Numerical Methods with Applications to Biochemical Networks

数值方法及其在生化网络中的应用

• 批准号: RGPIN-2020-05469
• 负责人: Ilie, Silvana
• 金额: $ 1.31万
• 依托单位: Ryerson University
• 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=740608
• 关键词: Numerical; Methods; Applications; Biochemical; Networks

My research is in the area of numerical analysis and scientific computing. The main objectives of this proposal are to develop and analyze numerical methods for approximating the solution of mathematical models of well-stirred and spatially distributed biochemical networks. This research will contribute to the improvement of existing software and will allow researchers in a crucial area of life sciences to solve more challenging problems than was previously possible, to effectively and reliably approximate the solution to their models and to analyze and predict the behaviour of complex systems. In the past, my research focused on the development of efficient strategies for solving numerically initial value problems for stochastic models of well-stirred and spatially distributed biochemical networks and initial value problems for differential algebraic equations. The application of mathematical modelling and simulations to study critical biological processes is an exciting and new area of research. Stochastic models of biochemical networks are of high interest today, due to their wide variety of important practical applications. Often, these mathematical models are highly complex. They may be non-linear and exhibit mathematical stiffness, due to the presence of multiple scales in time and molecular population numbers. Typically, such models cannot be solved by analytic mathematical tools. Then, numerical strategies are necessary to approximate their solution. Designing fast simulation techniques for studying complex stochastic models of biochemical systems which are also stiff is a challenging task. This proposal aims to (1) extend my previous work on stochastic models of well-stirred and spatially distributed biochemical systems, to improve the numerical methods for biologically relevant models, using adaptive time-stepping schemes and higher-order techniques, (2) design hybrid methods for approximating the solution of discrete stochastic models of reaction-diffusion systems, (3) develop effective and accurate strategies for sensitivity analysis of discrete stochastic models of biochemical systems, and (4) construct reliable and effective numerical techniques for identifiability analysis of discrete stochastic biochemical kinetic models.

我的研究领域是数值分析和科学计算。该提案的主要目标是开发和分析数值方法，用于近似求解良好搅拌和空间分布的生化网络的数学模型。这项研究将有助于改进现有软件，并使生命科学关键领域的研究人员能够解决比以前更具挑战性的问题，有效可靠地近似其模型的解决方案，并分析和预测复杂的行为系统。过去，我的研究重点是开发有效的策略来解决充分搅拌和空间分布的生化网络随机模型的数值初值问题以及微分代数方程的初值问题。 应用数学建模和模拟来研究关键的生物过程是一个令人兴奋的新研究领域。生化网络的随机模型由于其广泛的重要实际应用而引起了人们的高度关注。通常，这些数学模型非常复杂。由于时间和分子群体数量的多个尺度的存在，它们可能是非线性的并且表现出数学刚性。通常，此类模型无法通过分析数学工具来求解。然后，需要数值策略来近似其解决方案。设计快速模拟技术来研究生化系统的复杂随机模型也是一项具有挑战性的任务。 该提案的目的是（1）扩展我之前在充分搅拌和空间分布的生化系统的随机模型方面的工作，使用自适应时间步进方案和高阶技术改进生物相关模型的数值方法，（2）设计用于近似求解反应扩散系统离散随机模型的混合方法，(3) 开发有效且准确的生化系统离散随机模型敏感性分析策略，以及 (4) 构建可靠且有效的数值技术离散随机生化动力学模型的可识别性分析。