2 Fit Assessment
2.1 Comparing
Structure and Maps
Given a structural model of a protein (candidate model), a common
task is then to define how well its conformation “fits” in the map,
that is, how well does the structure describe the observed density of
the map.
2.2 Map Blurring
Direct comparison from a map, with density values in each voxel,
and no exact assignment of this density to atoms, to a structure,
with highly accurate position for each atom nucleus, is complicated.
It is possible to blur a structure, that is, to obtain a map with voxel
densities computed based on the proximity of atoms in the structure. However, many tools and scoring methods have been developed to describe how well two maps matches. These blurred maps
will be used in the following to evaluate the quality of proposed
structures, and to find regions of the maps that are missing or
ill-represented by the modeled structures.
In the TEMPy software, first, a grid is constructed around the
protein, with voxels of 1 A ˚ 3 . Then, the density value of voxels
containing heavy atom nuclei (i.e., the position of the atom) is
increased by the sum of the corresponding atomic number. The
blurring itself is done by convoluting that map with a gaussian
function. The gaussian sigma factor (controlling the width of the
gaussian function, and the level of blurring) is usually expressed as a
constant times the resolution, with different possible formulation
for the constant, with 0.225 and 0.187 the most common (also see
Note 1). These two choices make the width of the Fourier Transform of the gaussian distribution fall to 1/e and ½ at a wavenumber
of 1/resolution. Finally, if the blurred map is to be compared
against an existing map, it is resampled to ensure their grid matches.
2.3 Scoring
Functions
Finding an atomic structure with the best fit to a density map is an
issue central to cryo-EM. This can be assessed with a “scoring
function,” that provides a numerical value for any possible pair of
structure and map. The “best” structure, then, is dependent on the
definition of this scoring function. Global scoring functions are
useful to provide a general picture of the fit between candidate
structures and map but may miss smaller scale modeling errors.
Local scoring functions are needed to detect and potentially correct
those errors [7, 8].
In the following, we will describe scoring functions to estimate
the match between two maps, X and Y, and assume there is a oneto-one correspondence between their voxels. Although this condition is not guaranteed, it is usually possible to estimate the density
values for one map at voxel positions matching the other, thus
aligning them.
The map can also be transformed or filtered before the scoring
takes place, see Note 2.
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191
2.1 Comparing
Structure and Maps
Given a structural model of a protein (candidate model), a common
task is then to define how well its conformation “fits” in the map,
that is, how well does the structure describe the observed density of
the map.
2.2 Map Blurring
Direct comparison from a map, with density values in each voxel,
and no exact assignment of this density to atoms, to a structure,
with highly accurate position for each atom nucleus, is complicated.
It is possible to blur a structure, that is, to obtain a map with voxel
densities computed based on the proximity of atoms in the structure. However, many tools and scoring methods have been developed to describe how well two maps matches. These blurred maps
will be used in the following to evaluate the quality of proposed
structures, and to find regions of the maps that are missing or
ill-represented by the modeled structures.
In the TEMPy software, first, a grid is constructed around the
protein, with voxels of 1 A ˚ 3 . Then, the density value of voxels
containing heavy atom nuclei (i.e., the position of the atom) is
increased by the sum of the corresponding atomic number. The
blurring itself is done by convoluting that map with a gaussian
function. The gaussian sigma factor (controlling the width of the
gaussian function, and the level of blurring) is usually expressed as a
constant times the resolution, with different possible formulation
for the constant, with 0.225 and 0.187 the most common (also see
Note 1). These two choices make the width of the Fourier Transform of the gaussian distribution fall to 1/e and ½ at a wavenumber
of 1/resolution. Finally, if the blurred map is to be compared
against an existing map, it is resampled to ensure their grid matches.
2.3 Scoring
Functions
Finding an atomic structure with the best fit to a density map is an
issue central to cryo-EM. This can be assessed with a “scoring
function,” that provides a numerical value for any possible pair of
structure and map. The “best” structure, then, is dependent on the
definition of this scoring function. Global scoring functions are
useful to provide a general picture of the fit between candidate
structures and map but may miss smaller scale modeling errors.
Local scoring functions are needed to detect and potentially correct
those errors [7, 8].
In the following, we will describe scoring functions to estimate
the match between two maps, X and Y, and assume there is a oneto-one correspondence between their voxels. Although this condition is not guaranteed, it is usually possible to estimate the density
values for one map at voxel positions matching the other, thus
aligning them.
The map can also be transformed or filtered before the scoring
takes place, see Note 2.
CryoEM Density Fitting and Validation
191