Realization Theory and Functional Model Reduction in Biochemical Networks

目的系统生物学新兴领域的核心问题之一是大型复杂生化反应网络的分析和功能分类。这类网络正受到越来越多的仔细审查，它们的各个组成部分也被煞费苦心地详细调查。然而，从详细的网络描述中推断动态和功能行为的一般方法仍然非常缺乏。我们提出了一种方法，通过这种方法，这种网络的大型组件可以被具有类似功能的小得多的状态维度的组件所取代。我们将这个问题称为功能模型简化，以强调与传统模型简化技术的区别。这种方法背后的支持思想包括理解为规定功能（如逻辑或混合操作）而设计的动态系统如何能够通过具有特定类型构建块的动态网络来实现。我们调查它的具体背景下，可从基本的生化动力学构建块。有了这种分析，我们提出了反向进行这种分析的问题，也就是说，给定具有特定类型构建块的网络，我们询问它们代表什么类型的功能行为，以及是否有可能用低得多的动力系统来反映这种行为。我们的目标不是开发一种一般的非线性模型简化技术，而是一种专门针对生化动力学产生的微分方程的技术。需要开发系统理论的一些新方面，如预先指定网络组件的实现以及模型简化的功能目标。从生化反应网络的详细描述中揭示和分类功能是系统生物学和动力系统理论的核心问题。提出的工作将有助于技术，特别是量身定制的动态网络，从生化动力学产生。提出了一种基于网络函数的模型约简新范式。更广泛的影响这项工作的更广泛的影响包括将该项目开发的模型还原技术应用于正在开发的高阶缺血性中风复杂模型，这将使人们对这种疾病有新的认识和新的治疗方法成为可能。这项工作的多学科性质将确保来自动力系统和控制的研究生以及来自生命科学的研究生将从其他学科发展新的技能，并将帮助培养能够在其学科边界工作的毕业生。

Eccs-0802008BamiehObjectiveOne of the central problems in the emerging field of Systems Biology is the analysis and functional classification of large complex biochemical reaction networks. Such networks are increasingly being scrutinized and their individual components painstakingly investigated in detail. However, a general methodology for inferring dynamical and functional behavior from the detailed network description is still sorely lacking. We propose methodologies by which large components of such networks can be replaced by components of much smaller state dimension that have similar functionality. We term this problem Functional Model Reduction to emphasize distinctions with traditional model reduction techniques. The enabling ideas behind this methodology consist of understanding how dynamical systems that are designed for prescribed functions (such as logical or hybrid operations) can be implemented with dynamical networks constrained to have specific types of building blocks. We investigate it in the specific context of building blocks that are available from basic biochemical kinetics. Enabled with this analysis, we pose the problem of carrying out this analysis in reverse, that is, given networks with specific types of building blocks, we ask what type of functional behavior they represent, and whether it is possible to mirror that behavior with dynamical system of much lower dimension. Our goal is not to develop a general nonlinear model reduction technique, but rather one that is particularly tailored to the differential equations that result from biochemical kinetics. Some novel aspects of systems theory will need to be developed such as realizations with prespecified network components as well as functional objectives for model reduction.Intellectual MeritUncovering and classification of function from the detailed description of biochemical reaction networks is a central problem in systems biology and dynamical systems theory. The proposed work will contribute techniques that are particularly tailored to the dynamical network that arise from biochemical kinetics. A new paradigm for model reduction based on network function will be developed.Broader ImpactThe broader impacts of this work include the application of the model reduction techniques developed in this project to a high order complex model of ischemic stroke that is being developed, which will make possible new understanding of this disease and new treatments for it. The multi-disciplinary nature of this work will ensure that graduate students from dynamical systems and control and those from the life sciences will develop new skill sets from the other disciplines and will help create graduates who are comfortable working at the boundary of their disciplines.