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Structure determination of high-energy states in a dynamic protein ensemble


Macromolecular function frequently requires that proteins change conformation into high-energy states1,2,3,4. However, methods for solving the structures of these functionally essential, lowly populated states are lacking. Here we develop a method for high-resolution structure determination of minorly populated states by coupling NMR spectroscopy-derived pseudocontact shifts5 (PCSs) with Carr–Purcell–Meiboom–Gill (CPMG) relaxation dispersion6 (PCS–CPMG). Our approach additionally defines the corresponding kinetics and thermodynamics of high-energy excursions, thereby characterizing the entire free-energy landscape. Using a large set of simulated data for adenylate kinase (Adk), calmodulin and Src kinase, we find that high-energy PCSs accurately determine high-energy structures (with a root mean squared deviation of less than 3.5 angström). Applying our methodology to Adk during catalysis, we find that the high-energy excursion involves surprisingly small openings of the AMP and ATP lids. This previously unresolved high-energy structure solves a longstanding controversy about conformational interconversions that are rate-limiting for catalysis. Primed for either substrate binding or product release, the high-energy structure of Adk suggests a two-step mechanism combining conformational selection to this state, followed by an induced-fit step into a fully closed state for catalysis of the phosphoryl-transfer reaction. Unlike other methods for resolving high-energy states, such as cryo-electron microscopy and X-ray crystallography, our solution PCS–CPMG approach excels in cases involving domain rearrangements of smaller systems (less than 60 kDa) and populations as low as 0.5%, and enables the simultaneous determination of protein structure, kinetics and thermodynamics while proteins perform their function.

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Fig. 1: Paramagnetic enhanced NMR for structure determination of a high-energy state during catalysis.
Fig. 2: Maximum-likelihood classification method for high-energy structure determination.
Fig. 3: The high-energy state of Adk during enzyme catalysis.
Fig. 4: General applicability of PCS–CPMG methodology.

Data availability

The NMR assignments of G. stearothermophilus adenylate kinase in its Zn2+- and Co2+-bound states have been deposited in the BioMagResBank74 under accession codes 51232 and 51233, respectively. Peak lists for the tagged ubiquitin variants can be obtained from All relevant data are available from the corresponding author upon request.

Code availability

Any relevant code is available by request from the corresponding author. A general script for the Expectation Maximization algorithm and test datasets are made available at


  1. Sekhar, A. & Kay, L. E. NMR paves the way for atomic level descriptions of sparsely populated, transiently formed biomolecular conformers. Proc. Natl Acad. Sci. USA 110, 12867–12874 (2013).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  2. Orellana, L. Large-scale conformational changes and protein function: breaking the in silico barrier. Front. Mol. Biosci. 6, 117 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. Nussinov, R. Introduction to protein ensembles and allostery. Chem. Rev. 116, 6263–6266 (2016).

    PubMed  Google Scholar 

  4. Haliloglu, T. & Bahar, I. Adaptability of protein structures to enable functional interactions and evolutionary implications. Curr. Opin. Struct. Biol. 35, 17–23 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. Bertini, I., Luchinat, C. & Parigi, G. Magnetic susceptibility in paramagnetic NMR. Prog. Nucl. Magn. Reson. Spectrosc. 40, 249–273 (2002).

    CAS  Google Scholar 

  6. Kleckner, I. R. & Foster, M. P. An introduction to NMR-based approaches for measuring protein dynamics. Biochim. Biophys. Acta 1814, 942–968 (2011).

    CAS  PubMed  Google Scholar 

  7. Boehr, D. D., McElheny, D., Dyson, H. J. & Wright, P. E. The dynamic energy landscape of dihydrofolate reductase catalysis. Science 313, 1638–1642 (2006).

    CAS  PubMed  ADS  Google Scholar 

  8. Cianfrocco, M. A. et al. Human TFIID binds to core promoter DNA in a reorganized structural state. Cell 152, 120–131 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  9. Zhao, J., Benlekbir, S. & Rubinstein, J. L. Electron cryomicroscopy observation of rotational states in a eukaryotic V-ATPase. Nature 521, 241–245 (2015).

    CAS  PubMed  ADS  Google Scholar 

  10. Neudecker, P. et al. Structure of an intermediate state in protein folding and aggregation. Science 336, 362–366 (2012).

    CAS  PubMed  ADS  Google Scholar 

  11. Dethoff, E. A., Petzold, K., Chugh, J., Casiano-Negroni, A. & Al-Hashimi, H. M. Visualizing transient low-populated structures of RNA. Nature 491, 724–728 (2012).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  12. Zhao, B., Guffy, S. L., Williams, B. & Zhang, Q. An excited state underlies gene regulation of a transcriptional riboswitch. Nat. Chem. Biol. 13, 968–974 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  13. Fraser, J. S. et al. Accessing protein conformational ensembles using room-temperature X-ray crystallography. Proc. Natl Acad. Sci. USA 108, 16247–16252 (2011).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  14. Bonomi, M. & Vendruscolo, M. Determination of protein structural ensembles using cryo-electron microscopy. Curr. Opin. Struct. Biol. 56, 37–45 (2019).

    CAS  PubMed  Google Scholar 

  15. Vogeli, B., Olsson, S., Guntert, P. & Riek, R. The exact NOE as an alternative in ensemble structure determination. Biophys. J. 110, 113–126 (2016).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  16. Leung, H. T. et al. A rigorous and efficient method to reweight very large conformational ensembles using average experimental data and to determine their relative information content. J. Chem. Theory Comput. 12, 383–394 (2016).

    CAS  PubMed  Google Scholar 

  17. Clore, G. M. & Iwahara, J. Theory, practice, and applications of paramagnetic relaxation enhancement for the characterization of transient low-population states of biological macromolecules and their complexes. Chem. Rev. 109, 4108–4139 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Maltsev, A. S., Grishaev, A., Roche, J., Zasloff, M. & Bax, A. Improved cross validation of a static ubiquitin structure derived from high precision residual dipolar couplings measured in a drug-based liquid crystalline phase. J. Am. Chem. Soc. 136, 3752–3755 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Korzhnev, D. M., Religa, T. L., Banachewicz, W., Fersht, A. R. & Kay, L. E. A transient and low-populated protein-folding intermediate at atomic resolution. Science 329, 1312–1316 (2010).

    CAS  ADS  PubMed  Google Scholar 

  20. Nerli, S., McShan, A. C. & Sgourakis, N. G. Chemical shift-based methods in NMR structure determination. Prog. Nucl. Magn. Reson. Spectrosc. 106-107, 1–25 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Bertini, I. et al. Experimentally exploring the conformational space sampled by domain reorientation in calmodulin. Proc. Natl Acad. Sci. USA 101, 6841–6846 (2004).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  22. Hass, M. A. S. et al. A minor conformation of a lanthanide tag on adenylate kinase characterized by paramagnetic relaxation dispersion NMR spectroscopy. J. Biomol. NMR 61, 123–136 (2015).

    CAS  PubMed  Google Scholar 

  23. Xu, D. et al. Ligand proton pseudocontact shifts determined from paramagnetic relaxation dispersion in the limit of NMR intermediate exchange. J. Phys. Chem. Lett. 9, 3361–3367 (2018).

    CAS  PubMed  Google Scholar 

  24. Eichmuller, C. & Skrynnikov, N. R. Observation of microsecond time-scale protein dynamics in the presence of Ln3+ ions: application to the N-terminal domain of cardiac troponin C. J. Biomol. NMR 37, 79–95 (2007).

    PubMed  Google Scholar 

  25. Kerns, S. J. et al. The energy landscape of adenylate kinase during catalysis. Nat. Struct. Mol. Biol. 22, 124–131 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Moon, S., Bannen, R. M., Rutkoski, T. J., Phillips, G. N. Jr & Bae, E. Effectiveness and limitations of local structural entropy optimization in the thermal stabilization of mesophilic and thermophilic adenylate kinases. Proteins 82, 2631–2642 (2014).

    CAS  PubMed  Google Scholar 

  27. Hanson, J. A. et al. Illuminating the mechanistic roles of enzyme conformational dynamics. Proc. Natl Acad. Sci. USA 104, 18055–18060 (2007).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  28. Aden, J. & Wolf-Watz, M. NMR identification of transient complexes critical to adenylate kinase catalysis. J. Am. Chem. Soc. 129, 14003–14012 (2007).

    PubMed  Google Scholar 

  29. Pelz, B., Zoldak, G., Zeller, F., Zacharias, M. & Rief, M. Subnanometre enzyme mechanics probed by single-molecule force spectroscopy. Nat. Commun. 7, 10848 (2016).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  30. Mukhopadhyay, A. et al. Crystal structure of the zinc-, cobalt-, and iron-containing adenylate kinase from Desulfovibrio gigas: a novel metal-containing adenylate kinase from Gram-negative bacteria. J. Biol. Inorg. Chem. 16, 51–61 (2011).

    CAS  PubMed  Google Scholar 

  31. Carver, J. P. & Richards, R. E. General 2-site solution for chemical exchange produced dependence of T2 upon Carr–Purcell pulse separation. J. Mag. Res. 6, 89–105 (1972).

    CAS  ADS  Google Scholar 

  32. Aviram, H. Y. et al. Direct observation of ultrafast large-scale dynamics of an enzyme under turnover conditions. Proc. Natl Acad. Sci. USA 115, 3243–3248 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  33. Skrynnikov, N. R., Dahlquist, F. W. & Kay, L. E. Reconstructing NMR spectra of “invisible” excited protein states using HSQC and HMQC experiments. J. Am. Chem. Soc. 124, 12352–12360 (2002).

    CAS  PubMed  Google Scholar 

  34. Schwieters, C. D., Kuszewski, J. J., Tjandra, N. & Clore, G. M. The Xplor-NIH NMR molecular structure determination package. J. Mag. Res. 160, 65–73 (2003).

    CAS  ADS  Google Scholar 

  35. Fallon, J. L. & Quiocho, F. A. A closed compact structure of native Ca2+-calmodulin. Structure 11, 1303–1307 (2003).

    CAS  PubMed  Google Scholar 

  36. Cowan-Jacob, S. W. et al. The crystal structure of a c-Src complex in an active conformation suggests possible steps in c-Src activation. Structure 13, 861–871 (2005).

    CAS  PubMed  Google Scholar 

  37. Müntener, T., Kottelat, J., Huber, A. & Häussinger, D. New lanthanide chelating tags for PCS NMR spectroscopy with reduction stable, rigid linkers for fast and irreversible conjugation to proteins. Bioconjugate Chem. 29, 3344–3351 (2018).

    Google Scholar 

  38. Chou, J. J., Li, S., Klee, C. B. & Bax, A. Solution structure of Ca2+-calmodulin reveals flexible hand-like properties of its domains. Nat. Struct. Biol. 8, 990–997 (2001).

    CAS  PubMed  Google Scholar 

  39. Russel, D. et al. Putting the pieces together: integrative modeling platform software for structure determination of macromolecular assemblies. PLoS Biol. 10, e1001244 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  40. Häussinger, D., Huang, J. R. & Grzesiek, S. DOTA-M8: an extremely rigid, high-affinity lanthanide chelating tag for PCS NMR spectroscopy. J. Am. Chem. Soc. 131, 14761–14767 (2009).

    PubMed  Google Scholar 

  41. Morgado, L., Burmann, B. M., Sharpe, T., Mazur, A. & Hiller, S. The dynamic dimer structure of the chaperone Trigger Factor. Nat. Commun. 8, 1992 (2017).

    PubMed  PubMed Central  ADS  Google Scholar 

  42. Kovermann, M., Grundstrom, C., Sauer-Eriksson, A. E., Sauer, U. H. & Wolf-Watz, M. Structural basis for ligand binding to an enzyme by a conformational selection pathway. Proc. Natl Acad. Sci. USA 114, 6298–6303 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Li, D., Liu, M. S. & Ji, B. Mapping the dynamics landscape of conformational transitions in enzyme: the adenylate kinase case. Biophys. J. 109, 647–660 (2015).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  44. Stiller, J. B. et al. Probing the transition state in enzyme catalysis by high-pressure NMR dynamics. Nat. Catal. 2, 726–734 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  45. Saio, T. & Ishimori, K. Accelerating structural life science by paramagnetic lanthanide probe methods. Biochim. Biophys. Acta 1864, 129332 (2019).

    Google Scholar 

  46. Nitsche, C. & Otting, G. Pseudocontact shifts in biomolecular NMR using paramagnetic metal tags. Prog. Nucl. Magn. Reson. Spectrosc. 98-99, 20–49 (2017).

    CAS  PubMed  Google Scholar 

  47. Ma, R. S. et al. Determination of pseudocontact shifts of low-populated excited states by NMR chemical exchange saturation transfer. Phys. Chem. Chem. Phys. 18, 13794–13798 (2016).

    CAS  PubMed  Google Scholar 

  48. Gerstein, M., Lesk, A. M. & Chothia, C. Structural mechanisms for domain movements in proteins. Biochemistry 33, 6739–6749 (1994).

    CAS  PubMed  Google Scholar 

  49. Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589 (2021).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  50. Schmitz, C., Stanton-Cook, M. J., Su, X. C., Otting, G. & Huber, T. Numbat: an interactive software tool for fitting Delta chi-tensors to molecular coordinates using pseudocontact shifts. J. Biomol. NMR 41, 179–189 (2008).

    CAS  PubMed  Google Scholar 

  51. Cai, M., Huang, Y., Craigie, R. & Clore, G. M. A simple protocol for expression of isotope-labeled proteins in Escherichia coli grown in shaker flasks at high cell density. J. Biomol. NMR 73, 743–748 (2019).

    CAS  PubMed  Google Scholar 

  52. Otting, G., Ruckert, M., Levitt, M. H. & Moshref, A. NMR experiments for the sign determination of homonuclear scalar and residual dipolar couplings. J. Biomol. NMR 16, 343–346 (2000).

    CAS  PubMed  Google Scholar 

  53. Joss, D., Walliser, R. M., Zimmermann, K. & Häussinger, D. Conformationally locked lanthanide chelating tags for convenient pseudocontact shift protein nuclear magnetic resonance spectroscopy. J. Biomol. NMR 72, 29–38 (2018).

    CAS  PubMed  Google Scholar 

  54. Romero, P. R. et al. BioMagResBank (BMRB) as a resource for structural biology. Methods Mol. Biol. 2112, 187–218 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  55. Orton, H. W., Huber, T. & Otting, G. Paramagpy: software for fitting magnetic susceptibility tensors using paramagnetic effects measured in NMR spectra. Magn. Reson. 1, 1–12 (2020).

    Google Scholar 

  56. Ishima, R. & Torchia, D. A. Extending the range of amide proton relaxation dispersion experiments in proteins using a constant-time relaxation-compensated CPMG approach. J. Biomol. NMR 25, 243–248 (2003).

    CAS  PubMed  Google Scholar 

  57. Delaglio, F. et al. NMRPipe: a multidimensional spectral processing system based on UNIX pipes. J. Biomol. NMR 6, 277–293 (1995).

    CAS  PubMed  Google Scholar 

  58. Vranken, W. F. et al. The CCPN data model for NMR spectroscopy: development of a software pipeline. Proteins 59, 687–696 (2005).

    CAS  PubMed  Google Scholar 

  59. Lee, W., Rahimi, M., Lee, Y. & Chiu, A. POKY: a software suite for multidimensional NMR and 3D structure calculation of biomolecules. Bioinformatics. 37, 3041–3042 (2021).

    CAS  PubMed Central  Google Scholar 

  60. Niklasson, M. et al. Comprehensive analysis of NMR data using advanced line shape fitting. J. Biomol. NMR 69, 93–99 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  61. Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python (2014).

  62. Counago, R., Chen, S. & Shamoo, Y. In vivo molecular evolution reveals biophysical origins of organismal fitness. Mol. Cell 22, 441–449 (2006).

    CAS  PubMed  Google Scholar 

  63. Abele, U. & Schulz, G. E. High-resolution structures of adenylate kinase from yeast ligated with inhibitor Ap5A, showing the pathway of phosphoryl transfer. Protein Sci. 4, 1262–1271 (1995).

    CAS  PubMed  PubMed Central  Google Scholar 

  64. Berry, M. B. & Phillips, G. N. Jr. Crystal structures of Bacillus stearothermophilus adenylate kinase with bound Ap5A, Mg2+ Ap5A, and Mn2+ Ap5A reveal an intermediate lid position and six coordinate octahedral geometry for bound Mg2+ and Mn2+. Proteins 32, 276–288 (1998).

    CAS  PubMed  Google Scholar 

  65. Diederichs, K. & Schulz, G. E. The refined structure of the complex between adenylate kinase from beef heart mitochondrial matrix and its substrate AMP at 1.85 Å resolution. J. Mol. Biol. 217, 541–549 (1991).

    CAS  PubMed  Google Scholar 

  66. Schlauderer, G. J., Proba, K. & Schulz, G. E. Structure of a mutant adenylate kinase ligated with an ATP-analogue showing domain closure over ATP. J. Mol. Biol. 256, 223–227 (1996).

    CAS  PubMed  Google Scholar 

  67. Henzler-Wildman, K. A. et al. Intrinsic motions along an enzymatic reaction trajectory. Nature 450, 838–844 (2007).

    CAS  PubMed  ADS  Google Scholar 

  68. Muller, C. W., Schlauderer, G. J., Reinstein, J. & Schulz, G. E. Adenylate kinase motions during catalysis: an energetic counterweight balancing substrate binding. Structure 4, 147–156 (1996).

    CAS  PubMed  Google Scholar 

  69. Arnold, K., Bordoli, L., Kopp, J. & Schwede, T. The SWISS-MODEL workspace: a web-based environment for protein structure homology modelling. Bioinformatics 22, 195–201 (2006).

    CAS  PubMed  Google Scholar 

  70. Word, J. M., Lovell, S. C., Richardson, J. S. & Richardson, D. C. Asparagine and glutamine: using hydrogen atom contacts in the choice of side-chain amide orientation. J. Mol. Biol. 285, 1735–1747 (1999).

    CAS  PubMed  Google Scholar 

  71. Chattopadhyaya, R., Meador, W. E., Means, A. R. & Quiocho, F. A. Calmodulin structure refined at 1.7 Å resolution. J. Mol. Biol. 228, 1177–1192 (1992).

    CAS  PubMed  Google Scholar 

  72. Xu, W., Doshi, A., Lei, M., Eck, M. J. & Harrison, S. C. Crystal structures of c-Src reveal features of its autoinhibitory mechanism. Mol. Cell 3, 629–638 (1999).

    CAS  PubMed  Google Scholar 

  73. Bertini, I., Janik, M. B., Lee, Y. M., Luchinat, C. & Rosato, A. Magnetic susceptibility tensor anisotropies for a lanthanide ion series in a fixed protein matrix. J. Am. Chem. Soc. 123, 4181–4188 (2001).

    CAS  PubMed  Google Scholar 

  74. Ulrich, E. L. et al. BioMagResBank. Nucleic Acids Res. 36, D402–D408 (2007).

    PubMed  PubMed Central  Google Scholar 

  75. Tollinger, M., Skrynnikov, N. R., Mulder, F. A., Forman-Kay, J. D. & Kay, L. E. Slow dynamics in folded and unfolded states of an SH3 domain. J. Am. Chem. Soc. 123, 11341–11352 (2001).

    CAS  PubMed  Google Scholar 

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We thank I. Hertel-Hering and M. Rogowski for expression of the K6C and S20C ubiquitin constructs, respectively; and S. Hiller for the trigger factor expression plasmid. This work was supported by the Howard Hughes Medical Institute (HHMI) to D.K., the NIH (R01GM121384 and R01GM132499) to D.L.T., and the Department of Chemistry at University of Basel to D.H. Computational resources were provided by NSF XSEDE computing resources. We acknowledge computational support from the Brandeis HPCC which is partially supported by the NSF through DMR-MRSEC 2011846 and OAC-1920147.

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Authors and Affiliations



D.K. conceived the project idea. D.K. and J.B.S. developed the research plan and experimental strategy. J.B.S. purified Adk, performed NMR experiments, and analysed results. D.H. and P.S.R. synthesized lanthanide-binding tags and prepared tagged ubiquitin samples. R.O. purified PPD–SBD proteins and prepared lanthanide-bound samples. R.O. performed the NMR experiments for ubiquitin and PPD–SBD trigger factor. R.O., J.B.S., D.K., P.S.R. and D.H. analysed results from the NMR experiments. D.L.T. designed the expectation maximization algorithm. J.B.S. implemented the algorithm into the XPLOR-NIH software and performed calculations on simulated and real data. All authors discussed results leading to overall scientific findings. J.B.S. and D.K. wrote the manuscript. All authors reviewed and edited the manuscript.

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Correspondence to Dorothee Kern.

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Nature thanks Hashim Al-Hashimi and the other, anonymous reviewer(s) for their contribution to the peer review of this work. Peer review reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Diamagnetic and paramagnetic samples were assigned by triple resonance experiments.

Backbone assignment of Zn2+ (left) and Co2+ (right) Adk proteins under saturating nucleotide conditions plotted onto Ap5A bound crystal structure, PDB 4QBH26. Orange spheres depict residues where no assignment was determined. Prolines are shown as gray sticks. All other amides are assigned. For the cobalt species, many residues surrounding the metal binding site are lost due to either Curie relaxation or exchange on the intermediate timescale.

Extended Data Fig. 2 PCSs in different ligand states reflect the conformational state of Adk.

Fits of PCSs extracted from [1H-15N]-HSQC spectra in either 20 mM Mg2+ADP (a), 20 mM ADP (b), and apo (c) to the closed crystal structure (PDB 4QBH26). Notably, the Mg2+/ADP data fits reasonably well (Q = 11.6%), but reports on PCSs from both the closed crystal structure and the minor state (i.e., population averaged). In the absence of magnesium, the open/closing exchange rate is in the slow time regime, leading to PCSs that better fit the closed state (Q = 7.6%). The apo PCSs report on a more open state, and, therefore, fit significantly worse (Q = 47.9%) to the closed state. (d) Calculating tensors using either paramagnetic-induced RDCs (left) or PCSs (right) provide similar tensor values, indicating little ps-ns motion of the paramagnet.

Extended Data Fig. 3 In the absence of magnesium, the open/closed rate exchange rate is in the slow exchange regime, in agreement with earlier reports25.

(a) [1H, 15N]-HSQC spectra for Zn2+ and Co2+ samples with either 20 mM ADP or 20 mM Mg2+ADP. Residues that were broadened in the Mg2+ADP sample show reduced linewidths in the ADP sample, indicating a shift in exchange timescales from intermediate to slow exchange. Black lines trace the PCSs between diamagnetic and paramagnetic samples. For residue 38, the corresponding diamagnetic peaks are at 8.46 ppm (1H) and 123.5 ppm (15N) and are not shown for illustration purposes. (b) 1HN CPMG dispersion profiles for Co2+ Adk with 20 mM ADP and 0 mM Mg2+. Representative traces show slow exchange that is fit to the Tollinger equation75 (F-statistics were used to determine whether the description by a slow exchange model compared to a “no-exchange” model was justified at the 95% confidence interval; p>0.05). (c) Representative CPMG relaxation dispersion profiles for residues in the presence on 20 mM Mg2+ADP. Notably, the paramagnetic chemical shift differences in the absence and presence of magnesium are similar, whereas the timescale is significantly altered (kopen, ADP = 2.6 ± 0.3 s−1 vs kopen, ADP = 180 ± 36 s−1). Uncertainties (s.d.) in R2,eff are determined from the rmsd in the intensities of duplicate points (n = 3) according to the definition of pooled relative standard deviation. Uncertainties (s.d.) in chemical shift differences were calculated from the covariance matrix.

Extended Data Fig. 4 Comparison of PCS values determined during apo and turnover conditions and correlation of PCSs during turnover conditions with the open structure of Adk.

(a) Overlay of PCS values obtained for apo and Mg2+ADP conditions. Values were determined from [1H-15N]-HSQC comparison in Zn2+ and Co2+ states. Note the sizable loss of PCS in the apo state compared to the closed state, indicating a more open structure in the absence of ligand. (b) Difference in PCS values for apo and turnover conditions. Large absolute differences of > 0.1 ppm are observed for many residues. (c) Zoom in of [1H-15N]-HSQC spectra in either 20 mM Mg2+ADP or apo conditions of Co2+ Adk. Noticeable line broadening is observed for apo conditions. (d) Fit of open state (4AKE68) to observed PCS shift data during catalytic turnover. (e) Best-fit tensor for PCS to open state structure. (f) Calculated PCSs for open state structure when fit with observed PCSs. A poor fit is found as the observed PCSs do not report on the open state structure. (g) The PCS difference expected between the open and closed state structures. Differences of |0.5 ppm| or greater would be expected for residues in AMP lid and core domain near the ATP lid.

Extended Data Fig. 5 Expectation-maximization during simulated annealing leads to correct PCS identifications for nearly all residues.

All 12 structures are shown with incorrectly chosen PCS as gray spheres. Mistakes usually occur near the end of secondary structure units, where local differences between crystal structures are most prevalent. For each structure, the core domain, ATP-lid, and AMP-lid are colored in wheat, red, and blue, respectively. The cobalt metal is shown as a green sphere.

Extended Data Fig. 6 Starting from an open or closed starting structure of Adk in the PCS-CPMG maximum-likelihood calculations results in equivalent final Adk structures.

(a) Open (lighter colors) and closed (darker colors) crystal structures, PDBs 4AKE68 and 4QBH26, respectively. (b) RMSD, Co2+-Core distance, and AMP-lid angle results for four calculated structures, all started from the open state (PDB 4AKE68). Similar to starting from the closed state (Fig. 2f), starting from an open state result in excellent collective variables, and excellent agreement with the experimental structures (shown as black stars). (c) Alignment of inferred structures starting from a closed state (blue) and open state (red) compared to the target structure (gray), highlighting that the new method results in converged and accurate structures independent of the starting model.

Extended Data Fig. 7 Plots of likelihood versus RMSD to the target structures for the first simulated annealing run for all 12 simulated Adk structures.

Structures which possess relatively low likelihood also have higher RMSD.

Extended Data Fig. 8 Eight PCS choices possible in the case where CPMG is performed in the presence of one diamagnetic and two paramagnetic metals.

As the diamagnetic sign is shared between the two paramagnetic dispersions, choices 1/3 and 2/4 are linked. This reduces the possible PCS choice for a specific residue.

Extended Data Fig. 9 Expectation-maximization of ambiguous PCSs are solved during structural calculations for calmodulin and src kinase.

PCSs of the final structures for calmodulin (a) and src kinase (b) have low Q values for both metals as well as accurate PCS identifications (blue stars for the correct PCS identification, red spheres are incorrect PCS identifications, dark blue line indicates the calculated PCS).

Extended Data Fig. 10 Ubiquitin and the chaperone trigger factor support lanthanide-binding tag coordination and produce substantial paramagnetic tensors.

(a) [1H-15N]-HSQC spectra of ubiquitin mutants S20C (left) and K6C (middle, right) bound with either the DOTA-M7PyThiazole (left, middle) or DOTA-M8-(4R4S)-SSPy(right) lanthanide-binding tags. Each spectrum shows large PCSs induced by Tm3+ bound tags. (b) Correlation plots between each ubiquitin variant’s PCSs and the calculated PCSs. (c) [1H-15N]-HSQC spectra of WT PPD-SBD, V270C PPD-SBD, M8-Lu-V270C PPD-SBD, and M8-Tm-V270C PPD-SBD. (d) Zoom-in of center section of the [1H-15N]-HSQC spectra of (c) showing nearly identical spectra for each sample. (e) Correlation plots between each M8-Tm-V270C PPD-SBD PCSs and the calculated PCSs.

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Stiller, J.B., Otten, R., Häussinger, D. et al. Structure determination of high-energy states in a dynamic protein ensemble. Nature 603, 528–535 (2022).

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