Mathematical Modeling, Computational and Experimental Investigation of the Dynamics of Heterogeneity in Breast Cancer

尽管积极的临床治疗包括手术切除，放疗和化疗，肿瘤复发基本上是普遍的。治疗失败的部分原因是肿瘤细胞的异质性，来自遗传和非遗传来源，这有助于治疗抵抗和肿瘤进展。了解这种异质性是开发靶向癌症预防和治疗干预措施的关键。目前解释肿瘤内异质性的流行模型之一是癌症干细胞（CSC）假说。癌基因HER2是一种被充分研究的癌基因，其在促进癌细胞存活和增殖中的作用，最近与csc的产生和维持有关。因此，了解HER2信号传导对于开发新的癌症治疗策略至关重要，而肿瘤生长是一个非常复杂的现象，涉及许多相互关联的过程，跨越广泛的空间和时间尺度，这使得数学建模和计算非常具有挑战性。本研究旨在利用建模技术和计算研究，在数学、化学工程和生物学的界面上解决由肿瘤生长引起的复杂问题。该项目的成功完成也将对公共卫生产生重大影响，因为研究结果可用于开发更专门针对癌症干细胞的诊断、预后和治疗方法。提出的癌症细胞数学建模和实验研究的研究创造了一个独特的多学科研究环境，吸引了来自各个学科的本科生和研究生（特别是女性和少数民族学生）加入我们的研究团队。通过与实验的紧密结合，PI将对HER2信号在调节CSC群体在肿瘤生长中的时空动态进行多尺度建模和计算研究。为了更好地探索HER2信号通路，更好地了解乳腺癌的异质性，PI将开发细胞信号通路与细胞群体耦合的多尺度模型，研究CSCs的动力学控制。这种控制机制利用了文献中的新证据，并与新观察到的实验数据的最新发现相关联。人们普遍认为，维持细胞谱系发生的关键机制是干细胞生态位的形成和物质，干细胞在组织中存在的微环境。为了探索CSCs的肿瘤生长空间模式，PI还将开发一个连续的PDE模型，将HER2信号与多阶段细胞谱系模型和营养物质的空间效应结合起来。具体任务为：(1)研究HER2信号在CSCs控制和维持中的作用，建立和评估多尺度模型，探索控制肿瘤生长平衡的潜在机制和生物学因素；(2)进一步建立连续数学模型，更好地了解不同生物因子作用下肿瘤生长过程中CSC群体的空间结构；(3)设计快速、高效的数值方法求解具有运动和复杂域的数学模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Despite aggressive clinical treatment including surgical resection, radiation, and chemotherapy, tumor recurrence is essentially universal. Therapeutic failure is due, in part, to tumor cell heterogeneity, derived from both genetic and non-genetic sources, which contributes to therapeutic resistance and tumor progression. Understanding this heterogeneity is the key for the development of targeted cancer-preventative and -therapeutic interventions. One of the currently prevailing models explaining intratumoral heterogeneity is the cancer stem cell (CSC) hypothesis. Oncogene HER2 is a well-studied oncogene known for its role in promoting cancer cell survival and proliferation, and recently implicated in generation and maintenance of CSCs. Thus understanding the HER2 signaling is critical for development of novel strategies for cancer treatment, while tumor growth is a very complicated phenomenon involving many inter-related processes across a wide range of spatial and temporal scales, which makes the mathematical modeling and computation very challenging. This research seeks to employ modeling techniques and computational studies to address complex issues arising from tumor growth at the interface of mathematics, chemical engineering and biology. Successful completion of this project will also have a significant impact on public health, as the research findings can be used to develop diagnostics, prognostics, and therapeutics to more specifically target cancer stem cells. The proposed research of mathematical modeling and experimental studies for cancer cells creates a unique multidisciplinary research environment that attracts both undergraduate and graduate students (especially women and minority students) from all disciplines to join our research team.With a close integration with experiments, the PI will perform multi-scale modeling and computational investigation of HER2 signaling in modulating CSC population in cancer tumor growth with spatial-temporal dynamics. To better explore HER2 signaling for better understanding the heterogeneity in breast cancer, PI shall develop a multi-scale model coupled cell signaling with cell population to study the dynamics control of CSCs. This control mechanism capitalizes on emerging evidences in literature, and correlates with recent findings from new observed experimental data. It is widely believed that a key mechanism for proper maintenance of a cell lineage to occur is the formation and substance of the stem cell niche, a microenvironment where stem cells reside in a tissue. To explore the CSCs' spatial patterns for tumor growth, PI will also develop a continuum PDE model coupled HER2 signaling with multistage cell lineage models and spatial effects of nutrients. Specific tasks are: (1) to investigate the roles of HER2 signaling in controlling and maintenance of CSCs, and develop and evaluate multi-scale models to explore underlying mechanisms and biological factors to control the balance of tumor growth; (2) to further develop continuous mathematical models to better understand the spatial structures of CSC populations during tumor growth with different effects of various biological factors; (3) to design fast and efficient numerical methods for solving the mathematical models with moving and complex domains.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.