaction between the tumor and its supportive host tissue; in that case, as a function of host aging (Benzekry et al., 2014). This allowed us to predict a range of host changes that may be occurring with age that impact tumor dynamics. More generally, the basic formalism described here can be (and has been), extended to the therapeutic context using additional optimization criteria (Hahnfeldt et al., 1999). The model depends on three parameters: One for the tumor cell proliferation kinetics, one for the stimulation of the stromal support, and one for its inhibition, as well as two initial conditions. We describe here the numerical method to estimate these parameters from longitudinal tumor volume measurements.

Classical mathematical models for description and prediction of experimental tumor growth.

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

A proposed quantitative index for assessing the potential contribution of reprogramming to cancer stem cell kinetics.

Enrichment of cancer stem cells (CSCs) is thought to be responsible for glioblastoma multiforme (GBM) recurrence after radiation therapy. Simulation results from our agent-based cellular automata model reveal that the enrichment of CSCs may result either from an increased symmetric self-renewal division rate of CSCs or a reprogramming of non-stem cancer cells (CCs) to a stem cell state. Based on plateau-to-peak ratio of the CSC fraction in the tumor following radiation, a downward trend from peak to subsequent plateau (i.e., a plateau-to-peak ratio exceeding 1.0) was found to be inconsistent with increased symmetric division alone and favors instead a strong reprogramming component. The two contributions together are seen to be the product of a dynamic equilibrium between CSCs and CCs that is highly regulated by the kinetics of single cells, including the potential for CCs to reacquire a stem cell state and confer phenotypic plasticity to the population as a whole. We conclude that tumor malignancy can be gauged by a degree of cancer cell plasticity.

A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics.

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis--a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division--we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.

Proton irradiation augments the suppression of tumor progression observed with advanced age.

Proton radiation is touted for improved tumor targeting, over standard gamma radiation, due to the physical advantages of ion beams for radiotherapy. Recent studies from our laboratory demonstrate that in addition to these targeting advantages, proton irradiation can inhibit angiogenic and immune factors critical to "hallmark" processes that impact cancer progression, thereby modulating tumor development. Outside the therapeutic utilization of protons, high-energy protons constitute a principal component of galactic cosmic rays and thus are a consideration in carcinogenesis risk for space flight. Given that proton irradiation modulates fundamental biological processes known to decrease with aging (e.g. angiogenesis and immunogenicity), we investigated how proton irradiation impacts tumor advancement as a function of host age, a question with both therapeutic and carcinogenesis implications. Tumor lag time and growth dynamics were tracked, after injection of murine Lewis lung carcinoma (LLC) cells into syngeneic adolescent (68 day) vs. old (736 day) C57BL/6 mice with or without coincident irradiation. Tumor growth was suppressed in old compared to adolescent mice. These differences were further modulated by proton irradiation (1 GeV), with increased inhibition and a significant radiation-altered molecular fingerprint evident in tumors grown in old mice. Through global transcriptome analysis, TGFß1 and TGFß2 were determined to be key players that contributed to the tumor dynamics observed. These findings suggest that old hosts exhibit a reduced capacity to support tumor advancement, which can be further reduced by proton irradiation.

Global dormancy of metastases due to systemic inhibition of angiogenesis.

Autopsy studies of adults dying of non-cancer causes have shown that virtually all of us possess occult, cancerous lesions. This suggests that, for most individuals, cancer will become dormant and not progress, while only in some will it become symptomatic disease. Meanwhile, it was recently shown in animal models that a tumor can produce both stimulators and inhibitors of its own blood supply. To explain the autopsy findings in light of the preclinical research data, we propose a mathematical model of cancer development at the organism scale describing a growing population of metastases, which, together with the primary tumor, can exert a progressively greater level of systemic angiogenesis-inhibitory influence that eventually overcomes local angiogenesis stimulation to suppress the growth of all lesions. As a departure from modeling efforts to date, we look not just at signaling from and effects on the primary tumor, but integrate over this increasingly negative global signaling from all sources to track the development of total tumor burden. This in silico study of the dynamics of the tumor/metastasis system identifies ranges of parameter values where mutual angio-inhibitory interactions within a population of tumor lesions could yield global dormancy, i.e., an organism-level homeostatic steady state in total tumor burden. Given that mortality arises most often from metastatic disease rather than growth of the primary per se, this finding may have important therapeutic implications.

Beyond the cancer cell: progression-level determinants highlight the multiscale nature of carcinogenesis risk.

Over the last several decades, improved awareness of the prevalence of carcinogens in the environment, along with a growing appreciation of the complexity of the carcinogenesis process, has shifted policy on cancer risk from one of strict avoidance of carcinogens to one of adherence to exposure limits deemed "safe" based on quantitative risk estimation. Meanwhile, given the mutagenic nature of most carcinogens, attention has gravitated to developing a genetic rationale for measuring and comparing risks. This focus has culminated in the now well-established multistage mutational paradigm, which holds that a stepwise sequence of mutations drives cell "initiation" and the subsequent "transformation" of an initiated cell into a cancer cell, and that, once created, a cancer cell will inevitably undergo "progression" to become overt disease. Unanticipated by this paradigm is the effect progression-phase population- and tissue-level bottleneck events may have on this process. Attesting to this is the prevalence of tumor dormancy, a state of arrested growth of an otherwise fully malignant, often microscopic cancer mass, maintained by interactions among cancer cells and between cancer and host cells. The proper inclusion of such progression-modifying influences would clearly behoove risk estimation and improve our understanding of the natural history of cancer by accounting for the less-than-certain risk of eventual cancer disease even when cancer cells are present. Such an improved understanding, in turn, stands to better inform policy-making and influence such clinical practice decisions as whether to treat the increasingly smaller tumors detectable with advancing technologies.

Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers.

Although optimal control theory has been used for the theoretical study of anti-cancerous drugs scheduling optimization, with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously published model for metastatic development to define an optimal control problem at the scale of the entire organism of the patient. In silico study of the impact of different scheduling strategies for anti-angiogenic and cytotoxic agents (either in monotherapy or in combination) is performed to compare a low-dose, continuous, metronomic administration scheme with a more classical maximum tolerated dose schedule. Simulation results reveal differences between primary tumor reduction and control of metastases but overall suggest use of the metronomic protocol.

An integrated multidisciplinary model describing initiation of cancer and the Warburg hypothesis.

BACKGROUND: In this paper we propose a chemical physics mechanism for the initiation of the glycolytic switch commonly known as the Warburg hypothesis, whereby glycolytic activity terminating in lactate continues even in well-oxygenated cells. We show that this may result in cancer via mitotic failure, recasting the current conception of the Warburg effect as a metabolic dysregulation consequent to cancer, to a biophysical defect that may contribute to cancer initiation. MODEL: Our model is based on analogs of thermodynamic concepts that tie non-equilibrium fluid dynamics ultimately to metabolic imbalance, disrupted microtubule dynamics, and finally, genomic instability, from which cancers can arise. Specifically, we discuss how an analog of non-equilibrium Rayleigh-Benard convection can result in glycolytic oscillations and cause a cell to become locked into a higher-entropy state characteristic of cancer. CONCLUSIONS: A quantitative model is presented that attributes the well-known Warburg effect to a biophysical mechanism driven by a convective disturbance in the cell. Contrary to current understanding, this effect may precipitate cancer development, rather than follow from it, providing new insights into carcinogenesis, cancer treatment, and prevention.

Cancer Stem Cells: A Minor Cancer Subpopulation that Redefines Global Cancer Features.

In recent years cancer stem cells (CSCs) have been hypothesized to comprise only a minor subpopulation in solid tumors that drives tumor initiation, progression, and metastasis; the so-called "cancer stem cell hypothesis." While a seemingly trivial statement about numbers, much is put at stake. If true, the conclusions of many studies of cancer cell populations could be challenged, as the bulk assay methods upon which they depend have, by, and large, taken for granted the notion that a "typical" cell of the population possesses the attributes of a cell capable of perpetuating the cancer, i.e., a CSC. In support of the CSC hypothesis, populations enriched for so-called "tumor-initiating" cells have demonstrated a corresponding increase in tumorigenicity as measured by dilution assay, although estimates have varied widely as to what the fractional contribution of tumor-initiating cells is in any given population. Some have taken this variability to suggest the CSC fraction may be nearly 100% after all, countering the CSC hypothesis, and that there are simply assay-dependent error rates in our ability to "reconfirm" CSC status at the cell level. To explore this controversy more quantitatively, we developed a simple cellular automaton model of CSC-driven tumor growth dynamics. Assuming CSC and non-stem cancer cells (CC) subpopulations coexist to some degree, we evaluated the impact of an environmentally dependent CSC symmetric division probability and a CC proliferation capacity on tumor progression and morphology. Our model predicts, as expected, that the frequency of CSC divisions that are symmetric highly influences the frequency of CSCs in the population, but goes on to predict the two frequencies can be widely divergent, and that spatial constraints will tend to increase the CSC fraction over time. Further, tumor progression times show a marked dependence on both the frequency of CSC divisions that are symmetric and on the proliferation capacities of CC. Together, these findings can explain, within the CSC hypothesis, the widely varying measures of stem cell fractions observed. In particular, although the CSC fraction is influenced by the (environmentally modifiable) CSC symmetric division probability, with the former converging to unity as the latter nears 100%, the CSC fraction becomes quite small even for symmetric division probabilities modestly lower than 100%. In the latter case, the tumor exhibits a clustered morphology and the CSC fraction steadily increases with time; more so on both counts when the death rate of CCs is higher. Such variations in CSC fraction and morphology are not only consistent with the CSC hypothesis, but lend support to it as one expected byproduct of the dynamical interactions that are predicted to take place among a relatively small CSC population, its CC counterpart, and the host compartment over time.

Center of cancer systems biology second annual workshop--tumor metronomics: timing and dose level dynamics.

Metronomic chemotherapy, the delivery of doses in a low, regular manner so as to avoid toxic side effects, was introduced over 12 years ago in the face of substantial clinical and preclinical evidence supporting its tumor-suppressive capability. It constituted a marked departure from the classic maximum-tolerated dose (MTD) strategy, which, given its goal of rapid eradication, uses dosing sufficiently intense to require rest periods between cycles to limit toxicity. Even so, upfront tumor eradication is frequently not achieved with MTD, whereupon a de facto goal of longer-term tumor control is often pursued. As metronomic dosing has shown tumor control capability, even for cancers that have become resistant to the same drug delivered under MTD, the question arises whether it may be a preferable alternative dosing approach from the outset. To date, however, our knowledge of the coupled dynamics underlying metronomic dosing is neither sufficiently well developed nor widely enough disseminated to establish its actual potential. Meeting organizers thus felt the time was right, armed with new quantitative approaches, to call a workshop on "Tumor Metronomics: Timing and Dose Level Dynamics" to explore prospects for gaining a deeper, systems-level appreciation of the metronomics concept. The workshop proved to be a forum in which experts from the clinical, biologic, mathematical, and computational realms could work together to clarify the principles and underpinnings of metronomics. Among other things, the need for significant shifts in thinking regarding endpoints to be used as clinical standards of therapeutic progress was recognized.