Numerical Methods for Models of Biological Systems

生物系统模型的数值方法

• 批准号: RGPIN-2019-06946
• 负责人: Stinchcombe, Adam
• 金额: $ 1.17万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=739201
• 关键词: Numerical; Methods; Models; Biological; Systems

After experimentation and theory, computation is the third pillar of the scientific method. Especially in biology, computer simulations are used to understand phenomena, suggest illuminating and cost-effective experiments, and make predictions. Increasingly, our understanding of biological systems is being encapsulated in simulations. The incredible amount of available experimental data and a desire to have very detailed models necessitates having fast, accurate, and parallelizable numerical methods. Mathematics plays an essential role in creating and analysing numerical methods. I am developing numerical methods for large systems of ordinary differential equations that describe the electrical activity of and genetic-biochemical reaction networks in populations of cells. Examples of biological systems that couple genetics, biochemistry, and electrophysiology are the circadian (approximately 24) clock, the retina, and nearly all developmental processes. Populations of coupled oscillators are common in biological systems and have historically been the focus of mathematical analysis and simulation. Oscillator populations include the pacemaker of the heart, pancreatic islets that secrete insulin, populations of fireflies, and many regions of the brain. A numerical method of my creation, the population density particle method, enables fast and accurate simulation of populations of noisy coupled oscillators. I am working to make this method more broadly applicable, improve its performance, and put it on a sound theoretical foundation. With some modification, this method can also be used for parameter fitting, a common task for modellers. I am also studying a random walk based numerical method for partial differential equations that describe hydrodynamics, electrodiffusion, and spatially extended biochemical reactions. When these equations model biological systems, it is often the case that intricate boundaries and complicated boundary conditions prevent simulations from being fast or accurate. I expect my approach to overcome the challenges associated with boundaries. I will investigate high order methods for numerically stiff ordinary differential equations, parallelizable methods, pre-computation techniques, using graphical processing units for acceleration, low-rank approximation, machine learning techniques, grid-free methods, particle methods, and random walk methods to address numerical challenges commonly faced when simulating biological models. This will result in faster and more accurate simulations that will ultimately enable new insights into many biological problems. I will publicly distribute quality, usable implementations of my numerical methods so that they may be used as building blocks by others, creating a community of scientific discovery.

在实验和理论之后，计算是科学方法的第三支柱。特别是在生物学中，计算机模拟被用来理解现象，提出具有启发性和成本效益的实验，并做出预测。我们对生物系统的理解越来越多地被封装在模拟中。令人难以置信的大量可用实验数据和对非常详细的模型的渴望需要快速、准确和可并行化的数值方法。数学在创造和分析数值方法方面起着至关重要的作用。我正在为描述细胞群体中的电活动和遗传-生化反应网络的常微分方程组的大型系统开发数值方法。将遗传学、生物化学和电生理学结合起来的生物系统的例子有生物钟(大约24小时)、视网膜和几乎所有的发育过程。耦合振子种群在生物系统中很常见，历来都是数学分析和模拟的焦点。振荡器种群包括心脏的起搏器、分泌胰岛素的胰岛、萤火虫种群和大脑的许多区域。我创造的一种数值方法，布居密度粒子法，能够快速而准确地模拟噪声耦合振子的布居。我正在努力使这种方法更广泛地适用，提高其性能，并将其建立在坚实的理论基础上。经过一些修改，这种方法也可以用于参数拟合，这是建模人员的一项常见任务。我还在研究一种基于随机游走的数值方法，用于描述流体动力学、电扩散和空间扩展的生化反应的偏微分方程组。当这些方程模拟生物系统时，复杂的边界和复杂的边界条件通常会阻碍模拟的快速或准确。我希望我的方法能克服与边界相关的挑战。我将研究数值刚性常微分方程式的高阶方法、可并行化方法、预计算技术、使用用于加速的图形处理单元、低阶近似、机器学习技术、无网格方法、粒子方法和随机游走方法，以解决在模拟生物模型时经常面临的数值挑战。这将导致更快、更准确的模拟，最终将使人们能够对许多生物学问题有新的见解。我将公开发布我的数值方法的高质量、可用的实现，以便其他人可以将它们用作构建块，创建一个科学发现社区。