One well-studied model that might apply is bar-and-joint rigidity. Proteins can be modeled as bar-and-joint frameworks made up of fixed-length bars (the chemical bonds) connected via rotatable joints (the atoms). Identifying the rigid and flexible regions of a protein gives insight into the possible conformation space. In 2D, bar-and-joint rigidity can be tested efficiently using Laman's theorem. The corresponding result in 3D remains a major open question. In this talk, I will cover partial results from D.J. Jacobs on determining bar-and-joint rigidity of proteins. Jacobs observes that proteins fall under a special class of frameworks with underlying squared graphs. He uses this property in an algorithm for efficiently testing for rigidity in proteins.

Jacobs' paper comes from a biology discipline, and therefore emphasizes experimental results, rather than theoretical analysis, to prove correctness of the methods. I will present the results in the paper in a more formal manner, and present some of the algorithmic questions which are raised.

Reference: Jacobs, Donald J., Generic rigidity in three-dimensional bond-bending networks, in: J.Phys. A: Math. Gen. 31, volume 31, pages 6653-6668, 1998.