DynSyst_Special_Topics: Polynomial Dynamical s Systems Over Finite Fields: From Structure to Dynamics

DynSyst_Special_Topics：有限域上的多项式动力学系统：从结构到动力学

• 批准号: 0908201
• 负责人: Reinhard Laubenbacher
• 金额: $ 27.79万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908201&HistoricalAwards=false
• 关键词: DynSyst_Special_Topics; Polynomial; Dynamical; Systems; Over

Progress in our understanding of increasingly complex engineered and natural systems depends crucially on the use of mathematical models as the basis for computational analysis and prediction. Such models allow the simulation on a computer of dynamic processes that are driven by several different interacting forces. This is true in particular for systems studied in the life sciences, which form the basis for advances in biomedicine and bioengineering. Molecular networks inside human cells which process external signals and drive cellular metabolism provide important examples of such processes. Relatively little is currently known about the design principles of such networks. One approach to gaining increased understanding is to study properties of the mathematical models that capture their key features. An understanding of the relationship between structural features of the models and the constraints these features put on model dynamics will allow the formulation of hypotheses about design features of biological networks based on observed dynamics. These hypotheses can then be tested in the laboratory. The goal of this project is to study the relationship between structure and dynamics for a type of model that has proven to be very useful in capturing key features of a variety of intracellular molecular networks. Beyond molecular networks, aspects of this model type have been used in electrical engineering and computer science, so this project might have an impact beyond the life sciences. Time-discrete dynamical systems models are ubiquitous not only in engineering but also the life sciences. Especially during the last decade finite dynamical systems, that is, time-discrete dynamical systems with a finite state space, have been used increasingly in systems biology to model a variety of biochemical networks, such as gene regulatory networks and signal transduction networks. In many cases, the available data quantity and quality is not sufficient to build detailed quantitative models such as systems of ordinary differential equations, which require many parameters that are frequently unknown. In addition, discrete models tend to be more intuitive and more easily accessible to life scientists. The premise of this project is that polynomial dynamical systems over finite fields form a unified, mathematically rich class of dynamical systems that are increasingly used in systems biology. The goal of the project is to establish results that relate their structure to their dynamics. To obtain strong results it is necessary to focus on specific families of such systems. The choice for this project is the class of Boolean networks constructed from so-called nested canalyzing functions, and their multi-state generalizations. Many regulatory mechanisms in molecular biology can be described by such functions, and the resulting networks have good dynamic properties.

我们在理解日益复杂的工程和自然系统方面取得的进展，关键取决于使用数学模型作为计算分析和预测的基础。这样的模型允许在计算机上模拟由几种不同的相互作用力驱动的动态过程。这对于生命科学研究的系统来说尤其如此，这些系统构成了生物医学和生物工程进步的基础。人类细胞内处理外部信号和驱动细胞新陈代谢的分子网络提供了这种过程的重要例子。目前，人们对此类网络的设计原理知之甚少。获得更多理解的一种方法是研究数学模型的属性，这些属性捕捉到了它们的关键特征。了解模型的结构特征和这些特征对模型动力学的约束之间的关系，将允许根据观察到的动力学提出关于生物网络设计特征的假设。然后，这些假说就可以在实验室中得到验证。这个项目的目标是研究一种模型的结构和动力学之间的关系，该模型已被证明在捕捉各种细胞内分子网络的关键特征方面非常有用。除了分子网络，这种模型类型的方面已经被用于电气工程和计算机科学，所以这个项目可能会产生超出生命科学的影响。时间离散动力系统模型不仅在工程中普遍存在，在生命科学中也是如此。特别是在过去的十年里，有限动力系统，即具有有限状态空间的时间离散动力系统，在系统生物学中被越来越多地用于模拟各种生化网络，如基因调控网络和信号转导网络。在许多情况下，可用的数据量和质量不足以建立详细的量化模型，如常微分方程组，这些模型需要许多经常未知的参数。此外，离散模型往往更直观，更容易为生命科学家所用。这个项目的前提是有限域上的多项式动力系统形成了一类统一的、数学上丰富的动力系统，这类动力系统在系统生物学中越来越多地使用。该项目的目标是建立将它们的结构与它们的动态联系起来的结果。为了取得强有力的成果，有必要把重点放在这类系统的具体家族上。这个项目的选择是由所谓的嵌套分析函数及其多态推广构造的布尔网络类。分子生物学中的许多调控机制都可以用这样的函数来描述，由此产生的网络具有良好的动力学特性。