A short note on the analysis of distance measurements by electron paramagnetic resonance

Abstract

In electron paramagnetic resonance (EPR) distance distributions between site-directedly attached spin labels in soft matter are obtained by measuring their dipole-dipole interaction. The analysis of these distance distributions can be misleading particularly for broad distributions, because the most probable distance deviates from the distance between the most probable label positions. The current manuscript studies this effect using numerically generated spin label positions, molecular dynamics simulations, and experimental data of a model system. An approach involving Rice distributions is proposed to overcome this problem.

Symmetry-Constrained Analysis of Pulsed Double Electron–Electron Resonance (DEER) Spectroscopy Reveals the Dynamic Nature of the KcsA Activation Gate

“…The interprobe distance $r=\sqrt{\mathrm{\Delta }{x}^2+\mathrm{\Delta }{y}^2+\mathrm{\Delta }{z}^2}$ between two spin label centers, each normally distributed in space ( x, y, z ) with standard deviation σ S about its center, is described by the Rice 3D distribution, 27,28 generalized to n -dimensions as: $$f_{n}false(r;\mu ,{\sigma }_{R}false)=\frac{r^{(n/2)}}{{\mu }^{false(n/2false)-1}{\sigma }_R^2}\text{exp}true[\frac{-false(r^2+{\mu }^{2}false)}{2{\sigma }_R^2}true]I_{false(n/2false)-1}true(\frac{r\mu }{{\sigma }_R^2}true),r\ge 0$$ where the mean interprobe distance μ > 0 and Rice standard deviation σ R > 0 are real numbers; n is the dimension of the spin label normal random variables ( n = 3 for labeled membrane proteins in detergent micelles); I ν denotes the modified Bessel function of the first kind of real order ν. Assuming all spin labels have equal spatial variance, the Rice standard deviation is related to the spin label spatial standard deviation by ${\sigma }_R=\sqrt{2}{\sigma }_S$, which is a correction from that reported in 29 . The Rice 3D distribution can be simplified 29 to a more computationally efficient form using the relation $I_{1/2}false(xfalse)=\sqrt{\frac{2}{\pi x}}\text{sin}\mathrm{normalh}false(xfalse)$: $$f_{3}false(r;\mu ,{\sigma }_{R}false)=\frac{r}{\mu {\sigma }_R}\sqrt{\frac{2}{\pi }}\text{exp}true[\frac{-false(r^2+{\mu }^{2}false)}{2{\sigma }_R^2}true]\text{sin}\mathrm{normalh}true(\frac{r\mu }{{\sigma }_R^2}true),r\ge 0$$ The probability density function of the 2-component mixture of Rice 3D distributions is: $$Pfalse(r;\mathrm{bold\theta }false)=w{f}_{3}false($$…”

“…Assuming all spin labels have equal spatial variance, the Rice standard deviation is related to the spin label spatial standard deviation by ${\sigma }_R=\sqrt{2}{\sigma }_S$, which is a correction from that reported in 29 . The Rice 3D distribution can be simplified 29 to a more computationally efficient form using the relation $I_{1/2}false(xfalse)=\sqrt{\frac{2}{\pi x}}\text{sin}\mathrm{normalh}false(xfalse)$: $$f_{3}false(r;\mu ,{\sigma }_{R}false)=\frac{r}{\mu {\sigma }_R}\sqrt{\frac{2}{\pi }}\text{exp}true[\frac{-false(r^2+{\mu }^{2}false)}{2{\sigma }_R^2}true]\text{sin}\mathrm{normalh}true(\frac{r\mu }{{\sigma }_R^2}true),r\ge 0$$ The probability density function of the 2-component mixture of Rice 3D distributions is: $$Pfalse(r;\mathrm{bold\theta }false)=w{f}_{3}false(r;{\mu }_1,{\sigma }_{R,1}false)+false(1-wfalse)f_{3}false(r;{\mu }_2,{\sigma }_{R,2}false),r\ge 0$$ where w is the fraction of the 1 st mixture component and θ = (μ 1 , σ R ,1 , μ 2 , σ R ,2 , w ) is the set of all parameters that defines the bimodal distance distribution. The probability density function P ( r ; θ ) was fit to V exp ( t ) by minimization of Equation 2 using nonlinear least-squares regression.…”

A Straightforward Approach to the Analysis of Double Electron–Electron Resonance Data

“…The bottom row allows shapes other than Gaussian to be tried ( Square , Triangle , Circle , and Rice (Kohler, Spitzbarth, Diederichs, Exner & Drescher, 2011)). The next section ( Background) controls the parameters for the inter-object contribution to the DEER signal.…”

Long‐Range Distance Determination in a DNA Model System inside Xenopus laevis Oocytes by In‐Cell Spin‐Label EPR

“…This suggests partial reduction of spin labels during synthesis and a resulting incomplete labeling, however, without infringing reliable data analysis. [4,20] In general, the [a] M. Azarkh, O. Okle, Dr.width of the distance distribution ( Figure S1 in the Supporting Information) reflects both the flexibility of the macromolecule under study as well as the reorientational degree of freedom of the attached spin label, [22] while the errors of EPR distance measurements are much smaller than the variation of the distances due to conformational distribution. [15] Here, the narrow distance distribution (s = 0.43 nm) in combination with the distance constraint d represents a completely hybridized DNA duplex.For the in-cell DEER experiments 50 nL DNA solution (4 mm) was injected into each oocyte.…”