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...
A general theory for microstructure in systems of copolymers with strongly interacting groups (SIGs) is proposed. The so-called superstrong segregation limit, corresponding to rather short blocks containing SIGs and strong attraction between them, is considered in detail. In particular, multiplet formation in melts and solutions of ionomers (block ionomers) is studied. It is shown that as the interaction parameter increases, the most stable shape of a multiplet continuously changes from spherical to disklike (oblate ellipsoid). A further increase of the interaction parameter induces another (first order) transition from disklike multiplets to lamellae. The same transitions could be induced by decreasing the average length of ionic blocks in block ionomer systems. The relevant experimental observations are discussed.
The microdomain structure in block-copolymer melts with short A blocks which strongly attract each other separated by long B blocks is studied for the case of narrow interphases between the microdomains.It is shown that as the temperature is lowered (or attraction of A blocks becomes more intensive), the behavior of the system changes qualitatively: instead of the usual strong segregation regime a new regime emerges which we define as the "superstrong segregation regime". In this regime A chains within the micelles become practically completely extended and steric restrictions on the chain conformations in the micelles become important. Although the superstrong segregation regime is not characteristic for ordinary block copolymers, it is easily realized for the case when one of the blocks is ionomeric. By considering the limiting case of one monomer link in the A block we obtain the results for microdomain (multiplet) structure in random ionomers. In most cases multiplets in ionomers correspond to microdomains in block copolymers in the superstrong segregation regime. We calculate the limiting size of the multiplet, the average distance between the multiplets, and the expansion of the chains in ionomer melts. The comparison of multiplets for random and telechelic ionomers is also performed.
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