A Semi-Analytical Quantum-Cooperative Model of Proton Transport in Narrow Single-File Channels

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.