Graphical illustration of the effect of stepwise transforming the description of [(a)–(c)] TOFU and [(d)–(g)] elements into the interaction frame of the rf field, respectively. (a) The full TOFU rf field. (b) and (c) The TOFU rf field as in Eqs. (5) and (6), respectively. (d) The full rf field. The rf field after a transformation of a rotation about the (e) -axis, followed by a rotation about the (f) -axis, and succeeded by a rotation about the (g) -axis. To keep the graphics within reasonable space, [(a)–(c)] the TOFU field used and , and the [(d)–(g)] field used . These values are not the recommendable values for practical experiments (see text).
(a) Illustration of the effect of changing the phase between the horizontal modulations in a generalized TOFU experiment using and . The solid curve represents the coefficient for the normalized isotropic chemical shift in Eq. (28), while the dashed curve represents the coefficient for the recoupled dipole-dipole interaction in Eq. (33) for which and are set to unity for simplicity. (b) The solid curve represents the normalized isotropic chemical shift in Eq. (42) for a generalized experiment as a function of using , , and . The dashed curve represents the recoupled dipole-dipole coupling in Eq. (43) with , and the dashed-dotted curve represents the recoupled dipole-dipole coupling in Eq. (43) with . The recoupled dipole-dipole coupling is expressed in units of .
Schematic representation of the FOLD dipolar recoupling pulse sequences, with the main experiment shown in (a) and the reference experiment in (b). The refocusing pulses are of phase while the Gaussian pulses are of phase . The duration of each of the Gaussian pulses and each of the corresponding free evolution periods is in our setup four rotor periods. The overall duration of the free evolution periods bracketing the refocusing pulse is set to two rotor periods, but this choice is only intended as a guideline. The Gaussian pulses hinder refocusing of specific dipole-dipole interactions.
(a) Amplitude and (b) phase of the FOLD rf field element as implemented in our numerical simulations and experiments for the case , , and .
Numerical simulations of (a) -alanine, (b) -threonine, and (c) isoleucine (residue 13 in ubiquitin) FOLD (, , , or ) curves on top of an ideal Fresnel curve grid (solid lines). The numbers above/next to the Fresnel curves indicate the distance to measured in Å. The symbols represent numerically simulated curves reflecting dipole-dipole coupling to (filled circle), (open circle), or (filled square), (open square), and (filled triangle). The dashed Fresnel curves represent a distance of 2.4 Å in (b) and 3.8 Å in (c).
Experimental FOLD curves for -labeled samples of (a) -threonine and (b) ubiquitin plotted in a ideal Fresnel curve grid. The numbers above/next to the ideal Fresnel curves indicate the distance in Å to the nearest . Experimental data is obtained by integrating over the relevant part of the peak line shape in the detection dimension (for ubiquitin the relevant peaks are marked in Fig. 7). Data points reflecting the internuclear distance between and the nuclei in question are marked as: (filled circle), (open circle), or (filled square), (open square), and of residue 23 (filled triangle).
Experimental FOLD dephasing spectra obtained for -labeled ubiquitin using (a) the main experiment and (b) the reference experiment with an increasing number of FOLD blocks, (see Fig. 3), with the most intense spectrum in top representing .
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