  Self-assembly of polypeptides into fibrillar structures can be initiated by
planar surfaces that interact favorably with certain residues. Using a coarse
grained model, we systematically studied the folding and adsorption behavior of
a $\beta$-roll forming polypeptide. We find that there are two different
folding pathways depending on the temperature: (i) at low temperature, the
polypeptide folds in solution into a $\beta$-roll before adsorbing onto the
attractive surface, (ii) at higher temperature, the polypeptide first adsorbs
in a disordered state, and folds while on the surface. The folding temperature
increases with increasing attraction, as the folded $\beta$-roll is stabilized
by the surface. Surprisingly, further increasing the attraction lowers the
folding temperature again, as strong attraction also stabilizes the adsorbed
disordered state, which competes with folding of the polypeptide. Our results
suggest that to enhance the folding, one should use a weakly attractive
surface. They also explain the recent experimental observation of the
non-monotonic effect of charge on the fibril formation on an oppositely charged
surface [C. Charbonneau, et al., ACS Nano, 8, 2328 (2014)].
