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In this didactic paper, we present a theoretical modeling framework, called theG-function, that integrates both the ecology and evolution of cancer to understand oncogenesis. TheG-function has been used in evolutionary ecology, but has not been widely applied to problems in cancer. Here, we build theG-function framework from fundamental Darwinian principles and discuss how cancer can be seen through the lens of ecology, evolution, and game theory. We begin with a simple model of cancer growth and add on components of cancer cell competition and drug resistance. To aid in exploration of eco-evolutionary modeling with this approach, we also present a user-friendly software tool. By the end of this paper, we hope that readers will be able to construct basicGfunction models and grasp the usefulness of the framework to understand the games cancer plays in a biologically mechanistic fashion.

Therapeutic resistance is one of the main reasons for treatment failure in cancer patients. The polyaneuploid cancer cell (PACC) state has been shown to promote resistance by providing a refuge for cancer cells from the effects of therapy and by helping them adapt to a variety of environmental stressors. This state is the result of aneuploid cancer cells undergoing whole genome doubling and skipping mitosis, cytokinesis, or both. In this paper, we create a novel mathematical framework for modeling the eco-evolutionary dynamics of state-structured populations and use this framework to construct a model of cancer populations with an aneuploid and a PACC state. Using in silico simulations, we explore how the PACC state allows cancer cells to (1) survive extreme environmental conditions by exiting the cell cycle after S phase and protecting genomic material and (2) aid in adaptation to environmental stressors by increasing the cancer cell’s ability to generate heritable variation (evolvability) through the increase in genomic content that accompanies polyploidization. In doing so, we demonstrate the ability of the PACC state to allow cancer cells to persist under therapy and evolve therapeutic resistance. By eliminating cells in the PACC state through appropriately-timed PACC-targeted therapies, we show how we can prevent the emergence of resistance and promote cancer eradication.

Recent evidence suggests that a polyaneuploid cancer cell (PACC) state may play a key role in the adaptation of cancer cells to stressful environments and in promoting therapeutic resistance. The PACC state allows cancer cells to pause cell division and to avoid DNA damage and programmed cell death. Transition to the PACC state may also lead to an increase in the cancer cell’s ability to generate heritable variation (evolvability). One way this can occur is through evolutionary triage. Under this framework, cells gradually gain resistance by scaling hills on a fitness landscape through a process of mutation and selection. Another way this can happen is through self-genetic modification whereby cells in the PACC state find a viable solution to the stressor and then undergo depolyploidization, passing it on to their heritably resistant progeny. Here, we develop a stochastic model to simulate both of these evolutionary frameworks. We examine the impact of treatment dosage and extent of self-genetic modification on eco-evolutionary dynamics of cancer cells with aneuploid and PACC states. We find that under low doses of therapy, evolutionary triage performs better whereas under high doses of therapy, self-genetic modification is favored. This study generates predictions for teasing apart these biological hypotheses, examines the implications of each in the context of cancer, and provides a modeling framework to compare Mendelian and non-traditional forms of inheritance.

Bacteria under external stress can reveal unexpected emergent phenotypes. We show that the intensely studied bacteriumEscherichia colican transform into long, highly motile helical filaments poized at a torsional buckling criticality when exposed to minimum inhibitory concentrations of several antibiotics. While the highly motile helices are physically either right- or left-handed, the motile helices always rotate with a right-handed angular velocity$\overrightarrow{\omega }$, which points in the same direction as the translational velocity${\overrightarrow{v}}_T$of the helix. Furthermore, these helical cells do not swim by a “run and tumble” but rather synchronously flip their spin$\overrightarrow{\omega }$and thus translational velocity—backing up rather than tumbling. By increasing the translational persistence length, these dynamics give rise to an effective diffusion coefficient up to 20 times that of a normalE. colicell. Finally, we propose an evolutionary mechanism for this phenotype’s emergence whereby the increased effective diffusivity provides a fitness advantage in allowing filamentous cells to more readily escape regions of high external stress.

Cancer led to the deaths of more than 9 million people worldwide in 2018, and most of these deaths were due to metastatic tumor burden. While in most cases, we still do not know why cancer is lethal, we know that a total tumor burden of 1 kg—equivalent to one trillion cells—is not compatible with life. While localized disease is curable through surgical removal or radiation, once cancer has spread, it is largely incurable. The inability to cure metastatic cancer lies, at least in part, to the fact that cancer is resistant to all known compounds and anticancer drugs. The source of this resistance remains undefined. In fact, the vast majority of metastatic cancers are resistant to all currently available anticancer therapies, including chemotherapy, hormone therapy, immunotherapy, and systemic radiation. Thus, despite decades—even centuries—of research, metastatic cancer remains lethal and incurable. We present historical and contemporary evidence that the key actuators of this process—of tumorigenesis, metastasis, and therapy resistance—are polyploid giant cancer cells.