A generic statistical mechanical model is presented for the selfassembly of chiral rod-like units, such as ␤-sheet-forming peptides, into helical tapes, which with increasing concentration associate into twisted ribbons (double tapes), fibrils (twisted stacks of ribbons), and fibers (entwined fibrils). The finite fibril width and helicity is shown to stem from a competition between the free energy gain from attraction between ribbons and the penalty because of elastic distortion of the intrinsically twisted ribbons on incorporation into a growing fibril. Fibers are stabilized similarly. The behavior of two rationally designed 11-aa residue peptides, P 11-I and P11-II, is illustrative of the proposed scheme. P11-I and P11-II are designed to adopt the ␤-strand conformation and to selfassemble in one dimension to form antiparallel ␤-sheet tapes, ribbons, fibrils, and fibers in well-defined solution conditions. The energetic parameters governing self-assembly have been estimated from the experimental data using the model. The 8-nm-wide fibrils consist of eight tapes, are extremely robust (scission energy Ϸ200 kBT), and sufficiently rigid (persistence length lfibril Ϸ 20 -70 m) to form nematic solutions at peptide concentration c Ϸ 0.9 mM (volume fraction Ϸ0.0009 vol͞vol), which convert to self-supporting nematic gels at c > 4 mM. More generally, these observations provide a new insight into the generic self-assembling properties of ␤-sheet-forming peptides and shed new light on the factors governing the structures and stability of pathological amyloid fibrils in vivo. The model also provides a prescription of routes to novel macromolecules based on a variety of self-assembling chiral units, and protocols for extraction of the associated energy changes.P rospects for the large-scale production of low-cost peptides by genetic engineering (1) open up new opportunities for exploiting protein-like self-assembly as a route to novel biomolecular materials (2-5). In this context, the small-oligopeptide route has distinct processing advantages over the use of longer polypeptides. Previously, we have demonstrated that oligopeptides can be designed to self-assemble into micrometer-long ␤-sheet tapes (6). We now wish to show that, as a consequence of the amino acid chirality, an entire hierarchy of twisted self-assembling macromolecular structures is accessible, with tapes as the most primitive form: ribbons, fibrils, and fibers. These polymers are shown to give rise to nematic fluids and gels at concentrations determined by the characteristic flexibility and length of each type of polymer.The type of molecular assembly we discuss and exemplify here arises not only in the context of desirable engineered biomaterials, but also in pathological self-assembly of mis-folded proteins, when the aggregated assemblies are referred-to as ''amyloids.'' A very wide class of proteins may be induced into producing the tapefibril-fiber sequence of structures (7) We present a theoretical model that enables the morphology and properties of thes...

The process of making and breaking reversible bonds between associating groups (stickers) controls the dynamics of associating polymers. We develop a theory of “sticky reptation” to model the dynamics of entangled solutions of associating polymers with many stickers per chain. At a high degree of association, there are very few unassociated stickers. It is therefore very difficult for a sticker to find a new partner to associate with after breaking the bond with an old one. Typically a sticker returns to its old partner following an unsuccessful search for a new one, prolonging the effective lifetime of reversible bonds. In the sticky reptation model, the search for a new partner is restricted to a part of the tube confining the entangled chain. Another important effect is the increase of the fraction of the interchain associations at the expense of the intrachain ones with increasing polymer concentration. The sticky reptation model predicts a very strong concentration dependence of viscosity in good agreement with experiments.

An equilibrium mean−field theory for reversible network formation in solutions of associative polymers is presented. We study polymer solutions with many associating groups per chain and consider pairwise association of these groups. A simple analytical expression for the free energy of these systems is derived and is shown to be consistent with the classical gelation picture developed by Flory and Stockmayer. It is shown that association and formation of a reversible network is always accompanied by a tendency for phase separation which might occur even under marginal solvent conditions. The mean-field theory is also generalized to take into account the effect of local intrachain loops as well as excluded volume interactions (partial swelling of polymer chains). It is shown that phase separation might be suppressed by the excluded volume interactions.

Viscoelastic properties of reversible networks formed in solutions of associating polymers are considered theoretically in the Rouse−Zimm (unentangled) regime. It is shown that the dynamics is governed primarily by the network strand size and by the effective lifetime of reversible junctions. Both frequency and concentration dependencies of viscosity and dynamical moduli are considered. A novel model taking into account the possibility of multiple dissociation and recombination of the same pair of stickers is developed. It is shown that this effect gives rise to an increase of the apparent activation energy which is predicted to be substantially larger than the priming activation energy for dissociation of two stickers.