Evaluating the energetics of empty cavities and internal mutations in proteins

The energetics of cavity formation in proteins is evaluated with two different approaches and results are analyzed and compared to experimental data. In the first approach, free energy of cavity formation is extracted by RMS fitting from the distribution of numbers of cavities, N, with different volumes, Vcav, in 80 high-resolution protein structures. It is assumed that the distribution of number of cavities according to their volume follows the Boltzmann law, N(Vcav) = exp [(-a.Vcav-b)/kT], or its simplified form. Specific energy cost of cavity formation, a, extracted by RMS fitting from these distributions is compared to a values extracted from experimental free energies of cavity formation in T4 lysozyme fitted to similar expressions. It is found that fitting of both sets of data leads to similar magnitudes and uncertainties in the calculated free energy values. It is shown that Boltzmann-like distribution of cavities can be derived for a simple model of an equilibrium 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 mutation effects on protein stability in terms of specific free energy contributions. As an alternative approach, a direct molecular mechanics evaluation is attempted of T4 lysozyme destabilization by five single cavity-creating mutations. The calculations are based on the approach used in calculations of the energetics of packing defects in crystals. For all mutations calculated destabilizations agree with the corresponding experimental values within +/-0.6 kcal/mol. A computational relaxation of the mutant was most difficult to achieve for the mutation producing the smallest cavity. However, calculations do not always reproduce crystallographically observed contraction/expansion of cavities. It is suggested that this may be related to usually observed large RMS differences (> 1 A) between crystallographic and energy-minimized protein structures, and thus correct energetics might be easier to calculate than the correct geometry.