Mathematical Foundations for Nonlinear, Stochastic & Hybrid Biochemical Networks

非线性、随机的数学基础

• 批准号: 7161840
• 负责人: JOHN C DOYLE
• 金额: $ 36.28万
• 依托单位: CALIFORNIA INSTITUTE OF TECHNOLOGY
• 依托单位国家: 美国
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-05-01 至 2010-04-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7161840
• 关键词: chemical models; computational biology; computer program /software; computer system design /evaluation; mathematical model; model design /development; statistics /biometry

DESCRIPTION (provided by applicant): This proposal is for continued development and enhancement of existing and successful theory and software infrastructure developed at Caltech for the systems biology community, and builds on experience with SBML and engineering softwared. (1) Next-generation, multiscale, deterministic/stochastic simulation software. Computational models in biology are continually growing in complexity and size. Their accurate and effective simulation requires new algorithms and new software. Collaboration between the PI Doyle and Drs. Petzold (UCSB, creator of DASSL) and Dan Gillespie (creator of the stochastic simulation algorithm) have led to the development of combined deterministic/stochastic simulation algorithms that are much more efficient than existing stochastic algorithms, and can automatically determine the appropriate scale for different subsystems of a model. This program will support Dr. Gillespie's continued research and implementation of new algorithms in production-quality open-source software modules that will be made widely available. (2) Extension of SOSTOOLS. Recent Caltech research has developed mathematics for analyzing models, such as "this model cannot explain the data for any set of plausible parameters" and "this model is robust as parameters are varied." The theory builds on advances in several areas, including robust control and dynamical systems theory, computational complexity, real semi-algebraic geometry, semidefinite programming, and duality. The result of this work has been a new class of scalable algorithms for model analysis and (in)validation and iterative experimentation for large-scale, stochastic, nonlinear, nonequilibrium, hybrid (containing both continuous and discrete mathematics) networks with multiple time and spatial scales. The recent progress is implemented in SOSTOOLS, an open-source (GPL) MATLAB toolbox. This program will enhance and extend SOSTOOLS to exploit biological specific structure, treat stochastic models to complement simulation, make connections with Savageau's S-system formalism, perform model (in)validation from data, and develop provably correct model reduction for nonlinear biochemical models. (3) Integration of stochastic simulation and SOS analysis. Analysis of complex stochastic biochemical networks will require a blend of simulation and SOS analysis and model reduction, and this program will create an integrated suite of software tools with rigorous theoretical foundations.

描述(由申请人提供)：本提案是为了继续发展和加强加州理工学院为系统生物学社区开发的现有和成功的理论和软件基础设施，并建立在SBML和工程软件的经验基础上。(1)下一代、多尺度、确定性/随机模拟软件。生物学中的计算模型在复杂性和规模上都在不断增长。它们的准确和有效的模拟需要新的算法和新的软件。Pi Doyle和Petzold博士(UCSB，DASSL的创建者)和Dan Gillesbie(随机模拟算法的创建者)之间的合作导致了组合确定性/随机模拟算法的开发，这些算法比现有的随机算法效率高得多，并且可以自动确定模型不同子系统的适当比例。该计划将支持吉莱斯皮博士继续研究和实施生产质量的开源软件模块中的新算法，这些模块将被广泛使用。(2)SOSTOOLS的扩展。加州理工学院最近的研究已经开发出用于分析模型的数学方法，例如“这个模型不能解释任何一组合理参数的数据”和“这个模型是健壮的，因为参数是变化的。”该理论建立在几个领域的进展基础上，包括鲁棒控制和动态系统理论、计算复杂性、实半代数几何、半定规划和对偶。这项工作的结果是形成了一类新的可扩展的算法，用于多时间和空间尺度的大规模、随机、非线性、非平衡、混合(包括连续和离散数学)网络的模型分析、验证和迭代实验。最新的进展是在开源(GPL)的MatLab工具箱SOSTOOLS中实现的。该程序将增强和扩展SOSTOOLS，以开发生物特有的结构，处理随机模型来补充模拟，与萨瓦乔的S系统形式论相联系，从数据中执行模型验证，并开发可证明正确的非线性生化模型的模型降阶。(3)随机模拟与SOS分析相结合。对复杂的随机生化网络的分析将需要将模拟、SOS分析和模型简化结合在一起，该程序将创建一套具有严格理论基础的集成软件工具。