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

Gonzalez0102476，研究人员研究了DNA连续棒模型的本构关系，并开发了分析DNA和其他材料细丝的超卷绕和包装的新工具。该项目的主要目标是应用统计力学和随机微分方程组的理论来建立DNA连续体杆状模型的本构关系，这些本构关系被证明与碱基对水平上详细的、依赖于序列的结构信息一致；应用全局曲率的新概念来推导在DNA和其他生物细丝的超级卷曲和包装中发挥核心作用的自接触约束的年龄计量精确和易于计算的公式；以及为连续杆状模型开发有效和经证明准确的计算方法，该方法忠实地尊重全局几何约束以及基本系统的质量特征。生物学家和化学家现在认为，DNA分子上的碱基对线性序列不仅包含一个遗传密码，还包含一个结构密码，该密码支配着该分子的全球组织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真实的DNA机械模型。研究人员所从事的研究项目旨在进一步完善中到长尺度连续介质模式。特别是，开发了用于估计局部的、与序列相关的材料参数和描述全局的有限厚度效应的方法。这项研究的结果将有助于更好地理解DNA的物理和力学性质，建模DNA如何在自身上扭曲、弯曲和超级卷曲，以及研究DNA和其他材料细丝如何以最佳的限制几何形状堆积。

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.