SGER: Dynamic Evolution of DNA Supercoils and Loops

Noel Perkins和埃德加Meyhofer机械工程美国密歇根大学Ann Arbor，MI 48109- 2125我们提出的研究采用非线性动力系统的方法来探索DNA的基本生物功能。关键的生物学功能，如复制和转录，受到DNA形状或“结构”的影响。这种非常长的分子（长度是直径的一千倍）非常灵活，它可以进行非线性运动，可以调节（即控制）基因表达。 例如，蛋白质可以迫使DNA片段进入阻止转录的环。此外，热能激发DNA的振动，导致超螺旋状态的变化可以促进转录。上述运动发生在非常长的长度尺度（数百至数万纳米）和非常长的时间尺度（微秒至毫秒），相对于原子尺寸（埃）和分子动力学速率（皮秒和更小）。我们的研究计划的长期目标是通过DNA结构动力学的新理论和实验来理解这些动力学过程。 一个有前途的动力学理论，长的长度/时间尺度如下从治疗的长链分子作为一个动态连续杆。我们研究计划的第一步是建立一个DNA超螺旋和环的非线性计算杆模型。要考虑的主要挑战包括1）非线性变形，2）空间非均匀性和各向异性（例如，“序列相关”刚度和“固有”曲率和扭曲），3）自接触/静电和缠绕，4）耗散，和5）有效的数值算法。然后，我们将在两个战略案例研究中使用我们的计算模型。第一个案例研究的重点是在最近的单分子实验中观察到的受控末端旋转的股超螺旋的动态演变。第二个案例研究探讨了当受到一种被称为lac阻遏物的结合蛋白质的影响时，DNA的成环。我们的跨学科研究团队拥有动力系统和分子生物学的必要背景，能够通过工程科学的先进方法对DNA动力学进行这些基础研究。

DYNAMIC EVOLUTION OF DNA SUPERCOILS AND LOOPSNoel Perkins and Edgar MeyhoferMechanical EngineeringUniversity of MichiganAnn Arbor, MI 48109-2125Our proposed research employs methods of nonlinear dynamical systems to explore the fundamental biological functions of DNA. Critical biological functions such as replication and transcription are influenced by the shape or "structure" of DNA. This very long molecule (length is thousand times longer than diameter) is extraordinarily flexible, and it can undergo nonlinear motions that can regulate (i.e. control) gene expression. For example, proteins can force segments of DNA into loops that prevent transcription. In addition, thermal energy excites vibrations of DNA and resulting changes in supercoiled states can promote transcription. The motions described above occur over very long length scales (hundreds to tens of thousands of nanometers) and on very long time scales (microsecond to millisecond) relative to atomic dimensions (angstrom) and molecular dynamic rates (picosecond and smaller). It is the long-term objective of our research program to understand these dynamical processes through novel theories and experiments on DNA structural dynamics. A promising dynamical theory for long length/time scales follows from treating the long chain molecule as a dynamic continuum rod. The first step in our research plan is to develop a nonlinear computational rod model for DNA supercoils and loops. Major challenges to be considered include 1) the nonlinear deformation, 2) spatial non-uniformity and anisotropy (e.g., "sequence-dependent" stiffness and "intrinsic" curvature and twist), 3) self-contact/electrostatics and interwinding, 4) dissipation, and 5) efficient numerical algorithms. We will then employ our computational model in two strategic case studies. The first case study focuses on the dynamic evolution of supercoils for strands subjected to controlled end rotation as observed in recent single molecule experiments. The second case study explores the looping of DNA when subjected to a bound protein known as the lac repressor. Our interdisciplinary research team, which possesses the requisite background in dynamical systems and molecular biology, is well-positioned to make these fundamental investigations of DNA dynamics by advancing methods from the engineering sciences.