We argue that protein loops can be described by topological domain-wall solitons that interpolate between ground states which are the $\alpha$ helices and $\beta$ strands. We present an energy function that realizes loops as soliton solutions to its equation of motion, and apply these solitons to model a number of biologically active proteins including 1VII, 2RB8, and 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to numerically construct soliton solutions that reproduce secondary structural motifs such as $\alpha$-helix-loop-$\alpha$-helix and $\beta$-sheet-loop-$\beta$-sheet with an overall root-mean-square-distance accuracy of around $1.0\text{Å}$ or less for the central $\alpha$-carbons, i.e., close to the limits of current experimental accuracy.

• Received 1 April 2010

DOI:https://doi.org/10.1103/PhysRevE.82.011916