Mathematical Foundations for Nonlinear, Stochastic & Hybrid Biochemical Networks

描述（由申请人提供）：本提案旨在继续发展和增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不断增长。它们的准确有效的模拟需要新的算法和新的软件。多伊尔PI和博士的合作。Petzold （UCSB， DASSL的创造者）和Dan Gillespie（随机模拟算法的创造者）领导了确定性/随机模拟联合算法的发展，这种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规模。该计划将支持Gillespie博士继续研究和在生产质量的开源软件模块中实现新算法，这些软件模块将被广泛使用。(2) SOSTOOLS的延伸。加州理工学院最近的研究发展了分析模型的数学，比如“这个模型不能解释任何一组貌似合理的参数的数据”和“这个模型在参数变化时是稳健的”。该理论建立在几个领域的进步之上，包括鲁棒控制和动力系统理论、计算复杂性、真正的半代数几何、半定规划和对偶性。这项工作的结果是一种新的可扩展算法，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，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，以开发生物特异性结构，处理随机模型以补充模拟，与Savageau的s系统形式化建立联系，从数据中进行模型验证，并为非线性生化模型开发可证明正确的模型约简。(3)随机模拟与SOS分析相结合。分析复杂的随机生化网络将需要模拟和SOS分析以及模型简化的混合，该计划将创建一套具有严格理论基础的集成软件工具。

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.