Understanding stochasticity in cancer recurrence timing

突变引起的耐药是癌症治疗的主要障碍，经常导致治疗失败和肿瘤复发。癌症复发发生的时间（即治疗的生存获益）是由许多因素之间的复杂平衡决定的，如初始肿瘤大小、突变率、耐药机制的类型/数量、药物疗效和时间表。本研究旨在利用肿瘤生长的分支过程模型，对这些因素如何共同控制驱动癌症复发的进化过程的时间动力学进行全面的数学理解。工作的第一部分将侧重于在肿瘤细胞群“混合良好”的基本假设下，对癌症复发的时间动态进行详细的了解。在一个不断选择的环境中。该分析将描述由于人口统计学随机性和随机突变适应度变化而导致的系统平均动态和波动。在第二部分的工作中，研究人员将放宽这些基本假设，以量化和比较可能显著影响复发动力学的其他因素的影响。这些额外的因素包括时间变化的选择环境，空间结构和不均匀性，以及分层人口结构。所有这些研究都将使用逃逸灭绝的随机过程模型进行，并将利用分析和计算工具来研究递归动力学。这项研究将有助于更好地理解获得性耐药后癌症进展模式的变异性驱动机制。研究结果最终有助于开发更好的预后统计工具、评估药物疗效和改进治疗策略。例如，了解癌症复发的时间如何揭示有关肿瘤的组成或先前遗传史的信息可以帮助确定复发后的最佳治疗策略。此外，该项目将有助于对种群灭绝逃逸动力学的一般数学理解。因此，所开发的理论将广泛适用于理解进化、健康（例如细菌和病毒耐药性）和生态学中的类似问题，而不需要扩展。该项目将支持本科生、研究生和博士后在数学、生物学和医学领域进行研究。

Mutation-induced drug resistance represents a major obstacle in cancer treatment and often causes the failure of therapies and tumor recurrence. The time at which cancer recurrence occurs (i.e., survival benefit of therapy) is governed by a complex balance between many factors such as initial tumor size, mutation rates, the type/number of resistance mechanisms, and drug efficacy and schedule. This research aims to develop a comprehensive mathematical understanding of how these factors conspire to control the temporal dynamics of the evolutionary processes driving cancer recurrence, using branching process models of tumor growth. The first part of the work will focus on developing a detailed understanding of the temporal dynamics of cancer recurrence, under the basic assumptions that tumor cell populations are ?well-mixed? in a constant selective environment. The analysis will characterize both mean dynamics and fluctuations in the system due to both demographic stochasticity and random mutational fitness changes. In the second part of the work, the investigators will relax these basic assumptions to quantify and compare the effects of additional factors that may significantly impact recurrence dynamics. These additional factors include temporally varying selective environments, spatial structure and inhomogeneity, and hierarchical population structure. All of these investigations will be performed using stochastic process models of escape from extinction, and both analytical and computational tools will be utilized to study recurrence dynamics.This research will lead to a better understanding of the mechanisms driving variability in patterns of cancer progression following acquired resistance to treatment. The results can eventually aid in the development of better statistical tools for prognosis, evaluating drug efficacy, and improving treatment strategies. For example, an understanding of how the timing of cancer recurrence reveals information about the composition or prior genetic history of the tumor can aid in determining optimal treatment strategies post-recurrence. In addition, this project will contribute to a general mathematical understanding of the dynamics of escape from population extinction. Thus, the theory developed will be broadly applicable, with minimal extension, to understanding similar issues in evolution, health (e.g. bacterial and viral drug resistance), and ecology. This project will support for trainees at the undergraduate, graduate and postdoctoral levels in research at the interface of mathematics, biology, and medicine.