Minimum energy path methods and reactivity for enzyme reaction mechanisms: a perspective
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Neil R. McFarlane
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Jeremy N. Harvey
Abstract
In this perspective article, we discuss the link between minimum energy paths and activation parameters for reactions on complex potential energy surfaces involving many possible local minima, as are typically found for enzyme-substrate complexes. Such systems are frequently tackled with hybrid QM/MM methods in order to characterize reactivity. The link between local energy barriers along a minimum energy path, the so-called exponential average of such local energy barriers, and multiconformational transition state theory is discussed. Also, it is shown that in case of positive skewness of the distribution of barrier heights across sets of minimum energy paths, exponential averaging converges relatively quickly with the number of paths used.
Funding source: KU Leuven
Award Identifier / Grant number: C14/22/087
Acknowledgments
The authors thank Profs. Julianna Olah and Ulf Ryde for helpful discussions. They also acknowledge funding from KU Leuven research through grant C14/22/087.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission. The text was written by both authors. The Monte Carlo analysis was performed by N.M.
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Use of Large Language Models, AI and Machine Learning Tools: Non declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: KULeuven research funding, grant ref. C14/22/087.
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Data availability: Not applicable.
References
1. Mardirossian, N.; Head-Gordon, M. Mol. Phys. 2017, 115, 2315–2372. https://doi.org/10.1080/00268976.2017.1333644.Search in Google Scholar
2. Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. J. Chem. Phys. 2013, 139, 134101. https://doi.org/10.1063/1.4821834.Search in Google Scholar
3. Pulay, P. Molec. Phys. 1969, 17, 197–204. https://doi.org/10.1080/00268976900100941.Search in Google Scholar
4. Schlegel, H. B. J. Comput. Chem. 1982, 3, 214–218. https://doi.org/10.1002/jcc.540030212.Search in Google Scholar
5. Fukui, K. J. Phys. Chem. 1970, 74, 4161–4163. https://doi.org/10.1021/j100717a029.Search in Google Scholar
6. Miller, W. H.; Handy, N. C.; Adams, J. E. J. Chem. Phys. 1980, 72, 99–112. https://doi.org/10.1063/1.438959.Search in Google Scholar
7. Stillinger, F. H. Phys. Rev. E 1999, 59, 48–51. https://doi.org/10.1103/PhysRevE.59.48.Search in Google Scholar
8. Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi‐Ölçüm, N.; Houk, K. N. Angew. Chem. Int. Ed. 2008, 47, 7592–7601. https://doi.org/10.1002/anie.200800918.Search in Google Scholar
9. For some examples, see Vereecken, L.; Peeters, J. J. Chem. Phys. 2003, 119, 5159–5170. https://doi.org/10.1063/1.1597479, K. H. Møller, R. V. Otkjær, N. Hyttinen, T. Kurtén, H. G. Kjaergaard, J. Phys. Chem. A 120, 10072–10087 (2016), https://doi.org/10.1021/acs.jpca.6b09370.Search in Google Scholar
10. A very similar formalism has also been introduced to account for the kinetics of enzyme-catalyzed reactions observed at the single-molecule level, see Kou, S. C.; Cherayil, B. J.; Min, W.; English, B. P.; Xie, X. S. J. Phys. Chem. B 2005, 109, 19068–19081. https://doi.org/10.1021/jp051490q.Search in Google Scholar
11. Siegbahn, P. E. M.; Himo, F. WIREs Comp. Mol. Sci. 2011, 1, 323–336. https://doi.org/10.1002/wcms.13.Search in Google Scholar
12. For some reviews, see Senn, H. M.; Thiel, W. Angew. Chem. Int. Ed. 2009, 48, 1198–1229. https://doi.org/10.1002/anie.200802019; L. W. Chung, W. C. Sameera, R. Ramozzi, A. J. Page, M. Hatanaka, G. P. Petrova, T. V. Harris, X. Li, Z. Ke, F. Liu, H.-B. Li, L. Ding, K. Morokuma, Chem. Rev. 115, 5678–5796 (2015), https://doi.org/10.1021/cr5004419.Search in Google Scholar PubMed
13. Warshel, A.; Levitt, M. J. Mol. Biol. 1976, 103, 227–249. https://doi.org/10.1016/0022-2836(76)90311-9.Search in Google Scholar PubMed
14. Wlodawer, A.; Minor, W.; Dauter, Z.; Jaskolski, M. FEBS J. 2013, 280, 5705–5736. https://doi.org/10.1111/febs.12495.Search in Google Scholar PubMed PubMed Central
15. Lonsdale, R.; Harvey, J. N.; Mulholland, A. J. Chem. Soc. Rev. 2012, 41, 3025–3038. https://doi.org/10.1039/c2cs15297e.Search in Google Scholar PubMed PubMed Central
16. Klähn, M.; Braun-Sand, S.; Rosta, E.; Warshel, A. J. Phys. Chem. B 2005, 109, 15645–15650. https://doi.org/10.1021/jp0521757.Search in Google Scholar PubMed PubMed Central
17. Siegbahn, P. E. M.; Borowski, T. Faraday Discuss. 2011, 148, 109–117. https://doi.org/10.1039/C004378H.Search in Google Scholar
18. This is a very broad field of research, with too many methods and variants to cover in detail in this study. We cite here a few landmark methods: Bash, P. A.; Field, M. J.; Karplus, M. J. Am. Chem. Soc. 1987, 109, 8092–8094. https://doi.org/10.1021/ja00260a028.(b) Hu, H.; Lu, Z.; Yang, W. J. Chem. Theory Comput. 2007, 3, 390–406. https://doi.org/10.1021/ct600240y.Search in Google Scholar
19. For a recent example from our group, see Čivić, J.; Tuñon, I.; Harvey, J. N. ACS Catal. 2025, 15, 1684–1692. https://doi.org/10.1021/acscatal.4c06972.Search in Google Scholar
20. For an example showing how both types of method continue to be be developed, see Yagi, K.; Ito, S.; Sugita, Y. J. Phys. Chem. B 2021, 125, 4701–4713. https://doi.org/10.1021/acs.jpcb.1c01862.Search in Google Scholar PubMed PubMed Central
21. Ranaghan, K. E.; Mulholland, A. J. Int. Rev. Phys. Chem. 2010, 29, 65–133. https://doi.org/10.1080/01442350903495417.Search in Google Scholar
22. Henkelman, G.; Jónsson, H. J. Chem. Phys. 2000, 113, 9978–9985. https://doi.org/10.1063/1.1323224.Search in Google Scholar
23. Zimmerman, P. M. J. Chem. Phys. 2013, 138, 184102. https://doi.org/10.1063/1.4804162.Search in Google Scholar
24. Cooper, A. M.; Kästner, J. Chem. Phys. Chem. 2014, 15, 3264–3269. https://doi.org/10.1002/cphc.201402382.Search in Google Scholar
25. Ryde, U. J. Chem. Theory Comput. 2017, 13, 5745–5752. https://doi.org/10.1021/acs.jctc.7b00826.Search in Google Scholar
26. Kwak, S. G.; Kim, J. H. Korean J. Anesthesiol. 2017, 70, 144–156. https://doi.org/10.4097/kjae.2017.70.2.144.Search in Google Scholar
27. McFarlane, N. R.; Harvey, J. N. Phys. Chem. Chem. Phys. 2024, 26, 5999–6007. https://doi.org/10.1039/d3cp05772k.Search in Google Scholar
28. (a) Groeneveld, R. A.; Meeden, G. The Statistician 1984, 33, 391–399. https://doi.org/10.2307/2987742.(b) Joanes, D. N.; Gill, C. A. The Statistician 1998, 47, 183–189. https://doi.org/10.1111/1467-9884.00122.(c) Balanda, K. P.; MacGillivray, H. L. Am. Statistician 1988, 42, 111–119. https://doi.org/10.2307/2684482.Search in Google Scholar
29. Chook, Y. M.; Gray, J. V.; Ke, H.; Lipscomb, W. N. J. Mol. Biol. 1994, 240, 476–500. https://doi.org/10.1006/jmbi.1994.1462.Search in Google Scholar
30. Taskesen, E., 2020. distfit is a python library for probability density fitting. (version 1.4.0). https://erdogant.github.io/distfit.Search in Google Scholar
© 2025 IUPAC & De Gruyter
Articles in the same Issue
- Frontmatter
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- Minimum energy path methods and reactivity for enzyme reaction mechanisms: a perspective
- The quantum revolution in enzymatic chemistry: combining quantum and classical mechanics to understand biochemical processes
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- Research Articles
- O–Li⋯O and C–Li⋯C lithium bonds in small closed shell and open shell systems as analogues of hydrogen bonds
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Articles in the same Issue
- Frontmatter
- Review Articles
- Minimum energy path methods and reactivity for enzyme reaction mechanisms: a perspective
- The quantum revolution in enzymatic chemistry: combining quantum and classical mechanics to understand biochemical processes
- A quantum chemical perspective of photoactivated biological functions
- Does chemistry need more physics?
- Rotational dynamics of ATP synthase: mechanical constraints and energy dissipative channels
- Transforming dreams into reality: a fairy-tale wedding of chemistry with quantum mechanics
- The quantum chemistry revolution and the instrumental revolution as evidenced by the Nobel Prizes in chemistry
- Influence of symmetry on the second-order NLO properties: insights from the few state approximations
- The dichotomy between chemical concepts and numbers after almost 100 years of quantum chemistry: conceptual density functional theory as a case study
- How ‘de facto variational’ are fully iterative, approximate iterative, and quasiperturbative coupled cluster methods near equilibrium geometries?
- Electronic structure of methyl radical photodissociation
- Bridging experiment and theory: a computational exploration of UMG-SP3 dynamics
- Research Articles
- O–Li⋯O and C–Li⋯C lithium bonds in small closed shell and open shell systems as analogues of hydrogen bonds
- Metal–ligand bonding and noncovalent interactions of mutated myoglobin proteins: a quantum mechanical study
