Smith Alyssa L, Cekan Pavol, Rangel David P, Sigurdsson Snorri Th, Mailer Colin, Robinson Bruce H
Department of Chemistry, University of Washington, Seattle, Washington, USA.
J Phys Chem B. 2008 Jul 31;112(30):9219-36. doi: 10.1021/jp7111704. Epub 2008 Jul 2.
The weakly bending rod (WBR) model of double-stranded DNA (dsDNA) is adapted to analyze the internal dynamics of dsDNA as observed in electron paramagnetic resonance (EPR) measurements of the spin-lattice relaxation rate, R(1e), for spin probes rigidly attached to nucleic acid-bases. The WBR theory developed in this work models dsDNA base-pairs as diffusing rigid cylindrical discs connected by bending and twisting springs whose elastic force constants are kappa and alpha, respectively. Angular correlation functions for both rotational displacement and velocity are developed in detail so as to compute values for R(1e) due to four relaxation mechanisms: the chemical shift anisotropy (CSA), the electron-nuclear dipolar (END), the spin rotation (SR), and the generalized spin diffusion (GSD) relaxation processes. Measured spin-lattice relaxation rates in dsDNA under 50 bp in length are much faster than those calculated for the same DNAs modeled as rigid rods. The simplest way to account for this difference is by allowing for internal flexibility in models of DNA. Because of this discrepancy, we derive expressions for the spectral densities due to CSA, END, and SR mechanisms directly from a weakly bending rod model for DNA. Special emphasis in this development is given to the SR mechanism because of the lack of such detail in previous treatments. The theory developed in this paper provides a framework for computing relaxation rates from the WBR model to compare with magnetic resonance relaxation data and to ascertain the twisting and bending force constants that characterize DNA.
双链DNA（dsDNA）的弱弯曲杆（WBR）模型适用于分析dsDNA的内部动力学，这是在对刚性连接到核酸碱基上的自旋探针进行电子顺磁共振（EPR）测量自旋晶格弛豫率R(1e)时观察到的。本文中发展的WBR理论将dsDNA碱基对建模为通过弯曲弹簧和扭转弹簧连接的扩散刚性圆柱盘，其弹性力常数分别为κ和α。详细推导了旋转位移和速度的角关联函数，以便计算由于四种弛豫机制引起的R(1e)值：化学位移各向异性（CSA）、电子-核偶极（END）、自旋旋转（SR）和广义自旋扩散（GSD）弛豫过程。长度在50个碱基对以下的dsDNA中测得的自旋晶格弛豫率比将相同DNA建模为刚性杆时计算出的弛豫率快得多。解释这种差异的最简单方法是在DNA模型中考虑内部柔韧性。由于这种差异，我们直接从DNA的弱弯曲杆模型推导出CSA、END和SR机制引起的谱密度表达式。由于之前的处理中缺乏此类细节，因此在这一发展过程中特别强调了SR机制。本文发展的理论提供了一个框架，用于从WBR模型计算弛豫率，以便与磁共振弛豫数据进行比较，并确定表征DNA的扭转和弯曲力常数。
