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Enzymes as viscoelastic catalytic machines

Nature Physics volume 21, pages 787–798 (2025)Cite this article

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Abstract

The catalytic cycle involves internal motions and conformational changes that allow enzymes to specifically bind to substrates, reach the transition state and release the product. Such mechanical interactions and motions are often long ranged so that mutations of residues far from the active site can modulate the enzymatic cycle. In particular, regions that undergo high strain during the cycle give mechanical flexibility to the protein, which is crucial for protein motion. Here we directly probe the connection between strain, flexibility and functionality, and we quantify how distant high-strain residues modulate the catalytic function via long-ranged force transduction. We measure the rheological and catalytic properties of wild-type guanylate kinase and of its mutants with a single amino acid replacement in low-/high-strain regions and in binding/non-binding regions. The rheological response of the protein to an applied oscillating force fits a continuum model of a viscoelastic material whose mechanical properties are significantly affected by mutations in high-strain regions, as opposed to mutations in control regions. Furthermore, catalytic activity assays show that mutations in high-strain or binding regions tend to reduce activity, whereas mutations in low-strain, non-binding regions are neutral. These findings suggest that enzymes act as viscoelastic catalytic machines with sequence-encoded mechanical specifications.

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Fig. 1: Schematic and details of experiment.
Fig. 2: Strain computation and selection of mutants.
Fig. 3: Nano-rheology experimental results and model.
Fig. 4: Simulation of the pulled-apart enzyme.
Fig. 5: Enzymatic activity measurements.

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Data availability

Data for nano-rheology and enzymatic activity experiments are available in Supplementary Data. Additional data are available from the corresponding authors upon request.

Code availability

Code used to calculate the strain is available via GitHub at https://github.com/mirabdi/PDAnalysis.

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Acknowledgements

This work was supported by the National Research Foundation of Korea Grants NRF-RS-2025-00573354 funded by the Ministry of Science and ICT, and by the Institute for Basic Science, Project Code IBS-R020-D1. This work was supported by the Institute for Basic Science, Project Code IBS-R020-D1. E.M. and E.W. were supported in part by the Israel Science Foundation (grant no. 2767/20) and the Minerva Stiftung, Germany. J.-P.E. was partially supported by the Fonds National Suisse Swissmap. S.L.’s research is funded by M. de Botton and the Jacqueline and Marc Leland Foundation. We thank S. Sacquin-Mora and M. Baaden for providing the results of MD simulations of guanylate kinase bound to ADP, GDP and Mg.

Author information

Author notes

  1. These authors contributed equally: Eyal Weinreb, John M. McBride.

Authors and Affiliations

  1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel

    Eyal Weinreb & Elisha Moses

  2. Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan, Republic of Korea

    John M. McBride & Tsvi Tlusty

  3. Center for Algorithmic and Robotized Synthesis, Institute for Basic Science (IBS), Ulsan, Republic of Korea

    Marta Siek & Bartosz A. Grzybowski

  4. Département de Physique Théorique, Université de Genève, Geneva, Switzerland

    Jacques Rougemont & Jean-Pierre Eckmann

  5. Olfera, San Francisco, CA, USA

    Renaud Renault

  6. Structural Proteomics Unit (SPU), Department of Life Sciences Core Facilities (LSCF), Weizmann Institute of Science, Rehovot, Israel

    Yoav Peleg, Tamar Unger & Shira Albeck

  7. Department of Life Sciences Core Facilities (LSCF), Weizmann Institute of Science, Rehovot, Israel

    Yael Fridmann-Sirkis

  8. Department of Biomolecular Sciences, Weizmann Institute of Science, Rehovot, Israel

    Sofya Lushchekina

  9. Department of Chemical and Structural Biology, Weizmann Institute of Science, Rehovot, Israel

    Joel L. Sussman

  10. Institute of Organic Chemistry, Polish Academy of Sciences, Warsaw, Poland

    Bartosz A. Grzybowski

  11. Department of Chemistry, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea

    Bartosz A. Grzybowski

  12. Department of Physics and Astronomy, University of California, Los Angeles, CA, USA

    Giovanni Zocchi

  13. Section de Mathématiques, Université de Genève, Geneva, Switzerland

    Jean-Pierre Eckmann

  14. Department of Physics, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea

    Tsvi Tlusty

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  1. Eyal Weinreb
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Contributions

E.W.: conceptualization, methodology, software, formal analysis, investigation, visualization, writing (original draft). J.M.M.: methodology, software, formal analysis, investigation, visualization, writing (original draft). M.S.: methodology, investigation, visualization. J.R.: methodology, software, formal analysis. R.R.: conceptualization, methodology. Y.P.: methodology, resources, writing (original draft). T.U.: methodology, resources, writing (original draft). S.A.: methodology, resources, writing (original draft). Y.F.-S.: methodology, resources, investigation. S.L.: methodology, formal analysis, investigation, visualization. J.L.S.: methodology, resources, funding acquisition, writing (original draft). B.A.G.: supervision, resources. G.Z.: conceptualization, methodology, supervision. J.-P.E.: conceptualization, methodology, software, formal analysis, writing (original draft), supervision. E.M.: conceptualization, methodology, software, formal analysis, investigation, funding acquisition, writing (original draft), supervision. T.T.: conceptualization, methodology, software, formal analysis, funding acquisition, writing (original draft), supervision. All authors: writing (review and editing).

Corresponding authors

Correspondence to Elisha Moses or Tsvi Tlusty.

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Nature Physics thanks Dan Thomas Major, Qian-Yuan Tang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Strain analysis of alternate guanylate kinase structures.

a - Comparison of guanylate kinase structures before and after binding, colored by strain (residues with strain lower than median are grey, otherwise red). The same apo structure (1ZNW) is shown for all cases (differences between WT and WT* are not observable by eye). The holo structures are: PDB (1ZNY), WT bound to GDP; MD, WT bound to GDP, ADP and Mg; AF3, WT* bound to GDP, ADP and Mg. b - Strain due to binding for PDB, MD and AF3 structures (see ‘Strain evaluation and AlphaFold2 (AF) Analysis’ section of the Methods, and ‘Alternative calculations of binding strain’ section of the Supplementary Information). Locations of mutated sites for our 34 mutants are shown with black circles, with the groups indicated by colored circles; strain thresholds delineating High-Strain and Control groups are 0.04, 0.125 and 0.07.

Extended Data Fig. 2 Sequences of wild-type (WT) guanylate kinase and the cysteine-substituted variant (WT*).

Sequence alignment of the wild-type (WT) sequence with the sequence of the cysteine-substituted construct (WT*) which was used as the basis of all of our experiments and the 34 variants.

Extended Data Fig. 3 Nano-rheology for individual mutants.

Same as in Fig. 3a (a: phase vs frequency) and Fig. 3c (b: amplitude vs frequency), with curves shown for the individual mutants. Each curve represents the mean over all measurement days for an individual mutant, as specified in the Methods. Error bars show the standard error of the mean (No error bars are shown where only one measurement day was used). Mutants from the High-Strain, Control, and Binding groups are shown in reds, blues, and greens respectively. The number of measurements averaged for each mutant is detailed in Extended Data Table 1.

Extended Data Fig. 4 Effective potential-of-force profiles of cysteine-cysteine distances.

The potential of mean force (PMF) profiles for distance change between C75 and C171, calculated using the accelerated weight histogram method143,144 for the wild type (WT* - black), high-strain (E173N - red), and control (G62S - blue) mutants. Standard deviation is shown shaded and is calculated for 5 slices separated by 10 ns. The spring constants κ for the different mutants can be estimated using a second order fit to the PMF curves ΔG = ½ κ dx2 for small deviations from the minimum. The resultant spring constants are 200, 260 and 500 pN/nm respectively for the WT, G62S and E173N mutants. Errors in the fits are ~10%. This is consistent with both the MD pulling simulations (Fig. 4a) and the experimentally observed stiffer response of the E173N mutant to the pulling force.

Extended Data Fig. 5 Enzymatic activity for each mutant - with data points.

Same as shown in Fig. 5a, with individual data points added. Box-plot elements: center line, median; box-limits, upper and lower quartiles; whiskers, 1.5x interquartile range or the data range, whichever is lower. The number of measurements for each mutant is detailed in Extended Data Table 1.

Extended Data Fig. 6 Strain versus distance from binding sites.

a - Shortest distance from each residue’s Cα position to GDP versus ADP; mutated residues are highlighted, and colored by group. b - Strain versus the minimum distance to either GDP, ADP or Mg.

Extended Data Fig. 7 Melting temperature Tm versus enzymatic activity.

Enzymatic activity, normalized by wild type (WT*), versus melting temperature (Tm). We observe no dependence of activity on stability. Black line represents the fit to a power function. Pearson’s correlation coefficient r = 0.06 p = 0.83 (n = 17). Tm values for the individual mutants are detailed in Extended Data Table 1.

Extended Data Fig. 8 Enzymatic activity with different strain calculations.

a - Activity of variants, depicted according to different High-Strain / Control groupings according to different strain calculations: PDB, MD, AF3 (Extended Data Fig. 1). b, c - Strain - activity regression plots for different strain calculations, with (b) and without (c) mutants from the Binding group for PDB (left), MD (middle), and AF3 (right) calculations. Pearson’s correlation coefficients and p-values are displayed on the graphs. Sample sizes are 25 (B) and 34 (C). The number of measurements averaged for each mutant is detailed in Extended Data Table 1. All error bars show mean ± standard error. Variants are grouped according to the thresholds given in the caption of Extended Data Fig. 1.

Extended Data Fig. 9 Nano-rheology with groups chosen using different strain calculations.

a–c - Nano-rheology amplitude-phase response, as shown in Fig. 3e, depicted according to the different High-Strain / Control groupings generated by the different strain calculations (see also Extended Data Figs. 1 and 8). Groups, sample sizes, and error bar calculations same as in Fig. 3a. Error bars show mean ± standard error.

Extended Data Table 1 Mutant details and measurements
Full size table

Supplementary information

Supplementary Information

Supplementary Texts 1–5 and Figs. 1–13.

Reporting Summary

Supplementary Data 1

Data for nano-rheology and enzymatic activity experiments.

Supplementary Video 1

Wild-type guanylate kinase bound to GDP, ADP and Mg, morphing between closed and open (1ZNW) conformations. Created using the morph command in ChimeraX149.

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Weinreb, E., McBride, J.M., Siek, M. et al. Enzymes as viscoelastic catalytic machines. Nat. Phys. 21, 787–798 (2025). https://doi.org/10.1038/s41567-025-02825-9

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