Dynamical Model for a Bistable Contractile Molecular Injection System

Contractile Injection Systems (CIS) are biomolecular mechanisms used by viruses to puncture cells prior to infection. CIS consist of a stiff penetrating tube bound to a sixfold symmetric sheath consisting of a stack of identical ring-like structures. During injection this sheath transitions between an extended and contracted configuration. The injection is triggered by a localized conformational change in the baseplate which initiates a contraction wave in the sheath that propagates from the baseplate to the distal end. Drawing from recent structural evidence for the conformation changes at the molecular level, we model this molecular machine using a simplified geometry of inextensible filaments inspired by chebyshev nets. This geometry is fully described by a single angle that varies as a function of space and time. We show that the interaction of the bending of the chebyshev fibres and a local bistability of the sub-unit allows us to recover the contraction wave observed in computational and biological experiments, and validate our model by building mechanisms at the desktop scale. We further use our model to estimate the dynamics and forces observed during contraction that may be directly measured in the biological setting.