Parameter Distribution Analysis of Tau Fragment K18 Fibrillization

Abstract

Neural amyloid deposits of microtubule-associated protein tau are implicated in a number of neurodegenerative disorders, notably Alzheimer's disease (AD) and chronic traumatic encephalopathy (CTE). Fibrillization of tau, and of amyloid-forming proteins in general, appears to involve nucleation-dependent polymerization wherein small concentrations of “nuclei” form initially, followed by the rapid, highly favorable addition of further monomer to nuclei/fibril ends. Secondary nucleation, the formation of nuclei from fibrillar material, is a particularly important determinant of amyloid formation kinetics. When the reaction is monitored, this type of behavior results in highly cooperative, sigmoidal fibrillization curves. A number of small molecules derived from natural products have been shown to inhibit tau amyloid formation, but our understanding of their mechanistic effects is largely empirical. A thorough investigation of the kinetic and structural effects of these compounds could aid in the rational design of more potent, specific inhibitors.Toward this end, we are utilizing a combination of fluorescence spectroscopy, mathematical modeling and numerical simulation to evaluate the heparin-induced fibrillization of a fragment of tau, K18. This strategy enables us to examine entire distributions of model parameter values that describe the data with comparable accuracy, as opposed to the conventional approach of identifying a single “best-fit” set of parameters. Both for experimental K18 fibrillization timecourses and for simulated sets of test data, the parameter distribution approach appears to better reflect the true experimental uncertainties involved in studies of amyloid formation than conventional least-squares fitting. These parameter distributions are sensitive to relatively small changes in the underlying kinetic rates, and we discuss how they can be used to assign detailed effects to known small molecule inhibitors of tau amyloid formation in an effort to generate more detailed models for their mechanisms of action.