npo - Molecule and map plotting
npo [ XYZINn foo_in.brk ] [ mapin foo_in.map
] [ mapin2 foo_in2.map ] plot foo_out.plt
[Keyworded input]
NPO is a flexible program for plotting molecules and electron density maps, either separately or together. The molecule may be drawn as sticks, ball and stick, or space-filling, in parallel projection, perspective, or stereo-pairs with perspective (either side-by-side or red/green). Maps may be plotted as single sections or as stacks in mono or stereo, and two maps may be plotted together, so that for example a difference map may be superimposed on a 2Fo-Fc map.
The NPO program was originally written by Sam Motherwell (called `pluto') at the Chemical Laboratory, Cambridge. It has been modified for proteins by Eleanor Dodson, and for map plotting by Phil Evans.
The program can be used in 4 basic ways.
The various data control lines are identified by keywords, as follows, read in blocks depending on function. They are indicated in the table as compulsory (C), forbidden (F) or optional (O) for plotting of molecules and maps.
Group 1, initial settings
Molecule Map Comments
DATA O O If present, must be 1st for each drawing
TITLE O O Must be 1st after DATA
CELL C C not needed if present in MAPIN or XYZIN
SYMM C C not needed if present in MAPIN or XYZIN
PRINT O O May appear in group 4
USEORTEP O O (Works, just not very well.)
Group 2, map control
Molecule Map Comments
MAP C Must be 1st in group
CONTRS C
LIMITS O
MODE O
SECTNS C
SLAB O Must be after SECTNS
GRID O
Group 3, atom selection
Molecule Map Comments
INPUT C Must be 1st in group
BASE O
LABEL O
BOND O
RESIDU O
BOUNDS O F
BOX O F
SPHERE O F
STYLE O
LINK O
SKEW and/or TRANS O
Group 4, plotting style etc
Molecule Map Comments
JOIN C O Only one JOIN RESID RADII
VIEW or MATRIX C (F) Not to be used with map
ELLIPSOID O O (part of USEORTEP)
ESCALE O O (part of USEORTEP)
ELSTYLE O O (part of USEORTEP)
ORIG | OTRA | OROT O O (part of USEORTEP)
SOLID or STICK O O
RADII O O Must not precede JOIN
DCELL O F
STEREO | MONO O O
FONT O O
THICK O O
SIZE O O
COLOUR O O
Group 5, plot
Molecule Map Comments
PLOT C C Must be last (apart from END)
END 0 0
This keyword clears all arrays and flags (but not the view direction). It is only required to separate two independent drawings (or superimposed drawings).
If present, this card must be first (after DATA). The title is plotted at the head of the drawing. Also clear flags controlling plotting.
NB: Only to be used if there is an no input map, and if there are no CRYST1 and SCALEi cards in the XYZIN.
Enter cell constants and orthogonalisation switch, if only one number use as orthogonalisation code.
Cell dimensions in Angstrom and degrees. Angles default to 90. The cell dimensions are used for the conversion of orthogonal coordinates to fractional, and vice versa. If cell dimensions of 1 1 1 are given, then the conversion to fractional coordinates will have no effect, which will work, provided that no map is being plotted, and no translation (from symmetry or BOUNDS) is required.
Lorthogonalisation_Code=1 for Brookhaven orthogonalisation convention, and =2 (default) Rollett convention. (*) Cell dimensions given here override those on the map or PDB file. Sets up the calculation of orthogonalisation matrices.
Not to be used if MAPIN assigned.
Symmetry operations may be given in two ways: either in the style of International Tables, with different operators separated by * or on different cards
eg SYMM X,Y,Z * -X,1/2+Y,-Z
Translations may be given as 1/2 or 0.5 etc. Alternatively, the operation may be given as 12 numbers, a matrix S and translation vector t, in the order S11, S12, S13, t1, S21, S22, etc. Note that the symmetry operations act on fractional coordinates x' = Sx + t . At least the identity (X,Y,Z) must normally be given. (*) Symmetry operations will be read from the first map file, if any, but symmetry data given here on SYMM cards overrides that in the file. If no symmetry is given in either place, the identity is used.
This card may appear with the group 4 cards, and causes extensive diagnostic printing in the atom input, atom linking, and reading of the scratch file. Its main use is for debugging.
If given then uses ortep subroutines for drawing including bond overlap and anisotropic thermal ellipsoids: not recommended yet.
MAP keyword controls contours, mode and sections.
EJD - map order and sampling taken from map header - should be removed..
This card introduces map plotting. The three letters X, Y, and Z must
be given in the appropriate order to indicate the fast, medium and slow
(section) axes of the map (u, v, and w). They are accompanied by three
numbers giving the number of sampling intervals along the whole cell in
each direction. The optional keyword SCALE gives the scale in mm/A (this
is an alternative to the SIZE card). The 3D option produces contours in
three directions. Note that all contours will be seen on the plot ie perpendicular
contours will appear as lines. This option is only useful with map stacks.
(*) The axis order and sampling are not needed, but if present override
the data in the file. If the keyword NOBOX is present, the map is not surrounded
by a box.
eg MAP Y 104 X 152 Z 76 SCALE 2.5
Map has z sections in 1/76 ths with y running fastest (in 1/104) and x next (in 1/152). The scale is 2.5 mm/A.
The default orientation of the map on the plotter is with the fast axis u along the plotter Xp (to right), v along -Yp (down the paper) and w along +/- Zp (towards or away depending on the permutation of axes). The keyword INVERT on the MAP card interchanges u and v and inverts w relative to the plotter axes, ie it puts v along Xp, u along -Yp, and w along-/+ Zp. Alternatively, a viewpoint may be given but this is limited as the plot becomes distorted unless 3D option is used (see VIEW).
EJD: I haven't tested this and hate to think what would happen!
Keywords:
INVERT (optional) to put v axis along xp (default u along xp)
MAP AXIS ORDER MU,MV,MW, letters X,Y,Z, to give fast,medium,slow
directions in map
(optional, otherwise picked up from map)
3 Numbers giving sampling intervals
in these directions
SCALE (optional) scale in mm/a ( Picture_Scale )
NOBOX (optional) stop plotting of box around map
3D (optional) make contours in x, y, z directions
MAP Y 90 X 90 Z 120
CONTRS 0.25
SECTNS 23 32 10 10 1
LIMITS 51 62 93 106 23 32
This keyword sets the contour levels for the map. If two maps are to be plotted, this card will appear twice. The contours may either be given as a list, or as a lower and upper limits and interval.
eg CONTRS 200 400 600 800
CONTRS 200 TO 800 BY 200
Equivalent positive and negative contour levels may be specified by the keyword NEG before the specification of range and interval.
eg CONTRS NEG 20 TO 60 BY 20
will give contour levels 20 40 60 -20 -40 -60
Contours can be specified as sigma levels [SIG] (taken from map rms value) or as fractions of the maximum [MAX]. NEG can be used with either SIG or MAX but SIG and MAX cannot be used together. If NEG is used with MAX then the negative contours are taken has fractions of the minimum density.
eg CONTRS MAX 0.5 0.6 0.7
CONTRS NEG SIG 1.0 to 3.0 by 0.5
This limits the map to be drawn in x,y and z grid units. Obviously, the limits must be inside the original map limits as calculated from FFT. This keyword should not be used in conjunction with BOX, BOUNDS and SPHERE which limit the molecule.
>>> EJD - not useful - should use mapmask before plotting
This keyword MUST come AFTER the relevant CONTRS keyword.
Sets,
1) COLOUR and/or DASHED (optional, default black)
2) BELOW - Contour_Threshold, threshold for contour levels
3) COLOUR and/or DASHED, mode for levels BELOW Contour_Threshold
4) FIRST to set parameters for 1st section in a stack
DASHED keyword followed by 3 numbers, repeat,dash,dot
Mode for plotting contours. If two maps are plotted, each may have a MODE card, which must follow its corresponding CONTRS card. The mode is BLACK, RED, GREEN, BLUE, etc. (see Notes on Colours) or DASHED : DASHED may appear with a colour. If the keyword BELOW is present, a second mode is given for contour levels below the specified threshold. If the keyword FIRST is present, this mode is used for the first section in each map stack. This may be useful to plot sections in pairs, (SECTNS n1 n2 2 1) with one dashed or in a different colour. If no mode is given, the default colour is used (usually black, unless a COLOUR card is present). The keyword DASHED is followed by 3 numbers, repeat, dash, dot.
repeat repeat length in mm
dash dash length in mm (gap=repeat-dash)
dot length of dot for chain lines
eg MODE RED BELOW 0 RED DASHED 4 2 0
All red, negative contours dashed.
MODE BELOW 0 GREEN
Positive contours black
MODE DASHED 1 5 3.5
All dashed
BELOW
keyword below, store mode for higher levels and threshold
eg mode red below 0 red dashed 4 2 0
DASH
mode dashed 1 5 3.5
keyword dashed, store dash parameters, set mode negative
FIRST
(MODE FIRST not allowed with two maps)
keywords black,red,green,blue ...
Controls which sections to plot and how they are arranged. Multiple sections may be overlapped in stacks on the same plot (if StackSections > 1). By default these stacks will be contiguous (ie StepSections = StackSections), but StepSections maybe specified eg as < StackSections to allow staggered stacks with sections in common.
If the values are integers greater than the map range, then the program treats them as section numbers; but if they are less than the fractional map range, they are treated as fractions of the unit cell, and then converted within the program to section numbers.
If the FRAC subkeyword is included then the First_Section, Last_Section MUST be fractional. In this case the program will still check whether StepSections is <1 (i.e. a fraction) or >= 1 (i.e. a number-of-sections step).
eg SECTNS 3 14
plot sections 3 to 14 separately (the normal case)
SECTNS 3 11 4
plot 3 stacks of 4 sections :
3,4,5,6 ; 7,8,9,10 ; 11,12,13,14
ie start of each stack follows the end of the last one
SECTNS 3 11 4 2
plot 6 overlapping stacks of 4 sections
3,4,5,6 ; 5,6,7,8 ; 7,8,9,10 ; 9,10,11,12 ; etc
ie the start of each stack is 2 on from start of previous one
Set section limits for selection of atoms. Atoms will be stored on file if they lie between the sections specified plus 1 section thickness at each end. SLAB section1, section2
Only useful for large plots. If present, this card must follow the SECTNS
card. Normally atoms are stored in the scratch file if they lie between
the sections NFirst_Section-1 and NLast_Section+Nsections_in_Group. However,
in some cases plotting a map has to be split into several jobs, and it
may be better to select atoms for the whole map, and to save the scratch
file for the subsequent jobs (see the SAVED option on the INPUT card).
In this case, SLAB gives section limits for selection of atoms for the
scratch file: atom limits are section1-1 to section2+1, where section1
and section2 are the first and last sections of a series of plots.
eg SLAB 0 20
Read grid spacing along u and v in fractional or Angstrom (default Ugrid_Spacing=0.1,Vgrid_Spacing=Ugrid_Spacing)
and grid offset from map origin along u and v in fractional or Angstrom
(default=0). If the spacing is .lt. 1.0, it will be treated as fractional,
and any offset will be treated as fractional as well.
GRID Ugrid_Spacing,Vgrid_Spacing,Ugrid_Offset,Vgrid_Offset
Draw grid on map, at spacings of Ugrid_Spacing Angstrom along u and Vgrid_Spacing
along v
(default Ugrid_Spacing = 0.1, Vgrid_Spacing = Ugrid_Spacing).
Normally, the grid will pass through the map origin, but it may be offset by
Ugrid_Offset Angstrom along u and
Vgrid_Offset along v
(default=0),
ie the grid passes through the point
(Ugrid_Offset, Vgrid_Offset).
On map stacks, the grid is plotted only on the first section (with the lowest section number).
eg GRID 15
Draw grid at 15 A spacing in both directions
GRID
Draw grid at 0.1 (fractional) spacing.
GRID [U or V] <style for minor lines> EVERY <n> <style for major lines>
Set style for plotting grid lines (default full lines in current colour). If the first keyword is U or V, the card refers to grid lines across the u or v axes: otherwise the style refers to both directions. Two classes of grid lines may be defined, major and minor. The keyword EVERY gives the spacing of major grid lines, every n'th grid line from the origin (default=1, ie all grid lines major). The style specification may be a colour keyword (BLACK, RED, GREEN, BLUE, etc) and/or DASHED or FULL (default). DASHED is followed by 3 numbers (see MODE card). If the colour is not set, the current default colour is used (usually black). Up to three GRID cards may be given, to set the spacing and the style along u and v. Any one GRID card switches on grid plotting, so a style card may be given without a spacing card if the default spacing of 0.1 is wanted.
eg GRID RED DASHED 10 5 0 EVERY 5 FULL
Grid at default spacing 0.1, full line every 0.5.
GRID 10 25
GRID U RED EVERY 5 BLACK
GRID V RED EVERY 2 BLACK
GRID RED
Grid at 0.1 spacing in red.
This card introduces atom input. Initially the coordinate file is associated with the logical variable XYZIN1. Subsequently, when INPUT is specified the file will be associated with XYZIN2, then XYZIN3 etc.. Multiple input files maybe required when either superimposing plots (OVERPLOT) or generating several different plots from one command file. The exception to this is when 'INPUT SAVED' is specified as the coordinate information comes from a scratch file. Optional keywords are:
CA select alpha-carbon (CA) atoms only
SAVED for plotting into map, the scratch file has already
been created in a previous plot but in the same run
of the program. The scratch file is deleted when
the program is terminated.
If OVERPLOT is given on the card, this indicates that
the next drawing is superimposed on the previous one
(ie it is drawn at the same scale and position, without
advancing the paper). This provides a way of evading
the limit of (Max_Atoms) atoms in a drawing.
Label the given atom or atom type c1. If a number (n2) is given with an atom type, this label is only plotted if the residue number is an integral multiple of this number. The program by default tries to find the 'best' of 8 possible positions for each label. If two numbers are given with an atom name, they are used as the position of the start of the label, relative to the atom position, in mm. More than one LABEL card can be specified if you wish to label more than one atom or atom type
Optional keywords:
FIXED plot all labels to the right of the atoms. This saves
some time. FIXED must precede other keywords and
atom types.
ALL label all atoms (default if no atoms specified)
NONE no atoms are labelled
TEXT This is followed by a label (of up to 6 characters) to
be plotted on the following atom.
eg LABEL FIXED CA 10
label every 10th CA atom
LABEL O
label all the oxygen atoms, variable label
positions
LABEL TEXT IRON FE150 12 -5
Plot the label 'IRON' displaced by +12mm on
plotter x and -5mm on y from the atom
with name FE150 .
No tokens given LABEL ALL
FIX Expecting line of:-
LABEL FIX atom_name [increment number, default = 1]
label every j'th residue
Atom Expecting line of:-
name LABEL atom_name [increment number, default = 1]
label every j'th residue
ALL Expecting Line of :-
LABEL ALL
NONE Expecting line of :-
LABEL NONE
TEXT Expecting line of:-
LABEL TEXT string ATOM_ID [dx, dy]
i.e. atom plus residue number input, only label this atom if 2 numbers
on card, use as positions for this label relative to atom position, in
mm
default type NBType = 7 (using values from 'RADII ATOMS' for b(11) b(22) b(33) b(12) b(13) b(23)
with (Base)^{-D (b11*h**2 + b22*k**2 + b33*l**2 +
C*b12*h*k + C*b13*h*l + C*b23*k*l)}
NBType Base C D
0 e 2 1
1 e 1 1
2 2 2 1
3 2 1 1
10 e 2 2pi**2
or the coefficients U(ij)
with exp{ - D (a'**2 * U11 * h**2 +
b'**2 * U22 * k**2 +
c'**2 * U33 * l**2 +
C * a' * b' * U12 * h * k +
C * a' * c' * U13 * h * l +
C * b' * c' * U23 * k * l ) }
where a', b', c' are reciprocal cell dimensions
NBType C D
4 2 1/4
5 1 1/4
8 2 2 * pi**2
9 1 2 * pi**2
NBType = 6 allows for the Debye-Waller isotropic temperature
factor B which is used as follows:
exp ( -B sin^2(theta/lambda**2)
B is related to mean-square displacement of the atom
(rms) from its mean position by the relation
B = 8 pi**2 <rms**2>
the length of the axes are rms.
NBType = 7 allows for radii to be used
Atom limits in fractional coordinates. Only atoms within these limits are plotted. Unit cell translations are applied if necessary to put the atom into this volume. If maps are plotted, the bounds are set automatically. If the keyword CELL is present, the bounds are also stored as the cell edges, so that automatic scaling will be done on the bounds. Otherwise automatic scaling will be done on atoms only.
If keyword 'cell' absent, do not reset cell edges to bounds values, so auto scaling is done on real atoms only
word2 (optional) main, side, ca
2/3 (essential ) exclud, includ ,select, black, red,
green, blue, yellow, or bond
3/4 (optional)
4/5 (optional)
If a style (colour) keyword is used it must come in the second position e.g. RED, GREEN, PURPLE (see Notes on Colours).
Select residues for plotting, and plotting style. The second/third keyword may be a selection word SELECT, INCLUD or EXCLUD or BOND. If a residue is SELECTed, but not EXCLUDed, all symmetry operations are applied to its atoms. If a BOUNDS card is present or maps are plotted , the coordinates are tested against them, and unit cell translations are applied to try to bring them into the specified volume. Note that each symmetry operation can generate no more than one atom. INCLUDed atoms have no symmetry operations applied, and no bounds are tested.
The second keyword is optionally MAIN ,SIDE, or CA , to choose main chain, side chain, or Ca atoms only (main chain atoms are CA,C ,O ,N ). If none of the above keywords are specified then the RESIDUE keyword acts on all atoms in the residue.
Residue numbers may be given as a list, as a range n1 TO n2, or all residues by the keyword ALL. A style keyword may also be included as the last keyword on the card.
The BOND keyword is followed by two numbers, which give the bond types (specified on BOND cards) for main and side chain atoms.
Several RESIDU cards may be given, and their effect is cumulative. If no cards are given, the default is to SELECT all residues, but if any INCLUD or SELECT card is present, all other residues are excluded.
SELECT expects
Atom_name/Res_nam (TO Atom_name/Res_nam)
either as a list or as a range or ALL
INCLUDE/EXCLUDE expects
Atom_name/Res_nam (TO Atom_name/Res_nam)
either as a list or range or ALL (only include)
BOND expects
num, num, optionally followed by SELECT
Colour expects
MAIN, SIDE, CA, SELECT/INCLUDE or BOND.
Some examples:
RESIDU BOND 1 2 SELECT 100A TO 123A
RESIDU BOND 1 2 SELECT ALL
RESIDU RED BOND 3 4 50 TO 56
Draw residues 50 to 56 with bond types 3and4
in red, all others with bond types 1and2
RESIDU GREEN SELECT ALL
RESIDU SIDE EXCLUD 50 53 67
WARNING: use of a list of atom numbers
THESE MUST BE LAST on the line
RESIDUE RED BOND 2 2 SELECT 96L
RESIDUE BLACK BOND 1 1 SELECT 298H TO 302H
RESIDUE SELECT 404W
Read bond type or colour for symmetry numbers
2nd keyword black,red,green,blue,yellow, or bond
optional 3rd keyword trans: colour for all translated atoms
otherwise list of symmetry numbers
Read plotting style for molecules with the given symmetry numbers. Style keywords are BLACK, RED, GREEN, BLUE, etc and BOND. The BOND keyword is followed by two numbers giving the bond type for main and side chains. Colours given here take precedence over colours given on RESIDU cards. If the keyword TRANS is given with a colour, this colour is used for all atoms which have been translated to get them into the BOUNDS or the map, irrespective of symmetry operation. This takes priority over a symmetry colour.
eg STYLE RED 2 3
STYLE BOND 1 2 2
Bond types 1 and 2 for symmetry number 2
STYLE GREEN TRANS
STYLE Colour TRANS
STYLE Colour sym_numbers
STYLE BOND main side sym_numbers
bond type - first 2 numbers are bond types
for main and side chains
remaining numbers are symmetry numbers
Read bond type, bond radius, number of lines for dashed bond, keyword DASH followed by repeat,dash,dot BOND bond type, bond radius, number of lines
Defines a bond type, referred to on RESIDU and STYLE cards. The bond is defined by a cylindrical radius in A and a number of lines. Dashed bonds (one line only) are specified by the keyword DASHED and three numbers (see MODE card). Bond styles may also be defined by RADII BONDS card (qv) . The default style is radius 0.04, 8 lines.
eg BOND 1 0.04 5
BOND 3 DASHED 4 1.5 0
dashed line ( use default 0.04 8 0)
If the JOIN RESIDU option is used (qv, automatic for map plotting), residues are linked by recognizing the names of link atoms, by default N and C . These names may be changed on a LINK card. A number may be given for the maximum bond length between these atoms for a bond to be drawn (default=1.8).
eg LINK N C (=default, bondlength =1.8)
LINK CA CA 4.1 for CA plots
Two different LINK atom pairs may be given. They must both be given (no defaults) and must be in ascending order of bond distance. This may be useful for mixed main-chain and CA only drawings.
eg LINK N C 1.8
LINK CA CA 4.1
LINK P O3'
Read rotation matrix to rotate orthogonal atom coordinates to orthogonal
map frame:
SKEW S11,S12,S13,S21,S22,S23,S31,S32,S33
Read matrix S to rotate orthogonal atom coordinates into orthogonal map frame: Xo(map) = S * (Xo(atom) - t), where the vector t comes from a TRANS card (qv). This transformation will usually be required for a skew map, or other cases where the map and the molecule are not in the same frame. The program then works in the map frame (both orthogonal and fractional), which means that symmetry operations (if any) must also be transformed into the map frame. A blank SKEW card causes the skew transformation (rotation and translation) to be picked up from the map header, if it is present there.
Read translation vector to shift orthogonal atom coordinates to map
frame xormap=Skew_Matrix*(xor-tran)
TRANS tx, ty, tz
Translation vector for skew transformation. The vector t is the position of the map origin in the molecule frame.
BOX card, read coordinates of centre of box (A), and half-edges (either 1 number for all directions or 3 numbers) Select atoms in box centred at x,y,z (orthogonal coordinates in A), with half-edges hx,hy,hz A. If hy and hz are omitted, hx is used for all directions (default hx=10A). The limits are converted to fractional coordinates before use, so in a skew cell the box will be skew. The CELL keyword is the same as on the BOUNDS card.
If 6 numbers , separate half-edges for each direction If 4 numbers, 4th is half-edge, default = 10A
Select atoms in sphere centred at x,y,z A, radius r (default r=10A).
SPHERE x y z r
Define atoms to be classified as main-chain atoms. The first atom in
the list is considered as the CA atom for selection by RESIDU SELECT CA
and INPUT CAS. The default is MAIN CA C N O, for proteins.
eg MAIN C1' C2' C3' C4' C5' O4' O5' P O1P O2P O3' N9 N1
The element symbol is taken from columns 13:14 of the PDB file. For elements that are defined with two letters the program sets the second letter to lower case.
For example if we have the PDB file below the element symbols would be Xa, Xb and Cu. REMARK Written by O version 5.9.2 REMARK Tue Jun 13 17:26:21 1995 CRYST1 213.920 213.920 85.630 90.00 90.00 120.00 SCALE1 0.004675 0.002699 0.000000 0.00000 SCALE2 0.000000 0.005398 0.000000 0.00000 SCALE3 0.000000 0.000000 0.011678 0.00000 ATOM 1 XA JNK 1 120.040 19.308 -20.956 1.00 41.32 6 ATOM 2 XB JNK 1 145.538 0.306 7.347 1.00 42.84 6 ATOM 3 CU CU A 30 133.816 15.758 4.597 1.00 36.99 29 END Thus in the command lines in a script would have to be: # # Plot of molecule and fc map #!/bin/csh npo xyzin1 sketch.pdb plot z.plot << eof TITLE Test for NPO INPUT BROOK LABEL ALL BOND 1 0.5 5 JOIN RADII RESIDUE Cu 0.1 JOIN BOND 1 XA1 XB1 JOIN RADII RESIDUE Cu 0.01 Xa 0.01 RADII ATOM Cu 1.0 Xa 0.01 Xb 0.01 SOLID VIEW Z PLOT ! plot keyword is compulsory eof
As you can see dummy symbols are acceptable but follow the same rules as real symbols. However, dummy symbols should not contain numbers. Just to be confusing the actual atoms names are defined as set out in the PDB file (atom_name + res_number + chain_id); thus the copper atom would be CU30A. Note that the program presumes that anything beginning with C, N, O, or S is Carbon, Nitrogen, Oxygen or Sulphur resp., with the exceptions of, CA which is alpha carbon which gets special treatment in akwprotin, and OW - water. .
Checks:
Atom_Name contains a number first check for
CA1 i.e. calcium number 1
No number in Atom_Name
see if left justified heteroatom
here we have for example Ca for calcium -
left justified heteroatom
CA as Calpha is in columns 14/15
CA as Calcium is in columns 13/14
When labelling C-alpha atoms the atom name is
replaced by the residue name + number. For
WATER (wa) the atom name + number is used.
This card controls the way in which atoms are linked, either by explicit connection, or usually by search for atoms lying within the sum of their bonding radii (keyword RADII). A list of bonding radii is then given. The keyword RESIDU causes the distance search to be done only within residues, and this is usually preferable and faster than a search over all atoms. Residues are then linked by atom name (see LINK card).
eg JOIN RADII RESIDU CA 0.9 C 0.9 O 0.9 N 0.9 S 1.1
Note that CA is a different type from C and that only one card
should be given.
Hydrogen bonds may be generated with the keyword HBOND :
eg JOIN RADII HBOND 3 4 O 1.6 N 1.6
Search for connections between atoms of type O and type N with radii of 1.6 A. The first two numbers are the bond types (qv BOND) for mainchain-mainchain bonds and bonds involving sidechains respectively. The bond types may be 0 , in which case the bond style will be taken from the RADII BONDS card or from the default, or they may be -1, to suppress one type of bond (ie 1 -1 will find mainchain-mainchain bonds only). Mainchain-mainchain bonds are excluded within the same or adjacent residues in the same molecule, and sidechain-sidechain bonds in the same residue.
The H-bond search must be done before other bond searches (JOIN RADII ...... ).
Explicit connectivities may be given as a list of atom names, with breaks
indicated by end of card or by *. A number on a card of explicit connections
is used as a bond type, referring back to a BOND card. This option will
only work if both atoms in the bond are in the plot. Also, the CA atom
changes its name to the residue name i.e. ARG1 (see LABEL).
eg JOIN BOND 3 O243 N222 * N243 O251
If maps are plotted, the atoms are always joined by residue, and a JOIN card is only needed to change the radii from the default 0.9 A for all atoms. Explicit connections are not allowed.
JOIN EXCLUDE - exclude some bonds - Connections may also be explicitly removed from a previously generated list, (either connections between particular atoms, or less usefully all bonds between two atom types). Only one bond or bond type may be excluded on each card.
eg JOIN EXCLUD CA124 CA125
JOIN EXCLUD O N
eg JOIN RADII RESIDU CA 0.9 C 0.9 O 0.9 N 0.9 S 1.1
eg JOIN RADII HBOND 3 4 O 1.6 N 1.6
eg JOIN BOND 3 O243 N222 * N243 O251
eg JOIN NONE
eg JOIN BOND 3 O243 TO N222 N243 N251
JOIN NONE
JOIN RADII
JOIN RADII UNIQUE
JOIN RADII PRINT
JOIN RADII RESIDUE
JOIN RADII RESIDUE (Atom_Type n) ...
Atom_Type Given or Specifically named atom
JOIN RADII HBOND
Atom_Type Given or Specifically named atom
JOIN RADII ALL n
JOIN BOND
JOIN BOND bondtype
JOIN BOND n Atom1 TO list of atoms
join residue by residue
called for e.g.
JOIN RADII RESIDU CA 0.9 C 0.9 O 0.9 N 0.9 S 1.0 P 1.2
Controls ellipsoid type, not allowed with MAPS. See ORTEP-II manual for types, TYPE is entered either as a number greater than 700, the standard values, 1 to 6. (ortep values 701 to 706). If a number for TYPE is enter as 1 to 6 then it refers to a redefined ellipsoid type, entered via the keyword ELSTYLE. AtomType is either a group of atoms, i.e.
or it is a specifically named atom.
See ortep manual; default = 1.54. This is the Ellipse_ScaleFactor (the size of the probability ellipsoid).
Used to redefine an Ellipsoid style for an Ellipsoid type (number 1 to 6, i.e. ortep types 701 to 706)
NPLA sets NPLANES (in range 0 to 4 ) default 4 NDOT sets NDOTS (in range -6 to 6) default 0 NLIN sets NLINES (in range 0 to 9) default 8 NDAS sets NDASH (in range 0 to 9) default 0 ZERO sets AIN0 (in range 0 to 0.9) default 0.40 RATE sets AIN1 (in range 0 to 0.1) default 0.08 if NSOLID/NDOT negative whole number negated
Equivalent to ORTEP instruction 501. Define the reference Cartesian system explicitly.
Equivalent to ORTEP instruction 504. Translate the origin of the reference Cartesian system along the x, y, z axes of the reference system.
Equivalent to ORTEP instruction 502. <irot> = 1, 2 or 3 indicates a rotation by <phi> about the x, y or z axis respectively. <irot> = -1 or -2 indicates a rotation by 120 or 240 degrees respectively about the body diagonal.
This card defines the viewpoint for the drawing. For map plotting, the view is calculated from the map orientation, so a VIEW card should not normally be given, unless the atoms are not in the same fractional coordinate frame as the map (eg for skewed maps). The information on this card is used to construct a matrix to rotate the orthogonal molecule coordinates Orthogonal_XYZ into plotter coordinates. However it may be present before the MAP card to define the view direction. This is not recommended because unless it is used with the 3D option eg VIEW Y. It is preferable to calculate your map with different sections to the default.
Xp , Xp = R Orthogonal_XYZ .
Several options are available.
(a) View relative to axes.
X ( Yo along Xp
Y View along orthogonal axes ( Zo along Xp
Z towards origin ( Xo along Xp
AFACE View from (1,1/2,1/2)
BFACE (1/2,1,1/2)
CFACE (1/2,1/2,1) towards origin
LINE x y z view from fractional point xyz towards
origin
(b) View relative to named atoms
LINE n1 n2 view direction from atom n1 to n2. The vector v1
= (n1-n2) x (0,1,0) is along Xp.
BISECT n1 n2 n3 view along bisector of n1n2n3 towards n2,
perpendicular along Yp
PERP n1 n2 n3 view perpendicular to plane n1n2n3 , bisector
along Xp
(c) Rotation
After the matrix has been defined by one of the above options, it may be rotated about the plotter axes. A positive rotation is clockwise when looking along the axis towards the origin. Several rotations may be concatenated.
eg VIEW PERP O139 N36 CB72 X -30 rotate by -30 degrees about Xp from the specified orientation
The keyword MATRIX causes the current matrix to be modified. VIEW MATRIX alone preserves the current matrix (for superimposing drawings).
VIEW MATRIX Z 90
VIEW MATRIX
VIEW MATRIX [X,Y,Z] n
keywords defining a rotation matrix to be calculated.
VIEW [X,Y,Z]
VIEW [X,Y,Z] n
VIEW [AFACE, BFACE, CFACE]
VIEW LINE x y z
line is defined by two atom names
line defined by given point
from point to origin.
VIEW PERP n1 n2 n3
VIEW BISECT n1 n2 n3
Solid drawing, ie ball and spoke. The keyword NOHID suppresses the hidden line removal, making the program much faster. This should normally be done when plotting into maps. The keyword SHADE causes shading of the atom as if illuminated by a light source whose position is given by the angles a1 and a2. Zero angles give the light coming directly towards the viewer along the Zp axis. a1 and a2 are rotations about Yp and Zp (suitable values 120,-45). The SHADE option is useful for space-filling drawings (see RADII ATOMS). The Plotter_Step keyword (see also the DEVICE card) allows the plotter step size for circle drawing to be reset from its default of 0.25 mm to finer step eg 0.1 . The smaller step gives smoother circles but uses more time, particularly if the hidden lines option is used.
shade Shadelight_X Shadelight_Y nohid no hidden line removal Plotter_Step p reset Plotter_Step
This sets radii for atoms and bonds. There are several options for bond
specification, atom type, intermolecular, to list, specific atom pair.
we also enter number of lines for bond. Tapering of bonds may be controlled
also.
RADII ATOMS n1 r1 n2 r2 .....
This card sets the plotting radii for atom names or atom types n1, n2 etc to r1, r2 Angstrom . The default setting for all atoms is 0.3 A. Radii may be set to approximately Van der Waals radii to give a space-filling drawing. Radii may not be set for individual atoms when map plotting. If the radius is negative, the atoms are drawn with two concentric circles, the inner one with half the given radius. This is particularly useful for atoms such as waters which are not joined to other atoms.
When plotting maps, then only one radii can be specified for all atoms. It can be changed from the default by RADII ATOM ALL n.
This card may be used to set the bond radii, in a different way to the
BOND card. The bond style is given by a radius r in A and a number of lines
n. Alternatively, the style may be given as DASHED and three numbers (see
MODE card). The default values are 0.04 and 8.
The keyword ALL resets the default values.
eg RADII ATOMS CA 0.15 C 0.15 N 0.2 O 0.25 S 0.3 WA -0.2
RADII ATOMS ALL 0.5
RADII BONDS ALL 0.05 5
The keyword TO sets the bond style for all bonds to a
particular atom or atom type.
eg RADII BONDS TO FE 0 1
The bond style may also be given for a particular bond (not
when map plotting)
eg RADII BOND P2402 07402 0.08 6
The keyword TAPER applies exaggerated perspective to all
bonds. A factor m is given and is used to multiply the
ratio of the radii of the end points of the bonds.
eg RADII BONDS TAPER 25
packing diagram control
pack range x1,x2,y1,y2,z1,z2
Used by pack range instruction find molecules having their centre within the range given
moles to be plotted
OMIT atoms list or atom type list
Omit from plotting all specified atoms or all atoms of specified types. Up to eight atoms or types may be given on each OMIT card. This card may also appear in group 1 before INPUT to omit all atoms of one type from the atom selection (one OMIT card only).
Actually a useless option.
Draw unit cell as a box, with the origin and axes labelled. This is
not sensible to use when drawing map sections.
If a BOUNDS CELL card is present, the cell plotted is the bounds limits.
Causes a stereo pair to be drawn, as seen by an observer at a distance of d mm (default 600mm) from the top of the plotting coordinates, with an eye separation of 60mm. The keyword COLOUR selects red/green stereo, otherwise the two images are side by side. Note that if colours are defined for any part of the molecule, the red/green plot will not be correct.
The keyword SEP sets the separation of the two images to s mm. This separation will be altered if necessary by the program to a minimum value of the width of the drawing (default), and a maximum value of (paper width - drawing width) (see SIZE and DEVICE cards for paper width). If the drawing is wider than half the paper width, the stereo images will overlap.
NOTICKS option switches off the L and R page indicators. Useful when you have a red/green stereo drawing.
Draw perspective drawing, as seen from a distance d (default 600mm). If NOBOX is specified, no bounding box is drawn.
If neither MONO nor STEREO cards are present, the mono drawing is without perspective.
This card controls the scaling of the drawing. If the SCALE keyword is given, p is the scale in mm/A . If no scale is given (see also the MAP card), the scale factor is calculated to fit the drawing into size s1 mm. The scaling is normally done along the plotter Xp axis, but if the PLOT Y option is used, scaling is done along the plotter Yp axis. The default size is 250mm, 125mm for side-by-side stereo, or 244mm for PLOT Y.
The keyword CHAR sets the size for labels: the characters are spaced by s2 mm (default = 2mm).
The keyword PAPER (see also the DEVICE card) sets the paper width for scaling and calculation of stereo separation.
Note that a value for s1 must be given: this may be 0 if an explicit SCALE is given, either here or on the MAP card.
eg SIZE 0 CHAR 1.5 PAPER Paper_Width = FVALUEX(IWORK) SCALE Picture_Scale = FVALUEX(IWORK) CHAR Charcter_Size = fvaluex(iwork)
Matrix r11,r12,r13,r21,r22,r23,r31,r32,r33
Read view matrix R, Xp = R Xo . Alternative to the VIEW card.
Keywords BLACK, RED, GREEN, BLUE, MAGENTA, VIOLET, PURPLE, ORANGE or CYAN set the pen colour (where not overridden by other commands). Default is black. (See Notes on Colours).
Label the bond from atom1 to atom2 with the bond length. The second two numbers offset the label from the bond.
e.g. BNLA CB17 CG17 1 1
Font NFont_Number
Set font number for different style characters.
= 0 simple capitals
= 1 block letters (default)
= 2 italic
= 3 script
For GHOST NFont_Number = 0 not used in GHOST,
so used here as flag for italics
1 default Roman font
2 Greek
3 Cyrillic
Set line-thickness for Trilog, default =1 . If .gt. 1 (.le.9) the lines are thickened NPen_Thickness times. This is useful for large-scale plots.
The DEVICE card sets the paper size (and plotter step size) appropriate for a given device. The parameters may be set individually by a keyword/value pair:
WIDTH paper width in mm
LENGTH paper length in mm
STEP plotter step in mm (default = 0.25)
The paper size is used for scaling if a scale factor is not given, and for clipping the picture if a scale factor is given. The STEP keyword (see also the SOLID card) allows the plotter step size for circle drawing to be reset from its default of 0.25 mm to finer step eg 0.1 . The smaller step gives smoother circles but uses more time, particularly if the hidden lines option is used.
Alternatively, appropriate values may be set for standard devices:
Keyword Width Length Step
(default) TRILOG 330 508 default
BIG 330 2032 default
for Hewlett-Packard HP 275 350 0.1
eg DEVICE HP LENGTH 300 STEP 0.25
Set values for HP plotter, then change length
to 300mm, step to 0.25
Keywords WIDTH read paper width in mm Paper_Width
LENGTH read paper length in mm Paper_Length
STEP read plotter step in mm Plotter_Step
(default = 0.25)
GRID (X and Y are swapped here !)
set width = 253. length=320.
TRILOG set width = 328., length=508.
BIG set width = 328., length=2032.
HP set width = 275., length=350., step =0.1mm
(for Hewlett-Packard plotter)
Trilog
Paper_Width = 328.0
Paper_Length = 508.0
Big
Paper_Width = 328.0
Paper_Length = 2032.0
hp
Paper_Width = 275.0
Paper_Length = 350.0
Plotter_Step = 0.1
grid file (GHOST)
Paper_Width = 253.0
Paper_Length = 320.0
width
Paper_Width = FVALUEX(IWORK+1)
length
Paper_Length = FVALUEX(IWORK+1)
step
Plotter_Step = FVALUEX(IWORK+1)
Suppresses all titles, and other text around the plot, except labelling of map section axes, X and Y or U and V for pattersons, etc..
Read min and max of coords (as printed out by previous run) for producing
a series of pictures on same origin
Xmin,Xmax,Ymin,Ymax,Zmin,Zmax are in plot frame in A
This must be the last control card for a drawing, and starts the drawing process. Normally the plotter x axis Xp is across the paper, and the Yp axis along the roll, but the keyword Y rotates the whole drawing through 90 degrees, to put Xp along the roll.
This card may contain the number of traces and number of copies of the drawing to be made.
Y - yacross draw y axis across paper
THE DEFAULT AT emblhh and dl
X - xacross, Lpaper_Setting=0
THE DEFAULT USING plot84
TRACE LTrace_Flag
COPY Ncopies
End input.
There are three possible input files. Two map files and one PDB file. All of these are optional but obviously you need at least one of these.
MAPIN - first map to be contoured.
MAPIN2 - second map to be contoured. This is optional but useful for
superimposing 2Fo-Fc and Fo-Fc maps. Note that you need two
CONTRS keywords for each map and it is sensible to follow
those with two MODE keywords.
XYZIN1 - input PDB file containing the coordinates of the model.
If there are more INPUT keywords then the subsequent
coordinate files will be associated with XYZIN2,
XYZIN3 etc..
There is only one output file and that is the plot file. This can be plotted using xplot84driver. A PS file can be generated either from xplot84driver or from pltdev.
PLOT - output plot file.
A list of defined colours is given below along with their pen numbers:
1: BLACK 2: CYAN 3: RED 4: GREEN 5: BLUE 6: MAGENTA 7: YELLOW 8: PURPLE 9: ORANGE 10: BLACK
npo xyzin1 ../brk/arg96.brk plot cm.plt << eof
CELL 90.245 90.245 56.235 90.0 90.0 90.00
SYMM X,Y,Z
INPUT BROOK
LABEL TEXT Arg96L NE96L 8 1
LABEL TEXT Glu298 OE2298H -30 2
LABEL TEXT Asp300 CB300H 6 1
RESIDUE RED BOND 2 2 SELECT 96L
RESIDUE BLACK BOND 1 1 SELECT 298H TO 302H
RESIDUE SELECT 404W
BOND 1 .06 8
BOND 2 .06 2
BOND 3 DASHED 1 .5 0
JOIN BOND 3 WAT404W N301H
JOIN BOND 3 OE1298H NH296L
JOIN BOND 3 OE2298H NH196L
JOIN BOND 3 OE1298H WAT404W
JOIN BOND 3 O302H N299H
JOIN RADII RESIDU CA 0.9 C 0.9 O 0.9 N 0.9 S 1.0 P 1.2
MATRIX 0.97241 .09670 -.21231 .09231 -.99526 -.03052 -.21425 .01008 -.97673
VIEW MATRIX Y 15 X -15 Z 15
SOLID SHADE 45 -45 !PLOT 0.1
MONO NOTICKS
RADII ATOMS CA 0.225 C 0.225 O 0.275 N 0.255 S 0.275 P 0.3 OW -0.24
SIZE 250 CHAR 3.5
BNLA OE1298H NH296L 2.0 -3.5
BNLA OE2298H NH196L 2.0 -3.5
PLOT
eof
#
npo mapin m.map plot m.plt << eof
TITL skewing test
CELL 59.13770 59.13770 81.79250 90.00000 90.00000 120.00000
MAP
CONTRS .5 TO 4 BY .5
SECTNS 20 22 3
GRID 0.1
COLOUR BLACK
PLOT Y
eof
#
#!/bin/csh -f
# this plots in diff colours and dashed bonds
# but is complex isn't it ???
# colours/line thickness is whatever is in your .Xresources
# for xplot84
~ccp4/cadd/junk/npo xyzin ~/oppa/oppal/oppal_ortep.pdb\
plot kim.plt \
<< eof
CELL 110.600 77.080 71.240 90.00 90.00 90.00 1
SYMM X,Y,Z
INPUT BROOK
LABEL TEXT Glu32 N32A 8 1
LABEL TEXT Val34 VAL34A 8 1
#LABEL TEXT Asp419 CA419A 8 1
#LABEL TEXT Tyr109 CA109A 8 1
LABEL TEXT His405 HIS405A 8 1
LABEL TEXT Asp419 ASP419A 8 1
#LABEL TEXT Tyr109 TYR109A 8 1
LABEL TEXT Glu276 GLY276A 8 1
LABEL TEXT Arg404 ARG404A 8 1
LABEL TEXT Arg413 ARG413A 8 1
LABEL TEXT Cys417 CYS417A 8 1
LABEL TEXT Tyr245 TYR245A 8 1
LABEL TEXT Asn246 ASN246A 8 1
LABEL TEXT Asn247 ASN247A 8 1
LABEL TEXT Asn436 ASN436A 8 1
LABEL TEXT Thr438 THR438A 8 1
LABEL TEXT Trp397 TRP397A 8 1
LABEL TEXT Trp416 TRP416A 8 1
LABEL TEXT Leu401 LEU401A 8 1
LABEL TEXT Phe400 PHE400A 8 1
RESIDUE BLACK BOND 2 2 SELECT 24A TO 506A
RESIDUE BLACK BOND 1 1 SELECT 1B TO 3B
RESIDUE BLACK BOND 3 3 SELECT 15D TO 408D
RESIDUE BLACK BOND 2 2 SELECT 1E TO 5E
BOND 1 .08 10
BOND 2 .02 4
BOND 3 .04 2
BOND 4 DASHED 1 .5 0
!well it may be in doc but this line isn't in code
!JOIN RADII HBOND 4 4 O 1.6 N 1.6
! run first to get list of hbonds using
!JOIN RADII HBOND O 1.6 N 1.6
! then just edit log file to a set of
! JOIN BOND 4 ...... for
! second run --- do you really want all ???
! usually would only put in specific ones ???
JOIN BOND 2 SG271A SG417A ! disulphide bond
JOIN BOND 4 OE124A N32A
JOIN BOND 4 NE224A WAT48D
JOIN BOND 4 OE132A NE2405A
#JOIN BOND 4 OE132A OW048D
JOIN BOND 4 OE132A WAT48D
JOIN BOND 4 OE232A ND2436A
JOIN BOND 4 OE232A NZ2B
JOIN BOND 4 O32A N2B
JOIN BOND 4 O33A OG37A
JOIN BOND 4 N34A O2B
JOIN BOND 4 N36A OE136A
JOIN BOND 4 N37A OG37A
JOIN BOND 4 OD138A NH241A
JOIN BOND 4 OD138A WAT69D
JOIN BOND 4 ND238A WAT24D
JOIN BOND 4 NH141A WAT69D
JOIN BOND 4 NH141A WAT97D
JOIN BOND 4 OH109A OD2419A
JOIN BOND 4 O417A N1B
JOIN BOND 4 N417A O1B
JOIN BOND 4 OH109A N1B
JOIN BOND 4 OH245A OD21E
JOIN BOND 4 N246A OD1246A
JOIN BOND 4 O246A WAT74D
JOIN BOND 4 O246A WAT174D
JOIN BOND 4 OD1246A NZ3B
JOIN BOND 4 OD1246A WAT24D
JOIN BOND 4 ND2246A OD1487A
JOIN BOND 4 OD1247A NZ3B
JOIN BOND 4 OD1247A WAT25D
JOIN BOND 4 ND2247A WAT31D
JOIN BOND 4 ND2247A OD11E
JOIN BOND 4 OH269A WAT86D
JOIN BOND 4 OH274A WAT16D
JOIN BOND 4 OH274A WAT167D
JOIN BOND 4 OE1276A NH2404A
JOIN BOND 4 OE1276A OG1438A
JOIN BOND 4 OE1276A WAT167D
JOIN BOND 4 OE2276A NE404A
JOIN BOND 4 OD1366A NH1413A
JOIN BOND 4 ND2366A OD11E
JOIN BOND 4 NE2371A OD11E
JOIN BOND 4 NH1404A WAT39D
JOIN BOND 4 NH1413A OXT3B
JOIN BOND 4 NH2413A O3B
JOIN BOND 4 O415A WAT16D
JOIN BOND 4 O415A WAT39D
JOIN BOND 4 O415A N3B
JOIN BOND 4 NE1416A O425A
JOIN BOND 4 O418A WAT49D
JOIN BOND 4 N419A OG425A
JOIN BOND 4 O419A WAT176D
JOIN BOND 4 OD1419A N1B
JOIN BOND 4 OD2419A WAT62D
JOIN BOND 4 O425A OG425A
JOIN BOND 4 O425A WAT62D
JOIN BOND 4 OG425A WAT62D
JOIN BOND 4 N438A OG1438A
JOIN BOND 4 OH485A WAT25D
JOIN BOND 4 O504A WAT49D
JOIN BOND 4 O504A WAT387D
JOIN BOND 4 O505A WAT79D
JOIN BOND 4 OD2505A WAT344D
JOIN BOND 4 OD1506A WAT68D
JOIN BOND 4 OD1506A WAT387D
JOIN BOND 4 NZ1B WAT49D
JOIN BOND 4 NZ1B WAT176D
JOIN BOND 4 NZ1B WAT387D
JOIN BOND 4 O3B WAT25D
JOIN BOND 4 NZ3B WAT174D
JOIN BOND 4 NZ3B OD21E
JOIN BOND 4 OXT3B WAT39D
JOIN BOND 4 WAT24D WAT344D
JOIN BOND 4 WAT49D WAT86D
JOIN BOND 4 WAT49D WAT387D
JOIN BOND 4 WAT61D WAT167D
JOIN BOND 4 WAT68D WAT97D
JOIN BOND 4 WAT68D WAT176D
JOIN BOND 4 WAT68D WAT408D
JOIN BOND 4 WAT69D WAT79D
JOIN BOND 4 WAT74D WAT77D
JOIN BOND 4 WAT78D WAT167D
JOIN BOND 4 WAT79D WAT86D
JOIN BOND 4 WAT79D WAT344D
JOIN BOND 4 WAT79D WAT387D
JOIN BOND 4 WAT97D WAT107D
JOIN RADII RESIDU I 1.1 CA 0.9 C 0.9 O 0.9 N 0.9 S 1.1 Fe 1.1
VIEW Z
SOLID SHADE 120 -45 ! shade isn't done by xplot84 > postscript
STEREO NOBOX NOTICKS
RADII ATOMS CA 0.225 C 0.225 O 0.275 N 0.255 S 0.275 Fe 1.0 OWO -0.24
SIZE 65 CHAR 1.0
PLOT
eof
exit
Plotting a patterson with vectors
npo mapin isopatt plot $SCRATCH/isopatt5.plt xyzin1 emtsvectors.pdb << eof
notitle
map scale 4.0
sectns 0 0.1 1
contrs SIG 1
grid 0.1 0.1
#
input brook list
label all
solid
radii atoms VAA -0.3
plot
eof
If cell lengths are nearly the same then there can be problems with matrix/eigenvalue solution.