Fig. 5: Configuration of a tube with periodic boundary conditions along its axis.

A A tube made of a simple membrane. B A tube with spontaneous curvature (\(\bar{C}=0.4[{1/l}_{{dts}}]\)). C A tube with 20% protein coverage. The proteins are type 2 with \({k}_{1}=10[{k}_{B}T],{k}_{2}=0,{C}_{{||}0}=1.5[{d}_{{dts}}^{-1}],{C}_{\perp 0}=0\) and \({e}_{{inc},{inc}}=-{k}_{B}T(1+\cos [2(\Theta )])\). D A tube decorated with 40% proteins of type 1. \(\Delta \kappa=0\), \({c}_{0}=0.4[{d}_{{dts}}^{-1}],\Delta {\kappa }_{G}=0\) and \({e}_{{inc},{inc}}=-1\). The red lines and spheres are the proteins.