How to
Determine the Size of Folding Nuclei of Protofibrils
from the Concentration Dependence of the Rate and Lag-Time of Aggregation.
I. Modeling the Amyloid Protofibril Formation
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Abstract
The question about the size of nuclei
of formation of protofibrils
(which constitute mature amyloid fibrils) formed by different proteins
and peptides is yet open and debatable because of the absence of solid
knowledge of underlying mechanisms of amyloid formation. In this work,
a kinetic model of the process of formation of amyloid protofibrils
is suggested, which allows calculation of the size of the nuclei using
only kinetic data. In addition to the stage of primary nucleation,
which is believed to be present in many protein aggregation processes,
the given model includes both linear growth of protofibrils (proceeding
only at the cost of attaching of monomers to the ends) and exponential
growth of protofibrils at the cost of growth from the surface, branching,
and fragmentation with the secondary nuclei. Theoretically, only the
exponential growth is compatible with the existence of a pronounced
lag-period (which can take much more time then the growth of aggregates
themselves). The obtained analytical solution allows us to determine
the size of the primary and secondary nuclei from the experimentally
obtained concentration dependences of the time of growth and the new
parameterthe ratio <i>L</i><sub>rel</sub> of the
lag-time duration to the time of growth of amyloid protofibrils