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2017 ; 112
(5
): 868-880
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Inferring Mechanistic Parameters from Amyloid Formation Kinetics by Approximate
Bayesian Computation
#MMPMID28297646
Nakatani-Webster E
; Nath A
Biophys J
2017[Mar]; 112
(5
): 868-880
PMID28297646
show ga
Amyloid formation is implicated in a number of human diseases, and is thought to
proceed via a nucleation-dependent polymerization mechanism. Experimenters often
wish to relate changes in amyloid formation kinetics, for example, in response to
small molecules to specific mechanistic steps along this pathway. However,
fitting kinetic fibril formation data to a complex model including explicit rate
constants results in an ill-posed problem with a vast number of potential
solutions. The levels of uncertainty remaining in parameters calculated from
these models, arising both from experimental noise and high levels of degeneracy
or codependency in parameters, is often unclear. Here, we demonstrate that a
combination of explicit mathematical models with an approximate Bayesian
computation approach can be used to assign the mechanistic effects of modulators
on amyloid fibril formation. We show that even when exact rate constants cannot
be extracted, parameters derived from these rate constants can be recovered and
used to assign mechanistic effects and their relative magnitudes with a great
deal of confidence. Furthermore, approximate Bayesian computation provides a
robust method for visualizing uncertainty remaining in the model parameters,
regardless of its origin. We apply these methods to the problem of
heparin-mediated tau polymerization, which displays complex kinetic behavior not
amenable to analysis by more traditional methods. Our analysis indicates that the
role of heparin cannot be explained by enhancement of nucleation alone, as has
been previously proposed. The methods described here are applicable to a wide
range of systems, as models can be easily adapted to account for new reactions
and reversibility.