Chanalyzer: A Computational Geometry Approach for the Analysis of Protein Channel Shape and Dynamics

Abstract

Morphological analysis of protein channels is a key step for a thorough understanding of their biological function and mechanism. In this respect, molecular dynamics (MD) is a very powerful tool, enabling the description of relevant biological events at the atomic level, which might elude experimental observations, and pointing to the molecular determinants thereof. In this work, we present a computational geometry-based approach for the characterization of the shape and dynamics of biological ion channels or pores to be used in combination with MD trajectories. This technique relies on the earliest works of Edelsbrunner and on the NanoShaper software, which makes use of the alpha shape theory to build the solvent-excluded surface of a molecular system in an aqueous solution. In this framework, a channel can be simply defined as a cavity with two entrances on the opposite sides of a molecule. Morphological characterization, which includes identification of the main axis, the corresponding local radius, and the detailed description of the global shape of the cavity, is integrated with a physico-chemical description of the surface facing the pore lumen. Remarkably, the possible existence or temporary appearance of fenestrations from the channel interior towards the outer lipid matrix is also accounted for. As a test case, we applied the present approach to the analysis of an engineered protein channel, the mechanosensitive channel of large conductance.

Keywords: alpha shapes theory; channel and pore characterization; computational geometry; ion channels; molecular dynamics; molecular surface; skeletonization.

FIGURE 1

Pipeline of Chanalyzer. At the top, the basic flow is described. (A) Identification of the connected components of tetrahedra that are not entirely inside the SES. Each component represents a cavity (in blue the largest one, ascribed to the channel, in red the other ones, which are discarded); (B) the intersection of the blue component with the SES identifies the channel surface; (C) skeletonization (in green) revealing a footprint of the pentameric structure and the source-target path (in red); (D) centerline in red and several sections (in orange the central one).

FIGURE 2

Visible contour of a channel. On the left, is the visible contour of the channel (in light green) and the molecular surface (in grey). On the right, three sections of the visible contour: on the top, the section coinciding with the bifurcation of the skeleton; in the middle, the central section of the channel; at the bottom, a section clearly revealing the pentalobated nature of the channel. In each section, we spotlight some of the geometric features provided by the proposed approach. Specifically, in the top and in the bottom sections, the closest and the farthest points to the centerline are represented in blue and red, respectively. In the middle section, the ellipse (depicted in red) that best fits it is shown. Its knowledge allows retrieving further information about the local channel shape, such as its eccentricity.

FIGURE 3

(A) Solid lines, time-averaged channel radius along with the axial z position for each of the considered systems as obtained by Chanalyzer with associated SD (in the legend). Dashed lines, the same radius derived via the HOLE software. (B) Example of the dynamical behavior for the no-ligand system. The colormap is associated with the instantaneous value of the radius, as returned by Chanalyzer.

FIGURE 4

Average centerlines. Colors code for the size of the associated radius. Black dots are average ion positions for the permeating configurations. From top to bottom and left to right: (A) NL, (B) 1L, (C) 3L, and (D) 5L.