L. F. Ten Eyck

An efficient general-purpose least-squares refinement program for macromolecular structures

A package of programs has been developed for efficient restrained least-squares refinement of macromolecular crystal structures. The package has been designed to be as flexible and general purpose as possible. The process of refinement is divided into basic units and an independent computer program handles each task. Each functional unit communicates with other programs in the package by way of files of well defined format. To modify or replace any program, the user need only understand the function of that particular element. Stereochemical restraints are defined in a general way that can be applied to proteins, nucleic acids, prosthetic groups, solvent atoms and so on. Guide values for bond lengths and bond angles are specified in a straightforward direct manner. Designated groups of atoms can be held constant or constrained to behave as a rigid body during refinement. In order to make the package as efficient as possible, the fast Fourier transform algorithm is used for all the crystallographic transformations. To highlight potential errors in the refined structure the user can list those atoms that have the worst bond lengths and angles, or have the largest positional, temperature-factor or occupancy gradients. It is also possible to check that protein and solvent atoms do not sterically clash with symmetry-related neighbors. Applications of the program package to a bacteriochlorophyll-containing protein, thermolysin-inhibitor complexes and mutants of bacteriophage T4 lysozyme are described.

2.2 A refined crystal structure of the catalytic subunit of cAMP-dependent protein kinase complexed with MnATP and a peptide inhibitor.

. The crystal structure of a ternary complex containing the catalytic subunit of cAMP-dependent protein kinase, ATP and a 20-residue inhibitor peptide was refined at a resolution of 2.2 A to an R value of 0.177. In order to identify the metal binding sites, the crystals, originally grown in the presence of low concentrations of Mg(2+), were soaked in Mn(2+). Two Mn(2+) ions were identified using an anomalous Fourier map. One Mn(2+) ion bridges the gamma- and beta-phosphates and interacts with Asp184 and two water molecules. The second Mn(2+) ion interacts with the side chains of Asn171 and Asp l84 as well as with a water molecule. Modeling a serine into the P site of the inhibitor peptide suggests a mechanism for phosphotransfer.

Crystallographic fast Fourier transforms

This paper presents methods for incorporating crystallographic symmetry properties into complex Fourier transforms in a form particularly well suited for use with the Cooley-Tukey fast Fourier transform algorithm. The crystallographic transforms are expressed in terms of a small number of one-dimensional special cases. The algebra presented here has been used to write computer programs for both Fourier syntheses and Fourier inversions. Even for some quite large problems (7000 structure factors and 149000 grid points in the asymmetric unit) the rate-limiting step is output of the answers.

Efficient structure-factor calculation for large molecules by the fast Fourier transform

A method is presented for calculating structure factors by Fourier inversion of a model electron density map. The cost of this method and of the standard methods are analyzed as a function of number of atoms, resolution, and complexity of space group. The cost functions were scaled together by timing both methods on the same problem, with the same computer. The FFT method is 3½ to 7 times less expensive than conventional methods for non-centrosymmetric space groups.

Crystal Structure of the Potent Natural Product Inhibitor Balanol in Complex with the Catalytic Subunit of cAMP-Dependent Protein Kinase †

Endogenous protein kinase inhibitors are essential for a wide range of physiological functions. These endogenous inhibitors may mimic peptide substrates as in the case of the heat-stable protein kinase inhibitor (PKI), or they may mimic nucleotide triphosphates. Natural product inhibitors, endogenous to the unique organisms producing them, can be potent exogenous inhibitors against foreign protein kinases. Balanol is a natural product inhibitor exhibiting low nanomolar Ki values against serine and threonine specific kinases, while being ineffective against protein tyrosine kinases. To elucidate balanols specific inhibitory effects and provide a basis for understanding inhibition-regulated biological processes, a 2.1 A resolution crystal structure of balanol in complex with cAMP-dependent protein kinase (cAPK) was determined. The structure reveals conserved binding regions and displays extensive complementary interactions between balanol and conserved cAPK residues. This report describes the structure of a protein kinase crystallized with a natural ATP mimetic in the absence of metal ions and peptide inhibitor.

2.0 A refined crystal structure of the catalytic subunit of cAMP-dependent protein kinase complexed with a peptide inhibitor and detergent.

. A mutant (Serl39Ala) of the mouse recombinant catalytic (C) subunit of cAMP-dependent protein kinase was co-crystallized with a peptide inhibitor, PKI(5-24), and MEGA-8 (octanoyl-N-methylglucamide) detergent. This structure was refined using all observed data (30 248 reflections) between 30 and 1.95 A resolution to an R factor of 0.186. R.m.s. deviations of bond lengths and bond angles are 0.013 A and 2.3 degrees, respectively. The final model has 3075 atoms (207 solvent) with a mean B factor of 31.9 A(2). The placement of invariant protein-kinase residues and most C:PKI(5-24) interactions were confirmed, but register errors affecting residues 55-64 and 309-339 were corrected during refinement by shifting the affected sequences toward the C terminus along the previously determined backbone path. New details of C:PKI(5-24) interactions and the Ser338 autophosphorylation site are described, and the acyl group binding site near the catalytic subunit NH(2) terminus is identified.

DOT2: Macromolecular docking with improved biophysical models

Computational docking is a useful tool for predicting macromolecular complexes, which are often difficult to determine experimentally. Here, we present the DOT2 software suite, an updated version of the DOT intermolecular docking program. DOT2 provides straightforward, automated construction of improved biophysical models based on molecular coordinates, offering checkpoints that guide the user to include critical features. DOT has been updated to run more quickly, allow flexibility in grid size and spacing, and generate an infinitive complete list of favorable candidate configurations. Output can be filtered by experimental data and rescored by the sum of electrostatic and atomic desolvation energies. We show that this rescoring method improves the ranking of correct complexes for a wide range of macromolecular interactions and demonstrate that biologically relevant models are essential for biologically relevant results. The flexibility and versatility of DOT2 accommodate realistic models of complex biological systems, improving the likelihood of a successful docking outcome.

A method of obtaining a stereochemically acceptable protein model which fits a set of atomic coordinates

A method is proposed by which a protein model with acceptable stereochemistry can be fitted to a set of atomic coordinates. By expressing all constraints in terms of distances between pairs of atoms it is possible to enforce any desired stereochemistry in a physically realistic manner, and at the same time to substantially reduce computing time. Application of the technique to thermolysin is described. The method has been independently developed and applied to insulin by E. J. Dodson, N. W. Isaacs & J. S. Rollett [Acta Cryst. (1976). A32, 311-315].

Eigensystem analysis of the refinement of a small metalloprotein

The eigenvalues and eigenvectors of the least-squares normal matrix for the full-matrix refinement problem contain a great deal of information about the quality of a model; in particular the precision of the model parameters and correlations between those parameters. They also allow the isolation of those parameters or combinations of parameters which are not determined by the available data. Since a protein refinement is usually under-determined without the application of geometric restraints, such indicators of the reliability of a model offer an important contribution to structural knowledge. Eigensystem analysis is applied to the normal matrices for the refinement of a small metalloprotein using two data sets and models determined at different resolutions. The eigenvalue spectra reveal considerable information about the conditioning of the problem as the resolution varies. In the case of a restrained refinement, it also provides information about the impact of various restraints on the refinement. Initial results support conclusions drawn from the free R factor. Examination of the eigenvectors provides information about which regions of the model are poorly determined. In the case of a restrained refinement, it is also possible to isolate places where X-ray and geometric restraints are in disagreement, usually indicating a problem in the model.

The TNT refinement package

The TNT refinement package was created in the late 1970s and its development continued for about 25 years. Its design included many features not present in its contemporaries and allowed for the testing and addition of many novel tools during its lifespan. These include the implementation of stereochemical restraints to molecules in other asymmetric units (both bonded and non-bonded), space-group-optimized fast Fourier transforms, which allowed rapid crystallographic calculations, and a quick and easy method to model the scattering of bulk solvent, which allowed the use of low-resolution data in refinement. TNT is no longer being developed by its original authors but its code has been included in Global Phasing, Ltds program Buster, where considerable improvements have been made.