Temperature dependence of self-entanglements in protein backbones near the glass-like transition

Many proteins undergo a phase change whereby catalytic activity is switched on at a glass-transition temperature T* similar to 200 K. Over T*, large anharmonic motions dominate, most particularly on atoms coupled to the hydration layer. These changes are detectable in the positional disorder, e.g., in the Debye-Waller thermal B-factors. Yet. the glass transition is not detected in descriptors of backbone mean shape, e.g., the molecular size. In this work, we show that other descriptors of mean shape may be better at detecting the transition. We suggest that a property that uses the equilibrium geometry and the backbone connectivity can exhibit larger variations with thermal fluctuations. In particular, we contrast the effects of bond length fluctuations on the mean number of overcrossings and the radius of gyration. Using the glass transition of ribonuclease-A as a test example, we show that the change in Debye-Waller factors is also reflected in the mean overcrossing numbers computed with the backbones. The approach can be used to follow other configurational transitions and to assess the effect of various external perturbations.