How a protein functions depends both on having basic stable forms (tertiary structure) and having some residual flexibility supported within that structure. The modeling of protein flexibility and rigidity in terms imported from physics and engineering has been developed through the theory of generically rigid frameworks and a fast combinatorial algorithm is available in programs such as FIRST. Recent theoretical work on rigidity of frameworks has modified this generic analysis to include the basic symmetry and to predict additional motions. In particular, a framework which would normally count to be combinatorially minimally rigid in generic realizations has been shown to become flexible when realized with 2‐fold rotational symmetry in 3‐space.
Protein dimers, formed by two copies of a protein are a good case study for impact of this added flexibility due to 2‐fold rotational symmetry, as dimers generally self‐assemble with a 2‐fold rotational axis, for reasons of minimal energy. We describe an algorithm for predicting possible additional flexibility and consider the question: What is the significance of this for the behavior of dimers, such as tryptophan repressor?