Surveying the Energy Landscapes of Aβ Fibril Polymorphism

Many
unrelated proteins and peptides have been found spontaneously
to form amyloid fibers above a critical concentration. Even for a
single sequence, however, the amyloid fold is not a single well-defined
structure. Although the cross-β hydrogen bonding pattern is
common to all amyloids, all other aspects of amyloid fiber structures
are sensitive to both the sequence of the aggregating peptides and
the solvent conditions under which the aggregation occurs. Amyloid
fibers are easy to identify and grossly characterize using microscopy,
but their insolubility and aperiodicity along the dimensions transverse
to the fiber axis have complicated detailed experimental structural
characterization. In this paper, we explore the landscape of possibilities
for amyloid protofilament structures that are made up of a single
stack of peptides associated in a parallel in-register manner. We
view this landscape as a two-dimensional version of the usual three-dimensional
protein folding problem: the survey of the two-dimensional folds of
protein ribbons. Adopting this view leads to a practical method of
predicting stable protofilament structures of arbitrary sequences.
We apply this scheme to variants of Aβ, the amyloid forming
peptide that is characteristically associated with Alzheimer’s
disease. Consistent with what is known from experiment, we find that
Aβ protofibrils are polymorphic. To our surprise, however, the
ribbon-folding landscape of Aβ turned out to be strikingly simple.
We confirm that, at the level of the monomeric protofilament, the
landscape for the Aβ sequence is reasonably well funneled toward
structures that are similar to those that have been determined by
experiment. The landscape has more distinct minima than does a typical
globular protein landscape but fewer and deeper minima than the landscape
of a randomly shuffled sequence having the same overall composition.
It is tempting to consider the possibility that the significant degree
of funneling of Aβ’s ribbon-folding landscape has arisen
as a result of natural selection. More likely, however, the intermediate
complexity of Aβ’s ribbon-folding landscape has come
from the post facto selection of the Aβ sequence as an object
of study by researchers because only by having a landscape with some
degree of funneling can ordered aggregation of such a peptide occur
at in vivo concentrations. In addition to predicting polymorph structures,
we show that predicted solubilities of polymorphs correlate with experiment
and with their elongation free energies computed by coarse-grained
molecular dynamics.