Assembly of tubes in the stretching-dominated limit

Many biological and nanotechnological processes rely on the self-assembly of tubular structures. For this reason, theoretical models that offer insights into this process and ways to control its final outcome are essential. In this work, we study the conditions under which tubules are self-assembled spontaneously from free subunits in solution and explore the possible formation pathways using classical nucleation theory and an elastic model in the stretching-dominated regime. We find that a dimensionless number, B, that measures the relative importance of bending with respect to line tension, controls the fate and polymorphism of the tubules. In our model, the assembly process starts from the spontaneous formation of a curved patch that eventually closes into a tube following a combination of two generic mechanisms: (i) curvature fluctuations, which are dominant for B≤1 and (ii) aspect-ratio fluctuations, mainly occurring when B≫1. Using mesoscopic non-equilibrium thermodynamics, we describe the kinetics of formation of closed tubes and determine the final radii distribution of the assembled tubes, which can significantly differ from the equilibrium one. This work opens the way to optimize the efficiency of assembly and control the radius of different tubular nanostructures, such as viral, carboxysome, or DNA origami tubules.