THESEUS: maximum likelihood superpositioning and analysis of macromolecular structures

THESEUS is a command line program for performing maximum likelihood (ML) superpositions and analysis of macromolecular structures. While conventional superpositioning methods use ordinary least-squares (LS) as the optimization criterion, ML superpositions provide substantially improved accuracy by down-weighting variable structural regions and by correcting for correlations among atoms. ML superpositioning is robust and insensitive to the specific atoms included in the analysis, and thus it does not require subjective pruning of selected variable atomic coordinates. Output includes both likelihood-based and frequentist statistics for accurate evaluation of the adequacy of a superposition and for reliable analysis of structural similarities and differences. THESEUS performs principal components analysis for analyzing the complex correlations found among atoms within a structural ensemble. AVAILABILITY: ANSI C source code and selected binaries for various computing platforms are available under the GNU open source license from http://monkshood.colorado.edu/theseus/ or http://www.theseus3d.org.     

Methods for X-ray diffraction analysis of macromolecular structures.

A modern approach to protein crystallography relies as much on molecular biology as on the 'core' crystallographic disciplines. Some recent, biologically significant structure determinations have demonstrated this and show the importance of new third generation synchrotron sources. Novel uses of well known phasing techniques have also been valuable in these structure determinations. For the majority of structures, advances in phasing techniques, data collection and processing and the associated computer programs have led to more effective structure determinations.     

A new program for detecting the geometrical core of a set of structures of macromolecular complexes

Comparison of structures of homological proteins often helps to understand functionally significant features of these structures. This concerns not only structures of separate protein chains, but also structures of macromolecular complexes. In particular, a comparison of complexes of homologous proteins with DNA is significant for analysis of the recognition of DNA by proteins. We present program LCore for detecting geometrical cores of a family of structures; a geometrical core is a set of amino acid residues and nucleotides that disposed similarly in all structures of the family. We describe the algorithm of the program, its web interface, and an example of its application to analysis of complexes of homeodomains with DNA.     

AmbiPack: A systematic algorithm for packing of macromolecular structures with ambiguous distance constraints

The determination of structures of multimers presents interesting new challenges. The structure(s) of the individual monomers must be found and the transformations to produce the packing interfaces must be described. A substantial difficulty results from ambiguities in assigning intermolecular distance measurements (from nuclear magnetic resonance, for example) to particular intermolecular interfaces in the structure. Here we present a rapid and efficient method to solve the packing and the assignment problems simultaneously given rigid monomer structures and (potentially ambiguous) intermolecular distance measurements. A promising application of this algorithm is to couple it with a monomer searching protocol such that each monomer structure consistent with intramolecular constraints can be subsequently input to the current algorithm to check whether it is consistent with (potentially ambiguous) intermolecular constraints. The algorithm AmbiPack uses a hierarchical division of the search space and the branch-and-bound algorithm to eliminate infeasible regions of the space. Local search methods are then focused on the remaining space. The algorithm generally runs faster as more constraints are included because more regions of the search space can be eliminated. This is not the case for other methods, for which additional constraints increase the complexity of the search space. The algorithm presented is guaranteed to find all solutions to a predetermined resolution. This resolution can be chosen arbitrarily to produce outputs at various level of detail. Illustrative applications are presented for the P22 tailspike protein (a trimer) and portions of β-amyloid (an ordered aggregate). Proteins 32:26–42, 1998. © 1998 Wiley-Liss, Inc.     

SQUID: a program for the analysis and display of data from crystallography and molecular dynamics

SQUID is a flexible computer program that allows the analysis and display of molecular coordinates from crystallography, NMR, and molecular dynamics. The program can also display two-dimensional and three-dimensional data using many graph types, as well as perform array processing of data with numerous intrinsic functions. Graphics are based on the use of “move” and “draw” instructions, allowing easy development of new device drivers, including vector plotters.     

A data mining approach for analyzing density maps representing macromolecular structures

Results of electron microscopy-based three-dimensional reconstructions of macromolecules or their complexes are usually stored as density maps. Each point ("voxel") in the map represents a density value and one approach for studying details of the map is to display an isosurface enclosing areas of interest. We have taken a data mining approach not only focusing on the areas of immediate interest but determining all possible separate entities ("blobs") from a density map. After the entire density map is analyzed with our mining program BLOBBER, properties of all detected blobs can be browsed and sets of blobs can be visualized using our VIZBLOB program. Since BLOBBER analyzes density maps using only density information and relates it to spatial relationships, BLOBBER can be used to analyze symmetrical or asymmetrical density maps from any source. To test our program we have analyzed published bacteriophage PRD1 reconstructions. We identified various structural details ranging from individual proteins to major complexes such as the whole capsid shell and more elaborate details of possible connections between membrane interfaces. This approach can also be a useful preprocessing tool for visualizing reconstructions.     

XmMol: An X11 and motif program for macromolecular visualization and modeling

XmMol is a desktop tool designed to provide both interactive molecular graphics on X11 displays and easy interface with external applications. A kernel provides an interactive wire-frame display of macromolecules. It supports depth cueing, 3D clipping, and stereo. Various representations, coloring, and labeling modes are proposed. Docking and interactive back-bone deformation tools are also supported. Communication protocols allow the user to develop new external features or to use XmMol as a visualization tool for external numerical programs.     

Time-resolved analysis of macromolecular structures during reactions by stopped-flow electrooptics.

A stopped-flow field-jump instrument and its use for the analysis of macromolecular structure changes during reactions is described. The operation of the new instrument is simple and reliable, owing to a new type of cell construction with electrodes directly integrated in a quartz cuvette: major advantages are the relatively low demand on sample quantities and a high time resolution. The stopped flow is characterized by a dead time of approximately 0.5 ms. Electric field pulses with field strengths up to 20 kV/cm and rise times in the nanosecond range are applied at adjustable times after stop of the flow. The time resolution of the optical detection is up to the nanosecond time range. The instrument may be used for the combination of stopped flow with temperature-jump and field-jump experiments. A particularly useful new application is the analysis of macromolecular reactions by electrooptical measurements, because electrooptical data provide information about structures. This is demonstrated for the intercalation of ethidium into double-helical DNA. The transients, measured at 313 nm, where the signal is exclusively due to ethidium bound to the DNA, demonstrate a relatively high negative dichroism at 0.5 ms after mixing. The absolute value of this negative dichroism increases in the millisecond time range and approaches the equilibrium value within about a second. The dichroism decay time constants demonstrate a clear increase of the effective DNA length due to ethidium binding, already 0.5 ms after mixing; a further increase to the equilibrium value is found in the millisecond time range. The analysis of these data demonstrate the existence of up to three relaxation processes, depending on the conditions of the experiments. The dichroism amplitudes, together with the decay time constants, indicate that all the reaction states found in the present investigation are complexes with insertion of ethidium residues between basepairs. Moreover, the data clearly show the degree of intercalation in the intermediate states, which is very useful information for the quantitative assignment of the mechanism.     

Compressed representations of macromolecular structures and properties

We introduce a new and unified, compressed volumetric representation for macromolecular structures at varying feature resolutions, as well as for many computed associated properties. Important caveats of this compressed representation are fast random data access and decompression operations. Many computational tasks for manipulating large structures, including those requiring interactivity such as real-time visualization, are greatly enhanced by utilizing this compact representation. The compression scheme is obtained by using a custom designed hierarchical wavelet basis construction. Due to the continuity offered by these wavelets, we retain very good accuracy of molecular surfaces, at very high compression ratios, for macromolecular structures at multiple resolutions.     

Molecular chaperones: proteins essential for the biogenesis of some macromolecular structures

Many polypeptides can self-assemble into functional structures while others assemble only in the presence of additional proteins (molecular chaperones) which are not components of the final structure. We discuss here the effect that the recognition of the essential roles played by these proteins in assembly processes may have on the principle of spontaneous self-assembly.     

A program for predicting significant RNA secondary structures

We describe a program for the analysis of RNA secondary structure.There are two new features in this program. (i) To get vectorspeeds on a vector pipeline machine (such as Cray X-MP/24) wehave vectorized the secondary structure dynamic algorithm. (ii)The statistical significance of a locally ‘optimal’secondary structure is assessed by a Monte Carlo method. Theresults can be depicted graphically including profiles of thestability of local secondary structures and the distributionof the potentially significant secondary structures in the RNAmolecules. Interesting regions where both the potentially significantsecondary structures and ‘open’ structures (single-strandedcoils) occur can be identified by the plots mentioned above.Furthermore, the speed of the vectorized code allows repeatedMonte Carlo simulations with different overlapping window sizes.Thus, the optimal size of the significant secondary structureoccurring in the interesting region can be assessed by repeatingthe Monte Carlo simulation. The power of the program is demonstratedin the analysis of local secondary structures of human T-celllymphotrophic virus type III (HIV). Received on August 17, 1987; accepted on January 5, 1988     

The Phenix software for automated determination of macromolecular structures

X-ray crystallography is a critical tool in the study of biological systems. It is able to provide information that has been a prerequisite to understanding the fundamentals of life. It is also a method that is central to the development of new therapeutics for human disease. Significant time and effort are required to determine and optimize many macromolecular structures because of the need for manual interpretation of complex numerical data, often using many different software packages, and the repeated use of interactive three-dimensional graphics. The Phenix software package has been developed to provide a comprehensive system for macromolecular crystallographic structure solution with an emphasis on automation. This has required the development of new algorithms that minimize or eliminate subjective input in favor of built-in expert-systems knowledge, the automation of procedures that are traditionally performed by hand, and the development of a computational framework that allows a tight integration between the algorithms. The application of automated methods is particularly appropriate in the field of structural proteomics, where high throughput is desired. Features in Phenix for the automation of experimental phasing with subsequent model building, molecular replacement, structure refinement and validation are described and examples given of running Phenix from both the command line and graphical user interface.     

Multi-resolution contour-based fitting of macromolecular structures

A novel contour-based matching criterion is presented for the quantitative docking of high-resolution structures of components into low-resolution maps of macromolecular complexes. The proposed Laplacian filter is combined with a six-dimensional search using fast Fourier transforms to rapidly scan the rigid-body degrees of freedom of a probe molecule relative to a fixed target density map. A comparison of the docking performance with the standard cross-correlation criterion demonstrates that contour matching with the Laplacian filter significantly extends the viable resolution range of correlation-based fitting to resolutions as low as 30 A. The gain in docking precision at medium to low resolution (15-30 A) is critical for image reconstructions from electron microscopy (EM). The new algorithm enables for the first time the reliable docking of smaller molecular components into EM densities of large biomolecular assemblies at such low resolutions. As an example of the practical effectiveness of contour-based fitting, a new pseudo-atomic model of a microtubule was constructed from a 20 A resolution EM map and from atomic structures of alpha and beta tubulin subunits.     

Prediction and design of macromolecular structures and interactions

In this article, I summarize recent work from my group directed towards developing an improved model of intra and intermolecular interactions and applying this improved model to the prediction and design of macromolecular structures and interactions. Prediction and design applications can be of great biological interest in their own right, and also provide very stringent and objective tests which drive the improvement of the model and increases in fundamental understanding. I emphasize the results from the prediction and design tests that suggest progress is being made in high-resolution modelling, and that there is hope for reliably and accurately computing structural biology.     

MacMolecular: A program for visualization of molecular structures on the Macintosh

MacMolecular displays small- to medium-sized biomolecules, with particular emphasis on peptides. It has been developed to run on color Macintosh computers. The display can be stick, ball and stick, depth cued by thickness stick, or several types of space-filling representations. The program takes input from standard PDB files, simple Cartesian coordinate files, and, in addition, from Kinemage files in which atom information has been included. The program allows color changes of various types as well as the normal functions of translation, rotation, and zooming. In addition, animation files may be produced for subsequent display. Bonding of atoms is done by a distance algorithm (standard) or sequentially to properly display Cα traces and traces of peptides containing simplified representations of amino acids. Stereo viewing is available, and manipulated structures which were drawn from PDB files can be written out to new PDB files. In addition, PICT files of the drawing window can be generated.