Robert W. Harrison

Phase problem in crystallography

Phase recovery from unphased data is the central problem in the interpretation of crystal diffraction data. There are a number of experimental methods for determining phases, and for small molecules computational methods work very well. The problem of developing robust computational methods for large molecules is not yet solved. Most of the approaches for large molecules are variants of the Grechburg–Saxton algorithm [ Optik35, 237– 246 ( 1972)]; with sufficiently good initial phase estimates these converge, but in general they fail with phase stagnation similar to that seen in image processing [ DaintyJ. C.FienupJ. R., in Image Recovery: Theory and Application, StarkH., ed. ( Academic, Orlando, Fla., 1987); FienupJ. R.WackermanC. C., J. Opt. Soc. Am. A3, 1897– 1907 ( 1986)].

Stiffness and energy conservation in molecular dynamics: an improved integrator

Molecular dynamics is the integration of a set of coupled differential equations describing the motion of atoms over time. These equations exhibit the unfortunate property of stiffness, that is, terms of the equations (the forces on the atoms) are defined on several scales—ranging from tens of kcal/mol/Å to thousands of kcal/mol/Å. Additional nonconservative and stiff effects occur when a distance cutoff is used for the electrostatics and nonbonded potentials. Because the first derivative at the cutoff is essentially infinite, small variations in positions will cause large variations in energy and violate conservation of energy. The effects are demonstrated in a small system of 125 isolated water molecules. It is possible to greatly reduce and nearly eliminate the stiff integration effects with an improved integrator. The nonconservative effects of the distance cutoff cannot be removed by changing the integrator.

HUMAN BETA -CELL GLUCOKINASE : DUAL ROLE OF SER-151 IN CATALYSIS AND HEXOSE AFFINITY

Glucokinase is distinguished from yeast hexokinase and low Kmmammalian hexokinases by its low affinity for glucose and its cooperative behavior, even though glucose binding residues and catalytic residues are highly conserved in all of these forms of hexokinase. The roles of Ser-151 and Asn-166 as determinants of hexose affinity and cooperative behavior of human glucokinase have been evaluated by site-directed mutagenesis, expression and purification of the wild-type and mutant enzymes, and steady-state kinetic analysis. Mutation of Asn-166 to arginine increased apparent affinity for both glucose and ATP by a factor of 3. Mutation of Ser-151 to cysteine, alanine, or glycine lowered the Kmfor glucose by factors of 2-, 26-, and 40-fold, respectively, decreased Vmax, abolished cooperativity for glucose, and also decreased Kmfor mannose and fructose. The Ser-151 mutants had hexose Kmvalues similar to those of yeast hexokinase, hexokinase I, and the recombinantly expressed COOH-terminal half of hexokinase I. However, the Kivalues for the competitive inhibitors, N-acetylglucosamine and glucose-6-P, were unchanged, suggesting that Ser-151 is not important for inhibitor binding. Mutation of Ser-151 also increased the Kmfor ATP about 5-fold and abolished the enzymes low ATPase activity, which indicates it is essential for ATP hydrolysis. The substrate-induced change in intrinsic fluorescence of S151A occurred at a much lower glucose concentration than that for wild-type enzyme. The results implicate a dual role for Ser-151 as a determinant of hexose affinity and catalysis, exclusive of the glucose-induced conformational change, and suggest that the low hexose affinity of glucokinase is dependent on interaction of Ser-151 with other regions of the protein.

Molecular model of human beta-cell glucokinase built by analogy to the crystal structure of yeast hexokinase B.

Recent studies have shown that mutations in human β-cell glucokinase that impair the activity of this key regulatory enzyme of glycolysis can cause early-onset non-insulin-dependent diabetes mellitus (NIDDM). The amino acid sequence of human glucokinase has 31% identity with yeast hexokinase, a related enzyme for which the crystal structure has been determined. This homology has allowed us to model the three-dimensional structure of human glucokinase by analogy to the crystal structure of yeast hexokinase B. This model of human glucokinase provides a basis for understanding the effects of mutations on its enzymatic activity. Residues in the active site and on the surface of the binding cleft for glucose are highly conserved in both enzymes. Regions far from the active site are predicted to differ in conformation, and 10 insertions or deletions that range in size from 1 to 7 residues are located on the protein surface between elements of secondary structure. The model structure suggests that human glucokinase binds glucose in a similar manner to yeast hexokinase. The glucose-binding site contains a conserved aspartic acid, two conserved glutamic acids, and two conserved asparagines that form hydrogen bond interactions with the hydroxyls of the glucose similar to those observed in other sugar-binding proteins. Mutation of residues in the predicted glucose-binding site has been found to greatly reduce enzymatic activity. This model will be useful for future structure/function studies of glucokinase.

Crystallographic analysis of human immunodeficiency virus 1 protease with an analog of the conserved CA-p2 substrate -- interactions with frequently occurring glutamic acid residue at P2' position of substrates.

Human immunodeficiency virus type 1 (HIV-1) protease hydrolysis of the Gag CA-p2 cleavage site is crucial for virion maturation and is optimal at acidic pH. To understand the processing of the CA-p2 site, we have determined the structure of HIV-1 protease complexed with an analog of the CA-p2 site, the reduced peptide inhibitor Arg-Val-Leu-r-Phe-Glu-Ala-Ahx-NH2 [r denotes the reduced peptide bond and Ahx 2-aminohexanoic acid (norleucine), respectively]. The crystal structure was refined to an R-factor of 0.17 at 0.21-nm resolution. The crystals have nearly the same lattice as related complexes in P2(1)2(1)2(1) which have twofold disordered inhibitor, but are in space group P2(1). and the asymmetric unit contains two dimers of HIV-1 protease related by 180 degrees rotation. An approximate non-crystallographic symmetry has replaced the exact crystal symmetry resulting in well-ordered inhibitor structure. Each protease dimer binds one ordered inhibitor molecule, but in opposite orientations. The interactions of the inhibitor with the two dimers are very similar for the central P2 Val to P2 Glu residues, but show more variation for the distal P3 Arg and P4 Ahx residues. Importantly, the carboxylate oxygens of Glu at P2 in the inhibitor are within hydrogen-bonding distance of a carboxylate oxygen of Asp30 of the protease suggesting that the two side chains share a proton. This interaction suggests that the enzyme-substrate complex is additionally stabilized at lower pH. The importance of this interaction is emphasized by the absence of polymorphisms of Asp30 in the protease and variants of P2 Glu in the critical CA-p2 cleavage site.

A self-assembling neural network for modeling polymers

A central problem in modeling protein and other polymer structures is the generation of self‐avoiding chains which obey a priori distance restraint information which could include a folding potential function. This problem is usually addressed with a lattice model or a torsion space model of the polymer. Exhaustive searches in these spaces are of necessity exponentially complex. A new computer algorithm for modeling polymers and polymeric systems is described. This algorithm is a randomized algorithm based on a self‐assembling or Kohonen neural network. Given a defined chain topology, a defined spatial extent, and a prior probability distribution, it finds a set of coordinates which reproduce these properties. The convergence rate of the algorithm is linear with respect to the number of distance terms included. Modifications to the standard Kohonen algorithm to include a defined spatial metric, and a modified update rule improve the convergence of the standard algorithm and result in a highly efficient algorithm for building polymer models which are self avoiding and consistent with prior probability information and interatomic distance restraints.

Integrating quantum and molecular mechanics

A computer algorithm is developed for integrating density functional quantum mechanics into a molecular mechanics program. The computationally infeasible aspects of the standard LCAO‐MO approach (the iterative calculation of eigenvectors and the requirement of orthogonal expansions for the orbitals) are replaced with an efficient use of optimization via the trace theorem of linear algebra. The construction of a basis is also described for expanding the electron density that transforms with the molecular geometry. The combination of the trace method and the basis allow the solution for one configuration of atoms and electrons to be tracked over a wide range of internal conformations. The approach is readily adaptable to being used in the context of an imposed classical field that allows it to be used on part of a macromolecular complex. The initial implementation in the program AMMP is described.u2003©1999 John Wiley & Sons, Inc.u2003J Comput Chem 20: 1618–1633, 1999

Effects of different post‐crystallization soaking conditions on the diffraction of Mtcp1 crystals

The crystal structure of human Mtcp1 was determined at 2 A resolution after the X-ray diffraction limit was improved by post-crystallization soaking in 2.0 M ammonium sulfate for 1-5 months. The effects of varying the ammonium sulfate concentration and addition of polyethylene glycol to the soaking solution were examined in order to understand the phenomenon and to reduce the soaking time. Soaking the crystal for one week in a solution of 1.5 M ammonium sulfate and 2% PEG 3400 gave the desired improvement in diffraction quality. Therefore, different soaking conditions should be explored when crystals show disordered and low-resolution diffraction.

Improving the diffraction quality of MTCP-1 crystals by post-crystallization soaking.

Significant improvement in the resolution and quality of the X-ray diffraction of crystals of MTCP-1 protein was observed on post-crystallization soaking. The MTCP-1 crystals grown from 1.5 M ammonium sulfate diffracted to only 3.0 A resolution with some disorder in the diffraction. After post-crystallization soaking in a solution containing 2.0 M ammonium sulfate, the disorder was eliminated and diffraction extended to better than 2.0 A resolution. Both native and selenomethionine-enriched crystals demonstrated better diffraction after soaking for several months. This simple technique may be useful to improve the diffraction quality of protein crystals generally.

Models of HIV-1 protease with peptides representing its natural substrates

Abstract The substrate specificity of HIV-1 protease has been investigated by molecular modeling of HIV-1 protease with seven peptides representing the naturally occurring cleavage sites in the gag and gag–pol polyprotein precursors. These peptides contain a wide range of amino acids, although only hydrophobic residues are found at either side of the scissile peptide bond. Polar amino acid side chains in each substrate may form hydrogen bond interactions with atoms of HIV protease. HIV-1 protease residues Arg 8, Asp 29, Asp 30, Lys 45, Met 46, Gly 49 and Pro 81 were predicted to form hydrogen bond interactions with polar substrate side chains that may provide sequence specific recognition of the substrates. Several of these protease residues are mutated in inhibitor resistant strains of HIV. Residues equivalent to HIV-1 protease Asp 30 and Pro 81 have been shown to be critical components for substrate recognition. The calculated interaction energy betwen HIV protease and the tetrahedral intermediate of the substrates has a correlation coefficient of 71% with the differences in free energy calculated from kinetic measurements. The implications for the reaction pathway are discussed.