Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

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.

The development of a hot rolling process for variable cross-section I-beams

To meet targeted reductions in CO 2 emissions by 2050, demand for metal must be cut, for example through the use of lightweight technologies. However, the efficient production of weight optimized components often requires new, more flexible forming processes. In this paper, a novel hot rolling process is presented for forming I-beams with variable cross-section, which are lighter than prismatic alternatives. First, the new process concept is presented and described. A detailed computational and experimental analysis is then conducted into the capabilities of the process. Results show that the process is capable of producing defect free I-beams with variations in web depth of 30-50%. A full analysis of the process then indicates the likely failure modes, and identifies a safe operating window. Finally, the implications of these results for producing lightweight beams are discussed. © 2012 Elsevier B.V. All rights reserved.