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Abstract |
Flexible molecules can adopt their shape and diffuse through nanopores which are significantly more tight
than the average dimension of the molecules in bulk solution. This phenomenon is known for polymers which
can unfold, translocate through a tight pore and then refold again [1]. Recently, we have demonstrated that
the effect of molecule/pore flexibility is of crucial importance for the penetration of biologically related small
molecules, like nutrients and drugs, into bacterial cells [2,3].
Here, we will discuss a statistical approach [3] which allows one to separate the effect of steric hindrance
from other the molecule-pore-solute interactions. We will also define the concepts of the molecule and the
pore size adequate for the diffusive transport through nanopores. The average cross sectional area profile
along the channel and the average minimal projection area of the molecule are the two major quantities
determining the steric part of the free energy barrier for the translocation of the particle in the case of a small
rigid particle and a large rigid channel. In this case, the description is reduced to the Fick-Jacobs model.
However, the flexibility of the channel’s cross section and that of the molecule’s size play a crucial role when
a large molecule goes through a narrow channel. We treat the flexibility in terms of the equilibrium
fluctuations of the pore and of the molecule, independently.
For the case of gaussian fluctuations, we derived simple analytical expressions for the steric free energy
barrier and for the permeability coefficient of the pore. The model is compared with the all-atom MD
simulations of the transport of Van-der-Waals spheres of various radii through a biological nanochannel, as
well as of the transport of real molecules through artificial rigid pores of different radii.
[1] M. Muthukumar, “Polymer Translocation”, CRC Press, 2011
[2] Julia Vergalli, et.al. , “Porins and small-mol-ecule translocation across the outer membrane of Gram-
negative bacteria”, Nature Reviews Microbiology, 18,164–176 (2020); DOI: 10.1038/s41579-019-0294-2
[3] Igor V Bodrenko et.al, “Diffusion of large particles through small pores: From entropic to enthalpic
transport”, J. Chem. Phys., 150 (2019) 211102; DOI: 10.1063/1.5098868 |
