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We discuss the relation between the emergence of new phases with brokensymmetry within the framework of simple models of biopolymers. We start with aclassic model for a chain molecule of spherical beads tethered together, withthe steric constraint that non-consecutive beads cannot overlap, and with apairwise attractive square well potential accounting for the hydrophobic effectand promoting compaction. We then discuss the consequences of the successivebreaking of spurious symmetries. First, we allow the partial interpenetrationof consecutive beads. In addition to the standard high temperature coil phaseand the low temperature collapsed phase, this results in a new class ofmarginally compact ground states comprising conformations reminiscent of$\alpha$-helices and $\beta$-sheets, the building blocks of the native statesof globular proteins. We then discuss the effect of a further symmetry breakingof the cylindrical symmetry on attaching a side-sphere to the backbone beadsalong the negative normal of the chain, to mimic the presence of side chains inreal proteins. This leads to the emergence of a novel phase within thepreviously obtained marginally compact phase, with the appearance of morecomplex secondary structure assemblies. The potential importance of this newphase in the \textit{de novo} design of self-assembled peptides is highlighted.

Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptide