Section 14.2.1.6. Approaches to MAD phasing

There are two general approaches to MAD phasing. In the explicit approach, the MAD observational equation is solved directly (Hendrickson et al., 1988; Hendrickson & Ogata, 1997). In the pseudo-MIR approach, MAD phasing is treated as a special case of multiple isomorphous replacement (Burling et al., 1996; Terwilliger, 1997; Ramakrishnan & Biou, 1997). Both approaches have been quite successful, and each has advantages and disadvantages. For complete phase determination by either method, the partial structure of the anomalous scatterers must be determined. The explicit and pseudo-MIR approaches differ in when the partial structure is determined and in how it is refined.

The explicit approach provides the quantities , and by direct fit of the to the MAD observational equation (14.2.1.11). No anomalous-scatterer partial structure model is required in this first step of phasing. Estimates of the anomalous scattering factors at the wavelengths of data collection are required. These estimates can be refined (Weis et al., 1991), so they need not be highly accurate. Redundancies are merged to produce a unique data set at the level of the derived quantities , , and their error estimates. The anomalous-scatterer partial structure is determined from the derived estimates of and refined against these amplitudes. In the second step of phasing, is derived from the phase difference and weights are calculated for a Fourier synthesis from and . Phase probability distributions (ABCD coefficients; Hendrickson & Lattman, 1970) derived from the MAD observational equation (14.2.1.11) can be used directly in the explicit approach (Pähler et al., 1990). A probabilistic treatment based on maximum likelihood theory has also been developed (de La Fortelle & Bricogne, 1997). There are two advantages to the explicit approach. First, it is amenable to the `phase first, merge later' scheme of data handling because refinement of the anomalous-scatterer partial structure is entirely separate from phase calculation. The second principal advantage of the explicit approach is the calculation of an experimentally derived estimate of the normal structure amplitude for the anomalous scatterer. This is the quantity with which the partial structure of anomalous scatterers is most directly solved and refined. However, extraction of reliable estimates from data with low signal-to-noise can be difficult. Bayesian methods of estimation (Terwilliger, 1994a; Krahn et al., 1999) have been shown to be more robust than least-squares methods.

In the pseudo-MIR approach, data at one wavelength are designated as `native' data, which include anomalous scattering, and data at the other wavelengths as `derivative' data. This approach has the advantage that nothing need be known about the anomalous scattering factors at any time during phasing. These quantities are incorporated into heavy-atom atomic `occupancies' and refined along with other parameters. Of course, the partial structure of anomalous scatterers must be known, and its refinement is concurrent with phasing. This may be a principal advantage of the pseudo-MIR approach, because the anomalous-scatterer parameter refinement may be more reliable when incorporated into phasing than when done against estimates. Greater weight is given to the data set selected as `native' in refinement of the `heavy-atom' parameters in some implementations of the pseudo-MIR approach, although others treat data at all wavelengths equivalently (Terwilliger & Berendzen, 1997). The amplitudes are not a by-product of the pseudo-MIR approach.