The following comes straight from Appendix A in the README from MOLREP, and can now also be found in the CCP4 program documentation for MOLREP (which may be more up-to-date).
Molecular replacement method
There are two major steps in the Molecular replacement method: orientation and translation search. They are performed by Rotation and Translation function. Both of them are correlation functions (or overlapping functions) between observed and calculated model Pattersons.
ROT(R) = Irad Pobs(r) * Pcalc(R,r) dr
TR(s) = Icell Pobs(r) * Pcalc(s,r) dr = = Sum ( I Pobs(r) * Pcalc_ij_(s,r) dr) = i#j = Sum TRij(s) i#j
Translation function is the sum of translation functions for every pair of different cryst. symmetry operators.
The best rotation function algorithm is the Crowther Fast Rotation Function which is used in the program MOLREP. It utilizes FFT. The program can compute the Rotation Function for three different orientations of model and average them. That reduces the noise of Rotation function.
The translation function algorithm was developed by the author and performs calculations in reciprocal space using FFT. There are two major differences from other translation function:
Packing function is overlapping function:
P(s) = Sum ( I Roi(r) * Roj(r) dr ) i#j cell
where Roi(r) is the electron density of model which corresponds to ith cryst. symmetry operator. The algorithm of calculation of Packing function is similar to the one for translation function and performed by the same program.
Advanced translation function
The advanced Translation function is:
TR(s) = [ M TRij(s) ] * P(s) i#j
where M means multiplication of different TRij.
Secrets of success
Success of molecular replacement method depends on:
For scaling we use a completely new strategy based on scaling of two Patterson maps. This method makes it possible to have a very good approximation for scaling problem even if only low resolution data is available where other methods do not work. Scaling by Patterson also is useful for Cross rotation function where the cell is different for the model and the unknown structure.
Low resolution cut-off (Boff)
Low resolution cut-off introduces systematical errors in the electron density especially near the surface of the model. It is the series termination effect. Instead of using the usual low resolution cut-off, the program multiplies the modules of structure factors by a special coefficient:
Fnew = Fold (1-exp(-Boff*s^2))
where Boff = 4resmin^2. Boff is called "soft low resolution cut-off", which allows the removal of structure factors in this resolution range without introducing the series termination effect.
The use of a priori knowledge of similarity and completeness of the model
For low similarity the high resolution reflections are weighted down. Program uses for this additional overall factor Badd:
Fnew = Fold exp(-Badd*s^2)
Value of similarity 'SIM' can be : from 0.1 to 1.0. It directly corresponds to Badd ranging from (B_limit-Boverall) to (-Boverall), where B_limit refers to the so-called 'Optical Resolution'. SIM="1" means normalized F will be used.
For low completeness, e.g. when there are several molecules in the asymmetric unit, the contribution of low resolution reflections is weighted down. To manage the completeness of model, the program uses low resolution cut-off (Boff). Completeness of model 'COMPL' can be : from 0.2 to 1.0. It corresponds to Boff: from 400 to 1600.
Optical resolution is defined as an expected minimum distance between two resolved peaks in the electron density map. It is computed from the width of the Patterson origin peak. For reference, see MOLREP program documentation.
Functions of real space searching
Spherically averaged phased translation function (SAPTF)
SAPTF gives expected position of model in Electron density map by the comparison of spherically averaged density of model with locally spherically averaged observed density.
SAPTF(s) = Irad(s) Robs(r,s) * Rcalc(r) dr
Phased Rotation function (PRF)
PRF gives the orientation of model placed in some point of Electron density.
PROT(O) = Irad(s) Robs(r) * Rcalc(O,r) dr
Phased Translation function (PTF)
Translation search in Elecron density map.
PTR(s) = Icell Robs(r) * Rcalc(s,r) dr
Fitting two models
Fitting through Electron density. Second model (see MODEL_2) is the target model which is converted to electron density. To search the best overlapping of electron densities of models there are two algorithms:
For more information on the MOLREP program, see MOLREP.