We have applied molecular dynamics to investigate the structural properties and activity of recently synthesized amphiphilic polymethacrylate derivatives, designed to mimic the antimicrobial activity of natural peptides. The composition, molecular weight, and hydrophobicity (ratio of hydrophobic and cationic units) of these short copolymers can be modulated to achieve structural diversity, which is crucial in controlling the antimicrobial activity. We have carried out all-atom molecular dynamics to systematically investigate the conformations adopted by these copolymers in water and at the water-lipid interface as a function of sequence and the chemical nature of the monomers. For two sequences, we observe partial insertion into the bilayer. Formation of strong interactions between the lipid headgroups and the amine groups of the polymers assists in the initial association with the lipids. However, the primary driving force for the observed partial insertion appears to be the hydrophobic effect. Our results indicate sensitive dependence of the overall shape on the sequence, suggesting that experimentally observed changes in activity can be correlated with particular sequences, providing an avenue for rational design.