CAREER: Stochastic Models of Cancer Evolution

该项目将建立严格的数学框架，以了解癌症从健康组织开始，以及肿瘤微环境在抗癌治疗耐药性演变中的作用。在第一阶段，该项目将利用随机相互作用粒子系统和这些过程的介观近似，建立描述空间结构种群中繁殖、死亡和突变进化过程的随机模型。这些模型将被分析，以研究空间种群结构如何影响癌症起始过程和由此产生的组织遗传异质性。在第二阶段，该项目将利用非马尔可夫分支过程，建立肿瘤细胞群与其环境之间反馈的数学模型。我们将对这些模型进行分析，以帮助阐明肿瘤环境在耐药性进化中的作用。PI将与癌症生物学家合作，在肺癌实验系统中参数化和验证这些模型。本研究探讨了环境压力和空间人口结构对癌症进化的影响。这项研究可以开发更好的统计工具，用于评估癌前领域的癌症风险，预测生存，评估治疗效果，改进治疗方案的设计，以预防或延迟耐药性。本提案中开发的数学框架也将广泛适用于理解生态学和疾病动力学中的类似问题，例如细菌或病毒种群中抗生素耐药性的出现，或入侵植物物种和抗农药杂草的地理传播。该项目的一个教育目标是增加妇女在数学领域的代表性，重点是招收数学生物学和医学领域的妇女。明尼苏达大学每年将为当地高中女生举办为期一周的暑期课程，主题是“生物学和医学中的数学”。此外，将举办一个研讨会，将数学生物学领域的早期职业女性聚集在一起，目的是分享研究和讨论该领域的新兴领域，本科生将被纳入拟议的研究工作，为期一年的项目。这些项目将通过在线社区的发展联系起来，为校友提供支持、网络和指导，帮助他们在这些项目之外继续追求自己的目标。

This project will develop rigorous mathematical frameworks for understanding cancer initiation from healthy tissue, and the role of the tumor microenvironment on the evolution of resistance to anti-cancer therapies. In its first phase, this project will build stochastic models describing the evolutionary processes of reproduction, death and mutation in a spatially structured population, using stochastic interacting particle systems and mesoscopic approximations of these processes. These models will be analyzed to investigate how spatial population structure impacts the cancer initiation process and resulting genetic heterogeneity of the tissue. In its second phase, this project will develop mathematical models of the feedback between the evolving tumor cell population and its environment, using non-Markovian branching processes. These models will be analyzed to help elucidate the role of the tumor environment in the evolution of drug resistance. The PI will collaborate with cancer biologist to parametrize and validate these models a lung cancer experimental system. This research investigates how cancer evolution is shaped by environmental pressures and spatial population structure. This research can lead to the development of better statistical tools for assessment of cancer risk from premalignant fields, survival prediction, evaluation of treatment efficacy, and improved design of treatment regimens to prevent or delay drug resistance. The mathematical frameworks developed in this proposal will also be broadly applicable to understanding similar issues in ecology and disease dynamics, e.g. emergence of antibiotic resistance in bacterial or viral populations, or the geographic spread of invasive plant species and pesticide resistant weeds. An education goal of this project is to increase the representation of women in mathematics, with an emphasis on recruitment into the mathematical biology and medicine. A week-long summer program will be held each year at the University of Minnesota for local high school girls with the theme of "Mathematics in Biology and Medicine." In addition, a workshop will be held to bring together early career women in mathematical biology with the aim of sharing research and discussing emerging areas of the field, and undergraduate students will be integrated into the proposed research efforts for year-long projects. These programs will be linked through the development of an online community to provide support, networking and guidance to alumni, as they continue pursuing their goals beyond these programs.