Mathematical Foundations for Nonlinear, Stochastic & Hybrid Biochemical Networks

非线性、随机的数学基础

• 批准号: 7482413
• 负责人: JOHN C DOYLE
• 金额: $ 33.85万
• 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/7482413
• 关键词: Algorithms; Area; Biochemical; Biological; Biology; Class; Collaborations; Communities; Complement; Complex; Computer Simulation; Computer software; Data; Development; Engineering; Foundations; Hybrids; Mathematics; Modeling; Production; Research; Research Infrastructure; Software Tools; Son of Sevenless Proteins; Structure; System; Systems Biology; Systems Theory; Time; Validation; Work; biochemical model; experience; implementation research; next generation; open source; programs; simulation; size; theories

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）：该提案旨在继续开发和增强加州理工学院为系统生物学界开发的现有且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。生物学计算模型的复杂性和规模不断增长。他们准确有效的模拟需要新的算法和新的软件。 PI Doyle 和 Drs 之间的合作。 Petzold（UCSB，DASSL 的创建者）和 Dan Gillespie（随机模拟算法的创建者）开发了组合确定性/随机模拟算法，该算法比现有随机算法高效得多，并且可以自动确定模型的不同子系统的适当规模。该计划将支持 Gillespie 博士在生产质量的开源软件模块中继续研究和实施新算法，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开发了用于分析模型的数学，例如“该模型无法解释任何一组看似合理的参数的数据”以及“随着参数的变化，该模型是稳健的”。该理论建立在多个领域的进步之上，包括鲁棒控制和动力系统理论、计算复杂性、实半代数几何、半定规划和对偶性。这项工作的成果是一类新的可扩展算法，用于具有多个时间和空间尺度的大规模、随机、非线性、非平衡、混合（包含连续和离散数学）网络的模型分析和（中）验证和迭代实验。最近的进展是在开源 (GPL) MATLAB 工具箱 SOSTOOLS 中实现的。该计划将增强和扩展 SOSTOOLS 以利用生物特定结构，处理随机模型以补充模拟，与 Savageau 的 S 系统形式主义建立联系，根据数据进行模型（内）验证，并为非线性生化模型开发可证明正确的模型简化。 (3)随机模拟与SOS分析的结合。复杂随机生化网络的分析需要将模拟和 SOS 分析以及模型简化相结合，该程序将创建一套具有严格理论基础的集成软件工具。