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`157
`
`R. Stroud. A wholly digital version of the device, which allowed coordi(cid:173)
`nates to be both read out and entered through a control console (e.g., for
`model building from coordinates), was constructed at the University of
`California at San Diego, and subsequently at the University of Arizona. 4
`The motorized versions of this superposition device produce coordinates
`of comparable precision to the optical and acoustic devices described
`previously (at least ± 1 mm), and similarly allow for very rapid measure(cid:173)
`ments (one atomic position per 30 sec). However, construction of the
`former device is more complicated than either the AIMS (which can
`simply be rented) or acoustic coordinate measuring devices.
`With the advent of computer graphics and associated software for
`both map fitting and coordinate readout (this volume [12]), it appears only
`a matter of time before graphics obviates either building physical models
`of proteins in optical comparators or devising means for measuring their
`coordinates. Nevertheless, the techniques described here will undoubt(cid:173)
`edly continue to prove effective aids in determining crystal structures for
`some time to come. In addition, many modeling studies of protein confor(cid:173)
`mation and interaction continue to be most readily investigated in their
`initial stages by the construction of physical models. Subsequent model
`development and analysis by computer necessitates having accurate coor(cid:173)
`dinates, so that the technical feasibility of such studies depends on having
`an accurate and easy way of measuring model coordinates.
`
`4 F. R. Salemme and D. G. Fehr, J. Mol. Biol. 70, 697 (1972).
`
`[12] Interactive Computer Graphics: FRODO
`By T. ALWYN JoNES
`
`Introduction
`
`Computer graphics provides an elegant method of controlling the pro(cid:173)
`tein crystallographer's interaction with his model. The graphics display
`allows the model to "show" the crystallographer a part of its electron
`density such that he can decide how a molecular fragment best fits. Once
`the crystallographer has made his decision, the computer merely does the
`bookkeeping and minor improvements. The aim of the molecular fitting
`program, therefore, is to create the necessary environment to allow the
`crystallographer to decide what atoms he wants in what piece of density.
`
`METHODS IN ENZYMOLOGY, VOL. 115
`
`Copyright© 1985 by Academic Press, Inc.
`All rights of reproduction in any form reserved.
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`A great deal of effort has been spent to develop the necessary control
`software and, in some cases, to build the hardware. At present there are
`approximately 10 density-fitting program systems in active use. Most lab(cid:173)
`oratories are not able to build the necessary hardware, but high-perfor(cid:173)
`mance equipment is available from a number of vendors. The program
`FROD01•2•3•4 is presently implemented on the Vector General 3400 (with
`DEC, VAX, or PDP-11 computers), MMS-X, Evans & Sutherland PS 2
`(PDP-11), MPS (VAX or PDP-11), and PS300.
`The man-machine interface in FRODO varies with the available
`equipment. All systems use a data tablet to pick menu items and to iden(cid:173)
`tify atoms shown on the screen. The VG3400 and Evans & Sutherland
`PS300 systems use analog-to-digital converters to define the view direc(cid:173)
`tion, and other picture-related functions such as clipping, zooming, and
`intensities. Commands that invoke dihedral angle rotations, single atom,
`and fragment shifts are also coupled to the A-Ds. On the Evans & Suther(cid:173)
`land PS2 and MPS equipment, pseudo A-Ds are drawn on the screen and
`can be activated by the data tablet pen. The MMS-X version uses the
`standard user control panel.
`
`Program Flow
`
`The following is strictly applicable to only the VG3400 version of
`FRODO. Other versions have some minor differences.
`After starting the program the user must specify a control data set.
`This data set contains all of the important parameters needed by FRODO.
`It includes, for example, the data set name for the user's coordinate file
`and the regularization zone. It is a source file and can be edited (at one's
`own risk). The user then gets to the CHAT interface, which has a large
`number of menu items activated from a terminal keyboard. Every exit
`from CHAT causes an update of the control file. Control normally then
`passes to the display loop.
`To make the system easier to use an effort has been made to keep the
`display menu options to a minimum, and to a single "page." The data
`tablet pen position is marked on the screen by a cursor, and a menu item
`is activated by moving the pen so that the cursor is positioned over the
`
`1 T. A. Jones, J. Appl. Crystallogr. 11, 268 (1978).
`2 T. A. Jones, in "Computational Crystallography" (D. Sayre, ed.), p. 303. Oxford Univ.
`Press, London and New York, 1982.
`3 B. L. Bush, in "Computers & Chemistry," vol. 8, p. I. Pergamon, Oxford, 1984.
`4 J. W. Pfiugrath, M.A. Saper, and F. A. Quicho, in "Methods and Applications in Crystal(cid:173)
`lographic Computing" (S. Hall and T. Ashida, eds.), p. 404. Oxford Univ. Press, London
`and New York, 1984.
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`item and then pushing the pen into contact with the tablet. In principle,
`any number of commands can be activated and each is polled in turn. This
`means, for example, that an atom can be moved and have its contacts
`updated at the same time. In practice some care has to be taken, since
`there are a number of mixed options which may be disagreeable to the
`user. For example, if a group of atoms is being moved and the user
`activates the SA VE command, then the current fragment coordinates will
`get written to disk. The active commands can be seen at a glance because
`each has a star drawn next to it. To exit from the display loop, the user
`must pick a suitable menu item to either terminate the session or enter one
`of the utilities. Reentering the display loop causes a new loading of coor(cid:173)
`dinate information from the disk.
`The vectors drawn on the display are constructed from three data sets
`and normally show some of the atoms in the coordinate data set superim(cid:173)
`posed on a "chicken wire" representation of some sort of electron
`density.
`The coordinate data set contains more than just atomic coordinates.
`The atoms are grouped together to form a residue. There are residue
`records to describe the type of residue (e.g., PHE, MPD), the name of the
`residue (e.g., A2, lOG), the position in the data set of the atom records for
`this residue, the center of gravity, and the radius of the residue. The
`residues are grouped together to form a sequence. As far as the display
`loop is concerned, the sequence is only important when defining viewing
`zones, i.e., it does not necessarily force any chemical connectivity be(cid:173)
`tween residues (although it may exist). The data set can also contain extra
`information such as lattice type (P, I, R, F, A, B, C), unit cell constants,
`and crystal symmetry information. This information is optional but may
`be required for certain commands. The user must decide at the CHAT
`interface how he wishes to access this data set. There are three possibili(cid:173)
`ties: (1) Define the start and end residues of a zone. The program then
`displays all the atoms in the residues within the zone as defined by the
`sequence. (2) Define a point in space and a radius, and then display all of
`the atoms in the data set which are within the volume. (3) Define a mixture
`of IO display zones plus a sphere.
`In the sphere mode the user can choose an option to display any
`symmetry-related atoms which may fall within the volume. Both the
`sphere and symmetry options make use of the residue center of gravity
`information to decide what appears in the volume. Another option allows
`one to define by name which atoms are to be displayed; e.g., one can
`define just Ca to see the fold of a protein.
`After picking which atoms are to be displayed, one must decide on a
`connectivity, i.e., which atoms should have a line drawn between them.
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`The usual connectivity scheme in FRODO is based on distance criteria so
`that if atoms are closer than a certain distance they are joined. In sphere
`and mix modes all atoms are tested together. In zone mode the connectiv(cid:173)
`ity is built up a residue at a time, and a specific link is made between
`residues. An atom with no connections appears on the display as a three(cid:173)
`dimensional cross. If one is displayingjust C,. atoms, for example, there is
`an option to connect the first atom to the second, the second to the third,
`etc. The initial connectivity does not necessarily represent chemically
`correct bonds. It is simply there as an initial framework for the crystallog(cid:173)
`rapher to decide how he is to change his structure to fit the density.
`The second data set consists of linked vectors. It may represent den(cid:173)
`sity contoured at a number of different levels, or skeletonized electron
`density, or guide points, or a vectorized library of molecular data sets.
`The vectors are arranged in three-dimensional volume elements and in
`what are called contour commands (C-COMs). If the data set is a vector(cid:173)
`ized map, each C-COM corresponds to a contour level. In the vectorized
`molecular library each molecule is equivalent to a C-COM. The user can
`decide in the CHAT interface which (if any) C-COMs are to be chosen.
`The third data set is an electron density map. It is also arranged in
`three-dimensional volume elements with each density value packed into
`one byte. This data set is much smaller than an equivalent vectorized
`map, and has the advantage that the contour levels can be changed at any
`time. It is, however, slower to work with than the vectorized data set. The
`map can also be used to automatically fit molecular fragments to the
`density. One often uses both a map and vector data set where the contour
`level has been chosen after a brief inspection of the map.
`
`Building an Initial Model
`
`The crystallographer usually knows the rough fold of his molecule
`before starting work on the display. This is best determined by extensive
`study of minimaps plotted on stacked plastic sheets. The structure solu(cid:173)
`tion of retinol binding protein by Newcomer et al. 5 is one of the few
`exceptions to this rule. There are then four different ways of building the
`model on the display.
`The first method is a relic of working with Kendrew wire models in a
`Richards box. FRODO has extensive model-making features to produce
`coordinates from a given sequence which have standard bond lengths and
`angles and preferred torsion angles. A zone of residues can be made and
`
`5 M. E. Newcomer, T. A. Jones, J. Aqvist, J. Sundelin, U. Eriksson, L. Rask, and P. A.
`Peterson, The EMBO J. 3:7, 1451 (1984).
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`moved to the place in the map where one wishes to begin building (not
`necessarily the N terminus). The fragment can be translated and rotated
`by the display menu command FBRT so that the first residue sits close to
`its density. Up to six consecutive dihedral angles can be varied at a time,
`and by repeated FBRTs and TORs the fragment may be made to fit the
`density. These coordinates are written to disk when the user is satisfied
`by using the SA VE command. The model-making option can be used to
`extend the zone ofresidues and an attempt made to fit these. However, it
`rapidly gets more difficult to do this while maintaining the constrained,
`rigid geometry.
`In method two, by judicious choice of display zones, the user fits a few
`residues as described above but introduces a discontinuity in a peptide
`linkage by separately fitting the next zone of residues.
`In method three the user introduces discontinuities directly on the
`screen. The screen connectivity is used to decide which atoms are af(cid:173)
`fected by dihedral rotations and by fragment rotation/translation. Sup(cid:173)
`pose a zone of residues fits the density but the user sees that a side chain
`in the center of the zone would fit much better if he could change <f>
`(around the N-Ca bond) for the residue. If one changes this angle directly,
`all the other atoms to the end of the zone would be moved out of density.
`This is prevented by breaking the Ca-C bond of the residue using the
`menu BOBR command and then rotating around the N-Ca bond. This, of
`course, distorts the bond angles around the Ca atom. More commonly, the
`user disconnects the side chain from the main chain and moves the small
`fragment straight into the desired density. This is illustrated in Fig. la
`(which is drawn on a plotter directly from the picture on our display),
`where a growing chain has clear density for the phenylalanine side chain.
`The Ca-C,13 bond is broken and the ring moved into the density using
`FBRT (Fig. lb). The same coordinates are shown from a different view in
`Fig. le, where one can clearly see density for the carbonyl oxygen. In Fig.
`ld the oxygen has been moved into this density and we now have a very
`distorted residue.
`It should be clear that to simplify the fitting process we must introduce
`errors in bond lengths, angles, and fixed torsion angles. These can be
`removed by model regularization. To prevent the buildup of errors in
`particular variables, the regularization should have no built-in rigid con(cid:173)
`straints (such as fixed bond lengths, for example). FRODO uses the
`method described by Hermans and McQueen6 , which they call the
`method oflocal change. In this method each atom is shifted to minimize a
`weighted sum of terms representing the shift from its starting positions,
`
`6 J. Hermans and J. E. McQueen, Acta. Crystal/ogr., Sect. A. 30, 730 (1974).
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`162
`
`a
`
`b
`
`Fm. 1. Fitting a growing protein chain using method 3. (a) The growing chain with the
`Phe residue out of density. (b) The Phe ring is moved as a rigid group to fit the density. ( c) A
`different view showing density for the carbonyl oxygen. (d) The carbonyl oxygen is moved
`into density. (e) The result of regularization with certain atoms fixed. (f) The ring stays in
`density after regularization.
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`
`FIG. I. (continued)
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`Fm. 1. (continued)
`
`errors in bond lengths, bond angles, and fixed torsion angles. Extra terms
`can easily be added to maintain preferred values for normally variable
`torsion angles (e.g., for an a helix) and for distances between atoms (e.g.,
`to maintain hydrogen bond distances).
`To keep the atoms in density FRODO has a menu option FIX. Any
`atom hit with the FIX option will not move during regularization. Before
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`
`regularizing the atoms shown in Fig. ld, the peptide oxygens of residues
`230 and 231 were fixed together with Cf:l of residues 231. The result of
`regularization is shown in Figs. le and lf. Sometimes one carries out a
`second regularization with nothing fixed to remove some buildup of errors
`(normally in the CO bond). The skills to be learned in using FRODO are to
`decide how to distort the model to fit the density, and then to decide
`which atoms to fix so that the main group of atoms stay in density and the
`rest are pulled into it. Often the fit is a combination of actions such as a
`bond break to delimit a dihedral rotation, the dihedral rotation to line up
`some chain with some density, another bond break to separate the frag(cid:173)
`ment, and finally a rotation/translation shift into the density.
`The fourth method of fitting attempts to place atoms near their density
`before actually sitting in front of the display. Guide coordinates are read
`directly from the minimap. At most one picks (for a protein) a guess for
`the Ca, 0, and one side-chain atom. For regions of the molecule with
`secondary structure, FRODO's model-making options are used to gener(cid:173)
`ate the desired conformation. Another option is then used to find the best
`rigid body fit to the guide coordinates. The gaps between secondary struc(cid:173)
`ture are filled by first inserting guide atom coordinates into the data set
`and making these atoms fixed. The coordinates for the remaining atoms
`get added (rather roughly) by the regularizer option, provided coordinates
`already exist for the first residue in the regularization zone. Because the
`guide atoms are fixed, the newly added atoms are forced to move close to
`their density. A second cycle without fixes is normally required to pro(cid:173)
`duce good stereochemistry. The last residue of the regularization zone is
`used as the first of the next zone. Once the complete protein has been
`made, the map can be inspected and improvements made as described
`earlier.
`After making the first pass through the molecule in zone mode, the
`user must make a second pass in sphere mode. This is not just to ensure
`that chains do not interpenetrate. Since one rarely works at atomic resolu(cid:173)
`tion, the interpretation must be guided by contacts with neighboring resi(cid:173)
`dues. At this stage one can also decide how well the atoms fit the density.
`Atoms not fitting density are not used in later phase calculations.
`The advantages of building a model with FRODO rather than in a
`Richards box are as follows:
`
`1. Speed. One can normally build a model more quickly in a display.
`This gain can be lost by spending more time on details such as making
`better hydrogen bonds and trivial changes to improve the fit to the
`density.
`2. Accuracy. All parts of the map are equally accessible in the display,
`but not in the box. Their crystallographic R factors are noticeably better,
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`often below 40%. The chicken wire representation of the density in the
`display is usually clearer than stacked sections in a box, and if the crystal(cid:173)
`lographer can correctly interpret the density, he can build the model more
`accurately.
`3. Control. Once a newly positioned conformation has been SAVEed
`with FRODO, the coordinates are safely on disk. Backup and restore
`features are available on the display menu, so that accidental overwriting
`of coordinate information is not a disaster. The wire model is easily de(cid:173)
`graded by gravitational forces prior to measuring coordinates. These co(cid:173)
`ordinates must be regularized and their positions checked by plotting on
`density sections.
`4. Volume. For large enzymes and viruses the actual space occupied
`by a physical model becomes a problem, especially in mature laborato(cid:173)
`ries. A Kendrew model of the plant virus satellite tobacco necrosis virus
`(STNV) would have a volume of 18 m3.
`5. If the crystallographic asymmetric unit consists of more than one
`molecule, the model of the first molecule built in the display can be used
`as a good starting model for the second. This technique was used on
`southern bean mosaic virus, in which there are three different protein
`chains. 7 One can also use coordinates from related conformations as was
`done by Eklund et a/. 8 in their study of bolo-alcohol dehydrogenase,
`ADH. In this example the coordinates for the two domains of the apo(cid:173)
`ADH were rotated into the map, and then rebuilt to fit the density. The
`second chain of the molecule was then built using the transformed first
`chain as the initial model.
`The main disadvantage of building a model in the display is that there
`are usually so many people wanting to use it that one cannot just go and
`check out an idea on the spur of the moment.
`
`A Tool in Crystallographic Refinement
`FR ODO originated in the groups of Drs. Robert Huber and John Gass(cid:173)
`man in 1976. By that time it was known that protein molecules could be
`refined, provided the crystallographer had the necessary patience and
`computer power. At that time Huber's group used Diamond's constrained
`real space refinement program9•10 to improve the model fit in maps calcu-
`7 M. G. Rossmann, C. Abad-Zapatero, M. A. Hermodson, and J. W. Erickson, J. Mo/.
`Biol. 166, 37 (1983).
`8 H. Eklund, J-P. Samama, L. Wallen, C-1. Branden, A. Akeson, and T. A. Jones, J. Mo/.
`Biol. 146, 561 (1981) .
`9 R. Diamond, Acta. Crystallogr., Sect. A 27, 436 (1971).
`io J. Deisenhofer and W. Steigemann, Acta. Crysta/logr., Sect. B 31, 238 (1975).
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`lated with 2IF0! - !Fcl amplitudes and model phases. After some cycles
`the refinement would stop and it was then necessary to find out why. By
`studying various sorts of maps (with model or model/isomorphous com(cid:173)
`bined phases) it was usually possible to locate errors in the model but very
`difficult to correct them. Since then, refinement methods have improved,
`and mostly gone into reciprocal space. 11 •12•13 These programs are very
`good at removing small random errors from the model, but they cannot
`correct major nonrandom errors. 2 During refinement one hopes that the
`improvement in the phase angles is such that the nonrandom errors can be
`identified and corrected on the display.
`When building the first model in the MIR map, I find it useful to divide
`the atoms into three groups: the good, the bad, and the ugly. During
`refinement one hopes that the distribution is pushed in the direction of the
`good atoms. In Munich and Uppsala an atom flag in the FRODO coordi(cid:173)
`nate data set is used to decide if the atom is used in phase calculation.
`Normally during the course of the refinement more atoms are used, al(cid:173)
`though one frequently removes atoms for a few cycles if one distrusts
`their behavior. We often use chopped Fouriers, in which a portion of the
`structure is removed from the phase calculation and a Fourier calculation
`(normally 2jF0I - IFcl amplitudes) made around the region of interest.
`The bookkeeping qualities inherent in the computer system are an
`important aid in refinement. With FRODO the crystallographer can main(cid:173)
`tain a library of past models in the vector data set and check his present
`model against any past version. It is also helpful to keep a map copy of the
`MIR map since it is the only density unbiased by the model.
`The main disadvantage of working with FRODO is that one is often
`faced with one's own inadequacy, in that one can see everything perfectly
`and still not know what to do.
`
`FRODO Crystallographic Extensions
`An important development in computer graphics in the last few years
`has been the use of 32-bit computers to control the display. The increased
`computer power means that crystallographically meaningful calculations
`can be made on part of the structure when the user sits at the display. The
`first to be introduced is a real space refinement option. 14 This option is an
`
`11 W. A. Hendrickson and J. H. Konnert, in "Computing in Crystallography ," p. 13.01.
`Indian Acad. Science, Bangalore, 1980.
`12 J. L. Sussman, S. E. Holbrock, G. M. Church, and S. H. Kim, Acta Crysta/logr., Sect. A
`33, 800 (1977).
`n A. Jack and M. Levitt, Acta. Crystallogr., Sect. A 34, 931 (1978).
`14 T. A. Jones and L. Liljas, Acta Crystal/ogr., Sect. A 40, 50 (1984).
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`extension of the fragment rotate/translate menu option and is called fin(cid:173)
`gertip refinement. The fragment moves as a rigid body to maximize the
`grid sum convolution ~ Pea1ePobs, where Peale is the calculated density ob(cid:173)
`tained from a Gaussian function and Pobs the observed grid density. The
`user controls the number of grid points over which to sum and the rota(cid:173)
`tion/translation search range. The technique is illustrated in Fig. 2. The
`side chain Cp-C.y bond has been severed and the two fragments have been
`arbitrarily moved out of the density, as shown in Figs. 2a and b. The
`results of volume fitting each fragment are shown with the same views in
`Figs. 2c and d. A noninteractive version can refine a zone of residues.
`Each residue is split up into smaller fragments, each of which is refined as
`above. The result can be shown on the display so that the user can decide
`if there should be any fixes before regularization. These options are not
`seen as replacing reciprocal space refinement methods but as an aid to the
`FRODO user. They have, however, been used by Jones and Liljas 15 to
`carry out the first crystallographic refinement of a virus (satellite tobacco
`necrosis virus) to a resolution of 2.5 A.
`
`FRODO as a General Molecular Modeling System
`
`FRODO was designed as a tool for the practicing protein crystallogra(cid:173)
`pher. However some of its features make it of more general use:
`
`1. The flexible coordinate data set and the absence of any connectiv(cid:173)
`ity dictionary mean that any sort of molecular fragment can be displayed.
`2. There are a number of different options available for choosing
`which part of the coordinate data set should be displayed. However, on a
`16-bit computer there are space limitations as to how many atoms can be
`manipulated (200 atoms on a PDP 11/VG3400 system).
`3. The MOL option can be used to create quite complicated display
`lists. These can be made up of any combination of atoms, zones, spheres,
`residue types (i.e., all Phes, say) and molecular surfaces. Display lists are
`sets of vectors and as such take the place of the electron density normally
`displayed with FRODO.
`4. The fragment rotation/translation with neighbor calculations can be
`used to dock substrates into active sites. This has recently been enhanced
`to include local energy minimization (Cambillau et al. 16).
`5. The edit features in the SAM option allow one to change residue
`types and delete or insert new residues. If there are sequenoe similarities
`between two molecules, and if the X-ray structure has been solved for one
`
`15 T. A. Jones and L. Liljas, J. Mot. Biol. 177, 735 (1984).
`16 C. Cambillau, E. Horjales, and T. A. Jones, J. Molecular Graphics 2, 53 (1984).
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`0
`
`b
`
`Fm. 2. Fitting a fragment automatically using real-space volume fitting. (a) and (b) are
`different views of the starting coordinates. The dashed line represents the C11-C, bond,
`which is not drawn on the display because the atoms are too far apart. (c) and (d) are the
`results after refinement of each fragment.
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`MODELING
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`[12]
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`d
`
`FIG. 2. (continued)
`
`of them, then its coordinates can be used as a skeleton to hang on the
`other sequence.
`The program is cumbersome when one tries to compare two related
`molecules, because only one coordinate file can be active at a time. How-
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`ever, the main drawback of the program is that there is no entry to a
`complete protein data base system except via a single coordinate data set.
`
`Acknowledgments
`
`Drs. J. Gassmann and R. Huber encouraged me to develop a density-fitting program.
`Professor T. Blundell invited me to get FR ODO running on an Evans & Sutherland PS 2, and
`Dr. I. Tickle improved my efforts. Dr. L. Bush made the MPS and Drs. J. W. Pftugrath &
`M. A. Saper made the PS300 conversions. Drs. C. Cambillau and E. Horjales are responsi(cid:173)
`ble for the energy-minimization options. Dr. J. Hermans developed the regularization
`method.
`
`[13] Rationalization of Molecular Models
`
`By JAN HERMANS
`
`Introduction
`
`It is normal to represent the "solution" of a crystal structure, which
`itself approaches the electron density as closely as the accuracy of the
`structure factors permits, in terms of a molecular model, i.e., a collection
`of atoms. There are two principal reasons to do this: chemists and bio(cid:173)
`chemists would pay little or no attention to a structure that was presented
`in any other form, and the model is an indispensable part of the principal
`crystallographic refinement technique applicable to proteins. Available
`chemical information is invariably incorporated in the model; of a protein
`it is preferable to have the entire amino acid sequence. If the amino acid
`sequence is not known, a good deal of it may be inferred from the shape of
`the calculated electron density; the larger side chains are easily recog(cid:173)
`nized. However, individual C, N, and 0 atoms are not resolved in the first
`maps. Atomic resolution may be reached at the later stages of refinement,
`if the experimental data are of sufficiently high resolution.
`The fact that the map does not clearly indicate individual positions for
`the majority of atoms causes considerable uncertainty, which can be
`much reduced by making the model conform to standard stereochemistry,
`according to measured bond lengths and bond angles of small molecules
`such as amino acids and peptides. These were first established in the now
`classic work of Pauling and co-workers. Bond lengths and bond angles
`have been found to be very similar for each type of chemical group, even
`in somewhat different physical (i.e., nonbonded) or chemical environ(cid:173)
`ments. In addition, such groups as aromatic rings and the peptide group
`
`METHODS IN ENZYMOLOGY, VOL. 115
`
`Copyright© 1985 by Academic Press. Inc.
`All rights of reproduction in any form reserved.
`
`15 of 15
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`BI Exhibit 1127
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