Proline cis-trans isomerization in staphylococcal nuclease: multi-substrate free energy perturbation calculations.

Staphylococcal nuclease A exists in two folded forms that differ in the isomerization state of the Lys 116-Pro 117 peptide bond. The dominant form (90% occupancy) adopts a cis peptide bond, which is observed in the crystal structure. NMR studies show that the relatively small difference in free energy between the cis and trans forms (delta Gcis-->trans approximately 1.2 kcal/mol) results from large and nearly compensating differences in enthalpy and entropy (delta Hcis-->trans approximately delta TScis-->trans approximately 10 kcal/mol). There is evidence from X-ray crystal structures that the structural differences between the cis and the trans forms of nuclease are confined to the conformation of residues 112-117, a solvated protein loop. Here, we obtain a thermodynamic and structural description of the conformational equilibrium of this protein loop through an exhaustive conformational search that identified several substates followed by free energy simulations between the substrates. By partitioning the search into conformational substates, we overcame the multiple minima problem in this particular case and obtained precise and reproducible free energy values. The protein and water environment was implicitly modeled by appropriately chosen nonbonded terms between the explicitly treated loop and the rest of the protein. These simulations correctly predicted a small free energy difference between the cis and trans forms composed of larger, compensating differences in enthalpy and entropy. The structural predictions of these simulations were qualitatively consistent with known X-ray structures of nuclease variants and yield a model of the unknown minor trans conformation.

Assessment of phase accuracy by cross validation: the free R value. Methods and applications.

Analogies between the free R statistic [Brünger (1992). Nature (London), 355, 472-474] and the statistical methods of cross validation and bootstrap are discussed. Several new applications which make use of the previously observed correlation between the free R value and the phase accuracy of crystal structures are presented. One application concerns the relative weighting of individual restraint classes in macromolecular refinement. The free R value provides an objective statistical basis for the optimal choice of the weights. The results for the refinement of a penicillopepsin crystal structure at 1.8 A resolution indicate that overall bond length and bond angle weights, derived from uncertainties observed in small-molecule crystal structures, appear to be transferable to macromolecules. In another application, the landscape of the R value around the crystal structure was investigated for unrestrained modeling of diffraction data with equal atomic scatterers. Others have suggested applications to ab initio phasing because of the simplicity of the liquid-like system of equal atomic scatterers. However, there are a large number of incorrect configurations of the scatterers whose R values at 1.8 A resolution are close to that of the correct configuration given by the positions of the non-hydrogen atoms in the penicillopepsin crystal structure. A substantial number of the incorrect configurations have higher free R values than the correct one. It is therefore conceivable that the free R value could be used as a selection criterion to distinguish between certain incorrect configurations and configurations close to the correct one.