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.

Interfacial immobilization of monoclonal antibody and detection of human prostate-specific antigen.

Antibody orientation and its antigen binding efficiency at interface are of particular interest in many immunoassays and biosensor applications. In this paper, spectroscopic ellipsometry (SE), neutron reflection (NR), and dual polarization interferometry (DPI) have been used to investigate interfacial assembly of the antibody [mouse monoclonal anti-human prostate-specific antigen (anti-hPSA)] at the silicon oxide/water interface and subsequent antigen binding. It was found that the mass density of antibody adsorbed at the interface increased with solution concentration and adsorption time while the antigen binding efficiency showed a steady decline with increasing antibody amount at the interface over the concentration range studied. The amount of antigen bound to the interfacial immobilized antibody reached a maximum when the surface-adsorbed amount of antibody was around 1.5 mg/m(2). This phenomenon is well interpreted by the interfacial structural packing or crowding. NR revealed that the Y-shaped antibody laid flat on the interface at low surface mass density with a thickness around 40 Å, equivalent to the short axial length of the antibody molecule. The loose packing of the antibody within this range resulted in better antigen binding efficiency, while the subsequent increase of surface-adsorbed amount led to the crowding or overlapping of antibody fragments, hence reducing the antigen binding due to the steric hindrance. In situ studies of antigen binding by both NR and DPI demonstrated that the antigen inserted into the antibody layer rather than forming an additional layer on the top. Stability assaying revealed that the antibody immobilized at the silica surface remained stable and active over the monitoring period of 4 months. These results are useful in forming a general understanding of antibody interfacial behavior and particularly relevant to the control of their activity and stability in biosensor development.