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Optimal clustering for quantum refinement of biomolecular structures: Q|R#4

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Abstract

Quantum refinement (Q|R) of crystallographic or cryo-EM-derived structures of biomolecules within the Q|R project aims at using ab initio computations instead of library-based chemical restraints. An atomic model refinement requires the calculation of the gradient of the objective function. While it is not a computational bottleneck in classic refinement it is a roadblock if the objective function requires ab initio calculations. A solution to this problem adopted in Q|R is to divide the molecular system into manageable parts and do computations for these parts rather than using the whole macromolecule. This work focuses on the validation and optimization of the automatic divide-and-conquer procedure developed within the Q|R project. Also, we propose an atomic gradient error score that can be easily examined with common molecular visualization programs. While the tool is designed to work within the Q|R setting the error score can be adapted to similar fragmentation methods. The gradient testing tool presented here allows a priori determination of the computationally efficient strategy given available resources for the potentially time-expensive refinement process. The procedure is illustrated using a peptide and small protein models considering different quantum mechanical (QM) methodologies from Hartree–Fock, including basis set and dispersion corrections, to the modern semi-empirical method from the GFN-xTB family. The results obtained provide some general recommendations for the reliable and effective quantum refinement of larger peptides and proteins.

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References

  1. Shi Y (2014) A glimpse of structural biology through X-ray crystallography. Cell 159:995–1014. https://doi.org/10.1016/j.cell.2014.10.051

    Article  CAS  PubMed  Google Scholar 

  2. Branden CI, Tooze J (2012) Introduction to protein structure. Garland Science, New York. https://doi.org/10.1201/9781136969898

    Book  Google Scholar 

  3. Borbulevych OY, Plumley JA, Martin RI et al (2014) Accurate macromolecular crystallographic refinement: incorporation of the linear scaling, semiempirical quantum-mechanics program DivCon into the PHENIX refinement package. Acta Crystallogr Sect D Biol Crystallogr 70:1233–1247. https://doi.org/10.1107/S1399004714002260

    Article  CAS  Google Scholar 

  4. Senthil R, Sakthivel M, Usha S (2021) Structure-based drug design of peroxisome proliferator-activated receptor gamma inhibitors: ferulic acid and derivatives. J Biomol Struct Dyn 39:1295–1311. https://doi.org/10.1080/07391102.2020.1740790

    Article  CAS  PubMed  Google Scholar 

  5. Kordbacheh S, Kasko AM (2021) Peptide and protein engineering by modification of backbone and sidechain functional groups. Polym Int 70:889–896. https://doi.org/10.1002/pi.6208

    Article  CAS  Google Scholar 

  6. Urzhumtsev AG, Lunin VY (2019) Introduction to crystallographic refinement of macromolecular atomic models. Crystallogr Rev 25:164–262. https://doi.org/10.1080/0889311X.2019.1631817

    Article  Google Scholar 

  7. Waser J (1963) Least-squares refinement with subsidiary conditions. Acta Cryst 16:1091–1094. https://doi.org/10.1107/S0365110X63002929

    Article  CAS  Google Scholar 

  8. Engh R, Huber R (2001) International Tables for Crystallography, vol F, edited by MG Rossmann & E. Arnold, Kluwer Academic Publishers, Dordrecht, pp 382–392

  9. Groom CR, Bruno IJ, Lightfoot MP et al (2016) The Cambridge structural database. Acta Crystallogr B Struct Sci Cryst Eng Mater 72:171–179. https://doi.org/10.1107/S2052520616003954

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Taylor R, Wood PA (2019) A million crystal structures: the whole is greater than the sum of its parts. Chem Rev 119:9427–9477. https://doi.org/10.1021/acs.chemrev.9b00155

    Article  CAS  PubMed  Google Scholar 

  11. Vaitkus A, Merkys A, Gražulis S (2021) Validation of the crystallography open database using the crystallographic information framework. J Appl Crystallogr 54:661–672. https://doi.org/10.1107/S1600576720016532

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Berkholz DS, Shapovalov MV, Dunbrack RL Jr et al (2009) Conformation dependence of backbone geometry in proteins. Structure 17:1316–1325. https://doi.org/10.1016/j.str.2009.08.012

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Moriarty NW, Tronrud DE, Adams PD et al (2014) Conformation-dependent backbone geometry restraints set a new standard for protein crystallographic refinement. FEBS J 281:4061–4071. https://doi.org/10.1111/febs.12860

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Moriarty NW, Tronrud DE, Adams PD et al (2016) A new default restraint library for the protein backbone in Phenix: a conformation-dependent geometry goes mainstream. Acta Crystallogr D Struct Biol 72:176–179. https://doi.org/10.1107/S2059798315022408

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Liebeschuetz J, Hennemann J, Olsson T et al (2012) The good, the bad and the twisted: a survey of ligand geometry in protein crystal structures. J Comput Aided Mol Des 26:169–183. https://doi.org/10.1007/s10822-011-9538-6

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Janowski PA, Moriarty NW, Kelley BP et al (2016) Improved ligand geometries in crystallographic refinement using AFITT in PHENIX. Acta Crystallogr D Struct Biol 72:1062–1072. https://doi.org/10.1107/S2059798316012225

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Peach ML, Cachau RE, Nicklaus MC (2017) Conformational energy range of ligands in protein crystal structures: the difficult quest for accurate understanding. J Mol Recognit 30:e2618. https://doi.org/10.1002/jmr.2618

    Article  CAS  Google Scholar 

  18. Liebeschuetz JW (2021) The good, the bad, and the twisted revisited: an analysis of ligand geometry in highly resolved protein-ligand X-ray structures. J Med Chem 64:7533–7543. https://doi.org/10.1021/acs.jmedchem.1c00228

    Article  CAS  PubMed  Google Scholar 

  19. Brereton AE, Karplus PA (2015) Native proteins trap high-energy transit conformations. Sci Adv 1:e1501188. https://doi.org/10.1126/sciadv.1501188

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Jiang Z, Biczysko M, Moriarty NW (2018) Accurate geometries for “Mountain pass” regions of the Ramachandran plot using quantum chemical calculations. Proteins 86:273–278. https://doi.org/10.1002/prot.25451

    Article  CAS  PubMed  Google Scholar 

  21. Moriarty NW, Liebschner D, Tronrud DE et al (2020) Arginine off-kilter: guanidinium is not as planar as restraints denote. Acta Crystallogr D Struct Biol 76:1159–1166. https://doi.org/10.1107/S2059798320013534

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Qi HW, Kulik HJ (2019) Evaluating unexpectedly short non-covalent distances in x-ray crystal structures of proteins with electronic structure analysis. J Chem Inf Model 59:2199–2211. https://doi.org/10.1021/acs.jcim.9b00144

    Article  CAS  PubMed  Google Scholar 

  23. Moriarty NW, Janowski PA, Swails JM et al (2020) Improved chemistry restraints for crystallographic refinement by integrating the Amber force field into Phenix. Acta Crystallogr D Struct Biol 76:51–62. https://doi.org/10.1107/S2059798319015134

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Borbulevych O, Martin RI, Westerhoff LM (2018) High-throughput quantum-mechanics/molecular-mechanics (ONIOM) macromolecular crystallographic refinement with PHENIX/DivCon: the impact of mixed Hamiltonian methods on ligand and protein structure. Acta Crystallogr D Struct Biol 74:1063–1077. https://doi.org/10.1107/S2059798318012913

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Genoni A, Bučinský L, Claiser N et al (2018) Quantum crystallography: current developments and future perspectives. Chem Eur J 24:10881–10905. https://doi.org/10.1002/chem.201705952

    Article  CAS  PubMed  Google Scholar 

  26. Caldararu O, Manzoni F, Oksanen E et al (2019) Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data. Acta Crystallogr D Struct Biol 75:368–380. https://doi.org/10.1107/S205979831900175X

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Yan Z, Li X, Chung LW (2021) Multiscale quantum refinement approaches for metalloproteins. J Chem Theory Comput 17:3783–3796. https://doi.org/10.1021/acs.jctc.1c00148

    Article  CAS  PubMed  Google Scholar 

  28. Bergmann J, Oksanen E, Ryde U (2022) Combining crystallography with quantum mechanics. Curr Opin Struct Biol 72:18–26. https://doi.org/10.1016/j.sbi.2021.07.002

    Article  CAS  PubMed  Google Scholar 

  29. Merz KM Jr (2014) Using quantum mechanical approaches to study biological systems. Acc Chem Res 47:2804–2811. https://doi.org/10.1021/ar5001023

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Zheng M, Reimers JR, Waller MP et al (2017) Q|R: quantum-based refinement. Acta Crystallogr D Struct Biol 73:45–52. https://doi.org/10.1107/S2059798316019847

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Liebschner D, Afonine PV, Baker ML et al (2019) Macromolecular structure determination using X-rays, neutrons and electrons: recent developments in Phenix. Acta Crystallogr D Struct Biol 75:861–877. https://doi.org/10.1107/S2059798319011471

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Vagin AA, Murshudov GN (2004) IUCr. Comput Comm Newsl 4:59–72

    Google Scholar 

  33. Vagin AA, Steiner RA, Lebedev AA et al (2004) REFMAC5 dictionary: Organization of prior chemical knowledge and guidelines for its use. Acta Crystallogr Sect D Biol Crystallogr 60:2184–2195. https://doi.org/10.1107/S0907444904023510

    Article  CAS  Google Scholar 

  34. Senn HM, Thiel W (2009) QM/MM methods for biomolecular systems. Angew Chem Int Ed 48:1198–1229. https://doi.org/10.1002/anie.200802019

    Article  CAS  Google Scholar 

  35. Ryde U (2016) QM/MM calculations on proteins. Meth Enzymol 577:119–158. https://doi.org/10.1016/bs.mie.2016.05.014

    Article  CAS  Google Scholar 

  36. Canfield P, Dahlbom MG, Hush NS et al (2006) Density-functional geometry optimization of the 150 000-atom photosystem-I trimer. J Chem Phys 124:024301. https://doi.org/10.1063/1.2148956

    Article  CAS  PubMed  Google Scholar 

  37. Grimme S, Antony J, Ehrlich S et al (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132:154104. https://doi.org/10.1063/1.3382344

    Article  CAS  PubMed  Google Scholar 

  38. Kruse H, Grimme S (2012) A geometrical correction for the inter-and intra-molecular basis set superposition error in Hartree–Fock and density functional theory calculations for large systems. J Chem Phys 136:04B613. https://doi.org/10.1063/1.3700154

    Article  CAS  Google Scholar 

  39. Grimme S, Bannwarth C, Shushkov P (2017) A robust and accurate tight-binding quantum chemical method for structures, vibrational frequencies, and noncovalent interactions of large molecular systems parametrized for all spd-block elements (Z = 1–86). J Chem Theory Comput 13:1989–2009. https://doi.org/10.1021/acs.jctc.7b00118

    Article  CAS  PubMed  Google Scholar 

  40. Klamt A, Schüürmann G (1993) COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J Chem Soc Perkin Trans 2:799–805. https://doi.org/10.1039/P29930000799

    Article  Google Scholar 

  41. Carlsen M, Røgen P (2015) Protein structure refinement by optimization. Proteins 83:1616–1624. https://doi.org/10.1002/prot.24846

    Article  CAS  PubMed  Google Scholar 

  42. Titov AV, Ufimtsev IS, Luehr N et al (2013) Generating efficient quantum chemistry codes for novel architectures. J Chem Theory Comput 9:213–221. https://doi.org/10.1021/ct300321a

    Article  CAS  PubMed  Google Scholar 

  43. Herbert JM (2019) Fantasy versus reality in fragment-based quantum chemistry. J Chem Phys 151:170901. https://doi.org/10.1063/1.5126216

    Article  CAS  PubMed  Google Scholar 

  44. Gordon MS, Fedorov DG, Pruitt SR et al (2012) Fragmentation methods: A route to accurate calculations on large systems. Chem Rev 112:632–672. https://doi.org/10.1021/cr200093j

    Article  CAS  PubMed  Google Scholar 

  45. Collins MA, Bettens RP (2015) Energy-based molecular fragmentation methods. Chem Rev 115:5607–5642. https://doi.org/10.1021/cr500455b

    Article  CAS  PubMed  Google Scholar 

  46. Raghavachari K, Saha A (2015) Accurate composite and fragment-based quantum chemical models for large molecules. Chem Rev 115:5643–5677. https://doi.org/10.1021/cr500606e

    Article  CAS  PubMed  Google Scholar 

  47. Liu J, He X (2020) Fragment-based quantum mechanical approach to biomolecules, molecular clusters, molecular crystals and liquids. Phys Chem Chem Phys 22:12341–12367. https://doi.org/10.1039/D0CP01095B

    Article  CAS  PubMed  Google Scholar 

  48. Kitaura K, Ikeo E, Asada T et al (1999) Fragment molecular orbital method: an approximate computational method for large molecules. Chem Phys Lett 313:701–706. https://doi.org/10.1016/S0009-2614(99)00874-X

    Article  CAS  Google Scholar 

  49. Zheng M, Moriarty NW, Xu Y et al (2017) Solving the scalability issue in quantum-based refinement: Q| R# 1. Acta Crystallogr D Struct Biol 73:1020–1028. https://doi.org/10.1107/S2059798317016746

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Zheng M, Biczysko M, Xu Y et al (2020) Including crystallographic symmetry in quantum-based refinement: Q| R# 2. Acta Crystallogr D Struct Biol 76:41–50. https://doi.org/10.1107/S2059798319015122

    Article  CAS  PubMed  Google Scholar 

  51. Wang L, Kruse H, Sobolev OV et al (2020) Real-space quantum-based refinement for cryo-EM: Q| R# 3. Acta Crystallogr D Struct Biol 76:1184–1191. https://doi.org/10.1107/S2059798320013194

    Article  CAS  PubMed  Google Scholar 

  52. Schmitz S, Seibert J, Ostermeir K et al (2020) Quantum chemical calculation of molecular and periodic peptide and protein structures. J Phys Chem B 124:3636–3646. https://doi.org/10.1021/acs.jpcb.0c00549

    Article  CAS  PubMed  Google Scholar 

  53. Riek R (2017) The three-dimensional structures of amyloids. Cold Spring Harb Perspect Biol 9:a023572. https://doi.org/10.1101/cshperspect.a023572

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Burley SK, Berman HM, Bhikadiya C et al (2019) Protein Data Bank: the single global archive for 3D macromolecular structure data. Nucleic Acids Res 47:D520–D528. https://doi.org/10.1093/nar/gky949

    Article  CAS  Google Scholar 

  55. Afonine PV, Grosse-Kunstleve RW, Echols N et al (2012) Towards automated crystallographic structure refinement with phenix. refine. Acta Crystallogr Sect D Biol Crystallogr 68:352–367. https://doi.org/10.1107/S0907444912001308

    Article  CAS  Google Scholar 

  56. Hait D, Head-Gordon M (2018) How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values. J Chem Theory Comput 14:1969–1981. https://doi.org/10.1021/acs.jctc.7b01252

    Article  CAS  PubMed  Google Scholar 

  57. DeLano WL (2002) The PyMOL Molecular Graphics System, DeLano Scientific, San Carlos, CA, USA. http://www.pymol.org

  58. Larsen AH, Mortensen JJ, Blomqvist J et al (2017) The atomic simulation environment—a Python library for working with atoms. J Phys Condens Matter 29:273002. https://doi.org/10.1088/1361-648X/aa680e

    Article  Google Scholar 

  59. Seritan S, Bannwarth C, Fales BS et al (2021) TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics. Wiley Interdiscip Rev Comput Mol Sci 11:e1494. https://doi.org/10.1002/wcms.1494

    Article  CAS  Google Scholar 

  60. Ufimtsev IS, Martinez TJ (2009) Quantum chemistry on graphical processing units. 3. analytical energy gradients, geometry optimization, and first principles molecular dynamics. J Chem Theory Comput 5:2619–2628. https://doi.org/10.1021/ct9003004

    Article  CAS  PubMed  Google Scholar 

  61. Liu F, Luehr N, Kulik HJ et al (2015) Quantum chemistry for solvated molecules on graphical processing units using polarizable continuum models. J Chem Theory Comput 11:3131–3144. https://doi.org/10.1021/acs.jctc.5b00370

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

MB and YW acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 31870738). MB also acknowledges support of the COST Action CA21101 "COSY."

Funding

Malgorzata Biczysko and Yaru Wang received financial support from the National Natural Science Foundation of China (Grant No. 31870738).

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Authors and Affiliations

  1. Physics Department, International Center for Quantum and Molecular Structures, College of Sciences, Shanghai University, Shanghai, 200444, People’s Republic of China

    Yaru Wang & Malgorzata Biczysko

  2. Pending AI, The National Innovation Centre, Eveleigh, NSW, 2015, Australia

    Holger Kruse & Mark P. Waller

  3. Molecular Biosciences and Integrated Bioimaging, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Nigel W. Moriarty & Pavel V. Afonine

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  1. Yaru Wang
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  5. Pavel V. Afonine
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  6. Malgorzata Biczysko
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Contributions

MB, HK and PVA wrote the original manuscript text. HK developed tools described in the manuscript. YW performed all computations, analysis and prepared figures. PVA, NWM, MPW and HK developed the overall code. All authors reviewed and approved the final manuscript.

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Correspondence to Holger Kruse, Pavel V. Afonine or Malgorzata Biczysko.

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Wang, Y., Kruse, H., Moriarty, N.W. et al. Optimal clustering for quantum refinement of biomolecular structures: Q|R#4. Theor Chem Acc 142, 100 (2023). https://doi.org/10.1007/s00214-023-03046-0

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