Dissecting Amyloid Formation: Amyloid fibrils are associated with clinical disorders ranging from Alzheimer's disease to type II diabetes. Their self-assembly can be described by a master equation that takes into account nucleation-dependent polymerization and fragmentation. Knowles et al. (p. 1533 ) now present an analytical solution to the master equation, which shows that amyloid growth kinetics is often limited by the fragmentation rate rather than by the rate of primary nucleation. In addition, the results reveal relationships between system properties (scaling laws) that provide mechanistic insight not only into amyloid growth, but also into related self-assembly processes.

Advances in functionality and reliability of carbon nanotube (CNT) composite materials require careful formulation of processing methods to ultimately realize the desired properties. To date, controlled dispersion of CNTs in a solution or a composite matrix remains a challenge, due to the strong van der Waals binding energies associated with the CNT aggregates. There is also insufficiently defined correlation between the microstructure and the physical properties of the composite. Here, we offer a review of the dispersion processes of pristine (non-covalently functionalized) CNTs in a solvent or a polymer solution. We summarize and adapt relevant theoretical analysis to guide the dispersion design and selection, from the processes of mixing/sonication, to the application of surfactants for stabilization, to the final testing of composite properties. The same approaches are expected to be also applicable to the fabrication of other composite materials involving homogeneously dispersed nanoparticles.

A range of monodomain nematic liquid-crystal elastomers containing differing proportions of photoisomerizable mesogenic moieties, which turn from a rodlike to a kinked shape upon ultraviolet (uv) irradiation, was studied. Depending on the proportion and positional role of the photosensitive groups in the crosslinked polymer network, different types and magnitudes of response were found. The principle consequence of such photoisomerization is the destabilization of the nematic phase, whose order parameter depends on temperature in a near-critical fashion. Accordingly, the effect of uv irradiation is dramatically enhanced near the critical temperature, with the associated reduction in the nematic order parameter manifesting as a change in the macroscopic shape of the elastomer samples, producing a large uniaxial contraction. Theoretical analysis of this phenomenon gives a good quantitative agreement with experiment.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.