Research article Received: 3 June 2014
Revised: 23 September 2014
Accepted: 11 October 2014
Published online in Wiley Online Library: 22 January 2015
(wileyonlinelibrary.com) DOI 10.1002/mrc.4181
Direct prediction of residual dipolar couplings of small molecules in a stretched gel by stochastic molecular dynamics simulations Andreas O. Frank,a,† J. Christoph Freudenberger,b Alexey K. Shaytan,c,d Horst Kesslera,e and Burkhard Luyf,g* Residual dipolar couplings are highly useful NMR parameters for calculating and refining molecular structures, dynamics, and interactions. For some applications, however, it is inevitable that the preferred orientation of a molecule in an alignment medium is calculated a priori. Several methods have been developed to predict molecular orientations and residual dipolar couplings. Being beneficial for macromolecules and selected small-molecule applications, such approaches lack sufficient accuracy for a large number of organic compounds for which the fine structure and eventually the flexibility of all involved molecules have to be considered or are limited to specific, well-studied liquid crystals. We introduce a simplified model for detailed all-atom molecular dynamics calculations with a polymer strand lined up along the principal axis as a new approach to simulate the preferred orientation of small to medium-sized solutes in polymer-based, gel-type alignment media. As is shown by a first example of strychnine in a polystyrene/CDCl3 gel, the simulations potentially enable the accurate prediction of residual dipolar couplings taking into account structural details and dynamic averaging effects of both the polymer and the solute. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: NMR; 1H; orientational model
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C; residual dipolar couplings; MD simulations; stochastic dynamics; molecular alignment; RDC prediction;
Introduction
Magn. Reson. Chem. 2015, 53, 213–217
* Correspondence to: Burkhard Luy, Institute of Organic Chemistry and Institute for Biological Interfaces, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany. E-mail: [email protected] †
Present address: Novartis Institutes for BioMedical Research (NIBR), 5300 Chiron Way, Emeryville, CA 94608, USA.
a Institute for Advanced Study at the Department Chemie, Technische Universität München, Lichtenbergstr. 4, 85747, Garching, Germany b Bruker Biospin AG, Industriestr. 26, 8117, Fällanden, Switzerland c Institute of Polymer Science, University of Ulm, Albert-Einstein-Allee 47, 89069, Ulm, Germany d Biology Department, Moscow State University, 119991, Moscow, Russia e Chemistry Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia f Institut für Organische Chemie, Karlsruher Institut für Technologie (KIT), FritzHaber-Weg 6, 76131, Karlsruhe, Germany g Institut für Biologische Grenzflächen, Karlsruher Institut für Technologie (KIT), Postfach 3640, 76021, Karlsruhe, Germany
Copyright © 2015 John Wiley & Sons, Ltd.
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Residual dipolar couplings (RDCs) and other anisotropic NMR parameters nowadays can routinely be measured in partially aligned samples.[1–6] They contain very valuable information for determining three-dimensional molecular structures. However, the a priori unknown orientational alignment of solute molecules makes the interpretation of data difficult. To date, RDCs are usually interpreted using the concept of the Saupe matrix or alignment tensor, respectively, which assumes the molecule of interest to be rigid.[7] However, the Saupe matrix approach fails for molecules with inherent flexibility[8] or when specific structural questions are addressed like the multimeric state or the absolute configuration of a compound.[9,10] While inherent flexibility can be addressed by applying mean field approaches based on analytical models with continuous bond rotation[11–15] or by more general single-tensor and multitensor fits[16–22] if sufficient anisotropic parameters can be measured, the latter cases and instances when only insufficient experimental values are accessible, data interpretation requires the accurate a priori prediction of alignment. Prediction of RDCs can be achieved using a variety of techniques originally designed for large biomolecules like proteins and nucleic acids. One successful method for this type of molecules is the approximation of the alignment medium as unstructured walls or rods.[9,23] Other approaches take into account dynamic information from molecular dynamics (MD) simulations of the solute and derive alignment properties from its tensor of gyration or its charge distributions,[24,25] as, for example, implemented in the program MSpin.[26] These types of approaches neglect the detailed structural properties of the alignment medium. While the fine structure of the alignment medium is of minor importance for proteins and nucleic
acids, it certainly defines the main interactions for small molecules that weakly interact with the polymer matrix of the medium. Only recently, an atomistic model for the MD-based simulation of orientation in the liquid crystalline phase 5CB has been introduced and studied in great detail.[27,28] The complex simulations of the particular alignment medium and a number of small solute molecules resulted in relatively good agreement of prediction and experiment. Simultaneously, we have been working on the prediction of
A. O. Frank et al. alignment of stretched polymer gels using MD simulations,[29] which, however, requires a different approach with a specific model for representing the orientation. In this short article, we introduce a seemingly viable concept and a first example for such a model based on MD simulations that includes the fine structure of the polymer used for alignment. For a proof of principle, we use strychnine diffused into a stretched polystyrene (PS)/CDCl3 gel,[30–32] which has been the first RDC measurement achieved in our laboratory[30] and which could not be predicted satisfyingly by previously reported methods.
mechanical stress on the gel results in a net excess of PS strands oriented along the direction of stretching (Fig. 1(b)).[30–32] Because this excess induces the experimentally detectable alignment of a solute, we constructed a model with a single PS chain oriented along the z-axis (corresponding to the stretching axis of the polymer and the static magnetic field of an NMR spectrometer) to simulate the averaged net orientation of the alignment medium. Practically, the atactic PS used in our NMR measurements[30] was mimicked by six styrene subunits with differing chiralities. Throughout the MD simulations using Gromacs 3.3.3,[33] backbone chain end atoms were positionally restrained to preserve the directionality of the strand.
Basic Model for Alignment In contrast to liquid crystals with their small subunits calculating an atom-resolved MD trajectory of an entire polymer network with all solute and solvent molecules included is hardly feasible because of limited computational power. Hence, we were faced with several challenges when conceptualizing MD runs to predict partial alignment of a solute molecule. First, a simple model of a stretched polymer gel exhibiting all necessary properties for generating alignment has to be constructed. Furthermore, MD boundary conditions must be found, which allow for frequent and realistic interactions between the polymer and the solute. Finally, a calculation setup has to be defined that enables an exhaustive sampling of molecular orientations and interactions. Our PS model was build based on the following assumption: in a conventional PS/CDCl3 gel, all polymer strands are isotropically distributed (Fig. 1(a)). To cause a preferred alignment of a solute diffused into the gel, which is the prerequisite for measuring RDCs, the polymer must be stretched in at least one dimension. The
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Figure 1. Simplified model of a cross-linked polymer gel (solvent molecules are not shown). (a) In a freely swollen gel, individual polymer strands are isotropically distributed. (b) In contrast, a mechanically stretched gel leads to a net excess of polymer strands being oriented along the stretching axis (z-axis).
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Implementation and Results Subsequently, MD boundary conditions were adjusted, and a proper calculation setup was chosen. To avoid artificial alignment of the solute as a result of collisions with MD box walls and to guarantee frequent interactions between strychnine and the PS strand, the MD runs were carried out in small cubic boxes (1.65-nm edge lengths) including periodic boundary conditions with a short cutoff radius of 0.7 nm and corresponding shift functions for van der Waals and Coulomb interactions. Whereas shorter box edges in the x and y dimensions negatively influenced results as strychnine could no longer freely rotate around its center of mass, longer transversal edges did not impact the predicted RDCs. All MD runs were performed in the gas phase because trajectories including CDCl3 molecules did not display convergence of observables even after one microsecond of simulation time. By adding both random and frictional force terms to Newton’s equations of motion (Langevin dynamics),[34] the viscous influence of solvent molecules on the dynamics of the system at 300 K was mimicked. Although not parameterized for vacuum simulations, we decided to use the Optimized Potentials for Liquid Simulations/all-atom (OPLS/AA)[35] force field for our calculations because it provides a wealth of atom types and bonded parameters for rare molecular motifs, e.g. multibridged atoms as occurring in strychnine. As discussed in more detail in the succeeding text, an accurate parameterization of the solute’s bonded force field terms had an important impact on the quality of predicted RDCs. Because strychnine does not contain ionizable groups, the experimentally used solvent chloroform has a very low dielectric constant, and interactions with the polymer are expected not to be dominated by polar forces, we assumed that inaccuracies introduced by the use of OPLS/AA under vacuum conditions are relatively small. As a decisive step for the conceptual proof, we tested the described model and calculation setup with respect to a sufficient orientational sampling of strychnine with as little computation time as possible. Our attempt was therefore to simulate strychnine in an isotropic environment (without polymer) to find out about convergence criteria for isotropic sampling. With a self-written Gromacs-based tool called g_orient, we monitored the function ξ i = (with the angles φi between the CH vectors and the z-axis of the MD box and the brackets indicating averaging over time) as a measure for anisotropy for all 22 carbon–hydrogen bond vectors i of strychnine; almost full convergence with |ξ i| < 0.005 is obtained after a run of 500 ns (Fig. 2(a)). To further prove our concept, we performed a second MD run with the polymer strand being allowed to rotate around its center of mass. This case corresponds to an isotropically oriented, i.e. unstretched gel with no net alignment. Indeed, the ξ i values slowly
Copyright © 2015 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2015, 53, 213–217
Direct prediction of residual dipolar couplings by stochastic MD simulations RDCs,[36] experimental couplings (Supporting Information) were used for fitting the computational data with a single proportionality factor ( 75 Hz). In Fig. 3(a), three sets of predicted RDCs from different MD runs are plotted against the 19 experimentally determined RDCs (see Supporting Information for details, tables, and additional figures). In run 1, 13 calculated RDCs match the experimental ones within a maximum error of ±3.0 Hz. However, six RDCs show deviations between 4.0 and 6.3 Hz (standard deviation between experimental and calculated data sets σ [exp/calc] = 3.0 Hz). A comparison of the most representative MD structure of strychnine after 500-ns simulation time and the experimentally observed lowest energy conformation [root-mean-square deviation (RMSD) = 0.49 Å] revealed that the solute force field parameters were not optimally chosen. A redefinition of several MD atom types and dihedral angles
Figure 2. Convergence of averaged alignment of strychnine in various MD 2 simulations using ξ i = values for all 22 CH vectors as the measure. The orientations of freely tumbling strychnine (a) as well as strychnine in a box with a PS strand that can rotate around its center of mass (b) average over time to an isotropic distribution with no net alignment. In contrast, strychnine with a PS strand lined up along the z-axis results in a net orientation of CH vectors proportional to corresponding RDCs (c). Transparent images of strychnine and polystyrene represent different positions and orientations during a trajectory.
Magn. Reson. Chem. 2015, 53, 213–217
Figure 3. (a) Comparison of three sets of predicted and one set of 1 experimental DCH RDCs for strychnine in a PS/CDCl3 gel; open triangles, run 1; open squares, run 2; filled circles, run 3. (b) While the best MD run leads to a very good match of predicted and experimental RDCs (σ [exp/calc] = 1.3 Hz; filled circles), alternative approaches neglecting the fine structure of the alignment medium like PALES (σ [exp/calc] = 6.3 Hz; open triangles) or TRAMITE (σ [exp/calc] = 6.5 Hz; open diamonds) show a poor correlation.
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converge between 0.015 and +0.015 after 500 ns (Fig. 2(b)), which corresponds to the inherent statistical error of our prediction. In the final runs with the polymer strand orientationally restrained along the z-axis, corresponding ξ i values converge between 0.2 and +0.2 (Fig. 2(c)), clearly indicating preferred orientations of the solute molecule. As ξ i values are directly proportional to expected
A. O. Frank et al. (run2; see also Supporting Information) resulted in a better consensus between simulated and experimental strychnine structures (RMSD = 0.15 Å) and accordingly in a better match between predicted and experimental RDCs (σ [exp/calc] = 2.1 Hz). This outcome underpins the significance of a precise modeling of a small molecule’s fine structure on the accuracy of predicted RDCs. Stronger violations (≥3 Hz) are only found for vectors that belong to strychnine CH2 groups (carbons C12, C19, C21, and C24). These deviations might originate from a mismatch between the applied sp3-hybridized carbon force field parameters and the real geometry of the four affected CH2 groups; based on measured 1JCH coupling constants (Supporting Information), an sp2-contribution must be expected that influences equilibrium bond lengths, bond angles, and dihedral angles. Finally, we performed several additional simulations with varying starting conditions compared with run 2, e.g. we used differing initial positions of strychnine with respect to the polymer or different starting velocities. We observed that these conditions influence the quality of predicted RDCs, with σ [exp/calc] values usually varying by ±1 Hz. This variation meets the convergence criteria derived by the calculations shown in Fig. 2(b). For the best run, we obtained predicted data being in very good agreement with the measured ones (run 3; σ [exp/calc] = 1.3 Hz). As shown in Fig. 3(b), values from run 3 and RDCs predicted with Prediction of Alignment from Structure (PALES) and tracking alignment from the moment of inertia tensor (TRAMITE) demonstrate the very good correlation of our MD results with the experimental data compared with the two state-of-the-art approaches designed for biomacromolecules.[9,24]
Discussion and Potential Improvements
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The results obtained from simulating strychnine in a PS/CDCl3 gel model demonstrate the usefulness and potential of the proposed concept for predicting partial alignment. Please note that results of strychnine in PS/CDCl3 cannot be transferred to measurements using other alignment media like poly(γ-benzyl-L-glutamate)/ CDCl3[37] or poly(methyl methacrylate)/CDCl3[38] as the detailed structure of the alignment medium is part of the prediction. Our method is based on atomistic MD calculations of a polymer strand that is oriented along a principal axis. For a proof of principle, we developed and tested different calculation setups and identified simulation parameters for a first feasible implementation that provides a good coverage of all allowed solute orientations with respect to the polymer mimicking the alignment medium. However, the implementation could certainly be improved for a broader applicability. A technical problem is the frequent occurrence of local energy minima arising out of the omission of solvent molecules and the presence of fixed polymer end group atoms, which was found to be the main cause of impaired orientational sampling, resulting in a temporarily trapped strychnine molecule and therefore inaccurate results. In order to avoid misleading interactions of the solute and the polymer, we expect recently described algorithms that enable the simulation of infinitely long polymer strands crossing periodic box boundaries to be highly beneficial.[39] Describing PS as an infinite chain not only would eliminate artificial interactions with positionally restrained polymer end groups but also may generally be a better approximation of the overall structure and behavior (e.g. flexibility and elasticity) of the stretched alignment medium. It must also be recognized that the use of explicit solvent simulations is desirable and probably inevitable for the accurate description of polymer and solute molecules with
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considerable flexibility and/or polarity. However, explicit solvent runs drastically prolong MD simulation times because of the much greater particle numbers to be simulated and the less frequently occurring interactions between the solute and the polymer and require the use of cluster computing and enhanced sampling methods.[40] The treatment of charged alignment media, solute molecules, and solvent will, in addition, involve an adequate treatment of charges, as has been previously shown for Pf1-phage, and will further increase computation times. When comparing the different prediction methods, the biggest disadvantage of the presented approach is certainly the high effort and the special knowledge that is necessary to adequately parametrize polymer, solute, and eventually solvent molecules for the corresponding MD simulation. The relatively rough models designed for biomacromolecules allow the prediction of small molecule alignment in special cases[10,41] but did not lead to satisfying correlations with experimental data in most other cases in our hands (unpublished data). A more detailed and therefore much more elaborate model for the prediction of alignment of small to medium-sized organic molecules, like the one presented here, is probably necessary. Conventional methods for RDC prediction are usually much easier to apply, and the MD-based approach will only be applied if such methods fail. A solution with intermediate effort might also be the partial incorporation of fine structure or flexibility as additional dimensions in a grid search as used, for example, in the PALES program. The grid search would guarantee full averaging over all possible orientations with most reliable resulting couplings. The computational time for covering all structural and dynamic aspects, however, would by far exceed the time needed for the corresponding MD simulation, and practical feasibility must be questioned. Regarding the sampling of conformational space and multiple populated states, it must be ensured that all contributing timescales are covered by the simulation. It has been shown recently that MD trajectories can be calculated even in the millisecond range,[42,43] but more promising for actual calculations seem to be computational approaches enabling larger timescale coverage like replica exchange.[44,45] In principle, also Monte Carlo-based methods, which can massively be parallelized, should be applicable to RDC predictions, as calculating the explicit time course of molecular trajectories is not needed for orientational averaging.
Conclusion and Outlook Verified by experimental data, we have shown for strychnine in PS/CDCl3 that the accurate prediction of RDCs is possible based on MD calculations using a simple but atomistic model of the aligning polymer. As the general concept with a single polymer chain oriented along the principle axis should also work for other gel-based alignment media and possibly even for lyotropic, polymer-based liquid crystalline phases, we foresee a multitude of potential applications of the method where conventional fitting and prediction tools have failed, including, for example, the determination of the oligomeric state, the treatment of multiple conformers, or the absolute configuration of small molecules in (chiral) alignment media.[10,46,47] However, it remains to be proven in future studies how far the model can be applied to such cases. Acknowledgement We gratefully thank Prof. Dr. Wilfred F. van Gunsteren and his group at the Eidgenössische Technische Hochschule Zürich and
Copyright © 2015 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2015, 53, 213–217
Direct prediction of residual dipolar couplings by stochastic MD simulations Dr. Amr Fahmy (Harvard Medical School) for helpful discussions and suggestions. This work was supported by the Deutsche Forschungsgemeinschaft (Heisenberg fellowship LU 835/2,3,4,7,8; Forschergruppe FOR 934, Instrumentation facility Pro2NMR), the HGF program BioInterfaces, and the Center of Integrated Protein Science Munich.
References [1] A. Bax. Protein Sci. 2003, 12, 1–16. [2] J. H. Prestegard, C. M. Bougault, A. I. Kishore. Chem. Rev. 2004, 104, 3519–3540. [3] C. M. Thiele. Concepts Magn. Reson. 2007, 30A, 65–80. [4] G. Kummerlöwe, B. Luy. Trac-Trends Anal. Chem. 2009, 28, 483–493. [5] G. Kummerlöwe, B. Luy, G. Webb. Annu. Rep. NMR Spectrosc. 2009, 68, 193–230. [6] R. R. Gil. Angew. Chem.-Int. Ed. 2011, 50, 7222–7224. [7] A. Saupe. Angew. Chem.-Int. Ed. 1968, 7, 97–112. [8] R. Y. Dong, Nuclear Magnetic Resonance of Liquid Crystals, Springer, New York, 1997. [9] M. Zweckstetter, A. Bax. J. Am. Chem. Soc. 2000, 122, 3791–3792. [10] B. J. Luy. Indian Inst. Sci. 2010, 90, 119–132. [11] D. Catalano, L. Dibari, C. A. Veracini, G. N. Shilstone, C. Zannoni. J. Chem. Phys. 1991, 94, 3928–3935. [12] J. W. Emsley, G. R. Luckhurst, C. P. Stockley. Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 1982, 381, 117–138. [13] B. Stevensson, D. Sandstrom, A. Maliniak. J. Chem. Phys. 2003, 119, 2738–2746. [14] J. Thaning, B. Stevensson, J. Ostervall, K. J. Naidoo, G. Widmalm, A. Maliniak. J. Phys. Chem. B 2008, 112, 8434–8436. [15] G. Celebre, G. De Luca, M. E. Di Pietro. J. Phys. Chem. B 2012, 116, 2876–2885. [16] E. E. Burnell, C. A. Delange. Chem. Phys. Lett. 1980, 76, 268–272. [17] E. E. Burnell, C. A. Delange, O. G. Mouritsen. J. Magn. Reson. 1982, 50, 188–196. [18] M. E. Garcia, S. Pagola, A. Navarro-Vázquez, D. D. Phillips, C. Gayathri, H. Krakauer, P. W. Stephens, V. E. Nicotra, R. R. Gil. Angew. Chem.-Int. Ed. 2009, 48, 5670–5674. [19] C. Perez-Balado, H. Sun, C. Griesinger, A. R. de Lera, A. Navarro-Vázquez. Chem.-A Eur. J. 2011, 17, 11983–11986. [20] A. Schuetz, J. Junker, A. Leonov, O. F. Lange, T. F. Molinski, C. Griesinger. J. Am. Chem. Soc. 2007, 129, 15114–-15115. [21] H. Sun, U. M. Reinscheid, E. L. Whitson, E. J. d’Auvergne, C. M. Ireland, A. Navarro-Vázquez, C. Griesinger. J. Am. Chem. Soc. 2011, 133, 14629–14636. [22] C. M. Thiele, V. Schmidts, B. Böttcher, I. Louzao, R. Berger, A. Maliniak, B. Stevensson. Angew. Chem.-Int. Ed. 2009, 48, 6708–6712. [23] M. Zweckstetter, G. Hummer, A. Bax. Biophys. J. 2004, 86, 3444–3460.
[24] H. F. Azurmendi, C. A. Bush. J. Am. Chem. Soc. 2002, 124, 2426–2427. [25] B. Wu, M. Petersen, F. Girard, M. Tessari, S. S. Wijmenga. J. Biomol. NMR 2006, 35, 103–115. [26] A. Navarro-Vázquez. Magn. Reson. Chem. 2012, 50, S73–S79. [27] A. Pizzirusso, M. B. Di Cicco, G. Tiberio, L. Muccioli, R. Berardi, C. Zannoni. J. Phys. Chem. B 2012, 116, 3760–3771. [28] A. C. J. Weber, A. Pizzirusso, L. Muccioli, C. Zannoni, W. L. Meerts, C. A. de Lange, E. E. Burnell. J. Chem. Phys. 2012, 136, 174506. [29] B. Luy, Research Group Meeting "RDCs on Small Molecules". Darmstadt; 2010. [30] B. Luy, K. Kobzar, H. Kessler. Angew. Chem.-Int. Ed. 2004, 43, 1092–1094. [31] B. Luy, K. Kobzar, S. Knör, J. Furrer, D. Heckmann, H. Kessler. J. Am. Chem. Soc. 2005, 127, 6459–6465. [32] G. Kummerlöwe, S. Knör, A. O. Frank, T. Paululat, H. Kessler, B. Luy. Chem. Commun. 2008, 5722–5724. [33] D. Van der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark, H. J. C. Berendsen. J. Comput. Chem. 2005, 26, 1701–1718. [34] W. F. Van Gunsteren, H. J. C. Berendsen. Mol. Simul. 1988, 1, 173–185. [35] W. L. Jorgensen, D. S. Maxwell, J. TiradoRives. J. Am. Chem. Soc. 1996, 118, 11225–11236. [36] J. W. Emsley, J. C. Lindon, NMR Spectroscopy Using Liquid Crystal Solvents, Pergamon Press, Oxford, 1975. [37] C. M. Thiele. J. Org. Chem. 2004, 69, 7403–7413. [38] J. D. Snider, E. Troche-Pesqueira, S. R. Woodruff, C. Gayathri, N. V. Tsarevsky, R. R. Gil. Magn. Reson. Chem. 2012, 50, S86–S91. [39] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl. J. Chem. Theory Comput. 2008, 4, 435–447. [40] M. C. Zwier, L. T. Chong. Curr. Opin. Pharmacol. 2010, 10, 745–752. [41] J. C. Freudenberger, P. Spiteller, R. Bauer, H. Kessler, B. Luy. J. Am. Chem. Soc. 2004, 126, 14690–14691. [42] D. E. Shaw, P. Maragakis, K. Lindorff-Larsen, S. Piana, R. O. Dror, M. P. Eastwood, J. A. Bank, J. M. Jumper, J. K. Salmon, Y. B. Shan, W. Wriggers. Science 2010, 330, 341–346. [43] S. Piana, K. Lindorff-Larsen, D. E. Shaw. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 17845–17850. [44] M. Andrec, A. K. Felts, E. Gallicchio, R. M. Levy. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 6801–6806. [45] H. X. Lei, C. Wu, H. G. Liu, Y. Duan. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 4925–4930. [46] L. Ziani, P. Lesot, A. Meddour, J. Courtieu. Chem. Commun. 2007, 4737–4739. [47] R. Berger, J. Courtieu, R. R. Gil, C. Griesinger, M. Köck, P. Lesot, B. Luy, D. Merlet, A. Navarro-Vázquez, M. Reggelin, U. M. Reinscheid, C. M. Thiele, M. Zweckstetter. Angew. Chem.-Int. Ed. 2012, 51, 8388–8391.
Supporting Information Additional supporting information may be found in the online version of this article at the publisher’s website
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Copyright © 2015 John Wiley & Sons, Ltd.
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Revised: 23 September 2014
Accepted: 11 October 2014
Published online in Wiley Online Library: 22 January 2015
(wileyonlinelibrary.com) DOI 10.1002/mrc.4181
Direct prediction of residual dipolar couplings of small molecules in a stretched gel by stochastic molecular dynamics simulations Andreas O. Frank,a,† J. Christoph Freudenberger,b Alexey K. Shaytan,c,d Horst Kesslera,e and Burkhard Luyf,g* Residual dipolar couplings are highly useful NMR parameters for calculating and refining molecular structures, dynamics, and interactions. For some applications, however, it is inevitable that the preferred orientation of a molecule in an alignment medium is calculated a priori. Several methods have been developed to predict molecular orientations and residual dipolar couplings. Being beneficial for macromolecules and selected small-molecule applications, such approaches lack sufficient accuracy for a large number of organic compounds for which the fine structure and eventually the flexibility of all involved molecules have to be considered or are limited to specific, well-studied liquid crystals. We introduce a simplified model for detailed all-atom molecular dynamics calculations with a polymer strand lined up along the principal axis as a new approach to simulate the preferred orientation of small to medium-sized solutes in polymer-based, gel-type alignment media. As is shown by a first example of strychnine in a polystyrene/CDCl3 gel, the simulations potentially enable the accurate prediction of residual dipolar couplings taking into account structural details and dynamic averaging effects of both the polymer and the solute. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: NMR; 1H; orientational model
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C; residual dipolar couplings; MD simulations; stochastic dynamics; molecular alignment; RDC prediction;
Introduction
Magn. Reson. Chem. 2015, 53, 213–217
* Correspondence to: Burkhard Luy, Institute of Organic Chemistry and Institute for Biological Interfaces, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany. E-mail: [email protected] †
Present address: Novartis Institutes for BioMedical Research (NIBR), 5300 Chiron Way, Emeryville, CA 94608, USA.
a Institute for Advanced Study at the Department Chemie, Technische Universität München, Lichtenbergstr. 4, 85747, Garching, Germany b Bruker Biospin AG, Industriestr. 26, 8117, Fällanden, Switzerland c Institute of Polymer Science, University of Ulm, Albert-Einstein-Allee 47, 89069, Ulm, Germany d Biology Department, Moscow State University, 119991, Moscow, Russia e Chemistry Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia f Institut für Organische Chemie, Karlsruher Institut für Technologie (KIT), FritzHaber-Weg 6, 76131, Karlsruhe, Germany g Institut für Biologische Grenzflächen, Karlsruher Institut für Technologie (KIT), Postfach 3640, 76021, Karlsruhe, Germany
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Residual dipolar couplings (RDCs) and other anisotropic NMR parameters nowadays can routinely be measured in partially aligned samples.[1–6] They contain very valuable information for determining three-dimensional molecular structures. However, the a priori unknown orientational alignment of solute molecules makes the interpretation of data difficult. To date, RDCs are usually interpreted using the concept of the Saupe matrix or alignment tensor, respectively, which assumes the molecule of interest to be rigid.[7] However, the Saupe matrix approach fails for molecules with inherent flexibility[8] or when specific structural questions are addressed like the multimeric state or the absolute configuration of a compound.[9,10] While inherent flexibility can be addressed by applying mean field approaches based on analytical models with continuous bond rotation[11–15] or by more general single-tensor and multitensor fits[16–22] if sufficient anisotropic parameters can be measured, the latter cases and instances when only insufficient experimental values are accessible, data interpretation requires the accurate a priori prediction of alignment. Prediction of RDCs can be achieved using a variety of techniques originally designed for large biomolecules like proteins and nucleic acids. One successful method for this type of molecules is the approximation of the alignment medium as unstructured walls or rods.[9,23] Other approaches take into account dynamic information from molecular dynamics (MD) simulations of the solute and derive alignment properties from its tensor of gyration or its charge distributions,[24,25] as, for example, implemented in the program MSpin.[26] These types of approaches neglect the detailed structural properties of the alignment medium. While the fine structure of the alignment medium is of minor importance for proteins and nucleic
acids, it certainly defines the main interactions for small molecules that weakly interact with the polymer matrix of the medium. Only recently, an atomistic model for the MD-based simulation of orientation in the liquid crystalline phase 5CB has been introduced and studied in great detail.[27,28] The complex simulations of the particular alignment medium and a number of small solute molecules resulted in relatively good agreement of prediction and experiment. Simultaneously, we have been working on the prediction of
A. O. Frank et al. alignment of stretched polymer gels using MD simulations,[29] which, however, requires a different approach with a specific model for representing the orientation. In this short article, we introduce a seemingly viable concept and a first example for such a model based on MD simulations that includes the fine structure of the polymer used for alignment. For a proof of principle, we use strychnine diffused into a stretched polystyrene (PS)/CDCl3 gel,[30–32] which has been the first RDC measurement achieved in our laboratory[30] and which could not be predicted satisfyingly by previously reported methods.
mechanical stress on the gel results in a net excess of PS strands oriented along the direction of stretching (Fig. 1(b)).[30–32] Because this excess induces the experimentally detectable alignment of a solute, we constructed a model with a single PS chain oriented along the z-axis (corresponding to the stretching axis of the polymer and the static magnetic field of an NMR spectrometer) to simulate the averaged net orientation of the alignment medium. Practically, the atactic PS used in our NMR measurements[30] was mimicked by six styrene subunits with differing chiralities. Throughout the MD simulations using Gromacs 3.3.3,[33] backbone chain end atoms were positionally restrained to preserve the directionality of the strand.
Basic Model for Alignment In contrast to liquid crystals with their small subunits calculating an atom-resolved MD trajectory of an entire polymer network with all solute and solvent molecules included is hardly feasible because of limited computational power. Hence, we were faced with several challenges when conceptualizing MD runs to predict partial alignment of a solute molecule. First, a simple model of a stretched polymer gel exhibiting all necessary properties for generating alignment has to be constructed. Furthermore, MD boundary conditions must be found, which allow for frequent and realistic interactions between the polymer and the solute. Finally, a calculation setup has to be defined that enables an exhaustive sampling of molecular orientations and interactions. Our PS model was build based on the following assumption: in a conventional PS/CDCl3 gel, all polymer strands are isotropically distributed (Fig. 1(a)). To cause a preferred alignment of a solute diffused into the gel, which is the prerequisite for measuring RDCs, the polymer must be stretched in at least one dimension. The
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Figure 1. Simplified model of a cross-linked polymer gel (solvent molecules are not shown). (a) In a freely swollen gel, individual polymer strands are isotropically distributed. (b) In contrast, a mechanically stretched gel leads to a net excess of polymer strands being oriented along the stretching axis (z-axis).
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Implementation and Results Subsequently, MD boundary conditions were adjusted, and a proper calculation setup was chosen. To avoid artificial alignment of the solute as a result of collisions with MD box walls and to guarantee frequent interactions between strychnine and the PS strand, the MD runs were carried out in small cubic boxes (1.65-nm edge lengths) including periodic boundary conditions with a short cutoff radius of 0.7 nm and corresponding shift functions for van der Waals and Coulomb interactions. Whereas shorter box edges in the x and y dimensions negatively influenced results as strychnine could no longer freely rotate around its center of mass, longer transversal edges did not impact the predicted RDCs. All MD runs were performed in the gas phase because trajectories including CDCl3 molecules did not display convergence of observables even after one microsecond of simulation time. By adding both random and frictional force terms to Newton’s equations of motion (Langevin dynamics),[34] the viscous influence of solvent molecules on the dynamics of the system at 300 K was mimicked. Although not parameterized for vacuum simulations, we decided to use the Optimized Potentials for Liquid Simulations/all-atom (OPLS/AA)[35] force field for our calculations because it provides a wealth of atom types and bonded parameters for rare molecular motifs, e.g. multibridged atoms as occurring in strychnine. As discussed in more detail in the succeeding text, an accurate parameterization of the solute’s bonded force field terms had an important impact on the quality of predicted RDCs. Because strychnine does not contain ionizable groups, the experimentally used solvent chloroform has a very low dielectric constant, and interactions with the polymer are expected not to be dominated by polar forces, we assumed that inaccuracies introduced by the use of OPLS/AA under vacuum conditions are relatively small. As a decisive step for the conceptual proof, we tested the described model and calculation setup with respect to a sufficient orientational sampling of strychnine with as little computation time as possible. Our attempt was therefore to simulate strychnine in an isotropic environment (without polymer) to find out about convergence criteria for isotropic sampling. With a self-written Gromacs-based tool called g_orient, we monitored the function ξ i = (with the angles φi between the CH vectors and the z-axis of the MD box and the brackets indicating averaging over time) as a measure for anisotropy for all 22 carbon–hydrogen bond vectors i of strychnine; almost full convergence with |ξ i| < 0.005 is obtained after a run of 500 ns (Fig. 2(a)). To further prove our concept, we performed a second MD run with the polymer strand being allowed to rotate around its center of mass. This case corresponds to an isotropically oriented, i.e. unstretched gel with no net alignment. Indeed, the ξ i values slowly
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Direct prediction of residual dipolar couplings by stochastic MD simulations RDCs,[36] experimental couplings (Supporting Information) were used for fitting the computational data with a single proportionality factor ( 75 Hz). In Fig. 3(a), three sets of predicted RDCs from different MD runs are plotted against the 19 experimentally determined RDCs (see Supporting Information for details, tables, and additional figures). In run 1, 13 calculated RDCs match the experimental ones within a maximum error of ±3.0 Hz. However, six RDCs show deviations between 4.0 and 6.3 Hz (standard deviation between experimental and calculated data sets σ [exp/calc] = 3.0 Hz). A comparison of the most representative MD structure of strychnine after 500-ns simulation time and the experimentally observed lowest energy conformation [root-mean-square deviation (RMSD) = 0.49 Å] revealed that the solute force field parameters were not optimally chosen. A redefinition of several MD atom types and dihedral angles
Figure 2. Convergence of averaged alignment of strychnine in various MD 2 simulations using ξ i = values for all 22 CH vectors as the measure. The orientations of freely tumbling strychnine (a) as well as strychnine in a box with a PS strand that can rotate around its center of mass (b) average over time to an isotropic distribution with no net alignment. In contrast, strychnine with a PS strand lined up along the z-axis results in a net orientation of CH vectors proportional to corresponding RDCs (c). Transparent images of strychnine and polystyrene represent different positions and orientations during a trajectory.
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Figure 3. (a) Comparison of three sets of predicted and one set of 1 experimental DCH RDCs for strychnine in a PS/CDCl3 gel; open triangles, run 1; open squares, run 2; filled circles, run 3. (b) While the best MD run leads to a very good match of predicted and experimental RDCs (σ [exp/calc] = 1.3 Hz; filled circles), alternative approaches neglecting the fine structure of the alignment medium like PALES (σ [exp/calc] = 6.3 Hz; open triangles) or TRAMITE (σ [exp/calc] = 6.5 Hz; open diamonds) show a poor correlation.
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converge between 0.015 and +0.015 after 500 ns (Fig. 2(b)), which corresponds to the inherent statistical error of our prediction. In the final runs with the polymer strand orientationally restrained along the z-axis, corresponding ξ i values converge between 0.2 and +0.2 (Fig. 2(c)), clearly indicating preferred orientations of the solute molecule. As ξ i values are directly proportional to expected
A. O. Frank et al. (run2; see also Supporting Information) resulted in a better consensus between simulated and experimental strychnine structures (RMSD = 0.15 Å) and accordingly in a better match between predicted and experimental RDCs (σ [exp/calc] = 2.1 Hz). This outcome underpins the significance of a precise modeling of a small molecule’s fine structure on the accuracy of predicted RDCs. Stronger violations (≥3 Hz) are only found for vectors that belong to strychnine CH2 groups (carbons C12, C19, C21, and C24). These deviations might originate from a mismatch between the applied sp3-hybridized carbon force field parameters and the real geometry of the four affected CH2 groups; based on measured 1JCH coupling constants (Supporting Information), an sp2-contribution must be expected that influences equilibrium bond lengths, bond angles, and dihedral angles. Finally, we performed several additional simulations with varying starting conditions compared with run 2, e.g. we used differing initial positions of strychnine with respect to the polymer or different starting velocities. We observed that these conditions influence the quality of predicted RDCs, with σ [exp/calc] values usually varying by ±1 Hz. This variation meets the convergence criteria derived by the calculations shown in Fig. 2(b). For the best run, we obtained predicted data being in very good agreement with the measured ones (run 3; σ [exp/calc] = 1.3 Hz). As shown in Fig. 3(b), values from run 3 and RDCs predicted with Prediction of Alignment from Structure (PALES) and tracking alignment from the moment of inertia tensor (TRAMITE) demonstrate the very good correlation of our MD results with the experimental data compared with the two state-of-the-art approaches designed for biomacromolecules.[9,24]
Discussion and Potential Improvements
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The results obtained from simulating strychnine in a PS/CDCl3 gel model demonstrate the usefulness and potential of the proposed concept for predicting partial alignment. Please note that results of strychnine in PS/CDCl3 cannot be transferred to measurements using other alignment media like poly(γ-benzyl-L-glutamate)/ CDCl3[37] or poly(methyl methacrylate)/CDCl3[38] as the detailed structure of the alignment medium is part of the prediction. Our method is based on atomistic MD calculations of a polymer strand that is oriented along a principal axis. For a proof of principle, we developed and tested different calculation setups and identified simulation parameters for a first feasible implementation that provides a good coverage of all allowed solute orientations with respect to the polymer mimicking the alignment medium. However, the implementation could certainly be improved for a broader applicability. A technical problem is the frequent occurrence of local energy minima arising out of the omission of solvent molecules and the presence of fixed polymer end group atoms, which was found to be the main cause of impaired orientational sampling, resulting in a temporarily trapped strychnine molecule and therefore inaccurate results. In order to avoid misleading interactions of the solute and the polymer, we expect recently described algorithms that enable the simulation of infinitely long polymer strands crossing periodic box boundaries to be highly beneficial.[39] Describing PS as an infinite chain not only would eliminate artificial interactions with positionally restrained polymer end groups but also may generally be a better approximation of the overall structure and behavior (e.g. flexibility and elasticity) of the stretched alignment medium. It must also be recognized that the use of explicit solvent simulations is desirable and probably inevitable for the accurate description of polymer and solute molecules with
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considerable flexibility and/or polarity. However, explicit solvent runs drastically prolong MD simulation times because of the much greater particle numbers to be simulated and the less frequently occurring interactions between the solute and the polymer and require the use of cluster computing and enhanced sampling methods.[40] The treatment of charged alignment media, solute molecules, and solvent will, in addition, involve an adequate treatment of charges, as has been previously shown for Pf1-phage, and will further increase computation times. When comparing the different prediction methods, the biggest disadvantage of the presented approach is certainly the high effort and the special knowledge that is necessary to adequately parametrize polymer, solute, and eventually solvent molecules for the corresponding MD simulation. The relatively rough models designed for biomacromolecules allow the prediction of small molecule alignment in special cases[10,41] but did not lead to satisfying correlations with experimental data in most other cases in our hands (unpublished data). A more detailed and therefore much more elaborate model for the prediction of alignment of small to medium-sized organic molecules, like the one presented here, is probably necessary. Conventional methods for RDC prediction are usually much easier to apply, and the MD-based approach will only be applied if such methods fail. A solution with intermediate effort might also be the partial incorporation of fine structure or flexibility as additional dimensions in a grid search as used, for example, in the PALES program. The grid search would guarantee full averaging over all possible orientations with most reliable resulting couplings. The computational time for covering all structural and dynamic aspects, however, would by far exceed the time needed for the corresponding MD simulation, and practical feasibility must be questioned. Regarding the sampling of conformational space and multiple populated states, it must be ensured that all contributing timescales are covered by the simulation. It has been shown recently that MD trajectories can be calculated even in the millisecond range,[42,43] but more promising for actual calculations seem to be computational approaches enabling larger timescale coverage like replica exchange.[44,45] In principle, also Monte Carlo-based methods, which can massively be parallelized, should be applicable to RDC predictions, as calculating the explicit time course of molecular trajectories is not needed for orientational averaging.
Conclusion and Outlook Verified by experimental data, we have shown for strychnine in PS/CDCl3 that the accurate prediction of RDCs is possible based on MD calculations using a simple but atomistic model of the aligning polymer. As the general concept with a single polymer chain oriented along the principle axis should also work for other gel-based alignment media and possibly even for lyotropic, polymer-based liquid crystalline phases, we foresee a multitude of potential applications of the method where conventional fitting and prediction tools have failed, including, for example, the determination of the oligomeric state, the treatment of multiple conformers, or the absolute configuration of small molecules in (chiral) alignment media.[10,46,47] However, it remains to be proven in future studies how far the model can be applied to such cases. Acknowledgement We gratefully thank Prof. Dr. Wilfred F. van Gunsteren and his group at the Eidgenössische Technische Hochschule Zürich and
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Direct prediction of residual dipolar couplings by stochastic MD simulations Dr. Amr Fahmy (Harvard Medical School) for helpful discussions and suggestions. This work was supported by the Deutsche Forschungsgemeinschaft (Heisenberg fellowship LU 835/2,3,4,7,8; Forschergruppe FOR 934, Instrumentation facility Pro2NMR), the HGF program BioInterfaces, and the Center of Integrated Protein Science Munich.
References [1] A. Bax. Protein Sci. 2003, 12, 1–16. [2] J. H. Prestegard, C. M. Bougault, A. I. Kishore. Chem. Rev. 2004, 104, 3519–3540. [3] C. M. Thiele. Concepts Magn. Reson. 2007, 30A, 65–80. [4] G. Kummerlöwe, B. Luy. Trac-Trends Anal. Chem. 2009, 28, 483–493. [5] G. Kummerlöwe, B. Luy, G. Webb. Annu. Rep. NMR Spectrosc. 2009, 68, 193–230. [6] R. R. Gil. Angew. Chem.-Int. Ed. 2011, 50, 7222–7224. [7] A. Saupe. Angew. Chem.-Int. Ed. 1968, 7, 97–112. [8] R. Y. Dong, Nuclear Magnetic Resonance of Liquid Crystals, Springer, New York, 1997. [9] M. Zweckstetter, A. Bax. J. Am. Chem. Soc. 2000, 122, 3791–3792. [10] B. J. Luy. Indian Inst. Sci. 2010, 90, 119–132. [11] D. Catalano, L. Dibari, C. A. Veracini, G. N. Shilstone, C. Zannoni. J. Chem. Phys. 1991, 94, 3928–3935. [12] J. W. Emsley, G. R. Luckhurst, C. P. Stockley. Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 1982, 381, 117–138. [13] B. Stevensson, D. Sandstrom, A. Maliniak. J. Chem. Phys. 2003, 119, 2738–2746. [14] J. Thaning, B. Stevensson, J. Ostervall, K. J. Naidoo, G. Widmalm, A. Maliniak. J. Phys. Chem. B 2008, 112, 8434–8436. [15] G. Celebre, G. De Luca, M. E. Di Pietro. J. Phys. Chem. B 2012, 116, 2876–2885. [16] E. E. Burnell, C. A. Delange. Chem. Phys. Lett. 1980, 76, 268–272. [17] E. E. Burnell, C. A. Delange, O. G. Mouritsen. J. Magn. Reson. 1982, 50, 188–196. [18] M. E. Garcia, S. Pagola, A. Navarro-Vázquez, D. D. Phillips, C. Gayathri, H. Krakauer, P. W. Stephens, V. E. Nicotra, R. R. Gil. Angew. Chem.-Int. Ed. 2009, 48, 5670–5674. [19] C. Perez-Balado, H. Sun, C. Griesinger, A. R. de Lera, A. Navarro-Vázquez. Chem.-A Eur. J. 2011, 17, 11983–11986. [20] A. Schuetz, J. Junker, A. Leonov, O. F. Lange, T. F. Molinski, C. Griesinger. J. Am. Chem. Soc. 2007, 129, 15114–-15115. [21] H. Sun, U. M. Reinscheid, E. L. Whitson, E. J. d’Auvergne, C. M. Ireland, A. Navarro-Vázquez, C. Griesinger. J. Am. Chem. Soc. 2011, 133, 14629–14636. [22] C. M. Thiele, V. Schmidts, B. Böttcher, I. Louzao, R. Berger, A. Maliniak, B. Stevensson. Angew. Chem.-Int. Ed. 2009, 48, 6708–6712. [23] M. Zweckstetter, G. Hummer, A. Bax. Biophys. J. 2004, 86, 3444–3460.
[24] H. F. Azurmendi, C. A. Bush. J. Am. Chem. Soc. 2002, 124, 2426–2427. [25] B. Wu, M. Petersen, F. Girard, M. Tessari, S. S. Wijmenga. J. Biomol. NMR 2006, 35, 103–115. [26] A. Navarro-Vázquez. Magn. Reson. Chem. 2012, 50, S73–S79. [27] A. Pizzirusso, M. B. Di Cicco, G. Tiberio, L. Muccioli, R. Berardi, C. Zannoni. J. Phys. Chem. B 2012, 116, 3760–3771. [28] A. C. J. Weber, A. Pizzirusso, L. Muccioli, C. Zannoni, W. L. Meerts, C. A. de Lange, E. E. Burnell. J. Chem. Phys. 2012, 136, 174506. [29] B. Luy, Research Group Meeting "RDCs on Small Molecules". Darmstadt; 2010. [30] B. Luy, K. Kobzar, H. Kessler. Angew. Chem.-Int. Ed. 2004, 43, 1092–1094. [31] B. Luy, K. Kobzar, S. Knör, J. Furrer, D. Heckmann, H. Kessler. J. Am. Chem. Soc. 2005, 127, 6459–6465. [32] G. Kummerlöwe, S. Knör, A. O. Frank, T. Paululat, H. Kessler, B. Luy. Chem. Commun. 2008, 5722–5724. [33] D. Van der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark, H. J. C. Berendsen. J. Comput. Chem. 2005, 26, 1701–1718. [34] W. F. Van Gunsteren, H. J. C. Berendsen. Mol. Simul. 1988, 1, 173–185. [35] W. L. Jorgensen, D. S. Maxwell, J. TiradoRives. J. Am. Chem. Soc. 1996, 118, 11225–11236. [36] J. W. Emsley, J. C. Lindon, NMR Spectroscopy Using Liquid Crystal Solvents, Pergamon Press, Oxford, 1975. [37] C. M. Thiele. J. Org. Chem. 2004, 69, 7403–7413. [38] J. D. Snider, E. Troche-Pesqueira, S. R. Woodruff, C. Gayathri, N. V. Tsarevsky, R. R. Gil. Magn. Reson. Chem. 2012, 50, S86–S91. [39] B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl. J. Chem. Theory Comput. 2008, 4, 435–447. [40] M. C. Zwier, L. T. Chong. Curr. Opin. Pharmacol. 2010, 10, 745–752. [41] J. C. Freudenberger, P. Spiteller, R. Bauer, H. Kessler, B. Luy. J. Am. Chem. Soc. 2004, 126, 14690–14691. [42] D. E. Shaw, P. Maragakis, K. Lindorff-Larsen, S. Piana, R. O. Dror, M. P. Eastwood, J. A. Bank, J. M. Jumper, J. K. Salmon, Y. B. Shan, W. Wriggers. Science 2010, 330, 341–346. [43] S. Piana, K. Lindorff-Larsen, D. E. Shaw. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 17845–17850. [44] M. Andrec, A. K. Felts, E. Gallicchio, R. M. Levy. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 6801–6806. [45] H. X. Lei, C. Wu, H. G. Liu, Y. Duan. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 4925–4930. [46] L. Ziani, P. Lesot, A. Meddour, J. Courtieu. Chem. Commun. 2007, 4737–4739. [47] R. Berger, J. Courtieu, R. R. Gil, C. Griesinger, M. Köck, P. Lesot, B. Luy, D. Merlet, A. Navarro-Vázquez, M. Reggelin, U. M. Reinscheid, C. M. Thiele, M. Zweckstetter. Angew. Chem.-Int. Ed. 2012, 51, 8388–8391.
Supporting Information Additional supporting information may be found in the online version of this article at the publisher’s website
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