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Introduction to resolve
Why another density modification approach?
Although density modification (solvent flattening, non-crystallographic symmetry, phase extension, histogram matching, etc.) has been a very powerful tool, its potential is much greater than has been achieved so far. There are two reasons for this:
Problems with the phase recombination approach to density modification.
Resolve uses a maximum-likelihood approach to density modification, while other methods use an approach in which a map is modified to meet expectations and the new phases are recombined with experimental phases. For the mathematical details, see Terwilliger, T. C. (1999) Reciprocal-space solvent flattening, Acta Cryst. D55, 1863-1871. You might also wish to see the discussion and extensions in Kevin Cowtan's article "Gaussian Likelihoods in real and reciprocal space" in the CCP4 newsletter.
Principal problems with the phase recombination method
| What is the optimal relative weighting of modified and experimental phases? | Incorrect relative weighting means that the
final results will not be optimal
Incorrect weighting terms mean that the final figures of merit are almost always inflated |
| When do you stop iterating? | In some approaches the maps initially get better, then get worse unless you stop |
The maximum-likelihood approach to density modification
Density modification can be thought of as a way to adjust crystallographic phases (or amplitudes) to make them simultaneously consistent with the experimental data and with our expectations of what an electron density map should look like. The maximum-likelihood approach is a mathematical way to formulate this statement. By using this formulation, the weighting factors and problems with convergence are taken care of automatically.
In resolve, any set of structure factor amplitudes and phases has an associated likelihood composed of two simple parts:
Likelihood of a set of phases (and amplitudes)
| The likelihood of the experimental phases | This is the likelihood that you would have observed your experimental data if this set of phases (and amplitudes) were correct |
| The likelihood of the map | This is the likelihood that the electron density map calculated from this set of phases is drawn from the set of plausible electron density maps for this structure |
Resolve adjusts your crystallographic phases so as to maximize the total likelihood of those phases. The mathematics is a little complicated but the idea is very simple. To see the mathematics in detail, have a look at Terwilliger, T.C. (1999) "Reciprocal-space solvent flattening," Acta Crystallographica D, 1873-1871.
Using all the available information for density modification
Density modification is usually thought of as a process that is carried out on an experimental electron density map prior to model building, but iterative model-building methods such as ARP/wARP can also be thought of as density modification techniques. With the maximum-likelihood approach, partial model information can be seamlessly incorporated into the total expression for the likelihood of the phases. This allows a hierachical approach to incorporating information about phase likelihood:
Types of information that can be used in maximum-likelihood density modification
| Experimental phases (if available) |
| Low-resolution structural information (solvent boundary) |
| Non-crystallographic symmetry |
| Partial model information (molecular replacement or model building) |
| Full atomic model information |
The current version of resolve can incorporate the first two types of
information, which corresponds to carrying out solvent flattening and histogram
matching. The full version of resolve will incorporate all of them.