Self-assembly and structure transformations in living polymers forming fibrils

The classical isodesmic one-dimensional model for equilibrium polymerizatio n is generalized in order to describe self-assembly in systems forming fibr ils. The model was applied to peptide solutions forming beta -sheet tapes w hich can further aggregate into stacks of various thickness: double tapes a nd fibrils (several double tapes stacked together). We found that in some c ases the model yields several step-like transitions as the concentration in creases: first from monomers to single or double tapes, and then to fibrils . The abruptness of the first transition is controlled by the free energy p enalty for transformation of a peptide from random coil to a straight beta -strand conformation (the latter is characteristic for tapes). If both sing le and double tapes are allowed, the length of the aggregates after the fir st transition can be very large with high scission energies. For very low e nergies of attraction between double tapes, the transition from double tape s to fibrils happens separately (above the first transition), and it is eve n more abrupt and produces extremely long fibrils. The theoretical findings are used to extract the characteristic molecular parameters for the self-a ssembly of the de novo peptide DN1 forming polymeric beta -sheets in water.