Mutant evolution in spatially structured, hierarchical populations

无性种群的进化理论试图理解在各种环境中如何以及为什么发生遗传变化，从几代人的单细胞生物体到单个个体生命周期内多细胞生物体的衰老和疾病(体细胞进化)。虽然同质种群中的突变进化原理是众所周知的，通常是教科书的一部分，但它们并不直接适用于任何具有空间、等级结构的现实种群(例如维持组织的干细胞和执行组织功能的更具分化的细胞)。然而，这些特征是高等生物组织以及微生物种群(如生物膜形成细菌)的细胞动力学的共同主题，这些微生物种群也具有空间结构和等级结构(具有不同专业化的细胞子种群)的特征。这项研究项目将扩展进化的基本规律，使其适用于更多种类的生物系统。这一数学理论将应用于追踪横纹肌肉瘤小鼠模型细胞进化的实验数据，横纹肌肉瘤是一种儿科癌症。最后，该项目将开发一个新的指导计划，以促进学生和教授之间的互动，特别是针对代表性不足的学生。存在大量关于突变传播和入侵的数学文献，重点是衡量固定种群中的突变固定概率或突变固定的时间，以及不断增长的种群中的突变负载。推导了进化动力学的标度律，包括空间模型中的平衡种群密度、随机隧道率(少数单个突变体产生双突变体)和扩展菌落中的突变体含量。然而，在各种生物场景中，细胞和有机体在比进化理论传统上认为的更复杂的环境中进化。特别重要的是空间结构的、分级组织的细胞群体，它们由信号机制调节。例如，由干细胞和分化程度更高的细胞组成的组织、实体肿瘤和含有具有特殊功能的细菌细胞的生物膜。关于这种种群结构的全面进化理论目前还不存在。这个项目试图从数学上定义空间结构种群的进化比例法则，这些种群是按层次组织的，包含控制细胞命运决定的调控反馈循环。这将通过(A)开发描述空间扩展、进化的种群的高效数值方法，以及(B)推导空间种群动力学规律，包括适应度谷穿越速率和不同突变类型的突变负载的比例规律来实现。进化理论将应用于横纹肌肉瘤小鼠异种移植细胞进化的数据，具有空间结构和层次结构的特点。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Evolutionary theory for asexual populations seeks to understand how and why genetic change happens in a variety of contexts, from unicellular organisms over generations, to aging and disease of multicellular organisms within the lifespan of a single individual (somatic evolution). While the principles of mutant evolution in homogeneous populations are well-understood and are commonly part of textbooks, they do not directly apply to any realistic population with a spatial, hierarchical structure (such as stem cells that maintain the tissue and more differentiated cells that perform tissue function). These features are, however, a common theme of cell dynamics in tissues of higher organisms, as well as microbial populations such as biofilm forming bacteria, which are also characterized by both spatial and hierarchical structure (cell sub-populations with different specializations). This research project will extend fundamental laws of evolution to be applicable across a much greater variety of biological systems. The mathematical theory will be applied to experimental data that follow the evolution of cells in a mouse model of Rhabdomyosarcoma, which is a pediatric cancer. Finally, the project will develop a new mentoring program that facilitates interactions between students and professors, geared especially towards underrepresented students.A large mathematical literature exists about mutant spread and invasion, focusing on measures such as the mutant fixation probability or the time to mutant fixation in constant populations, as well as mutant load in growing populations. Scaling laws of evolutionary dynamics have been derived, including the equilibrium population density in spatial models, the rate of stochastic tunneling (double-mutant generation from a minority of single mutants), and the mutant content in expanding colonies. In various biological scenarios, however, cells and organisms evolve in more complex settings than those traditionally considered by evolutionary theory. Of particular importance are spatially structured, hierarchically organized cell populations that are regulated by signaling mechanisms. Examples include tissues consisting of stem and more differentiated cells, solid tumors, and biofilms containing bacterial cells with specialized functions. A comprehensive evolutionary theory for such population structures currently does not exist. This project seeks to mathematically define evolutionary scaling laws for spatially structured populations that are hierarchically organized and contain regulatory feedback loops that control cell fate decisions. This will be done by (a) developing efficient numerical methods that describe spatially expanding, evolving populations, and (b) deriving laws of spatial population dynamics, including rates of fitness valley crossing and scaling laws for the mutant load for different mutant types. The evolutionary theory will be applied to data on cellular evolution in Rhabdomyosarcoma mouse xenografts, which are characterized by both spatial and hierarchical structure.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.