CAREER: Rare Events in Cancer Evolution

这项学院早期职业发展(Career)基金将研究癌症的进化动力学。癌症被认为是一个多步骤的进化过程，将正常细胞转变为高度能动的细胞，具有不受限制的增殖能力和避免程序性细胞死亡信号。在拟议的工作中，我们的目标是利用进化原理来开发数学上易于处理的、参数化的和验证的随机模型，这些模型描述了癌症发生和治疗过程中的几个重要过程。癌症进化过程中的一个重要过程是肿瘤细胞从原发部位向远处扩散，即转移。这笔赠款的一个重要方面是研究抗癌治疗政策，将大转移负担的风险降至最低。癌症进化的另一个重要过程是治疗后疾病的复发。这项工作还将研究癌症治疗后复发的进化动力学。尤其重要的是，癌症在远离最初诊断地点的情况下异常复发。贯穿这项工作的一个共同主题是对罕见事件的数学研究，在这些事件中，癌细胞的进化行为与预期不同。将在本科阶段开设课程，介绍在医学中使用运筹学方法。此外，将有几次机会通过本科生研究体验(REU)让本科生参与该项目的研究方面。此外，还将在研究生阶段开设课程，研究随机模型和最优化在癌症治疗中的应用。这项拨款的工作将在随机粒子系统的随机建模和罕见事件模拟领域引入一些新问题。这些类型的过程已经被用来在不同的尺度上模拟许多生物过程，从细菌生物膜和肿瘤生长到动物种群的迁移。在这些系统中，罕见的随机事件往往会推动重要的变化，从而导致重大的进化变化。然而，针对这类模型的罕见事件模拟技术在很大程度上还没有开发出来。这项工作将建立随机粒子系统中罕见事件的新的极限定理，并发展新的估计其概率的重要抽样算法。因此，这项工作在罕见事件分析和模拟领域取得了进展。这项工作将通过提供工具来分析其他系统的类似模型中具有生物学重要性的罕见事件，从而使生物学和理论生物学社区受益。

This Faculty Early Career Development (CAREER) grant will study the evolutionary dynamics of cancer. Cancer is thought to arise from a multi-step evolutionary process that transforms normal cells into highly motile cells with unchecked ability to proliferate and avoid programmed cell death signals. In the proposed work, we aim to use evolutionary principles to develop mathematically tractable, parametrized and validated stochastic models of several important processes during carcinogenesis and treatment. One important process in the evolution of cancer is the dissemination of tumor cells from the primary site to distant sites, i.e., metastasis. An important aspect of this grant is the study of anti-cancer treatment policies that minimize the risk of large metastatic burden. Another important process in cancer evolution is the recurrence of the disease following treatment. This work will also study the evolutionary dynamics of cancer recurrence following treatment. Of particular importance, are scenarios where cancers recur abnormally far away from their initial site of diagnosis. A common theme throughout this work is the mathematical study of rare events, where the evolution of the cancer cells behaves differently than expected. Courses will be developed at the undergraduate levels that introduce the use of operations research methodologies in medicine. In addition, there will be several opportunities to involve undergraduates in the research aspects of the project through research experiences for undergraduates (REU). Furthermore, classes will be developed at the graduate level that study the use of stochastic models and optimization in the treatment of cancer.The work in this grant will introduce a number of new problems in the field of stochastic modeling and rare event simulation for stochastic particle systems. These types of processes have been used to model many biological processes at a variety of scales, from bacterial biofilms and tumor growth to migrating animal populations. Within these systems, rare stochastic events often drive important changes that lead to major evolutionary change. However, rare event simulation techniques for these types of models are largely undeveloped. The proposed work will establish new limit theorems for rare events in stochastic particle systems and develop new importance sampling algorithms for the estimation of their probabilities. Thus, this work makes advances to the field of rare event analysis and simulation. This work will benefit the biology and theoretical biology communities by providing tools to analyze biologically important rare events in similar models of other systems.