Directional interactions and cooperativity between mechanosensitive membrane proteins

Abstract

While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions. For the experimental model system of mechanosensitive ion channels we find that the sign and strength of elastic interactions depend on the protein shape, yielding distinct cooperative gating curves for distinct protein orientations. Our approach predicts how directional elastic interactions affect the molecular structure, organization, and biological function of proteins in crowded membranes.

Fig. 1

(Color online) Elastic interaction potentials obtained from eq. (11) between cylindrical membrane inclusions of constant hydrophobic thickness up to order n = N in the Fourier-Bessel series in eq. (9) between open, closed, and open and closed channel states (curves from top to bottom at d = 10 nm) for τ = 0. We use the same parameter values as in ref. [29]. Vertical lines and shaded regions indicate the minimum values of d mandated by steric constraints.

Fig. 2

(Color online) Directional interaction potentials obtained from eq. (11) at N = 12 for (a) open and (b) open and closed MscL. Bilayer-MscL interactions were parameterized as in ref. [69] but for a PC20 lipid bilayer with τ = 0. Thick curves denote the three MscL orientations in the insets, while thin curves correspond to intermediate MscL orientations rotated by π/20 or π/10 as indicated by arrows. The molecular models of MscL in the insets are reprinted, with permission, from Annual Review of Biophysics and Biomolecular Structure (Volume 31 © 2002 by Annual Reviews; www.annualreviews.org: ref. [45]), and the superimposed boundary curves were obtained from eq. (12) with R_i ≈ 3.49 nm and R_i ≈ 2.27 nm, and ε_i 0.11 and ε_i ≈ 0.22, for open and closed MscL.

Fig. 3

(Color online) Directional interaction potentials obtained from eq. (11) at N = 12 for cylindrical membrane inclusions of radius R_i = 3.5 nm [29] with the hydrophobic mismatch in eq. (13) using $U_i^0=-0.5$ nm [29] and δ_i = 0.7 nm. The lipid bilayer was parameterized as in ref. [29] with τ = 0. Thick curves denote the three inclusion orientations in the insets, while thin curves correspond to intermediate orientations rotated by π/45 as indicated by arrows.

Fig. 4

(Color online) Gating curves in eq. (14) for a pair of MscL proteins to transition from the open-closed to the open-open configuration (see figs. 2(b) and (a)) for the lipid bilayer parameter values in ref. [29] at d = 9 nm, d = 10 nm, and the value d = 100 nm corresponding to the far-field limit. All gating curves are obtained from eq. (11) at N = 12, and the protein orientations at d = 9 nm and d = 10 nm are labelled as in fig. 2(a). The molecular models of MscL in the insets are reprinted, with permission, from Annual Review of Biophysics and Biomolecular Structure (Volume 31 © 2002 by Annual Reviews; www.annualreviews.org; ref. [45]), and we use the same MscL shapes as in fig. 2.