A Semi-Analytical Quantum-Cooperative Model of Proton Transport in Narrow Single-File Channels
Abstract
Quantum behavior of protons in their transport through narrow, single-file water channels is an increasingly hot topic of discussion due to its possible far-reaching effects on fundamental biological and bioenergetic activities. It is well understood that ions move in an environment where there is electro-diffusion due to the electric field and concentration gradients which classical electro-diffusion models can explain. However, such models fall short of a full explanation of proton transport especially when quantum tunneling plays a role. This paper presents a semi-analytical approach based on combining Fick's law, the Poisson-Nernst-Planck equation, and the Wentzel-Kramers-Brillouin approximation to study through which pathways proton transfer in single and multiple proton regimes can be modulated by channel length and energy barriers. A proton tunnelling example revealed that tunneling really allows for the alternative crossing of the barrier besides just the extra parallel path. Yet, in cooperation, multi-proton systems may produce an even stronger flux. The computational work results suggested that tunneling probability is dependent on (bio)structural changes and thus proton flow may be regulated in vivo. Moreover, a transition state theory derived correction to a Gibbs barrier height demonstrates the quantum tunneling influence on the proton transfer energy surface. In conclusion, these findings highlight the importance of path-dependent quantum effects in the comprehension of proton transport in a restricting environment and thus, they set the stage for the future experimental and computational research work aiming to help biomimetic membranes and synthetic nanochannels for efficient proton transport.
Keywords
Biophysical Modelling, Proton Transport, Multi-Proton Effects, Quantum Tunneling, WKB Approximation
Supporting Institution
Ethical Statement
Thanks
References
- Hille, B. (2001). Ion Channels of Excitable Membranes (3rd ed.). Sinauer Associates.
- Weiss, T. F. (1996). Cellular Biophysics: Transport (Vol. 1). MIT Press.
- Agmon, N. (1995). The Grotthuss mechanism. Chemical Physics Letters, 244(5-6), 456-462. https://doi.org/10.1016/0009-2614(95)00905-J
- Marx, D. (2006). Proton transfer 200 years after von Grotthuss: Insights from ab initio simulations. ChemPhysChem, 7(9), 1848-1870. https://doi.org/10.1002/cphc.200600128
- Pomès, R., & Roux, B. (2002). Molecular mechanism of H+ conduction in the single-file water chain of the gramicidin channel. Biophysical Journal, 82(5), 2304-2316. https://doi.org/10.1016/S0006-3495(02)75576-8
- Voth, G. A. (2006). Computer simulation of proton solvation and transport in aqueous and biomolecular systems. Accounts of Chemical Research, 39(2), 143-150. https://doi.org/10.1021/ar0402098
- Pomès, R., & Roux, B. (1998). Free energy profiles for H+ conduction along hydrogen-bonded chains of water molecules. Biophysical Journal, 75(1), 33-40. https://doi.org/10.1016/S0006-3495(98)77492-2
- Li, C., & Voth, G. A. (2021). A quantitative paradigm for water-assisted proton transport through proteins and other confined spaces. Proceedings of the National Academy of Sciences of the United States of America, 118(49), e2113141118. https://doi.org/10.1073/pnas.2113141118
- Kratochvil, H. T., Watkins, L. C., Mravic, M., Thomaston, J. L., Nicoludis, J. M., Somberg, N. H., Liu, L., Hong, M., Voth, G. A., & DeGrado, W. F. (2023). Transient water wires mediate selective proton transport in designed channel proteins. Nature Chemistry, 15(7), 1012-1021. https://doi.org/10.1038/s41557-023-01210-4
- Gomez, A., Thompson, W. H., & Laage, D. (2024). Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange. Nature Chemistry, 16(11), 1838-1844. https://doi.org/10.1038/s41557-024-01593-y