Larry R. Dalton

Rotational diffusion studied by passage saturation transfer electron paramagnetic resonance

A comprehensive description is given of instrumental and theoretical methods employed to make accurate measurements of rotational correlation times using passage saturation transfer electron paramagnetic resonance (ST–EPR). Saturation transfer methods extend by several orders of magnitude the sensitivity of EPR to very slow motion; for example, for nitroxide spin labels, correlation times as long as 10−3 sec become accessible to measurement. Two ST–EPR detection schemes are discussed in detail: dispersion, detected 90° out of phase with respect to the 100 kHz field modulation, and absorption, detected 90° out of phase with respect to the second harmonic of the 50 kHz field modulation. The sensitivities of these configurations are illustrated with experimental spectra obtained from a system obeying isotropic Brownian rotational diffusion; namely, maleimide spin labeled human oxyhemoglobin in aqueous glycerol solutions. Two theoretical approaches, one employing coupled Bloch equations and the other utilizing the stochastic Liouville equation for the density matrix with the orientation variables treated by transition rate matrix or orthogonal eigenfunction expansion methods, are in excellent agreement with each other and with model system spectra. Both experimental and theoretical spectra depend on a number of relaxation processes other than rotational diffusion; consequently, considerable care must be taken to ensure the accuracy of measuredrotational correlation times. Although the absorption method is currently the more sensitive and convenient one to apply with most conventional (commercial) spectrometers, the dispersion ST–EPR method is potentially more powerful, providing strong motivation for future technological efforts to decrease noise levels in dispersion experiments.

Very slowly tumbling spin labels: adiabatic rapid passage

Abstract Rapid-passage EPR spectra from very slowly tumbling nitroxide radicals have been found to be sensitive in shape to the molecular motion. This is true even though the ordinary EPR spectra are substantially identical with that from a rigid powder. Rotational correlation times have been measured between 2×10 −7 and 2×10 −5 sec. The technique is potentially applicable to the study of motion of biological macromolecules with rigidly bound spin labels.

Molecular and applied modulation effects in electron electron double resonance. IV. Stationary ELDOR of very slowly tumbling spin labels

The investigation of very slowly tumbling spin labels by stationary electron electron double resonance (ELDOR) is discussed. When a Zeeman modulation frequency of 270 Hz was employed, spectra which were independent of modulation frequency but not modulation amplitude resulted. Under such conditions, the ELDOR technique permits characterization of rotational processes with correlation times from 10−7 to 10−3 sec even though normal electron spin resonance (ESR) spectra are insensitive to motion in these regions, appearing to be superimposable with the ESR powder pattern of a static random collection of molecules. Quantitative analysis of stationary ELDOR spectra is accomplished employing a density matrix treatment that explicitly includes the interaction of the spins with the applied electromagnetic radiation and Zeeman modulation fields. The effect of molecular motion inducing random modulation of the anisotropic hyperfine and electron Zeeman interactions can be calculated employing either an orthogonal ei...

Fast computer calculation of ESR and nonlinear spin response spectra from the fast motion to the rigid lattice limits

Abstract Fast computer simulation of the electron spin resonance and adiabatic rapid passage spectra of spin labels characterized by rotational correlation times ranging from the fast motion to the rigid lattice limits is demonstrated. Calculations are based upon a modification of the stochastic Liouville equation for the density matrix which explicitly includes interaction of the spins with applied radiation and modulation fields. Several mathematical simplifications of previous calculations are demonstrated, permitting computation with core and CPU requirements compatible with small computers.

EPR and saturation transfer EPR studies on glyceraldehyde 3‐phosphate dehydrogenase

Electron paramagnetic resonance (EPR) and saturation transfer–EPR (ST–EPR) techniques were employed to investigate the hydrodynamic properties of glyceraldehyde 3‐phosphate dehydrogenase (GAPDH). Both apo‐ and holoenzyme were spin‐labeled at the active site cysteine‐149 residue with N‐ (1‐oxyl‐2,2,6,6‐tetramethyl‐4‐piperidinyl) ‐ maleimide. The apo‐ and holoenzymes were observed to have the same hydrodynamic structure and the spectroscopic results were consistent with these complexes behaving as spheres with hydrated radii of 41 A. The environment of the paramagnetic electron was significantly more polar in the spin‐labeled holoenzyme than in the spin‐labeled apoenzyme, suggesting that either ionic residues are positioned closer to the active site in the holoenzyme or that ionic segments of coenzyme nicotinamide adenine dinucleotide (NAD+) itself may interact with the paramagnetic electron of the maleimide spin label. The dependence of the phase quadrature second harmonic absorption ST‐EPR signal upon mic...

EPR and saturation transfer EPR spectra at high microwave field intensities

Abstract The eight unique EPR signals at the first and second harmonies of the Zeeman modulation are sensitive to the very slow rotational diffusion of spin labeled biomolecules when these signals are recorded under conditions of microwave saturation and finite Zeeman modulation frequencies and amplitudes. Such saturation transfer sensitive spectra have been employed to study contractile proteins, hemoproteins, enzymes, etc. When these species or their supramolecular complexes are characterized by correlation times in the range 10 −8 to 10 −3 s. Published computer simulation reproduce quite well spectra at the longer correlation times and the general sensitivity of spectra to changing rotational correlation time; however, agreement between experimental and calculated spectral shapes is poor for rotational correlation time on the order of 10 −7 s and the dependence of experimental spectra upon microwave field intensity is not reproduced. In the present communication we show that the previously reported discrepancy between experimental and calculated spectra is due to the neglect of higher order cou magnetic interactions modulated by the molecular motion and involving the spin-microwave field interaction. When these “pseudodiagonal” terms of the spin density equation are explicitly included, experimental spectral lineshapes, spectral line positions, and the ratios of amplitudes of the various signal components are quantitatively reproduced. Plots of the ratios of the heights of the high and low field spectral extrema suggest a procedure for calibrating microwave field intensities as these ratios are found experimentally and theoretically to be nearly a linear function of microwave field intensity for intensities in the range 0.15 to 0.5 G. The separation of low and high field extrema was observed to increase with increasing microwave field intensity, suggesting the need to carefully consider saturation effects when determining rotational correlation times from this separation.

Rapid computer simulation of E.S.R. spectra

A fast computer algorithm is presented which permits simulation of the effects of rotational diffusion, electron and nuclear relaxation, microwave power, and modulation frequency upon saturation transfer (passage) E.S.R. spectra. Comparison of theoretical and experimental spectra for nitroxide spin-labelled biomolecules suggests that while the dependence of electron spin-lattice relaxation time upon rotational correlation time is weak, the variation of the ratio of the electron to nuclear spin-lattice relaxation times is significant and consideration of strong nuclear relaxation is necessary for the simulation of spectra characterized by correlation times near the reciprocal of the nitrogen nuclear resonance frequency.

Molecular and applied modulation effects in electron electron double resonance. V. Passage effects in high resolution frequency and field swept ELDOR

The observation of electron electron double resonance (ELDOR) linewidths for nitroxide radicals which are significantly less than the hyperfine envelope widths is reported. For a 1.5×10−3M solution of 2,2,6,6‐tetramethyl‐4‐piperidinol‐1‐oxyl (TANOL) in sec‐butylbenzene (SBB) between the temperatures of −40u2009°C and −70u2009°C, the ELDOR linewidths correspond to single spin packet widths determined by the effective electron spin–spin relaxation rates. An analysis of the precise dependence of frequency swept absorption and dispersion ELDOR signals upon microwave radiation field intensities and upon the details of the applied Zeeman modulation and accompanying phase‐sensitive detection is also presented. Quantitative prediction of molecular and applied modulation effects is accomplished employing a modified density matrix treatment. Best fit parameters for TANOL in SBB at −63u2009°C include we(0) = 1.75×105 Hz, Te1e(0) = 1.3×10−6 sec, Te2e(0) = 2.7×10−7 sec, wn(14N) = 2.6×105 Hz, wn(all 1H) = 0 Hz, τ2 = 2×10−10 sec, ?...

Molecular and applied modulation effects in electron—electron double resonance. III. Bloch equation analysis for inhomogeneous broadening

Abstract The dependence of electron—electron double resonance (ELDOR) reduction factors, obtained employing field or frequency swept modes of operation and dispersion or absorption modes detection, upon experimental condition such as Zeeman modulation frequency, Zeeman modulation phase, and pump microwave power and upon molecular conditions such as homogeneous and inhomogeneous broadening of the hyperfine lines are experimentally and theoretically investigated. Experimental studies were carried out on solutions of 2,2,6,6-tetramethyl-4-piperidenol-1-oxyl and perdeuterio-2,2,6,6-tetramethyl-4-piperidone-oxyl in sec-butylbenzene at −63 °C. For 1 × 10−3M tetramethylpiperidinol spin label, the methyl and methylene proton nuclear relaxation rates are significantly longer than nitrogen (14N) nuclear relaxation rates that the electron spin resonance (ESR) hyperfine lines demonstrate the characteristics of inhomogeneous broadening. Frequency swept dispersion and absorption ELDOR linewidths are observed to correspond to the linewidth (approximately one megahertz between points of maximum slope) of an ESR spin packet or superhyperfine line as compared to the ESR envelope or hyperfine linewidth (approximately four megahertz for the mI(14N) = +1 (low field) line when a peak to peak modulation field of 0.24 gauss is employed). Moreover, field dispersion ELDOR reduction factors are observed to depend strongly upon modulation frequency (in contrast to the behavior for homogeneous lines reported earlier), with reduction factors decreasing with modulation frequency. Theoretical calculations based upon a modified (interaction of the spins with Zeeman modulation and multiple radiation fields is introduced) decreasing equation Bloch treatment quantitatively reproduce the experimental results when interaction of the unpaired electron with nearby protons as well as with 14N is taken into account.

Computer simulation of EPR and ST-EPR spectra of nitroxide spin labels in the rigid-lattice limit

Abstract The rapid computer simulation of 9.5- and 35-GHz EPR and saturation transfer EPR spectra obtained employing finite Zeeman modulation amplitudes and microwave field intensities is discussed. The methodology outlined is relevant not only to the determination of magnetic tensors (e.g., electron Zeeman and electron-nuclear hyperfine) but also to the determination of molecular relaxation rates. Such data are in turn useful in the analysis of spectra from nitroxide spin labels undergoing rotational diffusion. The computer algorithms developed here are also relevant to the analysis of spectra of certain classes of oriented systems and certain classes of systems undergoing anisotropic rotational diffusion.