HASSP: Patterson searches by the superposition method
[Script for HASSP | More about HASSP | Analyzing a solution ]
HASSP is a program for automatically searching for solutions to a Patterson function. It is used by SOLVE as a means of generating plausible starting solutions for a MAD or MIR dataset. You can use it to analyze any Patterson or difference Patterson function that you have calculated with this package. Although HASSP is good at finding possible solutions to a Patterson, it is not as good as SOLVE at evaluating these solutions. It is a good idea to run HASSP on your Patterson functions to get an idea of what they look like, but you should really run SOLVE to get a complete solution to your dataset.
Using HASSP is very easy. Here is a script file that will run HASSP on a patterson that you have calculated and put into "patterson.patt".
!------------------Script for running HASSP --------------------------------- @solve.setup ! set up those standard keywords fftfile patterson.patt ! name of file with the patterson logfile hassp.prt ! write out the results to "hassp.prt" hassp ! run hassp !----------------------------------------------------------------------------
HASSP will then analyze your patterson in "patterson.patt" and will write out a sorted list of likely solutions to this patterson.
The HASSP routine uses a space-group symmetry minimum method to obtain sets of atomic sites consistent with a patterson function. The usual procedure followed in using this program is to search for single-atom solutions to patterson function, then to search for two-atom solutions to the patterson function. The two-atom solutions are obtained from two sources: combination of single-atom solutions (after figuring out origin shifts and translations along polar axes), and cross-vector searches. The idea behind a cross-vector search is that many of the peaks in general positions of a patterson are cross-vectors between sites. If you know the cross-vector between two sites then once you know the position of 1 site you know the position of the second. Considering a particular cross-vector, HASSP tests all possible positions for atom 1, generates the position of atom 2 and all the predicted peaks it the patterson. These are compared to the patterson itself and the solution is scored.
Searching for single-site solutions to patterson function.
A map is calculated over the range supplied (XS-XE; YS-YE; ZS-ZE), except that search is not carried out over axis which are not fixed (all three in space group P1). The value of the map at each grid point is the minimum of values of the patterson functon at the (NEQUIV-1) Harker vectors corresponding to this grid point. Peaks in this map are stored, sorted according to symmetry, and listed after elimination of redundancies.
For points in general positions, the peak height listed is simply the minimum value of the patterson function at the (NEQUIV-1) Harker vector associated with this point. For points in special positions, the listed height is the minimum of the values of the patterson function at each of the (NEQUIV-1) Harker vectors divided by the number of times a Harker vector associated with this point falls on that position. For example, in space group P222, an atom at (x,y,z) yields Harker vectors (0,0,0), (2x,2y,0), (2x,0,2z), and (0,2y,2z). If x=0 and y=0, though, (0,0,0)=(2x,2y,0) and (2x,0,2z)=(0,2y,2z) and there is only one unique Harker vector (excluding the origin), which is repeated twice. The value of the peak height listed would be 1/2 the height at (0,0,2z).
The probability that a given peak of height A in this function is due to a random combination of peaks is roughly given by:
P=(1.- (1.- p(A)**M )**N ) , where,
The noise in the map is taken to be the RMS value of the patterson function if this is a general position. If it is a position of higher symmetry, the noise = sqrt(SIGMA) * the symmetry number of this position. The number of independent grid points used in the search for peaks would roughly be equal to the number of reflections used to make up the map if reflections at all resolutions contributed equally. A better estimate of this numbr is probably the number of peaks+valleys in the patterson map. In this routine, we actually use 2* the number of peaks.
The grid used for all searches is exactly the same as the grid for the input patterson map, but each time a peak is found, all neighboring grid points are tested on a grid twice as fine and the highest of these test values is used. Values of the patterson function between grid points are interpolated. Do not use a grid coarser than 1/3 the resolution for the input patterson map. Also don't bother to use a grid finer than 1/6 the resolution. NOTE: the input patterson map must be on a grid such that the symmetry elements lie on grid points. That is, if there is a two-fold axis at 1/12 in z, then the z-axis must be divided into a number of grid points that is a multiple of 12. The easiest way to be safe is to make sure all unit cell translations are multiples of 12.
Significance tests
Difference patterson functions have a considerable amount of noise if acentric reflections are present. (For each acentric reflection, the expected error [|Fph-Fp| - |fh|] is roughly equal to |Fph-Fp|). It can be shown that SIGMA, the RMS noise in the map is roughly equal to the RMS value of the patterson function.
Peaks in the patterson map which have a height much less than SIGMA are therefore likely to be unrelated to atomic sites. On special positions, the RMS noise in the map will be sqrt(NSYM)*SIGMA, where NSYM is the symmetry number of this position.
In order not to include too many peaks due to this noise in any of the searches carried out, a significance test is made for each peak if ISIGNF=0 (default). A peak is rejected if there is a probability less than SIGNIF that no peak of this height or higher would occur by chance in this search.
Symmetry numbers of positions in real and patterson cells
For this program, the symmetry number of a position in a real or patterson cell is the number of ways that a symmetry operator in the group (patterson or real cell) can map the point onto itself (within a toler- ance of 2 grid units). The symmetry number of a general position is 1, for a point on a dyad, it is 2, etc..
Local symmetry
Local symmetry is not yet implemented in SOLVE
.
Obtaining an analysis of a solution that you input yourself.
In order to generate a list of local symmetry-related points and minimum self- and cross-vectors corresponding to a set of unique sites you specify, use ITYPE = -6 with a very small search region (keyword searchregion; if you set it to zero, though, it will replace your zeroes with the asymmetric unit of the cell as defined by your FFTGRID).
If ITYPE=-6 is specified along with a small (but non-zero) search region, an analysis of the sites you input on lines 9a-... will be printed. This analysis includes the minimum values of the self- and cross-vectors for this set of sites. This procedure will help you determine if there is anything unusual about your map.