Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

Modeling tumorspheres reveals cancer stem cell niche building and plasticity

Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the interactions between stem and non-stem cancer cell populations we develop a two-population mathematical model, which is suitable to describe tumorsphere growth. Both interspecific and intraspecific interactions, mediated by the microenvironment, are included. We show that there is a tipping point, characterized by a transcritical bifurcation, where a purely non-stem cell attractor is replaced by a new attractor that contains both stem and differentiated cancer cells. The model is then applied to describe the outcome of a recent experiment. This description reveals that, while the intraspecific interactions are inhibitory, the interspecific interactions stimulate growth. This can be understood in terms of stem cells needing differentiated cells to reinforce their niches, and phenotypic plasticity favoring the de-differentiation of differentiated cells into cancer stem cells. We posit that this is a consequence of the deregulation of the quorum sensing that maintains homeostasis in healthy tissues.Fil: Benitez, Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Barberis, Lucas Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Condat, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Hepatic stellate cells suppress NK cell-sustained breast cancer dormancy

The persistence of undetectable disseminated tumour cells (DTCs) after primary tumour resection poses a major challenge to effective cancer treatment; 1-3; . These enduring dormant DTCs are seeds of future metastases, and the mechanisms that switch them from dormancy to outgrowth require definition. Because cancer dormancy provides a unique therapeutic window for preventing metastatic disease, a comprehensive understanding of the distribution, composition and dynamics of reservoirs of dormant DTCs is imperative. Here we show that different tissue-specific microenvironments restrain or allow the progression of breast cancer in the liver-a frequent site of metastasis; 4; that is often associated with a poor prognosis; 5; . Using mouse models, we show that there is a selective increase in natural killer (NK) cells in the dormant milieu. Adjuvant interleukin-15-based immunotherapy ensures an abundant pool of NK cells that sustains dormancy through interferon-γ signalling, thereby preventing hepatic metastases and prolonging survival. Exit from dormancy follows a marked contraction of the NK cell compartment and the concurrent accumulation of activated hepatic stellate cells (aHSCs). Our proteomics studies on liver co-cultures implicate the aHSC-secreted chemokine CXCL12 in the induction of NK cell quiescence through its cognate receptor CXCR4. CXCL12 expression and aHSC abundance are closely correlated in patients with liver metastases. Our data identify the interplay between NK cells and aHSCs as a master switch of cancer dormancy, and suggest that therapies aimed at normalizing the NK cell pool might succeed in preventing metastatic outgrowth

Microenvironment-mediated cancer dormancy : insights from metastability theory

Dormancy is an evolutionarily conserved protective mechanism widely observed in nature. A pathological example is found during cancer metastasis, where cancer cells disseminate from the primary tumor, home to secondary organs, and enter a growth-arrested state, which could last for decades. Recent studies have pointed toward the microenvironment being heavily involved in inducing, preserving, or ceasing this dormant state, with a strong focus on identifying specific molecular mechanisms and signaling pathways. Increasing evidence now suggests the existence of an interplay between intracellular as well as extracellular biochemical and mechanical cues in guiding such processes. Despite the inherent complexities associated with dormancy, proliferation, and growth of cancer cells and tumor tissues, viewing these phenomena from a physical perspective allows for a more global description, independent from many details of the systems. Building on the analogies between tissues and fluids and thermodynamic phase separation concepts, we classify a number of proposed mechanisms in terms of a thermodynamic metastability of the tumor with respect to growth. This can be governed by interaction with the microenvironment in the form of adherence (wetting) to a substrate or by mechanical confinement of the surrounding extracellular matrix. By drawing parallels with clinical and experimental data, we advance the notion that the local energy minima, or metastable states, emerging in the tissue droplet growth kinetics can be associated with a dormant state. Despite its simplicity, the provided framework captures several aspects associated with cancer dormancy and tumor growth

Tumor cell dormancy

Metastasis is the primary cause of death in cancer patients and current treatments fail to provide durable responses. Efforts to treat metastatic disease are hindered by the fact that metastatic cells often remain dormant for prolonged intervals of years, or even decades. Tumor dormancy reflects the capability of disseminated tumor cells (DTCs), or micrometastases, to evade treatment and remain at low numbers after primary tumor resection. Unfortunately, dormant cells will eventually produce overt metastasis. Innovations are needed to understand metastatic dormancy and improve cancer detection and treatment. Currently, few models exist that faithfully recapitulate metastatic dormancy and metastasis to clinically relevant tissues, such as the bone. Herein, we discuss recent advances describing genetic cell-autonomous and systemic or local changes in the microenvironment that have been shown to endow DTCs with properties to survive and eventually colonize distant organs

Modeling the connection between primary and metastatic tumors

We put forward a model for cancer metastasis as a migration phenomenon between tumor cell populations coexisting and evolving in two different habitats. One of them is a primary tumor and the other one is a secondary or metastatic tumor. The evolution of the different cell phenotype populations in each habitat is described by means of a simple quasispecies model allowing for a cascade of mutations between the different phenotypes in each habitat. The cell migration event is supposed to be unidirectional and take place continuously in time. The possible clinical outcomes of the model depending on the parameter space are analyzed and the effect of the resection of the primary tumor is studied

How combination therapies shape drug resistance in heterogeneous tumoral populations

Treatment of cancer relies increasingly on combination therapies to overcome cancer resistance, but the design of successful combined protocols is still an open problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cancer populations competing for resources and with different susceptibilities to the action of immune system cells and therapies. The focus is on the effects of therapies that affect the rate of cancer growth, as in case of chemotherapy, used alone or in combination with immunotherapy, which boost the action of the immune system. Simulations show that a standard dose chemotherapy is effective when the sensitive clone has a marked competitive advantage, whereas combination of immuno- and chemotherapy works better in all the other cases. These results stress the importance to take into account competitive interactions among cancer clones to decide which therapeutic strategy should be adopted. Next the analysis is extended to protocols involving a drug holiday, i.e. periods in which no drug is administered. Finally, the model has been adapted to investigate combination therapies for non-small cell lung cancer: simulation results show that administration of standard dose of Erlotinib (a tyrosine kinase inhibitor), alone, has quite the same effect as a low-dose combination therapy, but the latter produces a slower increase of resistant cells

The Challenges of Detecting Circulating Tumor Cells in Sarcoma

Sarcomas are a heterogeneous group of malignant neoplasms of mesenchymal origin, many of which have a propensity to develop distant metastases. Cancer cells that have escaped from the primary tumor are able to invade into surrounding tissues, to intravasate into the bloodstream to become circulating tumor cells (CTCs), and are responsible for the generation of distant metastases. Due to the rarity of these tumors and the absence of specific markers expressed by sarcoma tumor cells, the characterization of sarcoma CTCs has to date been relatively limited. Current techniques for isolating sarcoma CTCs are based on size criteria, the identification of circulating cells that express either common mesenchymal markers, sarcoma-specific markers, such as CD99, CD81, or PAX3, and chromosomal translocations found in certain sarcoma subtypes, such as EWS-FLI1 in Ewing’s sarcoma, detection of osteoblast-related genes, or measurement of the activity of specific metabolic enzymes. Further studies are needed to improve the isolation and characterization of sarcoma CTCs, to demonstrate their clinical significance as predictive and/or prognostic biomarkers, and to utilize CTCs as a tool for investigating the metastatic process in sarcoma and to identify novel therapeutic targets. The present review provides a short overview of the most recent literature on CTCs in sarcoma