Water transport in aquaporins: osmotic permeability matrix analysis of molecular dynamics simulations

Abstract

Single-channel osmotic water permeability (p(f)) is a key quantity for investigating the transport capability of the water channel protein, aquaporin. However, the direct connection between the single scalar quantity p(f) and the channel structure remains unclear. In this study, based on molecular dynamics simulations, we propose a p(f)-matrix method, in which p(f) is decomposed into contributions from each local region of the channel. Diagonal elements of the p(f) matrix are equivalent to the local permeability at each region of the channel, and off-diagonal elements represent correlated motions of water molecules in different regions. Averaging both diagonal and off-diagonal elements of the p(f) matrix recovers p(f) for the entire channel; this implies that correlated motions between distantly-separated water molecules, as well as adjacent water molecules, influence the osmotic permeability. The p(f) matrices from molecular dynamics simulations of five aquaporins (AQP0, AQP1, AQP4, AqpZ, and GlpF) indicated that the reduction in the water correlation across the Asn-Pro-Ala region, and the small local permeability around the ar/R region, characterize the transport efficiency of water. These structural determinants in water permeation were confirmed in molecular dynamics simulations of three mutants of AqpZ, which mimic AQP1.

FIGURE 1

(a) Phylogenetic tree of the human and E. coli aquaporin family, drawn using Molphy (54). Aquaporins and aquaglyceroporins are colored blue and red, respectively. The molecules considered in the present study are shaded. (b) A multiple alignment of members of the aquaporin family. Residues on the channel surface are enclosed in a frame. The NPA motifs and ar/R region are shaded in yellow and blue, respectively. Magenta corresponds to Tyr²³ and Tyr¹⁴⁹ of AQP0, which occlude the channel. The mutation sites, Leu¹⁷⁰ and Asn¹⁸², of AqpZ are shaded in green and cyan, respectively. Asterisks indicate the residues whose main-chain oxygens protrude into the pore and form hydrogen-bonding sites for channel waters. (c) Superimposition of the aquaporins: AQP1 (green), AQP4 (pink), AqpZ (blue), GlpF (yellow), and AQP0 (magenta). This picture was prepared using PyMol (55). (d) Side view of the simulation system. The AQP1 tetramer was rendered as a cartoon representation in rainbow colors; for clarity, some helices are transparent. POPC molecules were rendered as gray sticks for aliphatic chains and as colored spheres for the headgroups: nitrogen (blue), phosphorus (orange), and oxygen (red). Water oxygen atoms are represented by cyan spheres. These diagrams were drawn using Molscript (56) with Raster3D (57). (e) Top view of the simulation system.

FIGURE 2

(a) The channel region of an AQP monomer drawn using the coordinates of AQP1. The pore is represented by light-blue meshes. The NPA motifs and the ar/R region are drawn in yellow and cyan sticks, respectively. Val¹⁷⁸ (AQP1) and Leu¹⁷⁰ (AqpZ) are indicated by green and red sticks, respectively. The hemihelices (HB and HE) are colored orange. The z-axis is aligned to the bilayer normal with the extracellular side on the right. (b) Channel radius r_c(z), AQP1 (red), AQP4 (green), AqpZ (blue), GlpF (cyan), and AQP0 (magenta), calculated by the method proposed by Smart et al. (58), which uses Monte Carlo simulated annealing to search the vacant area with a probe sphere in the x-y plane for a given z value. The radius profiles are averages over the eight monomers in the two independent 5-ns simulations. The NPA motifs and ar/R region are indicated by semitransparent yellow and cyan areas, respectively. The horizontal axis represents the z-axis. (c) Number density of channel waters. (d) Orientation of channel waters represented by the order parameter P₁(z) = 〈cosθ〉, where θ is the angle between the dipole moment of water and the z-axis.

FIGURE 3

The p_f matrices for the five AQPs: (a) AQP1, (b) AQP4, (c) AqpZ, (d) GlpF, and (e) AQP0. The vertical and horizontal axes are the z-axis of the channels. The same color scheme was used for all the AQPs except for AQP0. The broken lines indicate the position of the NPA motif.

FIGURE 4

(a) Diagonal elements p_ii of the p_f matrix: AQP1 (red), AQP4 (green), AqpZ (blue), GlpF (cyan), and AQP0 (magenta). The p_f correlation matrices: (b) AQP1, (c) AQP4, (d) AqpZ, (e) GlpF, and (f) AQP0. The vertical and horizontal axes are the z-axis of the channels. The broken lines indicate the position of the NPA motif.

FIGURE 5

(a) A side view of a carbon nanotube (CNT) system. The carbon nanotube and the carbon sheets mimicking the lipid bilayer are represented by gray sticks. Water molecules are rendered in red and white sticks. The water molecules inside the CNT form a continuous single-file, and are connected to each other by hydrogen bonds. (b) Diagonal elements p_ii of the p_f matrix. The p_f matrix for the CNT was calculated using the 10-ns trajectory. The diagonal terms p_ii of the p_f matrix show a flat profile. (c) The p_f correlation matrix {c_ij}. All the c_ij elements of the correlation matrix are ∼1.0. These features clearly indicate the prototypical characteristics of single-file permeation.

FIGURE 6

(a) Close-up view of the extracellular side of AqpZ showing the Asn¹⁸² mutation site. Green sticks and surface dots represent the side chain and the molecular surface of Asn¹⁸², respectively. Mutation of this residue to glycine removes the side chain. (b) Channel radius r_c, wild-type (red), L170V (green), N182G (blue), and L170V/N182G (cyan), calculated by the average of the eight monomers in the two independent 5-ns simulations. The NPA motifs and ar/R region are indicated in semitransparent yellow and cyan, respectively. The horizontal axis represents the z-axis. (c) Number density of channel waters. (d) The order parameter P₁(z) = 〈cosθ〉, where θ is the angle between the dipole moment of water and the z-axis.

FIGURE 7

(a) Single-channel water permeability p_f of AQP1, AqpZ wild-type, and its mutants, L170V, N182G, and L170V/N182G. (b) Diagonal terms p_ii of the p_f matrix: AQP1 (magenta), AqpZ wild-type (red), L170V (green), N182G (blue), and L170V/N182G (cyan). The p_f correlation matrices of AqpZ mutants: (c) L170V, (d) N182G, and (e) L170V/N182G.

FIGURE 8

(a) Average distances between a water located at position z and its adjacent channel waters in AqpZ wild-type and mutants: AqpZ wild-type (red), L170V (green), N182G (blue), and L170V/N182G (cyan). (b) The average number of hydrogen bonds of a water molecule with channel waters. (c) Same as panel b, but with the nitrogen atoms of the protein. (d) With the oxygen atoms of the protein. Hydrogen-bonded pairs were defined as being within 3.5 Å of each other.