A Structural-informatics approach for tracing beta-sheets: building pseudo-C(alpha) traces for beta-strands in intermediate-resolution density maps.

Abstract

We report the development of two computational methods to assist density map interpretation at intermediate resolutions: sheettracer for building pseudo-C(alpha) models of beta-sheets, and a deconvolution method for enhancing features attributed to major secondary structural elements. Sheettracer is tightly coupled with sheetminer, which was developed to locate sheet densities in intermediate-resolution density maps. The results from sheetminer are used as inputs to sheettracer, which employs a multi-step ad hoc morphological analysis of sheet densities to trace individual strands of beta-sheets. The methods were tested on simulated density maps from 12 protein crystal structures that represent a reasonably complete sampling of sheet morphology. The sheet-tracing results were quantitatively assessed in terms of sensitivity, specificity and rms deviations. Furthermore, sheettracer and the deconvolution method were rigorously tested on experimental maps of the lambda2 protein of reovirus at resolutions of 7.6A and 11.8A. Our results clearly demonstrate the capability of sheettracer in building pseudo-C(alpha) models of beta-sheets in intermediate-resolution density maps and the power of the deconvolution method in enhancing the performance of sheettracer. These computational methods, along with other related ones, should facilitate recognition and analysis of folding motifs from experimental data at intermediate resolutions.

Full text

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A Structural-informatics Approach for Tracing
b-Sheets: Building Pseudo-CaTraces for b-Strands in
Intermediate-resolution Density Maps
Yifei Kong1, Xing Zhang2, Timothy S. Baker2and Jianpeng Ma1,3,4*
1Graduate Program of
Structural and Computational
Biology and Molecular
Biophysics, Baylor College of
Medicine, One Baylor Plaza
Houston, TX 77030, USA
2Department of Biological
Sciences, Purdue University
West Lafayette, IN 47907, USA
3Department of Bioengineering
Rice University, Houston, TX
77005, USA
4Verna and Marrs McLean
Department of Biochemistry
and Molecular Biology, Baylor
College of Medicine, One
Baylor Plaza, Houston, TX
77030, USA
We report the development of two computational methods to assist
density map interpretation at intermediate resolutions: sheettracer for
building pseudo-Camodels of b-sheets, and a deconvolution method for
enhancing features attributed to major secondary structural elements.
Sheettracer is tightly coupled with sheetminer, which was developed to
locate sheet densities in intermediate-resolution density maps. The results
from sheetminer are used as inputs to sheettracer, which employs a multi-
step ad hoc morphological analysis of sheet densities to trace individual
strands of b-sheets. The methods were tested on simulated density maps
from 12 protein crystal structures that represent a reasonably complete
sampling of sheet morphology. The sheet-tracing results were quanti-
tatively assessed in terms of sensitivity, specificity and rms deviations.
Furthermore, sheettracer and the deconvolution method were rigorously
tested on experimental maps of the l2 protein of reovirus at resolutions
of 7.6 A˚and 11.8 A˚. Our results clearly demonstrate the capability of
sheettracer in building pseudo-Camodels of b-sheets in intermediate-
resolution density maps and the power of the deconvolution method in
enhancing the performance of sheettracer. These computational methods,
along with other related ones, should facilitate recognition and analysis
of folding motifs from experimental data at intermediate resolutions.
q 2004 Published by Elsevier Ltd.
Keywords: macromolecular complexes; intermediate-resolution density
maps; bioinformatics; secondary structural elements
*Corresponding author
Introduction
In this post-genomics era,1structural biologists
are faced with the challenges of analyzing increas-
ingly complex biological systems, many of which
only yield density maps at low to intermediate-
resolution.2This is particularly true for single-
particle electron cryomicroscopy (cryo-EM) of
supermolecular complexes.3–11In X-ray crystallo-
graphic structure determinations, crystals of large
complexes often fail to diffract beyond 4 A˚. More-
over, even for some well-diffracting crystals, the
structures have to be solved in a stepwise process
atprogressively enhanced
atomic resolution is achieved. This was certainly
resolutions before
true for the 50 S ribosomal subunit, which was
solved first at 9 A˚, and then at 5 A˚, and finally at
2.4 A˚.12–14In all such studies involving inter-
mediate-resolution density maps, it is nearly
impossible to build reasonably accurate atomic
models with conventional methods. However, it
would be enormously helpful if the locations of
major secondary structural elements could be
reliably defined, and this in turn would enable the
construction of accurate pseudo-atomic models.
Such models can facilitate structure determination
to higher resolutions and also assist further bio-
chemical studies and functional interpretation. In
fact, significant insights into the architecture and
organization of structures are often obtained once
major secondary structural elements are located.
a-Helices and b-sheets constitute the major
secondary structural elements in proteins. It has
recently been shown that a-helices, which have
an approximately cylindrical shape, can be located
in intermediate-resolution density maps via a
0022-2836/$ - see front matter q 2004 Published by Elsevier Ltd.
E-mail address of the corresponding author:
jpma@bcm.tmc.edu
Abbreviations used: cryo-EM, electron
cryomicroscopy; D, dimensional; PDB, Protein Data
Bank; rms, root-mean-square.
doi:10.1016/j.jmb.2004.03.038J. Mol. Biol. (2004) 339, 117–130

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five-dimensional cross-correlation search.15How-
ever, b-sheets are much more difficult to identify
in intermediate-resolution density maps because
they usually do not adopt a single, characteristic
shape. Moreover, variations in the number of
strands and the length of each strand result in
b-sheets of various sizes and shapes.
Despite such challenges, we have identified a set
of unique morphological features that can be used
to assist the location of b-sheets at intermediate
resolutions. This process is carried out in two
steps using the programs sheetminer and sheet-
tracer. We have recently shown that sheetminer is
able to locate reliably the regions belonging to
b-sheetsinintermediate-resolution
maps.16Here, we describe the development of
another tool, sheettracer, that traces pseudo-Ca
atoms in the b-sheet density maps output by
sheetminer.16A flowchart that depicts the overall
procedure of sheettracer is presented in Figure 1.
The integration of sheetminer16and sheettracer
with other methods such as helixhunter15will
enable the building of pseudo-Catraces in inter-
mediate-resolution density maps obtained from
any experimental measurements. This in turn will
enhance the interpretation of structural data at
intermediate resolutions. These methods offer a
distinctadvantage in
enhance model building experiments by narrowing
the volume of a density map that must be searched
density
thatthey significantly
and eliminating the need for global, brute-force
fitting procedures.
Results
Step-wise discerning of b-strands
The sheetminer16program outputs clusters of
voxels, with each cluster delineating a thin, but
continuousvolume of
representasingle
b-sheet.
employs a multi-step process to build pseudo-Ca
traces in each identified sheet. These steps are first
illustrated using as an example one b-sheet of the
apical domain of the molecular chaperonin GroEL,
also known as the minichaperone17(PDB code
1fy9).
In the first step, a local peak filter was applied to
each cluster of voxels (Figure 2(a)) output by sheet-
miner to identify voxels that are most likely
involved in forming the backbones of individual
strands (Figure 2(b)). The local peak-filtering
algorithm emphasizes high local density values
and thereby adjusts to variations in the magnitude
of densities throughout the map, which permits,
for example, effective selection of backbone voxels
even in regions of relatively weak density. The
next step involved condensing the selected voxels
using local first principal component axis projec-
tion, which acts to enforce the voxel distribution
along the longest axis and one meant to coincide
with a strand backbone (Figure 2(c)). This process
results in a significantly narrowed distribution of
voxels and makes subsequent local linearity filter-
ing more efficient. Surviving voxels were then sub-
jected to a local linearity filter that picks backbone
voxels exhibiting properties of good local linearity
(Figure 2(d)). This filtering method acts to remove
inter-strand voxels and results in a significantly
narroweddistribution
k-Segments clustering18was employed in the next
step to group voxels into smaller subsets, each of
which is expected to represent one part of a
b-strand (Figure 2(e)), and subsequently all subsets
belonging to the same strand were merged. At this
point, each cluster of voxels represents an inde-
pendent b-strand and a pseudo-Catrace was then
built for each strand.
density presumed
sheettracer
to
then
ofbackbonevoxels.
Discerning b-strands and building pseudo-Ca
traces in p21H-ras
The p21H-rasmolecule, which contains a single,
six-stranded b-sheet, was used to test sheettracer.
Analysis was performed on a relatively thin, but
continuous, sheet density map produced by sheet-
miner from a map of the protein simulated at 6 A˚
resolution (Figure 3(a)). A simulated density map
was obtained from the crystal structure using the
EMAN program19. Several steps of pre-processing,
as described in Methods, led to a set of points that
represent the topological features of the sheet
Figure 1. Flowchart for the computational procedure
of sheettracer in intermediate-resolution density maps.
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Tracing the b-Sheets

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(Figure 3(b)). The k-segments algorithm18was then
used to separate these points into groups. Cluster
cleaning and merging were then applied to each
group of points to ensure that each group
represents an independent strand (Figure 3(c),
groups are separately colored). Such groupings of
points permitted us to then make pseudo-Catraces
for all six strands (Figure 4(b)).
Discerning b-strands and building pseudo-Ca
traces in 12 proteins
As a further test of the ability of sheettracer to
discern individual b-strands in sheet densities of
different morphology, we examined simulated
density maps of 12 structurally unrelated proteins
whose high-resolution crystal structures are avail-
able from the Protein Data Bank (PDB). This set of
protein structures was chosen because the number,
size, and shape of b-sheets vary widely among
them and therefore they should provide a reason-
ably complete sampling of known b-sheet mor-
phologies. Four of the structures contain a single
b-sheet with varying size and number of strands:
carboxypeptidase A20(PDB code 5cpa), p21H-ras21
(PDB code 121p), flavodoxin22(PDB code 1ag9),
and VP1 protein of human rhinovirus 1423(PDB
code 4rhv). Four contain multiple independent
b-sheets: the GroEL minichaperone17(two sheets,
PDB code 1fy9), human class I major histocompati-
bility antigen24(three sheets, PDB code 1duz),
horse liver alcohol dehydrogenase25(five sheets,
PDB code 6adh), and MoFe protein of nitrogenase26
(six sheets, PDB code 1h1l). The last four contain
rich b-motifs such as the b-barrel and b-propeller:
bacteriophage P22 tailspike protein27(PDB code
1tsp), aldose reductase28(PDB code 1ads), retinol-
bindingprotein29
(PDB
phosducin30(PDB code 1b9x).
The sheet-tracing results on the 12 proteins are
shown in Figure 4 with the built pseudo-Catraces
superimposed on the crystal structures. The results
were statistically analysed in terms of three
separatemeasures: sensitivity, specificity, and
root-mean-square (rms) deviations. As had simi-
larly been used in quantitative analysis of sheet-
mining results,16sensitivity refers to the probability
of correctly identifying
whereas specificity defines the probability of cor-
rectly identifying non-sheet Ca-atoms. The rms
deviation is calculated by computing the average
distance of each built pseudo-Ca-atom from its
closest sheet Ca-atom in the superimposed crystal
structure. The average sensitivity and specificity
forall12 proteins are
respectively (Table 1). Moreover, regardless of
which b-sheet morphology is tested, the rms
deviations always remain smaller than 2.0 A˚, with
an average of 1.54 A˚(see footnote to Table 1 for
more details concerning the calculation of rms
deviation). Given the limited resolution upon
which our analysis was based, such statistical
results of trace building seem quite promising.
Note that sheettracer is unable to specify strand
directions, consequently these have been assigned
according to the known X-ray structures (Figure 4).
code 1aqb),and
true sheetCa-atoms,
79.5%and96.3%,
Figure 2. Step-wise processing of sheet density maps to discern individual b-strands, using the sheet in the GroEL
minichaperone as an example. (a) Sheet density identified by sheetminer shown in voxels. (b) Selected voxels by
local peak filter. (c) Surviving voxels after local first principal component axis projection using the voxels in (b) as
input. (d) Surviving voxels after local linearity filtering using the voxels in (c) as input. (e) Clustered backbone voxels
after k-segments processing. The lines are the fitted segments (the first principal component axes).
Figure 3. Sheet-tracing results based on a 6 A˚simulated density map of p21H-ras. (a) Isolated thin, but continuous,
sheet density map output from sheetminer. (b) Backbone voxels for delineating the strands. (c) Clusters of voxels
after k-segments processing. Each cluster represents one strand (in a different color).
Tracing the b-Sheets
119

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Figure 4. Sheet-tracing results for all 12 proteins based on 6 A˚simulated density maps. The pseudo-Catraces
depicted in darker color are superimposed on the X-ray structures of the proteins shown in lighter color using
MOLSCRIPT software.51The proteins are: (a) carboxypeptidase A; (b) p21H-ras; (c) flavodoxin; (d) VP1 protein of
human rhinovirus 14; (e) the GroEL minichaperone; (f) human class I major histocompatibility antigen; (g) horse liver
alcohol dehydrogenase; (h) MoFe protein of nitrogenase; (i) bacteriophage P22 tailspike protein; (j) aldose reductase;
(k) retinol-binding protein; and (l) phosducin. The arrows in the pseudo-Catraces are artificially assigned based on
the crystal structures.
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Tracing the b-Sheets

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A new method for deconvolution of
density maps
As demonstrated in the previous sections, we
can usually build the pseudo-Ca
reasonable confidence, but mistakes do occur,
especially when maps at lower resolutions are
analysed. Therefore, to help enhance our ability to
buildthe pseudo-Ca
traces
resolution density maps, we developed a new com-
putational method for deconvoluting the density
maps. The net result of deconvolution is to
enhance the features of secondary
elements in density maps. A simple example of
this is illustrated in Figure 5(a). The left panel
shows a synthetic two-dimensional (2D) geometri-
cal object and the middle panel shows the same
object contaminated with a level of noise that
nearly renders features in the original object
indistinguishable. The right panel shows the
results of a dramatic recovery of object features
after deconvolution is performed.
traces with
in intermediate-
structural
We then tested the method on a simulated 3D
density map (Figure 5(b)). A single b-sheet struc-
ture was blurred to 8 A˚(Figure 5(b), left), at which
point a straightforward building of pseudo-Ca
tracesbecamedifficult.
strands are more clearly resolved in the density
map (Figure 5(b), right). The subsequent building
of pseudo-Catraces on the deconvoluted map was
a trivial process.
Experimental density maps of the l2 protein of
reovirus were then used to further test the decon-
volution method. To perform the test in a more sys-
tematic and self-consistent way, the cryo-EM
structures of reovirus have been reconstructed to
7.6 A˚resolution from 7939 single-particle images
(100%-particle structure) and to 11.8 A˚resolution
from a subset (12.5%) of the same particle images
(12.5%-particle structure). Two helices in the l2
protein that are distinct in the 100%-particle struc-
ture (Figure 6(a)) are bridged by density that
appears to interconnect the helices in the 12.5%-
particle structure (presumably owing to the higher
After deconvolution,
Table 1. Quantitative analysis of the sheet-tracing results at 6 A˚
PDB
code
No.
total
Ca
No. sheet Ca
found by
STRIDE
No. true sheet
Cafound by
sheettracer
No. true sheet
Camissed by
sheettracer
No. false sheet
Cafound by
sheettracer
Specificity
(%)
Sensitivity
(%)
rms
deviations
(A˚)
5cpa
121p
1ag9
4rhv
1fy9
1duz
6adh
1h1l
1tsp
1ads
1aqb
1b9x
308
167
176
209
214
276
749
998
391
316
176
341
53
47
33
85
54
119
174
140
189
39
82
180
32
42
26
82
33
88
152
113
149
33
58
165
21
5
7
3
21
31
22
27
40
6
24
15
2
2
5
2
1
99.2
98.3
96.5
98.4
99.4
91.1
90.3
98.4
98.5
100.0
94.7
90.7
60.4
89.4
78.8
96.4
61.1
73.9
87.4
80.7
78.8
84.6
70.7
91.7
1.48
1.51
1.35
1.54
1.35
1.62
1.75
1.65
1.57
1.40
1.49
1.81
14
56
14
3
0
5
15
Average 96.379.5 1.54
The number of Ca-atoms of b-sheets in the crystal structures (third column) was determined by the method STRIDE.50The sheet-
tracing results were based on 6 A˚simulated density maps. The crystal structures were first superimposed on the simulated density
maps. The number of true sheet Ca-atoms found by sheettracer (fourth column) was then defined as the number of sheet Ca-atoms
in the atomic coordinates that spatially fall inside the sheet regions defined by sheettracer. The number of true sheet Ca-atoms missed
by sheettracer (fifth column) was defined as the number of sheet Ca-atoms in the atomic coordinates that spatially fall outside the
sheet regions defined by sheettracer. The number of false sheet Ca-atoms (sixth column) was defined as the number of non-sheet Ca-
atoms in the atomic coordinates that spatially fall inside the sheet regions defined by sheettracer. The specificity value (seventh
column) was calculated by the formula: 1 2 ðsixth column=ðsecond column 2 third columnÞÞ and the sensitivity value (eighth column)
was calculated by the formula: fourth column/third column. The rms deviations of built pseudo-Catraces were derived from the
distance of each pseudo-Ca-atom to its nearest Ca-atom on b-strands in the superimposed crystal structures. This calculation was
only performed for found pseudo-Ca-atoms. Please note, for all the calculations, no sequence identity of Ca-atoms was concerned.
As a result, the rms deviation calculated here is not the same as the conventional rms deviation based on atomic structures. The nearly
perfect specificity values are the results of the multi-step denoising process implemented in sheettracer.
Figure 5. A new deconvolution
method. (a) A simple 2D example
of deconvolution. The left is the
original image, the middle is the
image rendered with noises and
the right is deconvoluted image.
(b) A 3D example for deconvolution (right) on a piece of b-sheet density blurred to 8 A˚(left). The Catraces of the
sheet (red) are superimposed on the density.
Tracing the b-Sheets
121