The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity.

We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy.

Mathematical model reveals how regulating the three phases of T-cell response could counteract immune evasion.

T cells are key players in immune action against the invasion of target cells expressing non-self antigens. During an immune response, antigen-specific T cells dynamically sculpt the antigenic distribution of target cells, and target cells concurrently shape the host's repertoire of antigen-specific T cells. The succession of these reciprocal selective sweeps can result in 'chase-and-escape' dynamics and lead to immune evasion. It has been proposed that immune evasion can be countered by immunotherapy strategies aimed at regulating the three phases of the immune response orchestrated by antigen-specific T cells: expansion, contraction and memory. Here, we test this hypothesis with a mathematical model that considers the immune response as a selection contest between T cells and target cells. The outcomes of our model suggest that shortening the duration of the contraction phase and stabilizing as many T cells as possible inside the long-lived memory reservoir, using dual immunotherapies based on the cytokines interleukin-7 and/or interleukin-15 in combination with molecular factors that can keep the immunomodulatory action of these interleukins under control, should be an important focus of future immunotherapy research.

Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors.

Histopathological evidence supports the idea that the emergence of phenotypic heterogeneity and resistance to cytotoxic drugs can be considered as a process of selection in tumor cell populations. In this framework, can we explain intra-tumor heterogeneity in terms of selection driven by the local cell environment? Can we overcome the emergence of resistance and favor the eradication of cancer cells by using combination therapies? Bearing these questions in mind, we develop a model describing cell dynamics inside a tumor spheroid under the effects of cytotoxic and cytostatic drugs. Cancer cells are assumed to be structured as a population by two real variables standing for space position and the expression level of a phenotype of resistance to cytotoxic drugs. The model takes explicitly into account the dynamics of resources and anticancer drugs as well as their interactions with the cell population under treatment. We analyze the effects of space structure and combination therapies on phenotypic heterogeneity and chemotherapeutic resistance. Furthermore, we study the efficacy of combined therapy protocols based on constant infusion and bang-bang delivery of cytotoxic and cytostatic drugs.

Dispersal homogenizes communities via immigration even at low rates in a simplified synthetic bacterial metacommunity.

Selection and dispersal are ecological processes that have contrasting roles in the assembly of communities. Variable selection diversifies and strong dispersal homogenizes them. However, we do not know whether dispersal homogenizes communities directly via immigration or indirectly via weakening selection across habitats due to physical transfer of material, e.g., water mixing in aquatic ecosystems. Here we examine how dispersal homogenizes a simplified synthetic bacterial metacommunity, using a sequencing-independent approach based on flow cytometry and mathematical modeling. We show that dispersal homogenizes the metacommunity via immigration, not via weakening selection, and even when immigration is four times slower than growth. This finding challenges the current view that dispersal homogenizes communities only at high rates and explains why communities are homogeneous at small spatial scales. It also offers a benchmark for sequence-based studies in natural microbial communities where immigration rates can be inferred solely by using neutral models.

Publisher Correction: Dispersal homogenizes communities via immigration even at low rates in a simplified synthetic bacterial metacommunity.

In the original version of this article, the green and blue outlines in Figure 2b, top centre and right panels were inadvertently shifted left from the correct position. This has now been corrected in the PDF and HTML versions of the article.

Universal response in the RKO colon cancer cell line to distinct antimitotic therapies.

Both classic and newer antimitotics commonly induce a prolonged mitotic arrest in cell culture. During arrest, cells predominantly undergo one of two fates: cell death by apoptosis, or mitotic slippage and survival. To refine this binary description, a quantitative understanding of these cell responses is needed. Herein, we propose a quantitative description of the kinetics of colon carcinoma RKO cell fates in response to different antimitotics, using data from the single cell experiments of Gascoigne and Taylor (2008). The mathematical model is calibrated using the in vitro experiments of Gascoigne and Taylor (2008). We show that the time-dependent probability of cell death or slippage is universally identical for monastrol, nocodazole and two different doses of AZ138, but significantly different for taxol. Death and slippage responses across drugs can be characterized by Gamma distributions. We demonstrate numerically that these rates increase with prolonged mitotic arrest. Our model demonstrates that RKO cells exhibit a triphasic response - first, remain in mitosis, then undergo fast and slow transition, respectively- dependent on the length of mitotic arrest and irrespective of cell fate, drug type or dose.

Modeling Cancer Cell Growth Dynamics In vitro in Response to Antimitotic Drug Treatment.

Investigating the role of intrinsic cell heterogeneity emerging from variations in cell-cycle parameters and apoptosis is a crucial step toward better informing drug administration. Antimitotic agents, widely used in chemotherapy, target exclusively proliferative cells and commonly induce a prolonged mitotic arrest followed by cell death via apoptosis. In this paper, we developed a physiologically motivated mathematical framework for describing cancer cell growth dynamics that incorporates the intrinsic heterogeneity in the time individual cells spend in the cell-cycle and apoptosis process. More precisely, our model comprises two age-structured partial differential equations for the proliferative and apoptotic cell compartments and one ordinary differential equation for the quiescent compartment. To reflect the intrinsic cell heterogeneity that governs the growth dynamics, proliferative and apoptotic cells are structured in "age," i.e., the amount of time remaining to be spent in each respective compartment. In our model, we considered an antimitotic drug whose effect on the cellular dynamics is to induce mitotic arrest, extending the average cell-cycle length. The prolonged mitotic arrest induced by the drug can trigger apoptosis if the time a cell will spend in the cell cycle is greater than the mitotic arrest threshold. We studied the drug's effect on the long-term cancer cell growth dynamics using different durations of prolonged mitotic arrest induced by the drug. Our numerical simulations suggest that at confluence and in the absence of the drug, quiescence is the long-term asymptotic behavior emerging from the cancer cell growth dynamics. This pattern is maintained in the presence of small increases in the average cell-cycle length. However, intermediate increases in cell-cycle length markedly decrease the total number of cells and can drive the cancer population to extinction. Intriguingly, a large "switch-on/switch-off" increase in the average cell-cycle length maintains an active cell population in the long term, with oscillating numbers of proliferative cells and a relatively constant quiescent cell number.

Emergence of drug tolerance in cancer cell populations: an evolutionary outcome of selection, nongenetic instability, and stress-induced adaptation.

In recent experiments on isogenetic cancer cell lines, it was observed that exposure to high doses of anticancer drugs can induce the emergence of a subpopulation of weakly proliferative and drug-tolerant cells, which display markers associated with stem cell-like cancer cells. After a period of time, some of the surviving cells were observed to change their phenotype to resume normal proliferation and eventually repopulate the sample. Furthermore, the drug-tolerant cells could be drug resensitized following drug washout. Here, we propose a theoretical mechanism for the transient emergence of such drug tolerance. In this framework, we formulate an individual-based model and an integro-differential equation model of reversible phenotypic evolution in a cell population exposed to cytotoxic drugs. The outcomes of both models suggest that nongenetic instability, stress-induced adaptation, selection, and the interplay between these mechanisms can push an actively proliferating cell population to transition into a weakly proliferative and drug-tolerant state. Hence, the cell population experiences much less stress in the presence of the drugs and, in the long run, reacquires a proliferative phenotype, due to phenotypic fluctuations and selection pressure. These mechanisms can also reverse epigenetic drug tolerance following drug washout. Our study highlights how the transient appearance of the weakly proliferative and drug-tolerant cells is related to the use of high-dose therapy. Furthermore, we show how stem-like characteristics can act to stabilize the transient, weakly proliferative, and drug-tolerant subpopulation for a longer time window. Finally, using our models as in silico laboratories, we propose new testable hypotheses that could help uncover general principles underlying the emergence of cancer drug tolerance.

Applying ecological and evolutionary theory to cancer: a long and winding road.

Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic cellular selection and evolution being the fundamental processes leading to malignancy and its many manifestations (neoangiogenesis, evasion of the immune system, metastasis, and resistance to therapies). Historically, little attention has been placed on applications of evolutionary biology to understanding and controlling neoplastic progression and to prevent therapeutic failures. This is now beginning to change, and there is a growing international interest in the interface between cancer and evolutionary biology. The objective of this introduction is first to describe the basic ideas and concepts linking evolutionary biology to cancer. We then present four major fronts where the evolutionary perspective is most developed, namely laboratory and clinical models, mathematical models, databases, and techniques and assays. Finally, we discuss several of the most promising challenges and future prospects in this interdisciplinary research direction in the war against cancer.