Quantifying the protein core flexibility through analysis of cavity formation

We present an extensive analysis of cavity statistics in the interior of three different proteins, in liquid n-hexane, and in water performed using molecular-dynamics simulations. The heterogeneity of packing density over atomic length scales in different parts of proteins is evident in the wide range of values observed for the average cavity size, the probability of cavity formation, and the corresponding free energy of hard-sphere insertion. More interestingly, however, the distribution of cavity sizes observed at various points in the protein interior is surprisingly homogeneous in width. That width is significantly smaller than that measured for similar distributions in liquid n-hexane or water, indicating that protein interior is much less flexible than liquid hexane. The width of the cavity size distribution correlates well with the experimental isothermal compressibility data for liquids and proteins. An analysis of cavity statistics thus provides an efficient method to quantify local properties, such as packing, stiffness, or compressibility in heterogeneous condensed media.