Small molecule structure solution with SHELXD
SHELXD solves structures in two dual-space stages. The first stage -
(sub)structure solution - is determined by the FIND instruction,
plus optionally PATS or GROP, and the second stage -
structure completion - by PLOP. When SHELXD is used for
macromolecular substructure solution
this second stage is omitted. The use of SHELXD to solve small (and not
so small) molecule structures is described here.
The input to SHELXD consists of two files, name.ins and
name.hkl, both of which can conveniently be created using the
Bruker XPREP program and many GUIs. With the exception of a couple of
instructions in the .ins file, the input is very similar to that
for SHELXS. SHELXD is slower than SHELXS and requires a more realistic
estimate of the cell contents, but is more effective than SHELXS for
larger equal-atom structures and also for (pseudo-)merohedrally twinned
structures. We will use the 1.1Å data for the
linear polypeptide PN1A (PDB-code 1PEN), kindly provided by
Jenny Martin, as an example to illustrate the various approaches to
solving larger small-molecule structures with SHELXD. A resolution
of 1.1Å is borderline for small-molecule direct methods (0.9Å
or better would have been desirable), but if the Friedel pairs had not
been merged the structure would be a sitting duck for
sulfur-SAD phasing, e.g. using SHELXC/D/E (it was collected in-house with
CuKα radiation). The files pn1a.ins and pn1a.hkl
generated by XPREP are available as a zip archive.
The file pn1a.ins consists of:
TITL pn1a in P2(1)
CELL 1.54178 15.0000 19.8000 16.5000 90.000 113.400 90.000
ZERR 2.00 0.0030 0.0040 0.0033 0.000 0.030 0.000
SYMM -X, 0.5+Y, -Z
SFAC C H N O S
UNIT 130 254 38 44 8
PLOP 112 141 157
MIND 1.0 3
This solves the structure about 60 times in one or two minutes using
a 4-core desktop computer, so NTRY 100 would have been
adequate and faster. Alternatively NTRY can be omitted, in which
case the job runs for ever unless terminated
by creating a file name.fin in the same folder. The correct
solutions can be recognised by their high final correlation coefficients
between the structure and the native data (FCC) of over 80%.
A value of at least 70% usually indicates success given data to
1.0Å or better, but FCC is less decisive for lower resolution
data. The solution is written in SHELX format to the file pn1a.res
and in PDB format to pn1a.pdb. It is rather complete but does not
attempt to differentiate between C, N and O. Note that small-molecule
direct methods cannot determine the hand of the structure, so there
is a 50% chance that the solution will turn out to be a mirror image of
the true structure! In some cases (e.g. P41 or P43) this
will require inverting the space group as well as the atom coordinates.
A good way is to rename the .res file as .ins and
input it into SHELXE with the -i command line option. For a
few space groups this also requires an origin shift, but SHELXE takes
this into account.
Bootstrapping by solving the substructure first
An alternative approach is to use Patterson seeding
in the FIND stage instead of random starting atoms. The idea
is first to solve the substructure (in this case the four
sulfur atoms that make up the two disulfide bonds in the asymmetric
unit) and then to expand to the full structure with PLOP.
To use the highest Patterson peaks as two-atom translation search
fragments, the instructions between UNIT and HKLF in
the pn1a.ins file would be replaced by:
FIND 4 5
MIND -1.8 3
TEST 10 5
PLOP 50 80 120 160 160
This uses a super-sharp √(E³F)-Patterson
(PSMF -4), five dual-space cycles to find four heavy
atoms and a minimum interatomic distance of 1.8Å
(MIND -1.8 3). The negative sign for the first MIND
parameter causes the PATFOM figure of merit to be calculated (it
measures the agreement of the calculated interatomic vectors with
the Patterson function). TEST sets the
threshold for entering the PLOP stage and PLOP
specifies the number of atoms to be assigned in each PLOP
cycle. Alternatively the Patterson seeding
may be performed with a randomly oriented fixed length vector, e.g.
a disulfide bond with a length of 2.06Å:
FIND 4 5
MIND -1.8 3
TEST 10 5
PLOP 50 80 120 160 160
In principle it is also possible to search for a disulfide unit
using GROP, though this is really intended for larger
fragments (but larger 3D fragments would require a larger first
GROP 99 1.6 1.2
FIND 4 5
MIND -1.8 3
TEST 10 5
PLOP 50 80 120 160 160
ATOM 1 SG
0.000 0.000 0.000
ATOM 2 SG
0.000 0.000 2.060
Solving twinned structures with SHELXD
Under favorable conditions, SHELXD is also able to solve
(pseudo-)merohedrally twinned structures by ab initio methods.
Sometimes this succeeds without special action, but better results
may usually be obtained by using the SHELXL instructions TWIN
and BASF. The BASF parameter is held at a fixed value
(default 0.5) throughout. The Bruker AXS program XPREP can be
used to find the TWIN matrix and estimate the BASF
parameter value. TWIN and BASF are only applied at
the PLOP stage, and are ignored by PATS, GROP
Alphabetical list of SHELXD instructions
All instructions in the .ins file commence with a four (or less) letter
word (which may be an atom name) followed by numbers and other information in free
format, separated by one or more spaces. Upper and lower case input may be freely
mixed. Defaults are given in square brackets; '#' indicates that the program will
generate a suitable default value based on the rest of the available information.
Continuation lines are flagged by '=' at the end of a line, the instruction being
continued on the next line which must start with at least one space. Other lines
beginning with one or more spaces are treated as comments, so blank lines may be
added to improve readability. All characters following '!' or '=' in an instruction
are ignored, except after TITL or SYMM (for which continuation lines
are not allowed).
ATOM and HETATM
These instructions define PDB format atoms for use by GROP.
All correlation coefficients (CC) are calculated using weights
w = 1/[1+gσ²(E)]. If the σ(E) values
read from the .hkl file are known to be very unreliable, it might
be better to set g to zero. The correlation coefficients between
Ec and Eo are calculated using the formula:
CC = 100[ΣwEoEcΣw−ΣwEoΣwEc] /
CELL λ a b c α β γ
Wavelength and unit-cell dimensions in Ångstroms and degrees.
Converts the most suitable nss peaks into disulfide units
with S-S distances of 2.06Å. This is an improvement on treating
these atoms as super-sulfurs. Each disulfide counts as a single
peak for FIND, so MIND must be set to avoid both
sulfurs being found in the initial peaksearch (e.g.
MIND -3.5 3).
This is the last instruction in the rare cases when the
.ins file is not terminated by the HKLF
ESEL Emin[#], dlim[1.0]
Minimum E and high-resolution limit for FIND. The E²
values are normalized to 1 in resolution shells, then smoothed.
Emin defaults to 1.2 for ab initio structure solution
and to 1.5 for heavy atom location (the appropriate value is set as
default depending on whether a PLOP instruction is present
or not). It may be necessary to reduce Emin if the resolution
FIND na, ncy[#]
Search for na atoms in ncy dual space cycles. If
WEED is employed, na is the number of atoms remaining
after the random omit procedure. ncy defaults to the largest
of (20 or na) or, if PATS is used, to the smaller of
(3na and 20). If FIND is absent, PLOP expands
directly from the starting atoms.
Resolution of all Fourier syntheses (including the PSMF but excluding
the Patterson itself) in terms of the minimum ratio of the number of
grid points along an axis to the maximum reflection index used along
GROP nor, Eg[1.5], dg[1.2], ntr
The dual-space direct methods is seeded by a 6D search for small rigid
group to find a high value (not necessarily the global maximum) of
ΣEc²(Eo²−1) for the reflections with
E > Eg and d > dg, where d is the
resolution in Ångstroms. For each of nor random orientations,
the local maxima of this function are found starting from ntr
random translations, and the atom positions corresponding to the
orientation/translation combination that gives the highest value for this
function are used to initiate the dual-space recycling (FIND).
The search model is read from PDB-format ATOM or HETATM records in the
.ins file. All other PDB records should be removed. The atomic
number is deduced from the atom name applying PDB rules. A short piece of
alpha-helix might be used for solving small proteins and a diglucose
fragment might be suitable for cyclodextrins. In practice, a thorough
6-dimensional search (with a large nor value and
Eg = 0) using GROP is rather slow, but when
used in combination with TRIK, GROP is much faster because
then only a 3-dimensional search is required.
m = 4 for F² in .hkl file,
m = 3 for F (or FA or ΔF).
nh is the number of (heavy) atoms to retain as fixed atoms
during PLOP expansion. This will normally only be used when
expanding from starting atoms (PLOP without FIND,
GROP or PATS).
Lattice type: 1=P, 2=I, 3=rhombohedral obverse on hexagonal axes, 4=F,
5=A, 6=B, 7=C. N must be made negative if the structure is
MIND mdis[1.0], mdeq[-0.1]
|mdis| is the shortest distance allowed between atoms for
PATS and FIND. If mdis is negative PATFOM is
calculated, and the crossword table for the best PATFOM value so far
is output to the .lst file. In this case the solution is
passed on to the PLOP stage if either the CC is the
best so far or the PATFOM is the best so far. mdeq is the
minimum distance between symmetry equivalents for FIND (for
PATS the |mdis| distance is used). The default value of
-0.1 for mdeq allows heavy atom sites on special positions,
which is normally recommended for small molecules or for heavy atom
soaks for macromolecular phasing.
For the location of selenium or sulfur in macromolecular phasing
it is advisable to use a value of 3.0 to avoid spurious solutions
such as uraninum atom solutions that are incorrect but fit
the tangent formula. For PLOP the PREJ instruction can
be used to control whether peaks on special positions are selected.
MOVE dx dy dz sign
The coordinates of the atoms that follow this instruction
are changed to:
x' = dx + sign⋅x
y' = dy + sign⋅y
z' = dz +
Maximum number of (largest) TPR (triple phase relations) per reflection.
If ntpr is negative, E is replaced by E/[1+σ²(E)] in
the estimation of probabilities involved in the tangent formula and
minimal function, as recommended by Giacovazzo, Siliqi & Garcia-Rodriguez
Number of global tries if starting from random atoms, PATS or
GROP. If ntry is zero or absent, the program runs until
it is interrupted by creating a name.fin file in the current
working directory (e.g. using the UNIX command touch).
PATS +np or -dis , npt[#], nf
Calculates and stores Patterson. A random search is performed for
np two-atom vectors corresponding to Patterson peaks or for a
random orientation vector of length |dis|, using npt
random translations, selecting the one with the best Patterson minimum
function PMF (see PSMF). When selecting a vector from the list
of unique Patterson peaks, special vectors are ignored and the highest
vector is chosen from nf random selections. This favors the
highest peaks but (if nf is not too large) also allows lower
peaks a chance. For example, with the default np = 100
and nf = 5, the chance is 39.5% that one of the first
10 vectors will be chosen and 91.9% that one of the first 50 will be
chosen. The default value of npt is 9999 for space groups with
a floating origin and 99999 for other space groups. When the space
group is P1, an extra atom is placed on the origin in addition to the
two-atom vector employed for the translation search. In the special
case when FIND 1 is specified with PATS, a single
atom Patterson translation search is performed instead of using a
vector. If the first parameter is negative, nf randomly
oriented vectors of length |dis| are compared on the basis of
the corresponding Patterson densities and the best used for the
translation search. If PATS is used together with a second
FIND parameter ncy greater than zero (or FIND
followed by only one number) a full-symmetry Patterson
superposition minimum function (i.e. a superposition based on
the two peaks and all their symmetry equivalents) is used to locate
the starting atoms for the first FIND cycle. PATS and
GROP are mutually exclusive.
PLOP followed by up to 10 numbers
PLOP specifies the number of peaks to start with in each
cycle of the peaklist optimization algorithm of Sheldrick & Gould
(1995). Peaks are then eliminated one at a time until either the
correlation coefficient cannot be increased any more or 50% of the
peaks have been eliminated.
PREJ maxb, dsp[-0.01], mf
PREJ controls the assignment of atoms in the PLOP
stage. maxb is the maximum number of bonds to atoms or higher
peaks, the peak is deleted if there are more. Peaks are also deleted
if they are less than dsp Ångstroms from their
equivalents. Atoms are not output to the final .res file if
they are in a molecule that consists of less than mf atoms.
PSMF pres[3.0], psfac[0.34]
pres is the resolution of the Patterson in terms of minimum
ratio of the number of grid points along an axis and the maximum
reflection index along that axis. If nres is negative a
supersharp Patterson with coefficients √(E³F)
is calculated (in which case a finer grid is advisable, i.e.
PSMF -4), otherwise a normal F² Patterson is used.
psfac is the fraction of the lowest values in the sorted list
of Patterson heights that is summed to get the PMF.
Followed by a comment on the same line. This comment is ignored by the
program but is copied to the results file (.res).
SEED sets the random number seed so that exactly the same
results can be obtained if the job is repeated on an identical
computer with no changes in the other parameters. Each integer
nrand defines a different sequence of random numbers. If
nrand is omitted or zero, the seed is randomized so a new
sequence is always generated.
These element symbols define the order of scattering factors to be
employed by the program. The first 94 elements of the periodic system
are recognized. For some options, e.g. substructure solution, only
the first element type is used.
SHEL dmax [infinity], dmin
Resolution limits in Å for all calculations. Both limits must be
specified but it does not matter which is given first.
During FIND, if the second peak height is less than
min2 times the first, the first peak is rejected (before
applying WEED to reject other peaks). This is sometimes useful
to suppress uranium atom solutions. For large equal-atom
structures in space group P1, where there is a danger of an
uranium-atom pseudo-solution, it might be a good idea to specify
SKIP 0.99 so that the first peak is ALWAYS rejected!
SYMM symmetry operation
Symmetry operators, i.e. coordinates of the general positions as given in the
International Tables, volume A. The operator X, Y, Z is
always assumed, so may NOT be input. If the structure is centrosymmetric, the
origin MUST lie on a center of symmetry. Lattice centering should be indicated
by LATT, not SYMM. The symmetry operators may be specified using
decimal or fractional numbers, e.g. 0.5-x,0.5+y,-z or
Y-X,-X,Z+1/6; the three components are separated by
commas. At least one SYMM instruction must be present unless the
structure is triclinic.
TANG ftan[0.9], fex[0.4]
Fraction |ftan| of the ncy dual space (FIND) cycles are
performed using the tangent formula, the rest using a Sim-weighted E-map.
fex is the fraction of reflections with the largest Ecalc values to
hold fixed when doing tangent expansion to find the remaining phases.
WEED is only applied to the first |ftan|−ncy
cycles. If ftan is negative, the occupancies are refined for
the final (1−|ftan|)−ncy cycles. This is
particularly useful for the anomalous sites in halide soak experiments,
since these often have partial occupancies, but for other substructure
problems it also provides a good check as to how many heavy atom sites
are present. It is not recommended for normal ab initio
applications of SHELXD because the algorithm employed uses a large
amount of memory (in the interests of speed).
TEST CCmin[#], delCC[#]
After FIND, if CC is less than CCmin, FIND is
repeated with new starting atoms. Otherwise PATFOM is calculated
(if the first MIND parameter was negative) and the PLOP
stage entered. CCmin is reduced by 0.1% each cycle until a
solution passes this test. After PLOP has been entered at
least once, subsequent attempts go on to PATFOM and/or PLOP if CC
is within delCC of best CC value so far. If PATFOM is
calculated, then only solutions with either the best initial CC
(i.e. after FIND) so far or the best PATFOM so far go on
to the PLOP stage. Whether or not PATFOM is calculated, if
PLOP is absent the heavy atom sites with the best initial
CC so far are written to the .res and .pdb files. If
PLOP is specified, then the .res and .pdb files
are written after the PLOP stage. Since these files are closed
and reopened each time, they may be inspected with other programs
without stopping the SHELXD job. The defaults for CCmin and
delCC are 45 and 1 resp. for full ab initio solutions,
and 10 and 5 resp. for substructure solution (i.e. when PLOP
TITL [ ]
Title of up to 76 characters, to appear at suitable places in the output.
TRIC (or TRIK)
Expand data to non-centrosymmetric triclinic for all calculations.
UNIT n1 n2 ...
Number of atoms of each type in the cell, in SFAC order.
Randomly omit fraction fr of the atoms in the dual space
recycling (except in the last cycle and the cycles for which no tangent
refinement is performed - see TANG). WEED not applied in
the PLOP stage.
ZERR Z esd(a) esd(b) esd(c) esd(α) esd(β) esd(γ)
Z-value (number of formula units per cell) followed by the estimated errors in
the unit-cell dimensions. This information is not actually required by SHELXD
but is allowed for compatibility with SHELXL.