7.6. Solvent flattening It is assumed that the areas of the electron density map where protein lies have areas of greater positive electron density than the solvent areas. The solvent occupied areas inside the crystal have no rigid structure, so they can be `flattened' (all grids points in the solvent region obtain a single density value - usually zero). (B.C. Wang, Methods in Enzymology, 1985). Solvent flattening, when successfully applied, defines clear boundaries between solvent and protein regions and improves interpretability of an electron density map. There are several variations of the score map calculations available. They can be performed either in real or reciprocal space using linear or gaussian distance dependent density or RMS deviations of density weighting. I recommand the use of WEIGHT GAUSSIAN. First variables use later on throught the procedures are defined. > set vari MAP_DENS = 1 > set vari MAP_FO = 2 > set vari MAP_FOFC = 3 > set vari MAP_2FOFC = 4 > set vari MAP_MASK = 5 > set vari SOLV_RAD = 8.0 > set vari HIST_TEMP = 0.0 > set vari SOLV_CUT 0.40 and symmetry operators read. > read file >symm/c2.symm symm The MAP_ variables assign different maps, SOV_RAD is the sphere radius, HIST_TEMP is the B value of the atom used for local histogram matching and SOLV_CUT is the proportion of the map that will be flattened. You can either continue by reading an initial map > read file ../prodef_mir.xmap map xpl > read file ../refl/catl.fobs refl init resol 3.0 100. limit -99 0 -99 or calculating it from FOBS and MIR phases > read file cell.dat cell > read file ../refl/catl.fobs refl init resol 3.0 100. limit -99 0 -99 > set vari AGRID = 70 > set vari BGRID = 50 > set vari CGRID = 120 > make map MAP_DENS from 0 init 0 real grid AGRID BGRID CGRID cell > make map MAP_DENS conv complex > refl fill MAP_DENS defined > four map map MAP_DENS back > make map MAP_DENS rescale and then create all neccessary maps for the solvent falttening procedure. It is assumed that the map 1 (MIR_MAP) contains the whole unit cell density. The MIR_MAP is here never altered in order to allow variations of paramaters during different runs. At each restart the MAP_DENS map density should be COPIED into the MAP_FO (2) map. > make map MAP_FO from MAP_DENS init 9999 real cell copy > make map 3 from MAP_DENS init -9999 real cell > make map 4 from MAP_DENS init -9999 real cell 7.6.1. The real space procedure The calculation can be significantly accelerated if only points in an asymmetric unit are solvent flattened, however the BOX should be at least one grid larger then the actual asymetric unit. > make map MAP_MASK from MAP_FO init 9999 box 0 0 0 37 50 62 The procedure is faster then the original programs (Wang, Methods in Enzymology, 1985). The summ of density above the specified threshold value (CUT 0.0) at all grid points FROM map MAP_FO within the specified radius (SOLV_RAD) around the central point WEIGHTED LINEARLY by distance is stored into the equivalent central point in map MAP_MASK. > make map MAP_MASK from MAP_FO cut 0.0 radi SOLV_RAD \ > weight linear WEIGHT GAUSSIAN 2.0 replaces the linear weighting, it however introduces additional parameter: a gaussian sigma value exp( - dist**2 / radius**2 * sigma**2). The default sigma is 2.0. An additional keyword RMS calculates instead of density its RMS deviations within the specified sphere (Abrahams Acta. Cryst. D52, 30-42, 1996). 7.6.2. The reciprocal space (fast) procedure The difference between the standard solvent flattening procedure described by Wang and the herein described fast procedure is in the scrore map calculation. The standard procedure calculates the weighted sum of positive electron density within a sphere. The fast procedure is based on Parseval's theorem which allows to calculate the scoring map (basis of a molecular envelope) in reciprocal space. Fourier coefficients of the weighting scheme P1 map and Fourier coefficients of the positive parts of the map to be flattened are multiplied and then backtransformed. The resulting map is a score map: convolution of the weighting scheme and the posiive parts of the map (Leslie, Acta Cryst. A43, 134-136). The fast procedure is not numerically identical to the standard one because of Foruier series truncation error, however, it is sufficiently accurate to be used. The major advantage of the fast procedure is that it is incomparable faster than the standard one. It can be performed interactively at a workstation display. Its speed is not sphere radius dependent. WARNING: Accuracy of the reciprocal space procedure depends on the completness of the low resolution data. If substantial part of low resolution data is missing use the real space procedures only. You can generate the Leslie's analytical structure factors for the convlution sphere directly > reflect solv_flat SOLV_RAD or use your own form of weighting scheme by generating its density via atoms. I recommand use of the GAUSSIAN form. Initiate a unit cell with the density set to EMPTY and a density of an atom that is placed at coordinate system origin and which density FUNCTION uses LINEAR or GAUSSIAN distance dependance (1. - d / SOLV_RAD). Set the empty points to zero, Fourier transform the map and save its Fourier coeficients in the FWORKSET array. > make map MAP_SOLV from MAP_FO init -9999 cell real > make map MAP_SOLV atom function SOLV_RAD gaussian 2. > make map MAP_SOLV set -100000 0 0.0 > fourier map MAP_SOLV And then store in both cases the obtained FCALC structure factors in the FWORK set: > reflect set ampl phase fwork = fcalc * 1.0 Copy the MAP_FO into the MAP_SOLV, set all negative density values to zero and Fourier transform it. R-value calculation is performed in order to follow convergence of a further procedure. > make map MAP_SOLV from MAP_FO init 9999 cell real > make map MAP_SOLV from MAP_FO copy > make map MAP_SOLV set -99999 0 0.0 > fourier map MAP_SOLV > reflect shells 10 r-values Multiply FWORKSET (sphere model) and FCALCULATE (truncated MIR density) Fourier coeficients, convert the MAP_SOLV map to a convex map, fill it with the multiplied Fourier coefficients and Fourier BACK transform it. (The DEFINE option and application of all symmetry operators in the reflection fill-map command is OK too.) > reflect set ampl phase fwork = fwork * 1.0 * fcalc * 1.0 > make map MAP_SOLV conv complex > make map MAP_SOLV zero > refl fill-map MAP_MASK > four map MAP_SOLV back > make map MAP_SOLV rescale 7.6.3. The score map histogram The map MAP_MASK is further analyzed - a histogram of density points in the 256 density intervals is prepared. (Number of intervals can vary from 1 to the maximal number of atoms your MAIN can accept). This histogram serves for the envelope cut. Note that in the case of convoultion theorem based score MAP_SOLV should be equal to MAP_MASK. > analyze init > analyze map MAP_MASK step 256 > make map MAP_MASK analyzes range SOLV_CUT 7.6.4. Filling holes and removeing clouds > set vari HOLE_SIZE = 6 At this stage you can in addition influence the maps either by FILLING the holes or remove the cloudes of the scattered mask. The command can be iterated. > make map MAP_MASK + 1 from MAP_MASK init 9999 copy > make map MAP_MASK from MAP_MASK + 1 remove HOLE_SIZE > make map MAP_MASK + 1 from MAP_MASK init 9999 copy > make map MAP_MASK from MAP_MASK + 1 fill HOLE_SIZE 7.6.4. Geneartion of the unit cell The map MAP_SOLV is converted to a real*4 map empty map, with density values set to -9999. The regions occupied with molecule obtain density, while the solvent region remains empty. > make map MAP_MASK from MAP_FO copy > make map MAP_SOLV conv real > make map MAP_SOLV zero > make map MAP_SOLV set -1 1 -9999. > make map MAP_SOLV from MAP_MASK cell Note that in the case of convolution theorem based score map calculation no extra map is needed (MAP_MASK should be equal to MAP_SOLV) and that the unit cell generation step is superficial, so you only need to copy the density into the masked MAP_SOLV: > make map MAP_SOLV from MAP_FO copy 7.6.5. Flattening and flipping of the solvent region Keyword: solvent, fliping In order to flatten the solvent (empty) region its value can be simply set to zero or to some small negative value as -0.1. For current macro see "MAIN_UTILS:re_fft_map.com". > make map MAP_SOLV set -10000 -9900 0.0 For any other solvent region maipulations the solvent needs first to be converted into a mask > make map MAP_SOLV set -10000 -9900 9999.0 and then flipped > make map MAP_SOLV from MAP_FO invert reshift or set to its average value > make map MAP_SOLV from MAP_FO invert reshift scale 0.0 For further possibilities see "Command Reference Manual" MAKE MAP commands. 7.6.5. Fourier transformation of the solvent flattened map. > fourier map MAP_SOLV > reflect shells 10 r-values > reflect set ampl phase fwork = fcalc * 1.0 Use FOBS > reflect set ampl fwork = fobs * 1.0 or 2FOBS - FCALC map for further calculation > reflect set ampl scale fcalc fwork = fobs * 2.0 - fcalc * 1.0 At this point you can call the MAIN atomic probability function (See below the section "Local Histogram Matching".) > if ( HIST_TEMP .gt. 2.0 ) <>utils/hist_match or include phase combination (see the section "Phase Combination") > make map MAP_FO zero > make map MAP_FO conv complex > refl fill-map MAP_FO defined > four map MAP_FO back > make map MAP_FO rescale At this stage the procedure ends. The results can be stored or a new cycle started. > write over file FILE_MAP map MAP_FO xpl 7.7.3. Solvent flattening procedure based on a skeletonized map See menu items SKELETON and SOLV_MAS in menu block MAP_ATOM. In a while a better description will appear also here.