Theory for Spin−Lattice Relaxation of Spin Probes on Weakly Deformable DNA

Abstract

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 κ and R, 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.

Probing the Dynamics of the P1 Helix within the Tetrahymena Group I Intron

“…Nucleic acid duplexes of moderate length are rigid elements with defined, regular shapes so that dynamic properties can be predicted and compared to experimental measures 21,40. We therefore determined the FPA of 6-MI-labeled DNA duplexes of varying length and compared the experimental values to predicted values (see Supporting Information).…”

Conformational Equilibria of Bulged Sites in Duplex DNA Studied by EPR Spectroscopy

“…The dashed black line indicates a different linear correlation between spectral width and R 1e for the bulged samples. The R 1 e values, calculated on the basis of a rigid 14-mer,39,53 demonstrate that the experimental R 1 e values are about twice as large as the calculated values. The increased rate of experimental values arises from the internal motion of the spin probe over and above that of a rigid object 39.…”

“…The R 1 e values, calculated on the basis of a rigid 14-mer,39,53 demonstrate that the experimental R 1 e values are about twice as large as the calculated values. The increased rate of experimental values arises from the internal motion of the spin probe over and above that of a rigid object 39. The R 1e , like the spectral width $(2\langle A_{\mathrm{italiczz}}\rangle )$, indicates Ç/C has the least mobility of the Ç/X samples.…”

“…As a general principle, $2\langle A_{\mathrm{italiczz}}\rangle$ is determined in main part by dynamics processes that have rotational diffusion coefficients comparable to the width of the spectrum, which is on the order of 10 8 Hz . In contrast, the R 1 e is dominated by dynamics process that compete with the spectrometer frequency, which is 9.10 9 Hz (for X band spectrometers) 39,53,55. Therefore, the results from the simulated spectra (Figure 6 (top) , blue line) demonstrates that R 1 e for a sample with no internal motion does not depend strongly on the uniform mode of motion of the spin label, as the uniform mode for a ~14-mer is much slower than the spectrometer frequency.…”

“…The three parameters are 1 ) the full spectral splitting, called $2\langle A_{\mathrm{italiczz}}\rangle$, 2 ) the central linewidth, which is directly related to the mobility parameter of Hubbell,38 and 3 ) the spin lattice relaxation rate, R 1 e 39. Each parameter depends on the dynamics in different ways.…”