Studies In Applied Mathematics And Statistics

应用数学和统计学研究

• 批准号: 7296860
• 负责人: George H Weiss
• 金额: --
• 依托单位: CENTER FOR INFORMATION TECHNOLOGY
• 依托单位国家: 美国
• 资助国家: 美国
• 起止时间: 至
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/7296860
• 关键词: Studies; Applied; Mathematics; Statistics

Different parts of this project involves collaborative work with NIH scientists, in which sophisticated mathematical tools or an acquaintance with theoretical methods in the physical sciences are required for the research. Mainly these methods require an intimate acquaintance with techniques developed in statistical physics. To rationalize data on the partioning of PEG-3400 in the alpha-hemolysin channel as a function of function of polymer concentration we have developed a theory of polymer partitioning in cylindrical pores in non-ideal polymer solutions. The theory explains the highly nonlinear increase of partitioning with polymer concentration which has been observed in experiments. We discovered a very general property of particle dynamics in channels and similar systems, namely that the distributions of times spent in the channel by particles traversing the channel in opposite directions are always identical in spite of the fact that the translocation probabilities may be quite different. We developed an approach to extract information related to molecular transitions (e.g., protein folding, ligand dissociation, DNA unzipping) from single-molecule force experiments based on Kramers' theory of diffusive barrier crossing. The theory has been applied to experimental data on nanopore unzipping of individual DNA hairpin molecules. We have obtained simple analytical expressions for the time-dependent rate coefficients of diffusion-influenced reactions in the presence of spherically symmetric potentials. These should prove useful in the analysis of experimental data for essentially irreversible reactions such as fluorescence quenching.

该项目的不同部分涉及与 NIH 科学家的合作，其中研究需要复杂的数学工具或熟悉物理科学的理论方法。这些方法主要需要熟悉统计物理学中开发的技术。 为了使 PEG-3400 在 α-溶血素通道中的分配数据合理化为聚合物浓度的函数，我们开发了非理想聚合物溶液中圆柱形孔中聚合物分配的理论。该理论解释了实验中观察到的分配随聚合物浓度的高度非线性增加。 我们发现了通道和类似系统中粒子动力学的一个非常普遍的性质，即尽管易位概率可能相差很大，但沿相反方向穿过通道的粒子在通道中所花费的时间分布总是相同的。 我们开发了一种方法，根据 Kramers 的扩散势垒穿越理论，从单分子力实验中提取与分子转变（例如蛋白质折叠、配体解离、DNA 解压缩）相关的信息。该理论已应用于单个 DNA 发夹分子纳米孔解链的实验数据。 我们获得了在球对称势存在的情况下受扩散影响的反应的时间相关速率系数的简单解析表达式。这些在分析基本上不可逆反应（例如荧光猝灭）的实验数据时应该是有用的。