Hybrid Deterministic-Stochastic Methodology for Simulating Spatial Evolution in Large Populations

用于模拟大群体空间演化的混合确定性-随机方法

• 批准号: 1815406
• 负责人: Dominik Wodarz
• 金额: $ 40万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-15 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1815406&HistoricalAwards=false
• 关键词: Hybrid; Deterministic; Stochastic; Methodology; Simulating

The goal of this project is to develop new computational methods to study the growth and spread of initially small mutant populations that drive biological phenomena like spread of antibiotic resistance or development of treatment resistant tumors. One notoriously difficult problem in evolutionary simulations is the coexistence of very large and very small populations. This is a common occurrence, because random mutations give rise to relatively small clones, which could play an important role in evolution. For example, these small clones could at some later time harbor further mutations that lead to the formation of a 'super-mutant,' which eventually takes over the population. It is the simulation of such scenarios that presents serious computational problems, because the larger the overall population, the slower the computational process. In many realistic scenarios, further complications arise from spatial constraints. Examples include solid tumors and biofilms--bacterial communities with complex spatial structures, implicated both in public health and in industry. To illustrate application of the computational techniques, the optimization of melanoma (skin cancer) treatment will be studied in the presence of resistant mutants that have developed 'addiction' to the drug. Mathematics can guide how the on/off periods of therapy need to be timed to contain resistance. Similar considerations apply to antibiotic-resistant bacteria. Complementing the research will be efforts to introduce under-represented minority high-school students to the process of scientific inquiry through a summer school, with the opportunity to work on projects in computational biology. At the center of enhancing computational speed is the development of a versatile technique capable of efficiently simulating large heterogeneous stochastic populations. Spatial agent-based models of cellular growth will be considered that are common to a wide variety of ecological and evolutionary modeling endeavors. They take into account the processes of cell division and death, as well as mutations and spatial interactions. Deterministic (PDE) approximations of such spatial, stochastic processes generally do not yield accurate time series. In this project, first, deterministic representations of the agent-based models will be constructed by deriving the stochastic master equation of the agent-based model and using the moment closure techniques. This step will provide a fundamental correction to equations based on mean-field behavior. Then, a spatial hybrid stochastic-deterministic algorithm will be developed. The main problem is the 'stiffness' of typical evolutionary systems, resulting from the existence of small, fluctuating populations that can be essential to the final outcome. In traditional methods, this leads to a dramatic decrease of the step size for large populations. Here, a solution to this problem is proposed, by dynamically partitioning the population into small and large subpopulations, with the assumptions that large subpopulations are well described by deterministic laws and are decoupled from the influence of small subpopulations, while the stochasticity of small subpopulations is preserved (and the large populations still affect their dynamics). These approaches will enable simulation of evolutionary processes in large, multi-component, spatially structured evolutionary processes at manageable speeds.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.

该项目的目标是开发新的计算方法来研究最初较小的突变群体的生长和传播，这些突变群体驱动生物学现象，如抗生素耐药性的传播或耐药肿瘤的发展。 在进化模拟中，一个众所周知的难题是非常大和非常小的种群共存。这是一种常见的现象，因为随机突变会产生相对较小的克隆，这可能在进化中发挥重要作用。例如，这些小的克隆体可能在以后的某个时候携带进一步的突变，导致形成“超级突变体”，最终接管种群。正是对这种情景的模拟提出了严重的计算问题，因为总人口越大，计算过程就越慢。在许多现实的情况下，空间限制会带来进一步的复杂性。实例包括实体肿瘤和生物膜-具有复杂空间结构的细菌群落，涉及公共卫生和工业。为了说明计算技术的应用，将在对药物产生“成瘾”的耐药突变体存在的情况下研究黑色素瘤（皮肤癌）治疗的优化。数学可以指导治疗的开/关期需要如何定时以控制阻力。类似的考虑也适用于抗药性细菌。作为对研究的补充，将努力通过暑期学校向代表性不足的少数民族高中生介绍科学探究过程，并有机会从事计算生物学项目。在提高计算速度的中心是一个通用的技术，能够有效地模拟大型异质随机人口的发展。基于空间代理的细胞生长模型将被认为是常见的各种生态和进化建模的努力。它们考虑了细胞分裂和死亡的过程，以及突变和空间相互作用。这种空间随机过程的确定性（PDE）近似通常不会产生准确的时间序列。在这个项目中，首先，基于代理的模型的确定性表示将通过推导基于代理的模型的随机主方程，并使用矩封闭技术。这一步将提供一个基本的修正方程的基础上平均场的行为。然后，将开发一种空间混合随机-确定性算法。主要问题是典型进化系统的“刚性”，这是由于存在对最终结果至关重要的小的、波动的种群。在传统的方法中，这导致大群体的步长急剧减小。在这里，这个问题的解决方案，提出了动态划分的人口成小，大亚群，假设大亚群是很好地描述了确定性的法律和解耦的影响，小亚群的随机性被保存（和大人口仍然影响他们的动态）。这些方法将使大型的，多组件的，空间结构的进化过程在可控的speaker.This奖项反映了NSF的法定使命的进化过程的模拟，并已被认为是值得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的支持。

项目成果

Laws of Spatially Structured Population Dynamics on a Lattice

格子上空间结构种群动态规律

• DOI: 10.3390/physics4030052
• 发表时间: 2022
• 期刊: Physics
• 影响因子: 1.6
• 作者: Komarova, Natalia L.;Rodriguez-Brenes, Ignacio A.;Wodarz, Dominik
• 通讯作者: Wodarz, Dominik

Mutant Evolution in Spatially Structured and Fragmented Expanding Populations

空间结构和碎片化扩张种群的突变进化

• DOI: 10.1534/genetics.120.303422
• 发表时间: 2020
• 期刊: Genetics
• 影响因子: 3.3
• 作者: Wodarz, Dominik;Komarova, Natalia L.
• 通讯作者: Komarova, Natalia L.