Commensurability between protein nanotubes in contractile ejection nanomachines.

Contractile ejection nanomachines being sheath-tube assemblies create an opening in the cell membrane to translocate molecules or ions across it. Here, on the most structurally investigated examples of the bacteriophage T4 tail and pyocin R2, we show that the rearrangement of the sheath structure resulting in its contraction and twist occurs in such a way that the contracted sheath becomes commensurate with the inner tube. This fact dictates the previously unknown simple geometrical relationship between the nanotube symmetries.

Static and dynamic hidden symmetries of icosahedral viral capsids.

Viral shells self-assemble from identical proteins, which tend to form equivalent environments in the resulting assembly. However, in icosahedral capsids containing more than 60 proteins, they are enforced to occupy not only the symmetrically equivalent locations but also the quasi-equivalent ones. Due to this important fact, static and dynamic symmetries of viral shells can include additional hidden components.

Long-range protein coupling mediated by critical low-energy modes of tubular lipid membranes.

We develop a theory of a resonant effect in protein-membrane coupling taking place in the vicinity of instabilities in tubular lipid membranes (TLMs) under longitudinal force and pressure difference constraints. Two critical low-energy modes defining the stability domain boundaries are found. We show that these modes mediate long-range TLM-protein coupling and interactions between absorbed proteins.