Shape Selection of Surface-Bound Helical Filaments: Biopolymers on Curved Membranes

Abstract

Motivated to understand the behavior of biological filaments interacting with membranes of various types, we employ a theoretical model for the shape and thermodynamics of intrinsically helical filaments bound to curved membranes. We show that filament-surface interactions lead to a host of nonuniform shape equilibria, in which filaments progressively unwind from their native twist with increasing surface interaction and surface curvature, ultimately adopting uniform-contact curved shapes. The latter effect is due to nonlinear coupling between elastic twist and bending of filaments on anisotropically curved surfaces such as the cylindrical surfaces considered here. Via a combination of numerical solutions and asymptotic analysis of shape equilibria, we show that filament conformations are critically sensitive to the surface curvature in both the strong- and weak-binding limits. These results suggest that local structure of membrane-bound chiral filaments is generically sensitive to the curvature radius of the surface to which it is bound, even when that radius is much larger than the filament's intrinsic pitch. Typical values of elastic parameters and interaction energies for several prokaryotic and eukaryotic filaments indicate that biopolymers are inherently very sensitive to the coupling between twist, interactions, and geometry and that this could be exploited for regulation of a variety of processes such as the targeted exertion of forces, signaling, and self-assembly in response to geometric cues including the local mean and Gaussian curvatures.

Chiral twisting in cytoskeletal polymers regulates filament size and orientation

“…How does the intrinsic twist of MreB double protofilaments affect MreB conformation in vivo ? To answer this question, we utilized a coarse-grained model 28 in which an MreB double protofilament is represented as a beam, with its bending and twisting stiffness extracted from our all-atom MD simulations (Methods). Considering that the large turgor pressure across the bacterial cell envelope (∼1 atm 29 ) forces the membrane to adopt a shape matching that of the cell wall, we treated the membrane as a rigid cylindrical surface.…”

“…Considering that the large turgor pressure across the bacterial cell envelope (∼1 atm 29 ) forces the membrane to adopt a shape matching that of the cell wall, we treated the membrane as a rigid cylindrical surface. We calculated the Hamiltonian for an infinitely long MreB beam with intrinsic twist and bend 28 , and identified the local twist and bend angles that minimize its energy (Methods, Fig. 4d).…”

“…Intuitively, in the presence of a binding interaction between the filament and the membrane, a twisted filament can gain binding energy by untwisting so that more of its membrane-binding interface can bind the membrane, but the untwisting process also accumulates bending and twisting energy. Therefore, competition between membrane binding and filament mechanics ultimately determines the minimal-energy conformation, which involves periodic flat (untwisted) domains along the filament that are bound to the membrane 28 . For an infinitely long filament, these flat regions are separated by short regions of unbinding that introduce a local twist of 2π (Fig.…”

“…4f). We further performed sensitivity analyses by altering the parameters that affect filament conformation 28 . For instance, by varying the intrinsic bending k , we find that the limit-length predictions are largely unaffected, whereas larger values of k lead to pitch angles closer to 90° (Fig.…”

Stability of the helical configuration of an intrinsically straight semiflexible biopolymer inside a cylindrical cell

“…16 Within the cell, MreB can be either a helix or a ring. [3][4][5][6][7][8][9][10][26][27][28][29][30][31] It was found that MreB filaments have a persistence length 5 to 10 times larger than the bacterial cell size. 3,13 Consequently, the shape of the cell provides a strong constraint on the MreB filament.…”