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Catalytic cycle of formate dehydrogenase captured by single-molecule conductance

Nature Catalysis volume 6, pages 266–275 (2023)Cite this article

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Abstract

Understanding the mechanisms and kinetics of enzymatic reactions is essential for studies of life science and for bioengineering. Here the different reaction states in the catalytic cycle of formate dehydrogenase have been distinguished by their characteristic conductances, using the scanning tunnelling microscope break-junction technique, and these conductances have been further exploited as markers to monitor the catalytic mechanism of formate dehydrogenase from Candida boidinii. Combined with multiscale simulations, we demonstrate that the bound reduced form of nicotinamide adenine dinucleotide (NADH) converts to nicotinamide adenine dinucleotide (NAD+) directly via a hydride-transfer reaction in situ during the catalytic cycle of formate dehydrogenase. This conversion does not proceed via the apoenzyme state invoked in the conventional, generally accepted Theorell–Chance mechanism. This work provides intriguing insight into the mechanism of formate dehydrogenase and highlights the potential of the single-molecule technique in revealing the catalytic mechanism of NADH/NAD+-dependent oxidoreductases.

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Fig. 1: The conductance of single-molecule FDH junctions measured by STM-BJ.
Fig. 2: Single-molecule FDH reaction dynamics monitored using a hover model of STM-BJ.
Fig. 3: Investigations of the mechanism.

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Data availability

All data that support the findings of this study are available within this Article and its Supplementary Information. Source data are provided with this paper.

Code availability

The data analysis of conductance measurements in this work was performed using our open-source code XME analysis, which is available at Github (https://github.com/Pilab-XMU/XMe_DataAnalysis) and Zenodo (https://doi.org/10.5281/zenodo.6578853). The code used for data processing in this study is available from the website: https://github.com/JChonpca/Algorithm_for_STM-based_Single_Molecule_Enzymology_Time_Series_Data.

References

  1. Whiteley, A. T. et al. Bacterial cGAS-like enzymes synthesize diverse nucleotide signals. Nature 567, 194–199 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Xu, D. Q. et al. The gluconeogenic enzyme PCK1 phosphorylates INSIG1/2 for lipogenesis. Nature 580, 530–535 (2020).

    Article  CAS  PubMed  Google Scholar 

  3. Raju, T. N. K. The Nobel Chronicles—1955: Axel Hugo Theodor Theorell (1903-82). Lancet 353, 1807–1807 (1999).

    Article  CAS  PubMed  Google Scholar 

  4. Theorell, H. & Chance, B. Studies on liver alcohol dehydrogenase. II. The kinetics of the compound of horse alcohol dehydrogenase and reduced diphosphopyridine nucleotide. Acta Chem. Scand. 5, 1127–1144 (1951).

    Article  CAS  Google Scholar 

  5. Dalziel, K. & Dickinson, F. M. Aldehyde mutase. Nature 4981, 255–257 (1965).

    Article  Google Scholar 

  6. Nelson, D. & Cox, M. in Lehninger Principles of Biochemistry 7th edn, 1415–1416 (W. H. Freeman, 2017).

  7. Robin, T., Reuveni, S. & Urbakh, M. Single-molecule theory of enzymatic inhibition. Nat. Commun. 9, 779 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  8. Kim, T. H. et al. The role of dimer asymmetry and protomer dynamics in enzyme catalysis. Science 355, eaag2355 (2017).

    Article  PubMed  Google Scholar 

  9. Sui, X. W. et al. Structure and catalytic mechanism of a human triacylglycerol-synthesis enzyme. Nature 581, 323–328 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Reimer, J. M. et al. Structures of a dimodular nonribosomal peptide synthetase reveal conformational flexibility. Science 366, eaaw4388 (2019).

    Article  CAS  PubMed  Google Scholar 

  11. Enugala, T. R., Morato, M. C., Kamerlin, S. C. L. & Widersten, M. The role of substrate–coenzyme crosstalk in determining turnover rates in Rhodococcus ruber alcohol dehydrogenase. ACS Catal. 10, 9115–9128 (2020).

    Article  CAS  Google Scholar 

  12. Hamnevik, E. et al. Relaxation of nonproductive binding and increased rate of coenzyme release in an alcohol dehydrogenase increases turnover with a nonpreferred alcohol enantiomer. FEBS J. 284, 3895–3914 (2017).

    Article  CAS  PubMed  Google Scholar 

  13. Maurer, D. et al. Stereo- and regioselectivity in catalyzed transformation of a 1,2-disubstituted vicinal diol and the corresponding diketone by wild type and laboratory evolved alcohol dehydrogenases. ACS Catal. 8, 7526–7538 (2018).

    Article  CAS  Google Scholar 

  14. Smiley, R. D. & Hammes, G. G. Single molecule studies of enzyme mechanisms. Chem. Rev. 106, 3080–3094 (2006).

    Article  CAS  PubMed  Google Scholar 

  15. Yang, H. Protein conformational dynamics probed by single-molecule electron transfer. Science 302, 262–266 (2003).

    Article  CAS  PubMed  Google Scholar 

  16. Michalet, X., Weiss, S. & Jager, M. Single-molecule fluorescence studies of protein folding and conformational dynamics. Chem. Rev. 106, 1785–1813 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Guo, Q., He, Y. F. & Lu, P. Interrogating the activities of conformational deformed enzyme by single-molecule fluorescence-magnetic tweezers microscopy. Proc. Natl Acad. Sci. USA 112, 13904–13909 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Sanabria, H. et al. Resolving dynamics and function of transient states in single enzyme molecules. Nat. Commun. 11, 1231 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Galenkamp, N. S., Biesemans, A. & Maglia, G. Directional conformer exchange in dihydrofolate reductase revealed by single-molecule nanopore recordings. Nat. Chem. 12, 481–488 (2020).

    Article  CAS  PubMed  Google Scholar 

  20. Lu, H. P., Xun, L. & Xie, X. S. Single-molecule enzymatic dynamics. Science 282, 1877–1882 (1998).

    Article  CAS  PubMed  Google Scholar 

  21. Aragones, A. C. et al. Measuring the spin-polarization power of a single chiral molecule. Small 13, 1602519 (2017).

    Article  Google Scholar 

  22. Tang, C. et al. Identifying the conformational isomers of single-molecule cyclohexane at room temperature. Chem 6, 2770–2781 (2020).

    Article  CAS  Google Scholar 

  23. Aragones, A. C. et al. Single-molecule electrical contacts on silicon electrodes under ambient conditions. Nat. Commun. 8, 15056 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Zang, Y. P. et al. Directing isomerization reactions of cumulenes with electric fields. Nat. Commun. 10, 4428 (2019).

    Article  Google Scholar 

  25. Greenwald, J. E. et al. Highly nonlinear transport across single-molecule junctions via destructive quantum interference. Nat. Nanotechnol. 16, 313–317 (2021).

    Article  CAS  PubMed  Google Scholar 

  26. Bruot, C. et al. Piezoresistivity in single DNA molecules. Nat. Commun. 6, 8032 (2015).

    Article  PubMed  Google Scholar 

  27. Beall, E. et al. Effects of the backbone and chemical linker on the molecular conductance of nucleic acid duplexes. J. Am. Chem. Soc. 139, 6726–6735 (2017).

    Article  CAS  PubMed  Google Scholar 

  28. Guo, C. L. et al. Molecular rectifier composed of DNA with high rectification ratio enabled by intercalation. Nat. Chem. 8, 484–490 (2016).

    Article  CAS  PubMed  Google Scholar 

  29. Chang, S. et al. Tunnelling readout of hydrogen-bonding-based recognition. Nat. Nanotechnol. 4, 297–301 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Brisendine, J. M. et al. Probing charge transport through peptide bonds. J. Phys. Chem. Lett. 9, 763–767 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Zhang, B. T., Song, W. S., Brown, J., Nemanich, R. & Lindsay, S. Electronic conductance resonance in non-redox-active proteins. J. Am. Chem. Soc. 142, 6432–6438 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Ruiz, M. P. et al. Bioengineering a single-protein junction. J. Am. Chem. Soc. 139, 15337–15346 (2017).

    Article  CAS  PubMed  Google Scholar 

  33. Cahen, D., Pecht, I. & Sheves, M. What can we learn from protein-based electron transport junctions? J. Phys. Chem. Lett. 12, 11598–11603 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Zhuang, X. Y. et al. Coenzyme coupling boosts charge transport through single bioactive enzyme junctions. iScience 23, 101001 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Xu, B. & Tao, N. J. Measurement of single-molecule resistance by repeated formation of molecular junctions. Science 301, 1221–1223 (2003).

    Article  CAS  PubMed  Google Scholar 

  36. Albrecht, T., Guckian, A., Kuznetsov, A. M., Vos, J. G. & Ulstrup, J. Mechanism of electrochemical charge transport in individual transition metal complexes. J. Am. Chem. Soc. 128, 17132–17138 (2006).

    Article  CAS  PubMed  Google Scholar 

  37. Wang, M., Bugarski, S. & Stimming, U. Topological and electron-transfer properties of glucose oxidase adsorbed on highly oriented pyrolytic graphite electrodes. J. Phys. Chem. C 112, 5165–5173 (2008).

    Article  CAS  Google Scholar 

  38. Alvarez-Malmagro, J. et al. Bioelectrocatalytic activity of W-formate dehydrogenase covalently immobilized on functionalized gold and graphite electrodes. ACS Appl. Mater. Inter. 13, 11891–11900 (2021).

    Article  CAS  Google Scholar 

  39. Zhang, L., Liu, J., Ong, J., Fong, S. & Li, Y. Specific and sustainable bioelectro-reduction of carbon dioxide to formate on a novel enzymatic cathode. Chemosphere 162, 228–234 (2016).

    Article  CAS  PubMed  Google Scholar 

  40. Guan, J. X. et al. Direct single-molecule dynamic detection of chemical reactions. Sci. Adv. 4, eaar2177 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  41. Xie, X. S. et al. Enzyme kinetics, past and present. Science 342, 1457–1459 (2013).

    Article  CAS  PubMed  Google Scholar 

  42. Mehrabi, P. et al. Time-resolved crystallography reveals allosteric communication aligned with molecular breathing. Science 365, 1167–1170 (2019).

    Article  CAS  PubMed  Google Scholar 

  43. Otten, R. et al. How directed evolution reshapes the energy landscape in an enzyme to boost catalysis. Science 370, 1442–1446 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Hammes, G. G., Benkovic, S. J. & Hammes-Schiffer, S. Flexibility, diversity, and cooperativity: pillars of enzyme catalysis. Biochemistry 50, 10422–10430 (2011).

    Article  CAS  PubMed  Google Scholar 

  45. Agarwal, P. K. A biophysical perspective on enzyme catalysis. Biochemistry 58, 438–449 (2019).

    Article  CAS  PubMed  Google Scholar 

  46. Agarwal, P. K. Role of protein dynamics in reaction rate enhancement by enzymes. J. Am. Chem. Soc. 127, 15248–15256 (2005).

    Article  CAS  PubMed  Google Scholar 

  47. Yilmazer, B. et al. Structural insights into the NAD+-dependent formate dehydrogenase mechanism revealed from the NADH complex and the formate NAD+ ternary complex of the Chaetomium thermophilum enzyme. J. Struct. Biol. 212, 107657 (2020).

    Article  CAS  PubMed  Google Scholar 

  48. Ng, A. Y., Jordan, M. I. & Weiss, Y. On spectral clustering: analysis and an algorithm. Adv. Neural Inf. Process. Syst. 14, 849–856 (2002).

  49. Bei, Z., Huang, Y., Chen, Y., Cao, Y. & Li, J. Photo-induced carbocation-enhanced charge transport in single-molecule junctions. Chem. Sci. 11, 6026–6030 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Lin, L. C. et al. Spectral clustering to analyze the hidden events in single-molecule break junctions. J. Phys. Chem. C 125, 3623–3630 (2021).

    Article  CAS  Google Scholar 

  51. Schafer, R. W. What is a Savitzky–Golay filter? IEEE Signal Proc. Mag. 28, 111–117 (2011).

    Article  Google Scholar 

  52. Anastassiou, G. A. Fuzzy Mathematics: Approximation Theory (Springer, 2010).

  53. Whitley, D. A genetic algorithm tutorial. Stat. Comput. 4, 65–85 (1994).

    Article  Google Scholar 

  54. Trott, O. & Olson, A. J. AutoDock Vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. J. Comput. Chem. 31, 455–461 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  55. Pettersen, E. F. et al. UCSF Chimera—a visualization system for exploratory research and analysis. J. Comput. Chem. 25, 1605–1612 (2004).

    Article  CAS  PubMed  Google Scholar 

  56. Pavelites, J. J., Gao, J., Bash, P. A. & Mackerell, A. D. A molecular mechanics force field for NAD+, NADH, and the pyrophosphate groups of nucleotides. J. Comput. Chem. 18, 221–239 (1997).

    Article  CAS  Google Scholar 

  57. Walker, R. C., de Souza, M. M., Mercer, I. P., Gould, I. R. & Klug, D. R. Large and fast relaxations inside a protein: calculation and measurement of reorganization energies in alcohol dehydrogenase. J. Phys. Chem. B 106, 11658–11665 (2002).

    Article  CAS  Google Scholar 

  58. Wang, J., Wolf, R. M., Caldwell, J. W., Kollman, P. A. & Case, D. A. Development and testing of a general Amber force field. J. Comput. Chem. 25, 1157–1174 (2004).

    Article  CAS  PubMed  Google Scholar 

  59. Maier, J. A. et al. ff14SB: improving the accuracy of protein side chain and backbone parameters from ff99SB. J. Chem. Theory Comput. 11, 3696–3713 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Case, D. A. et al. AMBER 2018 (University of California, 2018).

  61. Hou, T., Wang, J., Li, Y. & Wang, W. Assessing the performance of the MM/PBSA and MM/GBSA methods. 1. The accuracy of binding free energy calculations based on molecular dynamics simulations. J. Chem. Inf. Model. 51, 69–82 (2011).

    Article  CAS  PubMed  Google Scholar 

  62. Hou, T., Wang, J., Li, Y. & Wang, W. Assessing the performance of the molecular mechanics/Poisson Boltzmann surface area and molecular mechanics/generalized Born surface area methods. II. The accuracy of ranking poses generated from docking. J. Comput. Chem. 32, 866–877 (2011).

    Article  CAS  PubMed  Google Scholar 

  63. Xu, L., Sun, H., Li, Y., Wang, J. & Hou, T. Assessing the performance of MM/PBSA and MM/GBSA methods. 3. The Impact of Force fields and ligand charge models. J. Phys. Chem. B 117, 8408–8421 (2013).

    Article  CAS  PubMed  Google Scholar 

  64. Torrie, G. M. & Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23, 187–199 (1977).

    Article  Google Scholar 

  65. Souaille, M. & Roux, B. T. Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations. Comput. Phys. Commun. 135, 40–57 (2001).

    Article  CAS  Google Scholar 

  66. Kumar, S., Rosenberg, J. M., Bouzida, D., Swendsen, R. H. & Kollman, P. A. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comput. Chem. 13, 1011–1021 (1992).

    Article  CAS  Google Scholar 

  67. Iannuzzi, M., Laio, A. & Parrinello, M. Efficient exploration of reactive potential energy surfaces using Car–Parrinello molecular dynamics. Phys. Rev. Lett. 90, 238302 (2003).

    Article  PubMed  Google Scholar 

  68. Laio, A. & Parrinello, M. Escaping free-energy minima. Proc. Natl Acad. Sci. USA 99, 12562–12566 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  69. Laio, A. & Gervasio, F. L. Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep. Prog. Phys. 71, 126601 (2008).

    Article  Google Scholar 

  70. CP2K Developers Group. CP2K version 5.0 (development version) (2016); https://www.cp2k.org/version_history

  71. VandeVondele, J. et al. Quickstep: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 167, 103–128 (2005).

    Article  CAS  Google Scholar 

  72. Laino, T., Mohamed, F., Laio, A. & Parrinello, M. An efficient real space multigrid QM/MM electrostatic coupling. J. Chem. Theory Comput. 1, 1176–1184 (2005).

    Article  CAS  PubMed  Google Scholar 

  73. Laio, A., VandeVondele, J. & Rothlisberger, U. A Hamiltonian electrostatic coupling scheme for hybrid Car–Parrinello molecular dynamics simulations. J. Chem. Phys. 116, 6941–6947 (2002).

    Article  CAS  Google Scholar 

  74. Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).

    Article  CAS  PubMed  Google Scholar 

  75. Pala, U. et al. Functional effects of active site mutations in NAD+-dependent formate dehydrogenases on transformation of hydrogen carbonate to formate. Protein Eng. Des. Sel. 31, 327–335 (2018).

    Article  CAS  PubMed  Google Scholar 

  76. Goedecker, S., Teter, M. & Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 54, 1703–1710 (1996).

    Article  CAS  Google Scholar 

  77. VandeVondele, J. & Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 127, 114105 (2007).

    Article  PubMed  Google Scholar 

  78. Guidon, M., Hutter, J. & VandeVondele, J. Auxiliary density matrix methods for Hartree–Fock exchange calculations. J. Chem. Theory Comput. 6, 2353–2364 (2010).

    Article  Google Scholar 

  79. Barducci, A., Bussi, G. & Parrinello, M. Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett. 100, 020603 (2008).

    Article  PubMed  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant numbers 21978245, B.F.; 22122305, B.W.; 22250003, 21722305, W.H.), the National Key R&D Program of China (grant number 2017YFA0204902, W.H.), and the National Postdoctoral Program for Innovative Talents (grant number BX20200197, A.Z.). W.H. thanks Y. Zhang (Xiamen University) for discussion on the catalytic mechanism of oxidoreductase. B.W. thanks Y. Zhao (Xiamen University) for discussion on the electron transfer mechanism.

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  1. These authors contributed equally: Aihui Zhang, Xiaoyan Zhuang, Jia Liu, Jiacheng Huang.

Authors and Affiliations

  1. State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, P. R. China

    Aihui Zhang, Xiaoyan Zhuang, Jia Liu, Jiacheng Huang, Luchun Lin, Yongxiang Tang, Shiqiang Zhao, Ruihao Li, Binju Wang, Baishan Fang & Wenjing Hong

  2. The Key Laboratory for Chemical Biology of Fujian Province, Key Lab for Synthetic Biotechnology of Xiamen City, Xiamen University, Xiamen, P. R. China

    Aihui Zhang, Xiaoyan Zhuang & Baishan Fang

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Contributions

B.F., W.H. and B.W. designed the experiments and co-supervised the project. B.F. conceived the idea and discussed with W.H. to probe the FDH catalytic cycle at the single-molecule level. A.Z. and B.W. wrote the manuscript with inputs from all authors. X.Z. was responsible for molecular synthesis and characterization. X.Z. and A.Z. carried out the BJ experiments and analysed the data. J.L. performed the theoretical modelling. J.H. performed the data processing method based on artificial intelligence. L.L and Y.T. carried out the data-clustering analysis. S.Z. and R.L. built the electrical measurement instrument. All authors participated in discussion of the work.

Corresponding authors

Correspondence to Binju Wang, Baishan Fang or Wenjing Hong.

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Nature Catalysis thanks Jens Ulstrup, Iñaki Tuñón, Sam Hay, Barış Binay, Giovanni Maglia, and the other, anonymous, reviewer for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Discussion, Figs. 1–33 and Tables 1–5.

Reporting Summary

Supplementary Data 1

The Cartesian coordinates of the truncated PDB (solvation waters 3 Å away from the protein are removed) of all species involved in the catalytic cycle (Fig. 3) from MD and QM/MM metadynamics.

Supplementary Data

Source Data Supplementary Figs. 1–12, 14, 16 and 23.

Source data

Source Data Fig. 1

SourceData for Fig. 1

Source Data Fig. 2

SourceData for Fig. 2

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Zhang, A., Zhuang, X., Liu, J. et al. Catalytic cycle of formate dehydrogenase captured by single-molecule conductance. Nat Catal 6, 266–275 (2023). https://doi.org/10.1038/s41929-023-00928-1

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