EVALUATING THE ENERGETICS OF EMPTY CAVITIES AND INTERNAL MUTATIONS INPROTEINS

The energetics of cavity formation in proteins is evaluated with two d ifferent approaches and results are analyzed and compared to experimen tal data. In the first approach, free energy of cavity formation is ex tracted by RMS fitting from the distribution of numbers of cavities, N , with different volumes, V-cav, in 80 high-resolution protein structu res. It is assumed that the distribution of number of cavities accordi ng to their volume follows the Boltzmann law, N(V-cav)=exp[(-a.V-cav-b )/kT], or its simplified form. Specific energy cost of cavity formatio n, a, extracted by RMS fitting from these distributions is compared to a values extracted from experimental free energies of cavity formatio n in T4 lysozyme fitted to similar expressions. It is found that fitti ng of both sets of data leads to similar magnitudes and uncertainties in the calculated foe energy values. It is shown that Boltzmann-like d istribution of cavities can be derived for a simple model of an equili brium interconversion between mutants in an extracellular system. We, however, suggest that a partitioning into cavity-dependent and cavity- independent terms may lose meaning when one attempts to describe mutat ion effects on protein stability in terms of specific free energy cont ributions. As an alternative approach, a direct molecular mechanics ev aluation is attempted of T4 lysozyme destabilization by five single ca vity-creating mutations. The calculations are based on the approach us ed in calculations of the energetics of packing defects in crystals. F or all mutations calculated destabilizations agree with the correspond ing experimental values within +/-0.6 kcal/mol. A computational relaxa tion of the mutant was most difficult to achieve for the mutation prod ucing the smallest cavity. However, calculations do not always reprodu ce crystallographically observed contraction/expansion of cavities. It is suggested that this may be related to usually observed large RMS d ifferences (>1 Angstrom) between crystallographic and energy-minimized protein structures, and thus correct energetics might be easier to ca lculate than the correct geometry.