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Self-assembly of polypeptides into fibrillar structures can be initiated byplanar surfaces that interact favorably with certain residues. Using a coarsegrained model, we systematically studied the folding and adsorption behavior ofa $\beta$-roll forming polypeptide. We find that there are two differentfolding pathways depending on the temperature: (i) at low temperature, thepolypeptide folds in solution into a $\beta$-roll before adsorbing onto theattractive surface, (ii) at higher temperature, the polypeptide first adsorbsin a disordered state, and folds while on the surface. The folding temperatureincreases with increasing attraction, as the folded $\beta$-roll is stabilizedby the surface. Surprisingly, further increasing the attraction lowers thefolding temperature again, as strong attraction also stabilizes the adsorbeddisordered state, which competes with folding of the polypeptide. Our resultssuggest that to enhance the folding, one should use a weakly attractivesurface. They also explain the recent experimental observation of thenon-monotonic effect of charge on the fibril formation on an oppositely chargedsurface [C. Charbonneau, et al., ACS Nano, 8, 2328 (2014)].

The competition between surface adsorption and folding of fibril-forming polypeptides