Generally, hydrophobic amino acids provide hydrophobic interactions during peptide aggregation. However, besides the hydrophobic amino acids, some hydrophilic amino acids, such as glutamine, are also considered to be essential elements in many self-aggregating peptides. For example, huntingtin contains polyglutamine at its N-terminus and the yeast prion Sup35 protein has the GNNQQNY sequence, a peptide well-known for its ability for amyloid fibril formation. However, despite the frequent emergence of glutamine in self-assembling systems, the molecular mechanism of amyloid formation involving this unique amino acid has not been well documented. It is still not clear how this hydrophilic amino acid is responsible for the hydrophobic interaction in the self-association process. Therefore, in this study, we have carried out classical molecular dynamics simulations of the GNNQQNY peptide and its derivatives in pure water. We quantify the propensity for the formation of beta-sheet conformation with an increasing glutamine number in the peptide sequence. In addition, we assess the importance of the hydrophobicity of the dimethanediyl group present in glutamine (as well as in glutamic acid) for the self-association of the peptides through nonpolar solvent medium simulations.