Shape transformations of protein-like copolymer globules

Shapes of globules formed by amphiphilic multi-block-copolymers in a selective solvent are considered theoretically. We focus on copolymers consisting mostly of insoluble H-units forming large core surrounded by a shell of soluble P-blocks. It is shown that the globule becomes non-spherical when the effective shell tension is low enough. The resultant shape depends on the shell bending energy: it is prolate if this energy is larger than the elastic energy of the core, and oblate in the opposite case. The central result is the prediction of the formation of a surface pattern of fingers accompanying or even preempting the shape transition mentioned above. We elucidate and discuss the following finger morphologies: 1) nearly spherical knob; 2) a necklace of spherical beads extending away from the surface; 3) mostly cylindrical fingers; 4) large thorn-like fingers. The first 3 morphologies develop at equilibrium as the shell area increases (or, equivalently, the shell tension decreases). Considering the relevant kinetical aspects we show that formation of fingers is a nucleation and growth process, and that the energy of their equilibrium nucleation is likely to be high. Therefore, the finger formation may be delayed, and may actually occur in the regime where the plain spherical surface is metastable. It is the last morphology (thorn-like fingers) that characterizes the metastable regimes when the finger formation is controlled by a high activation energy. The universal features of the above predictions inviting experimental tests are discussed.