The (4, +) energy surface of blocked alanine (N-acetyl-N'-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters-in the form of partial charges, atomic multipoles, or generalized atomic densities-were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) *~uthor to whom all correspondence should be addressed. Journal of Computational

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A procedure has been developed for global energy minimization of surface loops of proteins in the presence of a fixed core. The ECEPP potential function has been modified to allow more accurate representations of hydrogen bond interactions and intrinsic torsional energies. A computationally efficient representation of hydration free energy has been introduced. A local minimization procedure has been developed that uses a cutoff distance, minimization with respect to subsets of degrees of freedom, analytical second derivatives, and distance constraints between rigid segments to achieve efficiency in applications to surface loops. Efficient procedures have been developed for deforming segments of the initial backbone structure and for removing overlaps. Global energy minimization of a surface loop is accomplished by generating a sequence (or a trajectory) of local minima, the component steps of which are generated by searching collections of local minima obtained by deforming seven-residue segments of the surface loop. The search at each component step consists of the following calculations: (1) A large collection of backbone structures is generated by deforming a seven-residue segment of the initial backbone structure. (2) A collection of low-energy backbone structures is generated by applying local energy minimization to the resulting collection of backbone structures (interactions involving side chains that will be searched in this component step are not included in the energy). (3) One low-energy side-chain structure is generated for each of the resulting low-energy backbone structures. (4) A collection of lowenergy local minima is generated by applying local energy minimization to the resulting collection of structures. (5) The local minimum with the lowest energy is retained as the next point of the trajectory. Applications of our global search procedure to surface segments of bovine pancreatic trypsin inhibitor (BPTI) and bovine trypsin suggest that component-step searches are reasonably complete. The computational efficiency of component-step searches is such that trajectories consisting of about 10 component steps are feasible using an FPS-5200 array processor. Our procedure for global energy minimization of surface loops is being used to identify and correct problems with the potential function and to calculate protein structure using a combination of sequence homology and global energy minimization.

Structural parameters, derived from X‐ray crystallographic data, have been compiled for 35 derivatives of amino acids, peptides, and related compounds, which contain the N‐terminal benzyloxycarbonyl (Z) group. The geometry of the urethane moiety of this end group is closely similar to that of the tert‐butoxycarbonyl (Boc) group, except for a relaxation of some bond angles because the Z group is sterically less crowded than the Boc group. For the same reason, the Z group has greater conformational flexibility. As a result, packing forces in the crystal may cause greater deformations of bond angles, resulting in larger variations of observed bond lengths and bond angles than in Boc‐peptide crystals. The aromatic rings of the Z end groups tend to stack in crystals. Conformational energy calculations indicate that most conformations of Z‐amino acid‐N' ‐methylamides and of corresponding Boc derivatives have similar dihedral angles and relative energies, i.e. the nature of the N‐terminal end group has little effect on the conformational preferences of the residue next to it. In particular, the computed fraction of molecules with a cisurethane (C‐N) bond is similar for the two derivatives: 0.51 and 0.42 in Boc‐Pro‐NHCH3 and Z‐Pro‐NHCH3, respectively, and 0.02 in the two Ala derivatives. There exist several computed conformations of Z‐Ala‐NHCH3 and Z‐Pro‐NHCH3 in which the phenyl ring and the C‐terminal methylamide group are close to each other. Because of favorable nonbonded interactions, such conformations are of low energy.

A protein energy surface is constructed. Validation is through applications of global energy minimization to surface loops of protein crystal structures. For 9 of 10 predictions, the native backbone conformation is identified correctly. Electrostatic energy is modeled as a pairwise sum of interactions between anisotropic atomic charge densities. Model repulsion energy has a softness similar to that seen in ab initio data. Intrinsic torsional energy is modeled as a sum over pairs of adjacent torsion angles of 2-dimensional Fourier series. Hydrophobic energy is that of a hydration shell model. The remainder of hydration free energy is obtained as the energetic effect of a continuous dielectric medium. Parameters are adjusted to reproduce the following data: a complete set of ab initio energy surfaces, meaning one for each pair of adjacent torsion angles of each blocked amino acid; experimental crystal structures and sublimation energies for nine model compounds; ab initio energies over 1014 conformations of 15 small-molecule dimers; and experimental hydration free energies for 48 model compounds. All ab initio data is at the Hartree᎐Fockr6᎐31G U level.