Molecular orientation studies by pulsed electron-electron double resonance experiments

Abstract

Pulsed electron-electron double resonance (PELDOR) has proven to be a valuable tool to measure the distribution of long range distances in noncrystalline macromolecules. These experiments commonly use nitroxide spin labels as paramagnetic markers that are covalently attached to the macromolecule at specific positions. Unless these spin labels are flexible in such a manner that they exhibit an almost random orientation, the PELDOR signals will-apart from the interspin distance-also depend on the orientation of the spin labels. This effect needs to be considered in the analysis of PELDOR signals and can, moreover, be used to obtain additional information on the structure of the molecule under investigation. In this work, we demonstrate that the PELDOR signal can be represented as a convolution of a kernel function containing the distance distribution function and an orientation intensity function. The following strategy is proposed to obtain both functions from the experimental data. In a first step, the distance distribution function is estimated by the Tikhonov regularization, using the average over all PELDOR time traces with different frequency offsets and neglecting angular correlations of the spin labels. Second, the convolution relation is employed to determine the orientation intensity function, using again the Tikhonov regularization. Adopting small nitroxide biradical molecules as simple examples, it is shown that the approach works well and is internally consistent. Furthermore, independent molecular dynamics simulations are performed and used to calculate PELDOR signals, distance distributions, and orientational intensity functions. The calculated and experimental results are found to be in excellent overall agreement.

DEER Distance Measurements on Proteins

“…Orientation selection is not completely canceled by such field averaging (44). Averaging over different settings of pump and observer frequency was also proposed (45), but requires repetition of pulse channel setup for each new setting, whereas field averaging can be automated as a two-dimensional experiment.…”

“…Model-free analysis of orientation selection can be achieved by subjecting form factors F i (t) obtained at different observer/pump frequency settings i to two Tikhonov regularization steps (45). In the first step i F i (t) is converted to the distance distribution P (r).…”

Advanced EPR Methods for Studying Conformational Dynamics of Nucleic Acids

“…We have developed several approaches to analyze such data sets quantitatively. Simple geometrical modeling (Margraf et al, 2007;Schiemann et al, 2009) or comparison with MD simulations (Marko et al, 2009) can be used, if some prior knowledge about the molecule already exists. Analytical formula can be derived for specific cases and symmetries (Marko et al, 2010).…”

“…Because the orientation between both paramagnetic centers cannot be assumed to be randomly distributed, Tikhonov regularization (Chiang et al, 2005;Jeschke et al, 2006Jeschke et al, , 2002 cannot be used to obtain the distance distribution function directly from the PELDOR time trace. Instead, more elaborate simulation methods have to be used to disentangle distances and angular information (Denysenkov et al, 2006;Margraf, Bode, Marko, Schiemann, & Prisner, 2007;Marko et al, 2010Marko et al, , 2009Polyhach, Godt, Bauer, & Jeschke, 2007;Schiemann, Cekan, Margraf, Prisner, & Sigurdsson, 2009). …”

Conformational dynamics of nucleic acid molecules studied by PELDOR spectroscopy with rigid spin labels

“…Molecular dynamic studies of the molecule dissolved in a water box have been performed using the GROMACS program package with the AMBER 98 force field [78]. The equation of motion has been integrated with time steps of 2 fs over a total time span of 20 ns.…”