A Race between Tumor Immunoescape and Genome Maintenance Selects for Optimum Levels of (epi)genetic Instability

The human immune system functions to provide continuous body-wide surveillance to detect and eliminate foreign agents such as bacteria and viruses as well as the body's own cells that undergo malignant transformation. To counteract this surveillance, tumor cells evolve mechanisms to evade elimination by the immune system; this tumor immunoescape leads to continuous tumor expansion, albeit potentially with a different composition of the tumor cell population (“immunoediting”). Tumor immunoescape and immunoediting are products of an evolutionary process and are hence driven by mutation and selection. Higher mutation rates allow cells to more rapidly acquire new phenotypes that help evade the immune system, but also harbor the risk of an inability to maintain essential genome structure and functions, thereby leading to an error catastrophe. In this paper, we designed a novel mathematical framework, based upon the quasispecies model, to study the effects of tumor immunoediting and the evolution of (epi)genetic instability on the abundance of tumor and immune system cells. We found that there exists an optimum number of tumor variants and an optimum magnitude of mutation rates that maximize tumor progression despite an active immune response. Our findings provide insights into the dynamics of tumorigenesis during immune system attacks and help guide the choice of treatment strategies that best inhibit diverse tumor cell populations

Stochastic Tunneling of Two Mutations in a Population of Cancer Cells

Cancer initiation, progression, and the emergence of drug resistance are driven by specific genetic and/or epigenetic alterations such as point mutations, structural alterations, DNA methylation and histone modification changes. These alterations may confer advantageous, deleterious or neutral effects to mutated cells. Previous studies showed that cells harboring two particular alterations may arise in a fixed-size population even in the absence of an intermediate state in which cells harboring only the first alteration take over the population; this phenomenon is called stochastic tunneling. Here, we investigated a stochastic Moran model in which two alterations emerge in a cell population of fixed size. We developed a novel approach to comprehensively describe the evolutionary dynamics of stochastic tunneling of two mutations. We considered the scenarios of large mutation rates and various fitness values and validated the accuracy of the mathematical predictions with exact stochastic computer simulations. Our theory is applicable to situations in which two alterations are accumulated in a fixed-size population of binary dividing cells

Prediction of postoperative liver regeneration from clinical information using a data-led mathematical model

Although the capacity of the liver to recover its size after resection has enabled extensive liver resection, post-hepatectomy liver failure remains one of the most lethal complications of liver resection. Therefore, it is clinically important to discover reliable predictive factors after resection. In this study, we established a novel mathematical framework which described post-hepatectomy liver regeneration in each patient by incorporating quantitative clinical data. Using the model fitting to the liver volumes in series of computed tomography of 123 patients, we estimated liver regeneration rates. From the estimation, we found patients were divided into two groups: i) patients restored the liver to its original size (Group 1, n?=?99); and ii) patients experienced a significant reduction in size (Group 2, n?=?24). From discriminant analysis in 103 patients with full clinical variables, the prognosis of patients in terms of liver recovery was successfully predicted in 85–90% of patients. We further validated the accuracy of our model prediction using a validation cohort (prediction?=?84–87%, n?=?39). Our interdisciplinary approach provides qualitative and quantitative insights into the dynamics of liver regeneration. A key strength is to provide better prediction in patients who had been judged as acceptable for resection by current pragmatic criteria

Mathematical analysis identifies the optimal treatment strategy for epidermal growth factor receptor-mutated non-small cell lung cancer

IntroductionIn Asians, more than half of non-small cell lung cancers (NSCLC) are induced by epidermal growth factor receptor (EGFR) mutations. Although patients carrying EGFR driver mutations display a good initial response to EGFR-Tyrosine Kinase Inhibitors (EGFR-TKIs), additional mutations provoke drug resistance. Hence, predicting tumor dynamics before treatment initiation and formulating a reasonable treatment schedule is an urgent challenge.MethodsTo overcome this problem, we constructed a mathematical model based on clinical observations and investigated the optimal schedules for EGFR-TKI therapy.ResultsBased on published data on cell growth rates under different drugs, we found that using osimertinib that are efficient for secondary resistant cells as the first-line drug is beneficial in monotherapy, which is consistent with published clinical statistical data. Moreover, we identified the existence of a suitable drug-switching time; that is, changing drugs too early or too late was not helpful. Furthermore, we demonstrate that osimertinib combined with erlotinib or gefitinib as first-line treatment, has the potential for clinical application. Finally, we examined the relationship between the initial ratio of resistant cells and final cell number under different treatment conditions, and summarized it into a therapy suggestion map. By performing parameter sensitivity analysis, we identified the condition where　osimertinib-first therapy was recommended as the optimal treatment option.DiscussionThis study for the first time theoretically showed the optimal treatment strategies based on the known information in NSCLC. Our framework can be applied to other types of cancer in the future

Computational modeling of locoregional recurrence with spatial structure identifies tissue-specific carcinogenic profiles

IntroductionLocal and regional recurrence after surgical intervention is a significant problem in cancer management. The multistage theory of carcinogenesis precisely places the presence of histologically normal but mutated premalignant lesions surrounding the tumor - field cancerization, as a significant cause of cancer recurrence. The relationship between tissue dynamics, cancer initiation and cancer recurrence in multistage carcinogenesis is not well known.MethodsThis study constructs a computational model for cancer initiation and recurrence by combining the Moran and branching processes in which cells requires 3 or more mutations to become malignant. In addition, a spatial structure-setting is included in the model to account for positional relativity in cell turnover towards malignant transformation. The model consists of a population of normal cells with no mutation; several populations of premalignant cells with varying number of mutations and a population of malignant cells. The model computes a stage of cancer detection and surgery to eliminate malignant cells but spares premalignant cells and then estimates the time for malignant cells to re-emerge.ResultsWe report the cellular conditions that give rise to different patterns of cancer initiation and the conditions favoring a shorter cancer recurrence by analyzing premalignant cell types at the time of surgery. In addition, the model is fitted to disease-free clinical data of 8,957 patients in 27 different cancer types; From this fitting, we estimate the turnover rate per month, relative fitness of premalignant cells, growth rate and death rate of cancer cells in each cancer type.DiscussionOur study provides insights into how to identify patients who are likely to have a shorter recurrence and where to target the therapeutic intervention

Evolutionary dynamics of tumor progression with random fitness values

Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis. Other mutations, however, do not change the phenotype of the cell or even decrease cellular fitness. While much experimental effort is being devoted to the identification of the different functional effects of individual mutations, mathematical modeling of tumor progression generally considers constant fitness increments as mutations are accumulated. In this paper we study a mathematical model of tumor progression with random fitness increments. We analyze a multi-type branching process in which cells accumulate mutations whose fitness effects are chosen from a distribution. We determine the effect of the fitness distribution on the growth kinetics of the tumor. This work contributes to a quantitative understanding of the accumulation of mutations leading to cancer phenotypes.Comment: 33 pages, 2 Figure

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

Evolutionary dynamics of cancer in response to targeted combination therapy

In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics. DOI: http://dx.doi.org/10.7554/eLife.00747.00

The Therapeutic Implications of Plasticity of the Cancer Stem Cell Phenotype

The cancer stem cell hypothesis suggests that tumors contain a small population of cancer cells that have the ability to undergo symmetric self-renewing cell division. In tumors that follow this model, cancer stem cells produce various kinds of specified precursors that divide a limited number of times before terminally differentiating or undergoing apoptosis. As cells within the tumor mature, they become progressively more restricted in the cell types to which they can give rise. However, in some tumor types, the presence of certain extra- or intracellular signals can induce committed cancer progenitors to revert to a multipotential cancer stem cell state. In this paper, we design a novel mathematical model to investigate the dynamics of tumor progression in such situations, and study the implications of a reversible cancer stem cell phenotype for therapeutic interventions. We find that higher levels of dedifferentiation substantially reduce the effectiveness of therapy directed at cancer stem cells by leading to higher rates of resistance. We conclude that plasticity of the cancer stem cell phenotype is an important determinant of the prognosis of tumors. This model represents the first mathematical investigation of this tumor trait and contributes to a quantitative understanding of cancer