Since the dihedral angles of a beta-strand are close to 180 degrees, the backbone forms a zig-zag pattern, with the residues on alternating sides. Thus changes in phi and psi of period two also have coherent effects on the strand shape. Curl, a period two change also suggested in [1], decreases the phi and increases the psi of odd numbered residues, counting from the beginning of the strand, and does the opposite for even numbered residues. To fill out the four-dimensional space of period two changes to phi and psi, we added a fourth basis element, not described in [1], called braid. It increases both phi and psi for odd numbered residues, and decreases them for even numbered residues.
All these manipulations can be accessed through rollers in the Structure Dialog.
[1] Richardson, J.S. and Richardson, D.C., Principles and Patterns of Protein Conformation, in: Fassman, G.D., ed., Prediction of Protein Structure and the Principles of Protein Conformation, Plenum Press, New York, New York, 1989