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Phenomenological modeling of the nucleated polymerization of human islet amyloid polypeptide : a combined experimental and theoretical approach

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Title: Phenomenological modeling of the nucleated polymerization of human islet amyloid polypeptide : a combined experimental and theoretical approach
Author: Bailey, James
Degree Master of Science - MSc
Program Mathematics
Copyright Date: 2008
Publicly Available in cIRcle 2008-10-02
Subject Keywords Nucleated polymerization; Islet amyloid polypeptide
Abstract: The inverse scattering problem is based on the scattering theory in physics, where measured data such as radiation from an object is used to determine the unique structure of the object in question. This approach has been widely successful in fields ranging from geophysics and medical imaging, to quantum field theory. In 1996 Henrik Flyvbjerg suggested that a similar approach could be used to study a reaction far from equilibrium of the self-assembly of a nucleation dependent biopolymer and, under certain conditions, uniquely determine the kinetics of the assembly. Here we use this approach to elucidate the unique structure of human islet amyloid polypeptide, also known as amylin, in-vitro. We use a systematic phenomenological analysis of the amount of monomer in fibril, of amylin, for various initial concentrations from an unstructured monomer pool. Using the assumption that nucleation is the rate-limiting step in fibril formation, we invoke mass action to develop our model. We find that the fibrillogenesis of amylin is well described by a nucleation dependent polymerization event that is characteristic of the sigmoidal shape of the reaction profile generated by our data. Furthermore, we find a second nucleation event is needed to accurately match model predictions to the observed data for the kinetic profiles of fibril formation, and the experimental length distributions of mature fibrils from in-vitro assays. This analysis allows for the theoretical determination of each step of assembly in the nucleation process. Specifically, we find the number of steps to nucleation, the size of each oligomer formed in the nucleation process, the nucleus size, and the elongation kinetics of fibrils. The secondary nucleation process is found to be a fibril dependent surface mediated nucleation event and is similar in reaction order to the primary nucleation step. Model predictions are found to be congruent with experimental assay results of oligomer populations and monomer concentration. We demonstrate that, a persistent oligomer formation is a natural and necessary consequence of nucleated fibril formation, given certain qualitative features of the kinetic profile of fibril formation. Furthermore, the modeling assumptions about monomer and fibril mass are in agreement with experiment.
URI: http://hdl.handle.net/2429/2441

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