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. 1999 Nov;55(Pt 11):1863-71.
doi: 10.1107/s0907444999010033.

Reciprocal-space solvent flattening

T C Terwilliger  1
Affiliations

Reciprocal-space solvent flattening

T C Terwilliger. Acta Crystallogr D Biol Crystallogr. 1999 Nov.

Abstract

Solvent flattening is a powerful tool for improving crystallographic phases for macromolecular structures obtained at moderate resolution, but uncertainties in the optimal weighting of experimental phases and modified phases make it difficult to extract all the phase information possible. Solvent flattening is essentially an iterative method for maximizing a likelihood function which consists of (i) experimental phase information and (ii) information on the likelihood of various arrangements of electron density in a map, but the likelihood function is generally not explicitly defined. In this work, a procedure is described for reciprocal-space maximization of a likelihood function based on experimental phases and characteristics of the electron-density map. The procedure can readily be applied to phase improvement based on solvent flattening and can potentially incorporate information on a wide variety of other characteristics of the electron-density map.

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Figures

Figure 1
Figure 1
Flow diagrams for (a) real-space solvent flattening and (b) reciprocal-space solvent flattening.
Figure 2
Figure 2
Correlation of solvent-flattened phases with true phases [〈cos(Δϕ)〉] for model data in a unit cell containing 70% solvent as a function of resolution. Structure factors (6906 model data from ∞ to 3.0 Å) were generated based on coordinates from a dehalogenase enzyme from Rhodococcus species ATCC 55388 (American Type Culture Collection, 1992 ▶) determined recently in our laboratory (J. Newman, personal communication), except that only the N-terminal 174 residues (of 267) were included in the calculation in order to simulate a unit cell with 70% solvent. The calculation was performed in space group P21212 with unit-cell dimensions a = 94, b = 80, c = 43 Å and one molecule in the asymmetric unit. Electron density for the solvent region was introduced by calculating a model electron-density map based on protein atoms alone, setting the mean electron density in the solvent region (greater than 2.5 Å from any protein atom) to 0.32 e Å−3 and the mean electron density in the protein region to 0.43 e Å−3, respectively, smoothing the interface between solvent and protein region to minimize the introduction of high-frequency terms and calculating an inverse Fourier transform to obtain model phases and amplitudes. Phases with simulated errors were generated by adding phase errors with a distribution given by P(Δϕ) = exp[Acos(Δϕ) + Ccos2(Δϕ)], with the values A = 0.8 and C = 0.4 for acentric reflections and A = 0.4 and C = 0.2 for centric reflections. This led to an average value of the cosine of the phase error (i.e. the true figure of merit of the phasing) of 〈cos(Δϕ)〉 = 0.42 for acentric and 0.39 for centric reflections. The model data with simulated errors was then solvent flattened by the reciprocal-space method as described here and by the real-space method as implemented in the program dm (Cowtan & Main, 1996 ▶), version 1.8, using solvent flattening and omit mode. Although dm will carry out solvent flattening alone in this way, it should be noted that this is a non-recommended mode (all recommended modes also contain histogram matching, which we did not include in order to keep the comparison restricted to the use of solvent flattening). Circles, starting phases; squares, real-space solvent flattening; diamonds, reciprocal-space solvent flattening.
Figure 3
Figure 3
Sections of electron density in protein region of maps calculated as in Fig. 2 ▶ for the case with 70% solvent content. The maps shown are for (a) the starting phases, correlation coefficient to model map 0.42, (b) the real-space solvent-flattened phases, correlation coefficient 0.73, (c) the reciprocal-space solvent-flattened phases, correlation coefficient 0.93, and (d) model phases.
Figure 4
Figure 4
Correlation of solvent-flattened phases (diamonds, real space; squares, reciprocal space) with true phases (〈cos(Δϕ〉) for model data as in Fig. 2 as a function of the fraction of volume in the unit cell occupied by the solvent (see text).
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