Ground state instabilities of protein shells are eliminated by buckling

Abstract

We propose a hybrid discrete-continuum model to study the ground state of protein shells. The model allows for shape transformation of the shell and buckling transitions as well as the competition between states with different symmetries that characterize discrete particle models with radial pair potentials. Our main results are as follows. For large Föppl-von Kármán (FvK) numbers the shells have stable isometric ground states. As the FvK number is reduced, shells undergo a buckling transition resembling that of thin-shell elasticity theory. When the width of the pair potential is reduced below a critical value, then buckling coincides with the onset of structural instability triggered by over-stretched pair potentials. Chiral shells are found to be more prone to structural instability than achiral shells. It is argued that the well-width appropriate for protein shells lies below the structural instability threshold. This means that the self-assembly of protein shells with a well-defined, stable structure is possible only if the bending energy of the shell is sufficiently low so that the FvK number of the assembled shell is above the buckling threshold.

Finite Temperature Phase Behavior of Viral Capsids as Oriented Particle Shells

“…As indicated in the phase plot, we find a buckling threshold around γ B 75. The discrepancy between the computed and predicted values of the buckling threshold, which has been noted before [30], is a first measure of the importance of the discreteness effects. In order to apply TSET to melting, one can combine it with the Lindemann Melting Criterion (LMC), which states that melting occurs when the RMS of the fluctuations of particle displacements exceeds a certain fraction of the equilibrium interparticle spacing a.…”

Buckling transitions and soft-phase invasion of two-component icosahedral shells

“…We also emphasize that, as shown in Fig. 16, the elementary subunits of many viral-capsid proteins can be asymmetric in form, heterogeneous in protein composition, and nontrivial in their mutual interactions [3,9,28,29,31,97]. These features per se may severely impact the icosahedral appearance of some capsids (with planar tilings [222,223], e.g., being impossible to construct from these asymmetric structural elements).…”

“…The shape, self-assembly, and energetic stability of the generic icosahedra were rationalized in a large number of theoretical [18,23,33,38,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79], computer-simulations-based [15,[80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97], and experimental [25,98,[100][101][102][103][104][105]…”

A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes

“…This poses unique computational challenges. Current approaches impose constraints to anchor the particles on the substrate [ 21 ] or artificially restrict the particles to lie at the nodes of the mesh used to discretize the substrate [ 22 , 23 ]. Relying on constraints to force particles on the substrate is computationally expensive and cumbersome to implement, while restricting the particles’ positions to the nodes of the substrate mesh imposes undue restrictions on the allowed particle/substrate equilibrium configurations.…”