Mutant evolution in spatially structured, hierarchical populations

无性种群的进化理论试图理解遗传变化如何以及为什么在各种情况下发生，从单细胞生物的世代，到多细胞生物在单个个体的生命周期内的衰老和疾病（体细胞进化）。虽然同质群体中突变进化的原理是很好理解的，并且通常是教科书的一部分，但它们并不直接适用于具有空间层次结构的任何现实群体（例如维持组织的干细胞和执行组织功能的分化细胞）。然而，这些特征是高等生物组织中细胞动力学的共同主题，以及微生物种群如生物膜形成细菌，其特征也在于空间和层次结构（具有不同特化的细胞亚群）。该研究项目将扩展基本的进化规律，使其适用于更广泛的生物系统。数学理论将应用于实验数据，这些数据遵循横纹肌肉瘤小鼠模型中细胞的演变，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，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。大量的数学文献存在关于突变体的传播和入侵，侧重于测量，如突变体固定概率或固定在恒定的种群中的突变体固定的时间，以及在不断增长的种群中的突变负荷。演化动力学的标度律已经被推导出来，包括空间模型中的平衡种群密度、随机隧道效应（从少数单突变体产生双突变体）的速率以及扩展菌落中的突变体含量。然而，在各种生物学场景中，细胞和生物体在比传统进化理论所考虑的更复杂的环境中进化。特别重要的是由信号传导机制调节的空间结构化、分层组织的细胞群。实例包括由干细胞和更分化的细胞组成的组织、实体瘤和含有具有专门功能的细菌细胞的生物膜。目前还不存在一个关于这种种群结构的全面的进化理论。该项目旨在从数学上定义空间结构群体的进化比例律，这些群体是分层组织的，包含控制细胞命运决定的调节反馈回路。 这将通过（a）开发有效的数值方法来描述空间扩展，进化的种群，和（B）推导空间种群动态的规律，包括适应度谷交叉率和不同突变类型的突变负荷的比例法则。进化理论将应用于横纹肌肉瘤小鼠异种移植物的细胞进化数据，其特点是空间和层次结构。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值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.