A Floquet description of phase alternated sequences for efficient homonuclear recoupling in solid perdeuterated systems Sundaresan Jayanthi a,1 , Ümit Akbey b,⇑,1 , Boran Uluca c , Hartmut Oschkinat b , Shimon Vega a,⇑ a Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel b Department NMR-supported Structural Biology, Leibniz-Institut für Molekulare Pharmakologie (FMP), Robert-Rössle-Str. 10, D 13125 Berlin, Germany c Department of Chemistry, Fatih University, Istanbul, Turkey article info Article history: Received 4 March 2013 Revised 8 May 2013 Available online 5 June 2013 Keywords: Homonuclear recoupling Magic angle spinning Phase alternation PARIS irradiation schemes DONER abstract A Floquet description of a phase alternated homonuclear recoupling scheme for perdeuterated systems is presented. As a result, we demonstrate improvements in the recoupling efficiency of the DOuble Nucleus Enhanced Recoupling [DONER; J. Am. Chem. Soc. 131 (2009) 17054] technique by utilizing Phase Alter- nated Recoupling Irradiation Schemes [PARIS; Chem. Phys. Lett. 469 (2009) 342]. The effect of proton and deuterium radio frequency irradiation during recoupling has been systematically studied and theoretical observations have been verified experimentally using a deuterated model compound, L-Alanine, at 10 and 20 kHz magic angle spinning frequency. Experimental results are well in agreement with theoretical observations, thereby significantly increasing the recoupling efficiency of conventional DONER in perdeu- terated systems. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction The recent decade has witnessed the utility of solid state NMR to determine structure and dynamics of peptides and proteins in membranes, amyloid fibrils, etc. at an atomic resolution. Various technological developments have enriched the studies of complex biological systems and their aggregates in micro crystalline and non-crystalline forms [1–6]. The interactions in solids are aniso- tropic which leads to severe line broadening and hence reduces resolution and sensitivity. For high spectral quality and dispersion magic angle spinning (MAS) is usually applied to remove aniso- tropic interactions. By MAS, interactions which carry important structural information, e.g., internuclear distances are lost in the pursuit of resolution and sensitivity. As a result, dipolar recoupling techniques that selectively reintroduce these couplings were developed and are now necessary components in structural studies of solid samples. 13 C– 13 C homonuclear dipolar interactions can be recoupled in various ways, whereby the abundant protons in the system can be integrated into the recoupling realm, via the 1 H– 13 C heteronu- clear dipolar interaction, without or with radio frequency (RF) irra- diation on the protons. Since these latter interactions can become an order of magnitude larger than the 13 C– 13 C interactions, the first approach can be very effective leading to the Proton Driven Spin Diffusion (PDSD) mechanism promoting homonuclear recoupling [7]. The second approach will be the subject of this publication. Rotational Resonance (R 2 ) [8–10] is yet another recoupling scheme that restores homonuclear dipolar couplings of interacting ‘like’ spin pairs, directly and without proton assistance. This scheme becomes effective when the value of spinning frequency x r matches the isotropic resonance frequency difference D CS of the coupled spins, according to D CS = nx r ; where n = ±1, ±2. During R 2 recoupling of 13 C– 13 C interactions the protons are in general strongly irradiated eliminating the heteronuclear dipolar couplings. By applying simple sequences of RF pulses on coupled spin pairs synchronously with the sample spinning, their homonuclear di- pole–dipole couplings can also actively be recoupled during MAS experiments. Dipolar Recovery At the Magic Angle (DRAMA) [11,12] initiated the development of many recoupling sequences thereafter. It was shown in the early 90s that a series of rotor syn- chronized p-pulses can reintroduce the ‘‘flip-flop’’ part of the homonuclear dipolar interaction. Termed as radio-frequency driven recoupling (RFDR) [13], this sequence has been used frequently to record correlation spectra of biological systems. Several important recoupling sequences were developed utilizing RF irradiation on the coupled spins such as double quantum HOmonucleaR ROtary Resonance (HORROR) [14], Dipolar Recoupling Enhanced by Ampli- tude Modulation (DREAM) [15], symmetry based sequences such as POST-C7 [16], SPC5 [17] and stochastic recoupling [18]. Most of these have been reviewed extensively in the literature [19,20]. Yet another RF irradiation approach was introduced to recouple the interactions between heteronuclear spins. An example of this is the Rotary Resonance Recoupling (R 3 ) scheme [21], where an RF 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.05.007 ⇑ Corresponding authors. E-mail addresses: akbey@fmp-berlin.de (Ü. Akbey), Shimon.Vega@weizmann. ac.il (S. Vega). 1 These authors contributed equally to this work. Journal of Magnetic Resonance 234 (2013) 10–20 Contents lists available at SciVerse ScienceDirect Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr