Invariance of single-file water mobility in gramicidin-like peptidic pores as function of pore length

Abstract

We investigated the structural and energetic determinants underlying water permeation through peptidic nanopores, motivated by recent experimental findings that indicate that water mobility in single-file water channels displays nonlinear length dependence. To address the molecular mechanism determining the observed length dependence, we studied water permeability in a series of designed gramicidin-like channels of different length using atomistic molecular dynamics simulations. We found that within the studied range of length the osmotic water permeability is independent of pore length. This result is at variance with textbook models, where the relationship is assumed to be linear. Energetic analysis shows that loss of solvation rather than specific water binding sites in the pore form the main energetic barrier for water permeation, consistent with our dynamics results. For this situation, we propose a modified expression for osmotic permeability that fully takes into account water motion collectivity and does not depend on the pore length. Different schematic barrier profiles are discussed that explain both experimental and computational interpretations, and we propose a set of experiments aimed at validation of the presented results. Implications of the results for the design of peptidic channels with desired permeation characteristics are discussed.

FIGURE 1

Top and side view of the seven modeled polyalanine pores, of increasing number of residues, used for the study.

FIGURE 2

Effect of water collectivity on the underlying potential for motion along a single-file pore. The upper panel depicts a situation where two barriers are found at the entry/exit regions. The water molecules are sketched on top of the potential energy surface for illustration. Using the Monte Carlo method to sample the motion of a chain of water molecules, we can derive a free energy profile from the number density (lower panel). As a consequence of the imposed correlation between water positions, the emerging energetics seems to indicate the presence of local binding sites, whereas the true inner potential surface is actually flat.

FIGURE 3

Cumulative water-water displacements (taken as 2.75 Å, main frame) and complete water translocation (after correcting for half-permeation counting, inset) for all seven pores studied, averaged over two independent simulations.

FIGURE 4

Averaged (a) osmotic permeability coefficient (p_f) and (b) diffusive permeability coefficient (p_d) from two independent simulations as function of the number of residues forming the channel. Panel c displays the relationship between residue number and water occupancy as computed via N = p_f/p_d − 1 (black) and estimated from the simulation (red). Panel d illustrates water occupancy for p-ala15, p-ala21, and p-ala27.

FIGURE 5

Free energy profiles and their decomposition for the series of peptidic pores as obtained from force integration (see text). Total interaction (black), water-pore interaction (red), and water-water interaction (green) are plotted against the main pore axis. The panel on the lower right shows a comparison of free energy profiles as computed via water number density (orange) with force integration (black) for p-ala25.

FIGURE 6

Different PMF schemes for a chain of water molecules permeating a single file pore (left, shaded) lead to a different length dependence (right), expressed in permeability coefficients p_f (dash-dotted) and p_d (solid). Only panels d and e are consistent with the simulation results, suggesting that no binding sites for individual water molecules are present within the pore, and that the main barrier is independent of pore length.