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）：该提案是为了持续开发和增强加州科技在系统生物学社区开发的现有理论和软件基础架构，并以SBML和工程软件的经验为基础。 （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大小上不断增长。它们的准确有效仿真需要新的算法和新软件。 Pi Doyle和Drs之间的合作。 Petzold（UCSB，DASSL的创建者）和Dan Gillespie（随机仿真算法的创建者）导致了合并的确定性/随机仿真算法的发展，这些算法比现有的随机算法要高得多，并且可以自动确定模型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持续研究和实施新算法，这些算法将被广泛使用。 （2）Sostools的扩展。最近的Caltech研究开发了用于分析模型的数学，例如“此模型无法解释任何一组合理参数的数据”和“随着参数的变化，该模型都有坚固耐用”。该理论基于多个领域的进步，包括稳健的控制和动力学系统理论，计算复杂性，实际半代数几何，半决赛编程和二元性。这项工作的结果是用于模型分析的新型可扩展算法，以及（在）大规模，随机，非线性，非平衡，混合动力（包含连续和离散数学）网络的验证和迭代实验，具有多个时间和空间尺度。最近的进度在Sostools（开源（GPL）MATLAB工具箱）中实现。该程序将增强和扩展Sostools以利用生物学特定结构，对待随机模型以补充模拟，与Savageau的S-System形式主义建立联系，从数据中执行模型（IN）验证，并为非线性生物化学模型开发可证明正确的模型。 （3）随机模拟和SOS分析的整合。对复杂随机生物化学网络的分析将需要模拟，SOS分析和模型降低的融合，并且该程序将创建一套具有严格理论基础的软件工具的集成套件。