Numerical Methods with Applications to Biochemical Systems

数值方法及其在生化系统中的应用

• 批准号: RGPIN-2015-05723
• 负责人: Ilie, Silvana
• 金额: $ 1.02万
• 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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675423
• 关键词: Numerical; Methods; Applications; Biochemical; Systems

My research lies in the realm of numerical analysis and scientific computing. In the proposed research program, I plan to design and analyze numerical methods for approximating the solution of mathematical models of homogeneous and heterogeneous biochemical systems. This research will lead to improvement of existing software and will enable researchers in a key area of life sciences to model important biological processes much more productively, to effectively and reliably approximate the solution to their problems and to analyze and predict the behaviour of complex models. Previously, I developed efficient strategies for solving numerically initial value problems (IVP) for stochastic continuous models of homogeneous biochemical kinetics. In addition, I improved the computational cost of numerical algorithms for solving initial value problems for differential algebraic equations from existing exponential to polynomial cost.***Mathematical modelling and simulations provide indispensable tools for studying critical biological processes. In particular, stochastic models of biochemical kinetics are of high interest today due to their many important practical applications in life sciences that affect Canadians in many ways, including improving peoples' health. Most of these models are quite complex. They cannot be solved by analytic mathematical techniques and therefore numerical methods are required to approximate their solution. Often, these problems are nonlinear and exhibit mathematical stiffness, due to the presence of multiple interacting scales in time and molecular population amounts. Consequently, fast simulation of these models constitutes a difficult task. ***The objectives of this proposal are: (1) improving the speed of computation for solving numerically stochastic continuous and stochastic discrete models of homogeneous biochemical kinetics, by building adaptive time-stepping schemes (2) developing effective and accurate strategies for sensitivity analysis of discrete stochastic models of biochemical systems, (3) constructing more efficient and reliable schemes for approximating the solution of a stochastic discrete model of heterogeneous biochemical kinetics, that of the Reaction-Diffusion Master Equation, which prevent negative population numbers (4) designing strategies to overcome stiffness in the numerical integration of these models.**

我的研究属于数值分析和科学计算领域，我计划设计和分析用于近似求解同质和异质生化系统数学模型的数值方法。这项研究将改进现有软件。将使生命科学关键领域的研究人员能够更高效地对重要的生物过程进行建模，有效、可靠地近似解决他们的问题，并分析和预测复杂模型的行为。数值求解均相生化动力学随机连续模型的初始值问题 (IVP) 此外，我改进了求解微分代数方程初始值问题的数值算法的计算成本，从现有的指数成本改为多项式成本。***数学建模和模拟提供了。生化动力学的随机模型是研究关键生物过程不可或缺的工具，因为它们在生命科学中的许多重要实际应用影响着加拿大人。这些模型中的大多数都无法通过分析数学技术来解决，因此需要采用数值方法来近似其解决方案，并且由于其存在，这些问题通常是非线性的。经过检查，这些模型的快速模拟是一项艰巨的任务。 ***该提案的目标是：（1）提高求解数值随机连续和随机离散模型的计算速度。同质的生化动力学，通过构建自适应时间步长方案（2）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，（3）构建更有效和可靠的方案来逼近异质生化随机离散模型的解动力学，反应扩散主方程的动力学，它可以防止负总体数 (4) 设计策略来克服这些模型数值积分中的刚性。**