Bifurcations of Equilibria in DNA Elasticity

DNA 弹性平衡的分歧

• 批准号: 0514470
• 负责人: Bernard Coleman
• 金额: --
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0514470&HistoricalAwards=false
• 关键词: Bifurcations; Equilibria; DNA; Elasticity

For many problems in the theory of DNA elasticity, a DNA molecule can be treated as though it is a rod-like structure obtained by stacking dominoes one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. In molecular biology these "dominoes" are called base pairs, because each is formed by joining together with hydrogen bonds two nearly planar complementary nucleotide bases. Both the intrinsic geometry (e.g., curvature in the stress-free state) and the elastic properties (e.g., moduli governing bending, twisting, shearing, and coupling between such modes of deformation) are sensitive to the nucleotide sequence in the DNA molecule. Each base pair is covalently attached to the sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson-Crick structure, and as each phosphate group in the backbone chain bears one electronic charge, two such charges are associated with each base pair. The electrical force exerted on each base pair depends on the concentration of salt in the medium and the position in space of even remotely placed base pairs in the same DNA molecule. Calculations based on this model performed under a previous NSF grant indicate that the equilibrium configurations of an intrinsically curved DNA molecule in solution are very sensitive to the concentration c of salt in the medium. Bifurcation diagrams with c as the parameter can have great complexity and, under appropriate circumstances, contain regions in which several locally stable equilibrium configurations (each giving the molecule a distinct shape) occur at a single value of c. The goal of this project is to develop the mathematical theory of the model to the point where its conclusions are easily capable of experimental testing (e.g., by predicting that for particular DNA sequences experimentally detectable changes in configuration should occur at values of c near to calculated critical values).The attainment of a well developed theory of the influence of long-range electrostatic forces, and hence of changes in salt concentration, on the configurations of intrinsically curved (and in general non-homogeneous) DNA molecules is a matter of general interest in biophysics that has implications in bioengineering. The research in this project is expected to have applications to microdevices for imaging and sorting genomic-length DNA molecules. In one such device the DNA is elongated by confinement to a channel with a width of 0.1 microns, and the computational methods to be developed will aid in the attainment of an understanding of the way the amount of extension experienced by DNA confined in such a channel is related to the channel diameter, the concentration of salt, and the intrinsic curvature of the DNA. Another application of the theory is the investigation of the possibility that circularized molecules of DNA formed from appropriate sequences of several hundred base-pairs can serve as mesoscale mechano-chemical switches that undergo large changes in configuration upon small changes in salt concentration.

对于DNA弹性理论中的许多问题，DNA分子可以被看作是一个棒状结构，它是通过将多米诺骨牌一个叠在另一个的顶部而获得的，每个多米诺骨牌相对于其在堆栈中的直接前任旋转大约十分之一整圈。在分子生物学中，这些“多米诺骨牌”被称为碱基对，因为每一个都是通过氢键将两个几乎平面互补的核苷酸碱基连接在一起形成的。固有几何形状（例如，无应力状态下的曲率）和弹性特性（例如，控制弯曲、扭曲、剪切和这些变形模式之间的耦合的模量）对DNA分子中的核苷酸序列敏感。每个碱基对共价连接到两条DNA链之一的糖-磷酸主链上，这两条DNA链聚集在一起形成沃森-克里克结构，并且由于主链中的每个磷酸基团携带一个电子电荷，因此每个碱基对与两个这样的电荷相关联。施加在每个碱基对上的电场力取决于介质中盐的浓度，以及同一DNA分子中即使相距较远的碱基对在空间中的位置。基于该模型的计算表明，在溶液中的固有弯曲的DNA分子的平衡构型对介质中盐的浓度C非常敏感。以c为参数的分叉图可能具有很大的复杂性，在适当的情况下，包含几个局部稳定的平衡构型（每一个都赋予分子不同的形状）出现在一个单一的c值的区域。 该项目的目标是将模型的数学理论发展到其结论易于进行实验测试的程度（例如，通过预测对于特定的DNA序列，实验上可检测的构型变化应该发生在接近计算临界值的c值处）。关于内在弯曲的DNA分子（并且通常是非均质的）是生物物理学中普遍感兴趣的问题，其在生物工程中具有意义。该项目的研究预计将应用于成像和分选基因组长度DNA分子的微型设备。在一个这样的装置中，DNA通过限制在宽度为0.1微米的通道中而伸长，并且待开发的计算方法将有助于理解限制在这样的通道中的DNA所经历的延伸量与通道直径、盐浓度和DNA的固有曲率相关的方式。 该理论的另一个应用是研究由数百个碱基对的适当序列形成的环状DNA分子可以作为介观机械化学开关的可能性，该开关在盐浓度的微小变化时经历构型的巨大变化。