Superlinear growth reveals the Allee effect in tumors

A modelling framework for cancer ecology and evolution

Cancer incidence increases rapidly with age, typically as a polynomial. The somatic mutation theory explains this increase through the waiting time for enough mutations to build up to generate cells with the full set of traits needed to grow without control. However, lines of evidence ranging from tumour reversion and dormancy to the prevalence of presumed cancer mutations in non-cancerous tissues argue that this is not the whole story, and that cancer is also an ecological process, and that mutations only lead to cancer when the systems of control within and across cells have broken down. Aging thus has two effects: the build-up of mutations and the breakdown of control. This paper presents a mathematical modelling framework to unify these theories with novel approaches to model the mutation and diversification of cell lineages and of the breakdown of the layers of control both within and between cells. These models correctly predict the polynomial increase of cancer with age, show how germline defects in control accelerate cancer initiation, and compute how the positive feedback between cell replication, ecology and layers of control leads to a doubly exponential growth of cell populations.

Testing Adaptive Therapy Protocols Using Gemcitabine and Capecitabine in a Preclinical Model of Endocrine-Resistant Breast Cancer

Adaptive therapy, an ecologically inspired approach to cancer treatment, aims to overcome resistance and reduce toxicity by leveraging competitive interactions between drug-sensitive and drug-resistant subclones, prioritizing patient survival and quality of life instead of killing the maximum number of cancer cells. In preparation for a clinical trial, we used endocrine-resistant MCF7 breast cancer to stimulate second-line therapy and tested adaptive therapy using capecitabine, gemcitabine, or their combination in a mouse xenograft model. Dose modulation adaptive therapy with capecitabine alone increased survival time relative to MTD but not statistically significantly (HR = 0.22, 95% CI = 0.043-1.1, p = 0.065). However, when we alternated the drugs in both dose modulation (HR = 0.11, 95% CI = 0.024-0.55, p = 0.007) and intermittent adaptive therapies, the survival time was significantly increased compared to high-dose combination therapy (HR = 0.07, 95% CI = 0.013-0.42, p = 0.003). Overall, the survival time increased with reduced dose for both single drugs (p < 0.01) and combined drugs (p < 0.001), resulting in tumors with fewer proliferation cells (p = 0.0026) and more apoptotic cells (p = 0.045) compared to high-dose therapy. Adaptive therapy favors slower-growing tumors and shows promise in two-drug alternating regimens instead of being combined.

Stronger Together: Cancer Clones Cooperate to Alleviate Growth Barriers in Critical Cancer Progression Transitions

Hershey and colleagues recently showed how clones in a triple-negative breast cancer cell line cooperate for their mutual fitness benefit. In this system, clones exchange soluble metabolites to increase their in vitro growth rate at low population densities, therefore mitigating the documented growth barrier that reduces individual fitness in small tumor cell populations (Allee effect). Such cooperation could aid important transitions in cancer progression in which cancer cell populations are small, like invasion or metastasis. Using orthotopic transplantation, the authors demonstrate that this cooperation is functional in one such transition in vivo, increasing the metastatic load and number of metastases, which are usually polyclonal. Together, these findings highlight the need to consider ecologic interactions to properly understand tumor growth dynamics, and how they complement the standing evolutionary model of cancer progression in our quest to understand and treat cancer.

Testing Adaptive Therapy Protocols using Gemcitabine and Capecitabine on a Mouse Model of Endocrine-Resistant Breast Cancer

Highly effective cancer therapies often face limitations due to acquired resistance and toxicity. Adaptive therapy, an ecologically inspired approach, seeks to control therapeutic resistance and minimize toxicity by leveraging competitive interactions between drug-sensitive and drug-resistant subclones, prioritizing patient survival and quality of life over maximum cell kill. In preparation for a clinical trial in breast cancer, we used large populations of MCF7 cells to rapidly generate endocrine-resistance breast cancer cell line. We then mimicked second line therapy in ER+ breast cancers by treating the endocrine-resistant MCF7 cells in a mouse xenograft model to test adaptive therapy with capecitabine, gemcitabine, or the combination of those two drugs. Dose-modulation adaptive therapy with capecitabine alone increased survival time relative to MTD, but not statistically significant (HR: 0.22, 95% CI 0.043- 1.1 P = 0.065). However, when we alternated the drugs in both dose modulation (HR = 0.11, 95% CI: 0.024 - 0.55, P = 0.007) and intermittent adaptive therapies significantly increased survival time compared to high dose combination therapy (HR = 0.07, 95% CI: 0.013 - 0.42; P = 0.003). Overall, survival time increased with reduced dose for both single drugs (P < 0.01) and combined drugs (P < 0.001). Adaptive therapy protocols resulted in tumors with lower proportions of proliferating cells (P = 0.0026) and more apoptotic cells (P = 0.045). The results show that Adaptive therapy outperforms high-dose therapy in controlling endocrine-resistant breast cancer, favoring slower-growing tumors, and showing promise in two-drug alternating regimens.

Modeling the Role of Immune Cell Conversion in the Tumor-Immune Microenvironment

Tumors develop in a complex physical, biochemical, and cellular milieu, referred to as the tumor microenvironment. Of special interest is the set of immune cells that reciprocally interact with the tumor, the tumor-immune microenvironment (TIME). The diversity of cell types and cell-cell interactions in the TIME has led researchers to apply concepts from ecology to describe the dynamics. However, while tumor cells are known to induce immune cells to switch from anti-tumor to pro-tumor phenotypes, this type of ecological interaction has been largely overlooked. To address this gap in cancer modeling, we develop a minimal, ecological model of the TIME with immune cell conversion, to highlight this important interaction and explore its consequences. A key finding is that immune conversion increases the range of parameters supporting a co-existence phase in which the immune system and the tumor reach a stalemate. Our results suggest that further investigation of the consequences of immune cell conversion, using detailed, data-driven models, will be critical for greater understanding of TIME dynamics.

Invasion front dynamics of interactive populations in environments with barriers

Invading populations normally comprise different subpopulations that interact while trying to overcome existing barriers against their way to occupy new areas. However, the majority of studies so far only consider single or multiple population invasion into areas where there is no resistance against the invasion. Here, we developed a model to study how cooperative/competitive populations invade in the presence of a physical barrier that should be degraded during the invasion. For one dimensional (1D) environment, we found that a Langevin equation as [Formula: see text] describing invasion front position. We then obtained how [Formula: see text] and [Formula: see text] depend on population interactions and environmental barrier intensity. In two dimensional (2D) environment, for the average interface position movements we found a Langevin equation as [Formula: see text]. Similar to the 1D case, we calculate how [Formula: see text] and [Formula: see text] respond to population interaction and environmental barrier intensity. Finally, the study of invasion front morphology through dynamic scaling analysis showed that growth exponent, [Formula: see text], depends on both population interaction and environmental barrier intensity. Saturated interface width, [Formula: see text], versus width of the 2D environment (L) also exhibits scaling behavior. Our findings show revealed that competition among subpopulations leads to more rough invasion fronts. Considering the wide range of shreds of evidence for clonal diversity in cancer cell populations, our findings suggest that interactions between such diverse populations can potentially participate in the irregularities of tumor border.

Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.