Section 19.6.4.7. Visualization, modelling and interpretation of results

Once a reliable 3D map is obtained, computer graphics and other visualization tools may be used as aids in interpreting morphological details and understanding biological function in the context of biochemical and molecular studies and complementary X-ray crystallographic and other biophysical measurements.

Initially, for low-resolution studies (>10 Å) and where the structure is unknown, the gross shape (molecular envelope) of the macromolecule is best visualized with volume-rendering programs (e.g. Conway et al., 1996; Sheehan et al., 1996; Spencer et al., 1997). Such programs establish a density threshold, above which all density is represented as a solid and below which all density is invisible (representing possible solvent regions). Choice of the threshold that accurately represents the solvent-excluded density can prove problematic, especially if the microscope CTF is uncorrected (e.g. Conway et al., 1996). For qualitative examination of maps, a threshold at 1.5 or 2 standard deviations above the background noise level provides a practical choice. Another, semi-quantitative, approach is to adjust the threshold to produce a volume consistent with the expected total molecular mass. This procedure is prone to error because the volume is sensitive to small changes in contour level, which, in turn, is highly sensitive to scaling and CTF correction. Caution should therefore be exercised in drawing conclusions based on volume fluctuations of less than 20% of that expected. As a general guide, solid-surface rendering in the range 80 to 120% of the expected volume gives reasonable shape and connectivity.

A complete description of available graphical tools for visualizing 3D density maps is beyond the scope of this discussion, but it is worth noting several of the principles by which 3D data can be rendered. Stereo images (e.g. Liu et al., 1994; Agrawal et al., 1996; Taveau, 1996; Winkler et al., 1996; Nogales et al., 1997; Kolodziej et al., 1998; Gabashvili et al., 2000) provide a powerful way to convey the 3D structure. Also, as in X-ray crystallographic applications, stereo viewing is essential for exploring details of secondary and tertiary structural information in high-resolution 3D maps (e.g. Henderson et al., 1990; Böttcher, Wynne & Crowther, 1997). Additional visualization tools include: use of false colour to highlight distinct components (e.g. Yeager et al., 1994; Cheng et al., 1995; Hirose et al., 1997; Metoz et al., 1997; Zhou et al., 1999) and a variety of computer `sectioning' or image-projection algorithms that produce cut-open views (e.g. Vigers et al., 1986; Cheng et al., 1994; Fuller et al., 1995), spherical sections (e.g. Baker et al., 1991), icosahedrally cut surfaces (Böttcher, Kiselev et al., 1997), polar sections (Fuller et al., 1995), cylindrical sections (e.g. Hirose et al., 1997), radial projections (e.g. Dryden et al., 1993), and radial depth cueing (Spencer et al., 1997), which conveys an immediate, and often quantitative, view of the radial placement of details in a map (Grimes et al., 1997). Animation also provides an alternative approach to enhance the viewer's perception of the 3D structure (e.g. van Heel et al., 1996; Frank et al., 1999). All these rendering methods should always be carefully described so the reader may distinguish representation from result.

Difference imaging and density-map modelling are examples of two additional techniques that can sometimes enhance interpretation of 3D cryo EM data.

Difference imaging is a very powerful tool, long employed by structural biologists outside the cryo EM field, that permits small (or large) differences among closely related structures to be examined. One of the great advantages of cryomicroscopy of ice-embedded specimens over microscopy using negative stains is that cryo EM difference imaging yields more reliable results as confirmed by correlation with biochemical and immunological data (e.g. Baker et al., 1990; Stewart et al., 1993; Vénien-Bryan & Fuller 1994; Yeager et al., 1994; Hoenger & Milligan, 1997; Lawton et al., 1997; Stewart et al., 1997; Böttcher et al., 1998; Conway et al., 1998; Sharma et al., 1998; Zhou, Mcnab et al., 1998). However, reliable interpretation is only possible if the difference maps are carefully calculated (i.e. from two maps calculated to the same resolution and scaled in such a way that the differences are minimized). Subtraction of two maps, each having an intrinsic noise level, guarantees that the difference map will always be noisier than either of the parent maps, and noise in the difference map is what determines the significance of features in it. Careful statistical analysis is an important prerequisite in attributing significance to and interpreting particular features. One critical test is to see whether a difference of a similar size can be found between independent determinations of the same structure. Differences that occur at symmetry axes must be treated cautiously, because the noise level there is greater.

The combination of X-ray and cryo EM data provides a powerful tool for interpreting structures [e.g. see the review by Baker & Johnson (1996)]. A high-resolution X-ray model can be docked into a cryo EM density map with greater precision than the nominal resolution of the map. Several similar protocols have been developed for fitting X-ray data to cryo EM reconstructions (e.g. Wikoff et al., 1994; Che et al., 1998; Volkmann & Hanein, 1999; Wriggers et al., 1999). First, because magnification in an electron microscope can vary, the absolute magnification of the reconstruction to within a few per cent must be established. In addition, the relative scale factor for the density must be calculated. Determination of absolute magnification and relative scaling may be accomplished by several means: (1) comparing the EM map with clear features in the X-ray structure of an individual component (Stewart et al., 1993), (2) using radial density profile information derived from scattering experiments (e.g. Cheng et al., 1995), or (3) using the X-ray structure of an entire assembly when this is available (e.g. Speir et al., 1995). When a single component is used for scaling, it is necessary to refine the scale as the proper position and orientation of that component become better determined. Next, the resolution of the density distribution of the reconstruction must be matched to that in the X-ray structure. For example, fitting of the high-resolution model of the adenovirus hexon to the EM density map of the virus itself was accomplished by convoluting the X-ray structure with the point-spread function for the EM reconstruction (Stewart et al., 1993). An alternative procedure is simply to normalize the EM map so that it has the same range of density values as the corresponding X-ray map (e.g. Luo et al., 1993; Wikoff et al., 1994; Ilag et al., 1995). A maximum-entropy approach (Skoglund et al., 1996) was also used to treat CTF effects to improve the correspondence between the adenovirus hexon X-ray structure and the corresponding density in the EM map (Stewart et al., 1993).

The next step in the modelling procedure is to fit the X-ray structure interactively to the cryo EM density using a display program such as O (Jones et al., 1991), at which point a subjective estimate of the quality of the fit can be made. One criterion for the quality of the fit is whether the hand of the structure can be identified. Because 3D density maps are generated from projected views of the structure, an arbitrary hand will emerge during refinement unless explicit steps are taken to determine the absolute hand. Thus, in the absence of relatively high resolution data (which, for example, would reveal the hand of features like α-helices), the absolute hand must be determined from other types of data such as shadowing (e.g. Belnap et al., 1996) or comparison of the orientations of the same particle imaged at different tilt angles (e.g. Finch, 1972; Belnap et al., 1997). The match with X-ray data (of known hand) serves as an unambiguous determination of hand for the EM map. At this stage of fitting it is important to determine whether the X-ray model should be fitted as a single rigid body (e.g. Stewart et al., 1993) or as two or more partly independent domains (e.g. Grimes et al., 1997; Che et al., 1998; Volkmann & Hanein, 1999).

The quality and uniqueness of the X-ray/EM map fit is then assessed, often simply by calculating an R factor between the two maps. It may be necessary first to mask out density that is not part of the structure being fitted by the X-ray data (e.g. Stewart et al., 1993; Liu et al., 1994; Cheng et al., 1995). The uniqueness of the fit is then tested by rotating and shifting the X-ray model in the EM map and noting changes in the R factor (e.g. Che et al., 1998). An objective fitting procedure, either in reciprocal or real space, is necessary for refining and checking the uniqueness of the result of the interactive fitting. The program X-PLOR (Brünger et al., 1987) can be used for reciprocal-space refinement after the two maps are modified to avoid ripple and edge effects due to masking and differences in contrast (e.g. Wikoff et al., 1994; Grimes et al., 1997; Hewat et al., 1997). Real-space refinement has been performed using other programs (e.g. Volkmann & Hanein, 1999; Wriggers et al., 1999). A few examples include fitting the Sindbis capsid protein to the Ross River virion map (Cheng et al., 1995), fitting the VP7 viral protein into the bluetongue virus core map (Grimes et al., 1997), fitting the Ncd motor domain to microtubules (Wriggers et al., 1999), and fitting of two separate macromolecules, the myosin S1 subfragment and the N-terminal domain of human T-fimbrin, to reconstructions of complexes between these molecules and actin filaments (Volkmann & Hanein, 1999). Comparison between results of real- and reciprocal-space fitting can prove informative. For example, reciprocal-space fitting is usually not constrained to avoid interpenetration of the densities, an issue more easily addressed in real-space fitting. If the two approaches yield different fits, it may be necessary to consider conformation changes between the X-ray and the EM structure. This type of analysis is best performed with quantitative model-fitting routines such as those currently being developed (e.g. Volkmann & Hanein, 1999; Wriggers et al., 1999).