William N. Lipscomb

The synchronous-transit method for determining reaction pathways and locating molecular transition states

Abstract In the synchronous-transit method, a model linear synchronous transit pathway is first constructed and is then refined by optimizing one or more intermediate structures subject to the constraint that the optimized structure retain the same relative position along the path ( orthogonal optimization ). The method yields a series of energy estimates which progressively bound the energy of the transition state from above and from below. High computational efficiency is attainable, and sufficient flexibility is provided to deal with asynchronous processes. Comparisons are made to the alternative “reaction-coordinate” approach, which is shown to be subject to several serious deficiencies. The method is applied to a model two-dimensional energy surface and to the allowed electrocyclic interconversions of the cyclopropyl and allyl cations and of cyclobutene and cis -butadiene.

Theory of Polyhedral Molecules. I. Physical Factorizations of the Secular Equation

An LCAO—MO systematization of polyhedral molecules such as BNHN is undertaken. Peculiarities of polyhedral systems, such as inapplicability of nearest‐neighbor assumption and increased number of parameters are discussed within the framework of a Huckel type of theory. It is found that inclusion of hydrogen atoms does not affect predictions of closed shells, but is important in determining electronic transitions. Various physical factorizations of the secular equations, such as the in‐surface, apex‐equatorial, and ring‐polar separations are critically examined. A computer program for calculations on molecules of up to 15 atoms is described and used to obtain the energy levels of a variety of polyhedral molecules.

Perturbed Hartree—Fock Calculations. I. Magnetic Susceptibility and Shielding in the LiH Molecule

The limited basis set Hartree—Fock problem is solved in the presence of a perturbation term in the Hamiltonian to obtain the first‐order perturbed wavefunction. The formulation is applied to the calculation of electric polarizability, magnetic susceptibility, and magnetic shielding. The effect of the limited basis set on the gauge invariance of the magnetic quantities is discussed. The magnetic susceptibility and shielding, the rotational magnetic moment, and the spin rotational constants are calculated for lithium hydride using two different wavefunctions. The agreement with experiment is reasonably good for the spin rotational constants and rotational magnetic moment. It is felt that further refinement of the calculation would not change the results by more than a few percent.

Boron Hydrides: LCAO—MO and Resonance Studies

The results of an LCAO—MO calculation for the boron hydrides and hydride ions B2H6, B4H10, B5H9, B5H11, B6H10, B9H15, B10H14, B10H16, BH4—, B3H8—, B9H14—, B10H10—2, B10H14—2, B12H12—2 are reported. Charge distributions and overlap populations are calculated from the wavefunctions for real distances and for idealized molecules with all distances equal. The three‐center bond theory is extended to incorporate unsymmetric equivalent structures with concomitant improvement in charge distributions. These are compared with the presumably better LCAO—MO charges. The valence structure of a new boron hydride, B18H22, is discussed.

Carboxypeptidase A: A Protein and an Enzyme

Publisher Summary This chapter discusses the relationship of the three-dimensional structures of bovine carboxypeptidase A (CPA), and of its complexes with substrates and inhibitors, to the functional behavior of this enzyme. In particular, it discusses the basis for substrate specificity, modes of binding, and possible mechanisms of hydrolytic cleavage of substrates for this enzyme. CPA is a zinc-containing proteolytic enzyme, which catalyzes the hydrolysis of carboxy-terminal peptide bonds in protein and peptide substrates. Removal of Zn2+, either by lowering the pH below 5.5 or by the use of a variety of chelating agents at neutral pH, yields an inactive enzyme, apocarboxypeptidase A. Peptidase activity is known for Co2+, Ni2+, Mn2+ and Fe2+ in place of Zn2+, but substitution of Cu2+ for Zn2+ yields an enzyme that is inactive toward all substrates. Esters are also cleaved by CPA and the substitution of Hg2+, Cd2+, or Pb2+ retains esterase activity, although these heavy metal derivatives are not peptidases in solution. However, the crystals of the mercury derivative have shown some peptidase activity.

The crystal structure of Haelll methyltransferase covalently complexed to DNA: An extrahelical cytosine and rearranged base pairing

Many organisms expand the information content of their genome through enzymatic methylation of cytosine residues. Here we report the 2.8 A crystal structure of a bacterial DNA (cytosine-5)-methyltransferase (DCMtase), M. HaeIII, bound covalently to DNA. In this complex, the substrate cytosine is extruded from the DNA helix and inserted into the active site of the enzyme, as has been observed for another DCMtase, M. HhaI. The DNA is bound in a cleft between the two domains of the protein and is distorted from the characteristic B-form conformation at its recognition sequence. A comparison of structures shows a variation in the mode of DNA recognition: M. HaeIII differs from M. HhaI in that the remaining bases in its recognition sequence undergo an extensive rearrangement in their pairing. In this process, the bases are unstacked, and a gap 8 A long opens in the DNA.

Theory of Polyhedral Molecules. III. Population Analyses and Reactivities for the Carboranes

Population analyses of the molecular orbitals of the polyhedral carboranes, BN—2C2HN, are computed. All the geometrical isomers of the trigonal, tetragonal, pentagonal bipyramid, and the icosahedron geometries are analyzed, and predictions made of the reactivities of these compounds and their derivatives. A comparison is also made between an LCAO‐MO charge distribution and one derived from the three‐center bond formalism.

Refined crystal structure of the potato inhibitor complex of carboxypeptidase A at 2.5 A resolution.

The exopeptidase carboxypeptidase A forms a tight complex with a 39 residue inhibitor protein from potatoes. We have determined the crystal structure of this complex, and refined the atomic model to a crystallographic R-factor of 0.196 at 2.5 A resolution. The structure of the inhibitor protein is organized around a core of disulfide bridges. No α-helices or β-sheets are present in this protein, although there is one turn of 3_(10) helix. The four carboxy-terminal residues of the inhibitor protein bind in the active site groove of carboxypeptidase A, defining binding subsites S′_1, S_1, S_2 and S_3 on the enzyme. The carboxy-terminal glycine of the inhibitor is cleaved from the remainder of the inhibitor in the complex, and remains trapped in the back of the active site pocket. Interactions between the inhibitor and residues Tyr248 and Arg71 of carboxypeptidase A resemble possible features of binding stages for substrates both prior and subsequent to peptide bond hydrolysis. Not all of these interactions would be available to different types of ester substrates, however, which may be in part responsible for the observed kinetic differences in hydrolysis between peptides and various classes of esters. With the exception of residues involved in the binding of the inhibitor protein (such as Tyr248), the structure of carboxypeptidase A as determined in the inhibitor complex is quite similar to the structure of the unliganded enzyme (Lipscomb et al., 1968), which was solved from an unrelated crystal form.

Structure determination and refinement of bovine lens leucine aminopeptidase and its complex with bestatin

The three-dimensional structure of bovine lens leucine aminopeptidase (EC 3.4.11.1) complexed with bestatin, a slow-binding inhibitor, has been solved to 3.0 A resolution by the multiple isomorphous replacement method with phase combination and density modification. In addition, this structure and the structure of the isomorphous native enzyme have been refined at 2.25 and 2.32 A resolution, respectively, with crystallographic R-factors of 0.180 and 0.159, respectively. The current structural model for the enzyme includes the two zinc ions and 481 of the 487 amino acid residues comprising the asymmetric unit. The enzyme is physiologically active as a hexamer, which has 32 symmetry, and is triangular in shape with a triangle edge length of 115 A and maximal thickness of 90 A. Monomers are crystallographically equivalent. Each is folded into two unequal alpha/beta domains connected by an alpha-helix to give a comma-like shape with approximate maximal dimensions of 90 A x 55 A x 55 A. The secondary structural composition is 35% alpha-helix and 23% beta-strand. The N-terminal domain (160 amino acid residues) mediates trimer-trimer interactions and does not appear to participate directly in catalysis, while the C-terminal domain (327 amino acid residues) is responsible for catalysis and binds the two zinc ions, which are less than 3 A apart. These two metal ions are located near the edge of an eight-stranded, saddle-shaped beta-sheet. The zinc ion that has the lower temperature factor is co-ordinated by one carboxylate oxygen atom from each of Asp255, Asp332 and Glu334, and the carbonyl oxygen of Asp332. The other zinc ion, presumed to be readily exchangeable, is co-ordinated by one carboxylate oxygen atom of each of Asp273 and Glu334 and the side-chain amino group of Lys250. The active site also contains two positively charged residues, Lys262 and Arg336. The six active sites are themselves located in the interior of the hexamer, where they line a disk-shaped cavity of radius 15 A and thickness 10 A. Access to this cavity is provided by solvent channels that run along the 2-fold symmetry axes. Bestatin binds to one of the active site zinc ions, and its phenylalanine and leucine side-chains occupy hydrophobic pockets adjacent to the active site. Finally, the relationship between bovine lens leucine aminopeptidase and the homologous enzyme pepA from Escherichia coli is discussed.

Self‐consistent‐field wavefunctions for complex molecules. The approximation of partial retention of diatomic differential overlap

A new approach, based on partial retention of diatomic differential overlap over an orthogonalized basis, is described for approximating LCAO SCF molecular orbital wavefunctions at the minimum basis set level for closed‐shell molecules containing hydrogen and first‐row atoms. The SCF equations are solved explicitly, retaining all one‐electron integrals and approximating two‐electron Coulomb integrals, hybrid integrals, and exchange integrals of the forms (iAjA | iAjA) and (iAjB | jAjB) for centers A and B. Single‐center averaging processes otherwise required for rotational invariance are avoided by the use of local atomic‐centered axes which are unique in anisotropic environments. The result is accuracy comparable to that of much more elaborate methods such as STO‐3G, in computing times only moderately longer than for simpler methods based on neglect of differential overlap such as CNDO and INDO. Both unparameterized and parameterized methods are reported. Comparison of parameterized results with ab initi...