Repeat protein architectures predicted by a continuum representation of fold space

It is an open question whether nature has utilized all possible protein folds. For a simple protein architecture, the helical repeats, we report a method to address this question based on a mapping between the set of repetitive curves and a space of parameters specifying the curve. The exploration of the parameter space for a particular architecture enables a systematic exploration of the fold space for that protein architecture. In a planar subspace of the parameter space of helical repeats we have identified points corresponding to both naturally occurring folds and potential folds not observed so far.