Mathematical modeling, analysis and computation arising in continuum mechanical descriptions of DNA

DNA 连续力学描述中出现的数学建模、分析和计算

• 批准号: 0102476
• 负责人: Oscar Gonzalez
• 金额: $ 10.2万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0102476&HistoricalAwards=false
• 关键词: Mathematical; modeling; analysis; computation; arising

Gonzalez0102476 The investigator studies constitutive relations forcontinuum rod models of DNA and develops new tools for analyzingthe supercoiling and packaging of DNA and other materialfilaments. The main objectives of the project are to apply thetheories of statistical mechanics and stochastic differentialequations to develop constitutive relations for continuum rodmodels of DNA that are provably consistent with detailed,sequence-dependent structural information at the base-pair level;to apply the new concept of global curvature to develop ageometrically exact and computationally tractable formulation ofthe self-contact constraint that plays a central role in thesupercoiling and packaging of DNA and other biological filaments;and to develop efficient and provably accurate computationalmethods for continuum rod models that faithfully respect globalgeometric constraints as well as qualitative features of theunderlying system. Biologists and chemists now believe that the linear sequenceof base-pairs along a DNA molecule contains not only a geneticcode, but also a structural code that governs the globalorganization of the molecule and its susceptibility tointeractions with other molecules. An understanding of thisstructural code requires realistic mechanical models of DNA overa wide range of length scales. The research project pursued bythe investigator is aimed at the further refinement of medium- tolong-scale continuum models. In particular, methods aredeveloped for estimating local, sequence-dependent materialparameters and for describing global, finite-thickness effects.Results from this research will be useful in developing a greaterunderstanding of the physical and mechanical properties of DNA,in modeling how DNA may twist, bend and supercoil upon itself,and in studying how DNA and other material filaments may beoptimally packed in confined geometries.

冈萨雷斯0102476 研究人员研究了DNA的连续杆模型的本构关系，并开发了分析DNA和其他材料细丝的超螺旋和包装的新工具。 该项目的主要目标是应用统计力学和随机微分方程的理论，为DNA的连续杆模型建立本构关系，这些模型可证明与碱基对水平上的详细的、依赖于序列的结构信息一致;应用全局曲率的新概念，发展了几何精确的和计算易处理的自接触约束在DNA和其他生物细丝的螺旋盘绕和包装中起着核心作用;并为连续体杆模型开发有效和可证明准确的计算方法，忠实地尊重全局几何约束以及底层系统的定性特征。 生物学家和化学家现在认为，DNA分子中沿着的碱基对线性序列不仅包含遗传密码，而且还包含结构密码，它控制着分子的整体结构及其与其他分子相互作用的敏感性。 要理解这种结构密码，需要在大范围的长度尺度上建立DNA的真实力学模型。 研究者所从事的研究项目旨在进一步完善中长期尺度的连续体模型。 特别是，方法被开发用于估计本地，序列相关的materialparameters和用于描述全局，有限厚度的effects.结果，从这项研究将是有用的，在开发一个更好的理解DNA的物理和机械性能，在建模如何DNA可能扭曲，弯曲和supercoil在自己，并在研究如何DNA和其他材料细丝可能bestoptimally包装在有限的几何形状。