  Understanding the influence of macromolecular crowding and nanoparticles on
the formation of in-register $\beta$-sheets, the primary structural component
of amyloid fibrils, is a first step towards describing \emph{in vivo} protein
aggregation and interactions between synthetic materials and proteins. Using
all atom molecular simulations in implicit solvent we illustrate the effects of
nanoparticle size, shape, and volume fraction on oligomer formation of an
amyloidogenic peptide from the transthyretin protein. Surprisingly, we find
that inert spherical crowding particles destabilize in-register $\beta$-sheets
formed by dimers while stabilizing $\beta$-sheets comprised of trimers and
tetramers. As the radius of the nanoparticle increases crowding effects
decrease, implying smaller crowding particles have the largest influence on the
earliest amyloid species. We explain these results using a theory based on the
depletion effect. Finally, we show that spherocylindrical crowders destabilize
the ordered $\beta$-sheet dimer to a greater extent than spherical crowders,
which underscores the influence of nanoparticle shape on protein aggregation.
