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.

An investigation of the kinetics of CO2 uptake by a synthetic calcium based sorbent

This study examines the kinetics of carbonation by CO2 at temperatures of ca. 750 °C of a synthetic sorbent composed of 15 wt% mayenite (Ca12Al14O33) and CaO, designated HA-85-850, and draws comparisons with the carbonation of a calcined limestone. In-situ XRD has verified the inertness of mayenite, which neither interacts with the active CaO nor does it significantly alter the CaO carbonation–calcination equilibrium. An overlapping grain model was developed to predict the rate and extent of carbonation of HA-85-850 and limestone. In the model, the initial microstructure of the sorbent was defined by a discretised grain size distribution, assuming spherical grains. The initial input to the model – the size distribution of grains – was a fitted parameter, which was in good agreement with measurements made with mercury porosimetry and by the analysis of SEM images of sectioned particles. It was found that the randomly overlapping spherical grain assumption offered great simplicity to the model, despite its approximation to the actual porous structure within a particle. The model was able to predict the performance of the materials well and, particularly, was able to account for changes in rate and extent of reaction as the structure evolved after various numbers of cycles of calcination and carbonation.

An investigation of the kinetics of CO 2 uptake by a synthetic calcium based sorbent

This study examines the kinetics of carbonation by CO 2 at temperatures of ca. 750°C of a synthetic sorbent composed of 15wt% mayenite (Ca 12Al 14O 33) and CaO, designated HA-85-850, and draws comparisons with the carbonation of a calcined limestone. In-situ XRD has verified the inertness of mayenite, which neither interacts with the active CaO nor does it significantly alter the CaO carbonation-calcination equilibrium. An overlapping grain model was developed to predict the rate and extent of carbonation of HA-85-850 and limestone. In the model, the initial microstructure of the sorbent was defined by a discretised grain size distribution, assuming spherical grains. The initial input to the model - the size distribution of grains - was a fitted parameter, which was in good agreement with measurements made with mercury porosimetry and by the analysis of SEM images of sectioned particles. It was found that the randomly overlapping spherical grain assumption offered great simplicity to the model, despite its approximation to the actual porous structure within a particle. The model was able to predict the performance of the materials well and, particularly, was able to account for changes in rate and extent of reaction as the structure evolved after various numbers of cycles of calcination and carbonation. © 2011 Elsevier Ltd.

Measurement of the Interaction Between Recombinant I-domain from Integrin alpha 2 beta 1 and a Triple Helical Collagen Peptide with the GFOGER Binding Motif Using Molecular Force Spectroscopy.

The role of the collagen-platelet interaction is of crucial importance to the haemostatic response during both injury and pathogenesis of the blood vessel wall. Of particular interest is the high affinity interaction of the platelet transmembrane receptor, alpha 2 beta 1, responsible for firm attachment of platelets to collagen at and around injury sites. We employ single molecule force spectroscopy (SMFS) using the atomic force microscope (AFM) to study the interaction of the I-domain from integrin alpha 2 beta 1 with a synthetic collagen related triple-helical peptide containing the high-affinity integrin-binding GFOGER motif, and a control peptide lacking this sequence, referred to as GPP. By utilising synthetic peptides in this manner we are able to study at the molecular level subtleties that would otherwise be lost when considering cell-to-collagen matrix interactions using ensemble techniques. We demonstrate for the first time the complexity of this interaction as illustrated by the complex multi-peaked force spectra and confirm specificity using control blocking experiments. In addition we observe specific interaction of the GPP peptide sequence with the I-domain. We propose a model to explain these observations.