Henrik Gesmar

The applicability of the magnetization-transfer NMR technique to determine chemical exchange rates in extreme cases. The importance of complementary experiments

Abstract It is shown that a conventional two-site magnetization-transfer experiment provides an insufficient amount of information to allow a reliable determination of the exchange rate, unless |λ2| ⪢ |λ1|, where λ1 and λ2 are the time constants of the two exponentials involved. This difficulty, which is often met, is further hampered when the linewidths as well as the longitudinal relaxation rates of the two exchanging signals are different, when a perturbation of the noninverted signal occurs, or when the signal intensities are difficult to determine. However, by including a complementary experiment, in which the perturbed and unperturbed signals are interchanged, additional, independent information about the parameters involved is provided, allowing all of the unknown parameters including the exchange rate to be determined in most cases. The significant increase in the applicability of the technique when the complementary experiment is included, as well as the considerable errors that may be introduced when it is omitted, is illustrated by examples of the rate of exchange between the NH and H2O protons in the water/N-methylacetamide system. In addition these experiments demonstrate that exchange rates covering about three orders of magnitude (0.06 to 45 sec−1) can be determined by the method when applied in the form presented here, as exchange rates which are at least seven times slower than the fastest relaxation rate can be evaluated.

Quantitative analysis of complicated nonideal fourier transform NMR spectra

Abstract The exact expression for the discrete Fourier transform of a sum of exponentially damped sinusoids is derived, and its applicability for describing the general, discrete Fourier transform spectrum is demonstrated. It is shown that the frequency, the linewidth, the intensity, and the phase of each individual signal can be determined by fitting the derived expression to the real and imaginary part of experimental spectra. The results are not influenced by aliasing, truncation errors, widely different signal intensities, nonlinear phase distortions, and partly overlapping signals.

Two-dimensional linear-prediction NMR spectroscopy

Abstract A two-dimensional linear-prediction procedure, applying the linear-prediction principle to both dimensions, is described in detail. It is demonstrated that a two-dimensional linear-prediction calculation is feasible because the most time-consuming parts of the procedure are only performed once for a given 2D data set. Deviations from ideality caused by noise and short data records are discussed, and it is shown how to obtain maximum information in these cases. The advantages of the method as compared to the two-dimensional Fourier analysis are illustrated on a 1 H COSY free-induction decay of threonine.

Optimizing the multisite magnetization-transfer experiment

Abstract It is shown that a magnetization-transfer experiment can provide reliable rate constants from a spin system consisting of n exchanging sites only if the experiment is separated into n individual inversion experiments containing complementary information. In this case, however, it is possible to determine the n(n − 1) 2 exchange rates as well as the n longitudinal relaxation rates even if the inverting rf pulses are not completely selective. The influence from other kinds of cross relaxation is also described.

Applicability of magnetization transfer nuclear magnetic resonance to study chemical exchange reactions

Publisher Summary This chapter discusses the magnetization transfer technique in its general form. This includes cases where the relaxation rates of all exchanging signals are different, unintentional signal perturbations occur, and the exponents of the involved multi exponential functions are almost identical. Also cases with phase- and baseline- distorted spectra, low signal-to-noise ratios, and partly overlapping signals are considered. In particular, this chapter shall concentrate on the experimental procedure necessary to obtain spectra that are sufficiently informative, and the data analysis that must be used to retrieve the maximum information from these spectra. In nuclear magnetic resonance (NMR) studies of enzymes and other biological systems, overlapping signals often hamper the analysis. Because of the limited dynamic range of the spectrometer, further problems can arise when weak signals from biological molecules are present together with a strong solvent signal, in particular, the proton signal from water. Although effective procedures for solvent suppression are available, the application of these procedures may often result in phase- and baseline-distorted spectra preventing a correct evaluation of the signal intensities from the spectra.

Specific and Nonspecific Interactions in Ultraweak Protein–Protein Associations Revealed by Solvent Paramagnetic Relaxation Enhancements

Weak and transient protein–protein interactions underlie numerous biological processes. However, the location of the interaction sites of the specific complexes and the effect of transient, nonspecific protein–protein interactions often remain elusive. We have investigated the weak self-association of human growth hormone (hGH, KD = 0.90 ± 0.03 mM) at neutral pH by the paramagnetic relaxation enhancement (PRE) of the amide protons induced by the soluble paramagnetic relaxation agent, gadodiamide (Gd(DTPA-BMA)). Primarily, it was found that the PREs are in agreement with the general Hwang-Freed model for relaxation by translational diffusion (J. Chem. Phys.1975, 63, 4017–4025), only if crowding effects on the diffusion in the protein solution are taken into account. Second, by measuring the PREs of the amide protons at increasing hGH concentrations and a constant concentration of the relaxation agent, it is shown that a distinction can be made between residues that are affected only by transient, nonspecific protein–protein interactions and residues that are involved in specific protein–protein associations. Thus, the PREs of the former residues increase linearly with the hGH concentration in the entire concentration range because of a reduction of the diffusion caused by the transient, nonspecific protein–protein interactions, while the PREs of the latter residues increase only at the lower hGH concentrations but decrease at the higher concentrations because of specific protein–protein associations that impede the access of gadodiamide to the residues of the interaction surface. Finally, it is found that the ultraweak aggregation of hGH involves several interaction sites that are located in patches covering a large part of the protein surface.

Quantitative information from complicated nuclear magnetic resonance spectra of biological macromolecules.

Publisher Summary This chapter discusses a series of examples that illustrate the way optimum, quantitative information about biomacromolecules in solution can be obtained from NMR spectra by a nonlinear least-squares (LSQ) analysis of the frequency spectra in combination with a linear prediction (LP) analysis of the time-domain signal (free induction decay, FID). The examples include (1) determination of the exchange rates of slowly exchanging amide protons in a protein from a single two-dimensional (2D) nuclear Overhauser effect spectroscopy (NOESY) spectrum, (2) estimation of the intensities of overlapping signals in 2D NMR spectra, and (3) characterization of structural changes in a protein as function of pH. In all three cases, the LSQ analyses are based on the complete analytical expression for the discrete Fourier transform NMR spectrum. To elucidate the importance of using this expression, a short introductory review of its form and its deviation from a true Lorentzian is presented.

Fast orthogonal decomposition of rank deficient Toeplitzmatrices

A 9mn-algorithm for computing an orthogonal factorization of a well-conditionedm×n Toeplitz matrixT was presented in Cybenko [8]. In the present paper we discuss extensions of this algorithm to cover rank deficient Toeplitz matrices that do not have many consecutive ill-conditioned submatricesT(:, 1:i) fori=1, ...,n. Our algorithms are stillO(mn).

Linear prediction enhancement of 2D heteronuclear correlated spectra of proteins

SummaryLinear prediction has been used to extrapolate the t1 domain of natural abundance1H−13C correlated two-dimensional (2D) FIDs of insulin. The FIDs were obtained by two different heteronuclear correlation experiments, one that utilizes heteronuclear multiple-quantum coherence during t1, and one that utilizes13C single-quantum coherence. It is shown that the enhancement of the resolution and sensitivity in the F1 dimension of the Fourier transform spectrum that results from the linear prediction extrapolation allows the t1 domain to be confined to a relatively short time period where the signal intensity is at maximum. In particular, it is found that the enhancement thus obtained is sufficiently good to allow an observation of the difference between the F1 line widths in the single-quantum and double-quantum coherence spectra.