Molecular Surfaces
3. Electron Density Fitting

Michael L. Connolly

1259 El Camino Real, #184
Menlo Park, CA 94025

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This section describes the application of molecular graphics to X-Ray Crystallography. It concentrates on protein crystallography. First we review the methods used by protein crystallographers before the advent of molecular graphics.

Myoglobin was the first protein whose three-dimensional structure was determined at high resolution (Kendrew, Dickerson, Strandberg, Hart, Davies, Phillips and Shore, 1960). The electron density and molecule were represented by metal models. The scale was 5 cm per angstrom. A forest of vertical steel rods was created, with electron density represented by colored clips attached to the rods. There were 2500 rods in a cube 6 ft. on a side. The molecular model was made out of brass wire. The large number of rods obscure the view of the molecular model and make it hard to make adjustments to it.

In 1968 Fred Richards (1968) introduced an optical comparator, which became the standard way to build a molecular model into electron density contours. The contours are drawn on thin acetate sheets and mounted on 36" X 36" Perspex sheets. Both the model and the density are illuminated by light bulbs. The model is supported by metal rods and piano wire. Both the model and the density are made to the same scale, typically 2 cm = 1 Å. The correct placement of a half-silvered mirror makes it possible to superimpose images of the electron density contours and the molecular model, so that the quality of fit of the model to the map is immediately apparent. Measurements of atomic positions are made using sliders with cross hairs. Measurements must be made in two orthogonal directions to get all three Cartesian coordinates. Accuracy is typically 0.1 Å.

Richards (1985b) comments that after he invented his optical comparator it was brought to his attention that a half-silvered mirror had been used much earlier to superimpose images for stage magic illusions. But Richards made five related contributions: (1) the idea to use a half-silvered mirror to superimpose images; (2) the idea that (1) could be applied to fitting a molecular model into electron density; (3) actually building the device; (4) using the device (and Hal Wyckoff) to solve the structure of ribonuclease-S; and (5) promoting the device so that it became a standard method in protein crystallography. Only the first of these contributions has been found to be anticipated. Some improvements in the optical comparator are described by Salemme (1985).

During 1975-1981 Richards boxes were gradually replaced by computer graphical systems, sometimes called electronic Richards boxes. By the early eighties several protein crystallographic modeling systems had been developed, including ones at the University of Leeds (North, Denson, Evans, Ford and Willoughby, 1981), the University of Utah (Russell Athay, personal communication), the University of California at San Diego (Steve Dempsey, personal communication) and the University of California at San Francisco (Oliver Jones, personal communication). But only the following four systems were widely used: (1) MMS-X, developed at the Computer Systems Laboratory at Washington Univesity in St. Louis (Barry, Bosshard, Ellis and Marshall, 1974; Miller, Abdel-Meguid, Rossmann and Anderson, 1981), (2) GRIP-75 at the Computer Science Department of the University of North Carolina at Chapel Hill (Tsernoglou, Petsko, McQueen, and Hermans, 1977; Brooks, 1977; Wright, 1981; Lipscomb, 1981; Britton, Lipscomb and Pique, 1978), (3) BILDER developed at the Medical Research Council Laboratory for Molecular Biology in Cambridge, England (Diamond, 1981ab), and (4) FRODO (Jones, 1978; Jones, 1981; Jones, 1985).

Before we discuss these four systems, let me describe the general features of an electronic Richards box. Such a system does several things: (1) it displays electron density contours as a net of vectors, (2) it displays the molecular model as a stick figure, (3) it allows one to change and move the model so that it fits into the electron density, (4) it allows one to read and write the atomic coordinates and to read electron density contours, (5) it allows a simple regularization algorithm to run that improves the stereochemistry and/or the fit to the electron density. The original systems typically had a minicomputer driving the graphics, and a mainframe for crystallographic computations.

The electron density contours are generally computed off-line. Usually they are displayed in three perpendicular planes. This makes the electron density contours look like a net. More than one contour level can be displayed at a time, but this is confusing without. Because of limitations on the number of vectors the display system can display and transform, it is not possible to display the whole map at once, but only selected regions of it. Molecular geometry is changed by pen and tablet or analog input devices in two ways: (1) changing torsional angles, and (2) moving an atom to a new position. The main problem in electron density fitting is that moving two different, but connected parts of the molecule into their appropriate electron density may cause these two parts not to join properly (e.g., long covalent bonds). This problem is generally handled by fitting fragments of several amino acid residues separately, and then joining them together and regularizing using an optimization algorithm. The model and density are made to appear three dimensional by various methods: stereo pairs, rotation interactively controlled by analog input device, and intensity depth cueing.

The computer graphics programs have the following advantages over a Richards box: speed, accuracy, control, size of molecule that can be handled, and the ability to look at symmetry-related molecules.

Let us now discuss the four systems listed above. The MMS-X system (MMS stands for molecular modeling system) was designed at Washington University primarily by Dave Barry, who had worked on earlier modeling systems with Cyrus Levinthal in the U.S. and Tony North in the U.K. It had four predecessors at Washington University, the last being the MMS-4 system (Barry Bosshard, Ellis and Marshall, 1974). The MMS-X system is made up of a Texas Instruments 980B minicomputer, a Pertec dual disc drive, a Hewlett-Packard 1321A cathode ray tube, and a Beehive terminal. Besides the original fitting software developed in St. Louis, other software has been developed at Purdue University (Miller, Abdel-Meguid, Rossmann and Anderson, 1981) and the University of Alberta at Edmunton by Colin Broughton. The MMS-X system has been sold to about 16 crystallographic laboratories.

The GRIP-75 system grew out of the GRIP-71 system of Bill Wright (1971, 1972). GRIP stands for Graphical Interaction with Proteins. The GRIP-75 system was designed and built by E.G. Britton, J.S. Lipscomb, M.E. Pique, W.V. Wright and F. P. Brooks, Jr. Brooks' laboratory is interested in human factors and the man-machine interface and scientists who came to Chapel Hill to use the system were observed while using it (Brooks, 1977). The system had very convenient analog input devices, stereo with a shuttered viewing device, Ramachandran plots, and used the Hermans and McQueen (1974) idealization algorithm. The GRIP-75 system was written almost entirely in PL/I. The hardware consisted of a Vector General model 3 display, a PDP-11/45 minicomputer and an IBM 360 model 75 mainframe. Numerous protein structures have been solved using the system, include the snake venom alpha-neurotoxin (Tsernoglou, Petsko, McQueen, and Hermans, 1977), Cu-Zn superoxide dismutase (Tainer, Getzoff, Beem, Richardson and Richardson, 1982), and transfer RNA (Sussman, Holbrook, Warrant, Church and Kim, 1978). Tom Williams (of UNC) has developed a ridge-line program called GRINCH (Williams, 1982) for fitting electron density that is used by Duncan McRee's XTALVIEW (McRee, 1993).

The Bilder system was written by Robert Diamond of the MRC laboratory in Cambridge. Diamond (1971) had earlier invented the real-space refinement technique. "Bilder" is German for pictures. All input is controlled by pen and tablet. Bilder was written for a PDP 11/50 minicomputer and an Evans and Sutherland Picture System 1. Because of memory limitations, the program is extensively overlayed. The functions of the program are divided into four pages, with only one page being resident in memory at a time. Each page has its associated menu. All input is by means of pen and tablet.

The part of the molecule that can be modified is called the "molten zone". The positions of atoms in the molten zone are modified by selecting target positions that the user wants the atoms to assume, and then applying an optimizer that changes dihedral angles to move the atoms towards these positions. Targets for conformational angles may also be set. The electron density map is displayed as contours (Diamond, 1981c). The contours are divided into "bricks", which are stored on disk. The relevant bricks are displayed on the screen. The contour level may be changed interactively.

Bilder has been modified and extended by Bob Ladner at Harvard to run on an E&S MultiPicture System and VAX computer operating under VMS. Ladner has added new optimizer features. The VAX version has been installed at UCLA, NIH and Scripps Clinic (in La Jolla). It has been applied to the tobacco mosaic virus disc (Diamon, 1981a) and influenza virus hemagglutinin (Wilson, Skehel and Wiley, 1981).

Frodo was originally written by Alwyn Jones in Robert Huber's group at the Max Planck Institute in Munich. The first version ran on a DEC PDP 11/40 and a Vector General 3404 display. Crystallographic computations were performed on a Siemens 4004. The program is menu-driven, using pen and tablet. Atoms are positioned into the density by (1) moving entired residues, (2) rotating around torsional angles, (3) regularizing using a method developed by Jan Hermans and John McQueen, (4) the MOVE command, which moves an atom to where on wants it. The part of the molecule to be displayed is specified either by sequence ranges or inclusion within a sphere of a particular center and radius. Up to 5 contour levels can be displayed simultaneously, distinguished by line type and color. Frodo uses terminal menus and analog input devices.

The port to the Evans and Sutherland Picture System 2 was done by Jones, and improved by Ian Tickle of Birkbeck College in London. The program was ported to the VAX-11/780 (VMS) and Evans and Sutherland MultiPicture System by Bruce Bush of Merck (Rahway, New Jersey). Bush made numerous enhancements (Bush, 1984). The port to the E&S PS 300 was done by Pflugraph, Saper and John Sack working in Flo Quicho's laboratory at Rice University in Houston (Pflugraph, Saper and Quicho, 1984). At the Department of Chemistry of the University of California at San Diego, the late Stuart Oatley ported Frodo to the Silicon Graphic IRIS workstation. During the 1980's, FRODO was the standard electronic Richards box program.

Recently, Jones has written a new crystallographic package called O(Jones, Zou, Cowan and Kjeldgaard, 1991).

Duncan McRee of the Scripps Research Institute has developed protein crystallographic software, XTALVIEW, that displays its graphics via the UNIX X11 window system (McRee, 1992, 1993). The software is distributed by the San Diego Supercomputer Center CCMS .

[ 1. Introduction ] [ 2. Physical Molecular Models ] [ *** 3. Electron Density Fitting *** ] [ 4. Molecular Graphics ] [ 5. Solvent-Accessible Surfaces ] [ 6. Molecular Surface Graphics ] [ 7. Molecular Volume and Protein Packing ] [ 8. Shapes of Small Molecules and Proteins ] [ 9. Structure-based Drug Design ] [ 10. Protein-Protein Interactions ] [ 11. Surface Biology, Chemistry and Physics ] [ 12. Bibliography ]

All material in ths article Copyright © 1996 by Michael L. Connolly

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