Computational Prediction of Atomic Structures of Helical Membrane
Proteins Aided by EM Maps
Julio A. Kovacs,* Mark Yeager,*yz§and Ruben Abagyan*
*Department of Molecular Biology,yDepartment of Cell Biology, The Scripps Research Institute, La Jolla, California;
zDivision of Cardiovascular Diseases, Scripps Clinic, La Jolla, California; and§Department of Molecular Physiology
and Biological Physics, University of Virginia, Charlottesville, Virginia
ing of transmembrane a-helices. However, when an intermediate-resolution electron microscopy (EM) map is available, it can be
used to provide restraints which, in combination with a suitable computational protocol, make structure prediction feasible. In this
work we present such a protocol, which proceeds in three stages: 1), generation of an ensemble of a-helices by flexible fitting into
each of the density rods in the low-resolution EM map, spanning a range of rotational angles around the main helical axes
and translational shifts along the density rods; 2), fast optimization of side chains and scoring of the resulting conformations; and
3), refinement of the lowest-scoring conformations with internal coordinate mechanics, by optimizing the van der Waals,
through a so-called tethering map, derived from the EM map, which restrains the positions of the a-helices. The protocol was
validated on three test cases: GpA, KcsA, and MscL.
Integral membrane proteins pose a major challenge for protein-structure prediction because only ?100 high-
Ab initio prediction of membrane protein structure, in the
absence of additional experimental data, remains a difficult
problem, in part due to the small number (?100) of high-re-
solution structures that are known, compared to the .30,000
protein structures that have been solved by x-ray crystallog-
raphy. Nevertheless, membrane protein structural biology is
important because it is estimated that approximately one-
third of genes code for membrane proteins (1) and because
.50% ofthe pharmaceuticals inuse are targetedtomembrane
proteins (2). This is so mainly because of technical problems
in the expression and crystallization of this class of proteins
(3–5). (See Michel’s membrane protein website: http://www.
White’s membrane protein website: http://blanco.biomol.uci.
Advances in electron microscopy (EM) have produced
an increasing number of intermediate-resolution (9–6 A˚)
structures of membrane proteins, which can be utilized as
restraints to make the prediction calculations more tractable.
In this work we restrict ourselves to the major class of
membrane proteins formed by bundles of transmembrane
(TM) a-helices and describe a protocol for predicting their
structure that uses a given EM map as an aid to restrain the
position of the helices.
A number of approaches have been developed in the last
several years regarding the structure prediction of membrane
proteins. (Extensive lists of references are given in other
reviews (6,7).) One of the most widespread approaches is
homology modeling, which constructs models that are homol-
ogous to other protein(s) (templates) whose three-dimensional
structure is known. An important example of the application
of this approach is the modeling of ion channels (8) based on
the structure of KcsA (9).
In general, methods differ in the kind of energy function
they use and/or their sampling strategy to search for low-
energy conformations. The core of all of these procedures is
the docking of flexible helices. Abagyan et al. (10) first dem-
onstrated that the correct association of two a-helices could
be predicted from scratch by global energy optimization. The
sampling protocol was capable of identifying the correct ar-
rangement of the two helices, and the energy function, which
included van der Waals, torsional, hydrogen bonding, elec-
trostatic and solvation terms, distinguished parallel, anti-
parallel, and crossed helical conformations. Kim et al. (11)
used only the van der Waals energy term, and, starting from a
set of random orientations of a pair of helices, optimized the
parameters by a Monte Carlo search. In this way, they were
able to model simple homo-oligomers (a straight helix re-
peated two, four, or five times). Gottschalk (12) used only
four degrees of freedom for each helix to generate a sparse
set of conformations, which were then evaluated using van
der Waals and electrostatic energy terms. Park et al. (13) de-
scribed a scoring function, which they used to perform an
exhaustive search of the six degrees of freedom between two
helices. A similar approach was used by Fleishman and Ben-
Tal (14), while Dobbs et al. (15) used an empirical energy
function derived from statistical analyses of known mem-
brane protein structures (16). The replica-exchange Monte
Carlo method has been used successfully (17) to reproduce
Submitted November 28, 2006, and accepted for publication April 27, 2007.
Address reprint requests to Julio Kovacs, Tel.: 858-784-8904, E-mail:
Editor: Peter Tieleman.
? 2007 by the Biophysical Society
1950Biophysical JournalVolume 93September 20071950–1959
the NMR structure of Glycophorin A (GpA). For this, the
authors performed a long replica-exchange Monte Carlo sim-
ulation starting from a single conformation of the pair of he-
lices. Molecular dynamics (MD) simulations have also been
used in the modeling of transmembrane helices (18). Goddard
and co-workers (19) have specifically tailored a method
called MembStruk to predict the structures of G-protein
coupled receptors. Physicochemical data are used to build an
initial coarse-grained model, which is subsequently refined
by stochastic sampling and MD simulations. The TASSER
method has also been adapted to membrane proteins (20).
This approach threads the given sequence on parts of solved
protein structures, and then refines the resulting template.
Lastly, the Rosetta algorithm for structure prediction has
been implemented for TM proteins (21). However, only
backbone coordinates are derived due to the computational
intractability of a full-atom prediction for membrane
proteins, which are usually larger than the small soluble
proteins amenable to Rosetta.
Despite the promising progress exemplified by the success
of the above methods, they are in general very time-consum-
ing, which makes them applicable only to simple or small
cases, such as the fitting of rigid a-helices, or they can only
be performed by a sparse search, which degrades their reli-
ability. This is alleviated when some additional constraints
are imposed (22). For instance, Sale et al. (23) combined mea-
sures derived from statistical analyses with experimental dis-
tance constraints to refine an ensemble of initial conformations
that matched a set of distance constraints. Beuming and
Weinstein (24) proposed a related approach, using distance
restraints obtained from EM maps to assemble bundles of
ideal a-helices, each of which was individually oriented ac-
servation with their propensities to be exposed to the lipid.
A similar methodology was independently suggested by
Fleishman et al. (25), which, unlike Beuming and Weinstein
(24), provides only Cacoordinates but does not involve any
The present work also belongs to this category. However,
unlike those approaches, we allowed the a-helices to be flex-
ible and performed a fast exhaustive search (made possible
by the use of a novel tree-decomposition algorithm) com-
bined with energy minimization. In this way, we were able
to obtain predictions that were close to the experimental
structures—between 0.9 and 1.9 A˚root mean-square devi-
ation (RMSD) for the backbone atoms, depending on the size
of the complex.
In our approach we assume that an intermediate-resolution
that the helical segments of the sequence have been deter-
mined beforehand. We use these input data to construct
another map, called a tethering map, which has low values
around thehelices’ backbone atoms,andgrowsquicklyaway
from them. This map is used as a penalty term (acting on the
backbone atoms only) during the energy minimization stage
to keep the helices close to their experimental positions as
given by the density map. The energy function includes van
der Waals, electrostatic, hydrogen bonding, and torsional
terms. The effect of desolvation is included by correcting the
energies through a solvent-accessibility map, which provides
an efficient way to consider this contribution.
A schematic flow chart of our method is presented in Fig. 1. Details of the
various steps are described below. They were performed within the internal
coordinate mechanics (ICM) software environment (10); the ICM scripts
used in this work are available upon request.
Three-dimensional map and TM a-helix sequences
The input data consisted of an intermediate-resolution density map and the
ments are assumed to have been identified beforehand by standard hydrop-
athy analysis (26,27) as well as experimental methods such as antibody
labeling (28–30). For our simulated test cases, the sequences of the TM
segments were based on the experimental structures. We also used the
identities of the three amino acids before andthe three amino acids after each
TM segment, to build initial straight helices as described in the next step.
Modeling the TM a-helices
Using the given sequences, a family of ideal, straight a-helices was con-
structed by assigning the values ?62? and ?41? to the f- and c-backbone
torsion angles, respectively. As mentioned above, this family of a-helices
included shifts along the sequence of up to three amino acids in each di-
rection (keeping the length of each helix fixed, so when a residue was added
at one end, another was deleted from the other end).
FIGURE 1 Schematic flow chart of our prediction methodology.
Prediction of Helical TM Proteins1951
Biophysical Journal 93(6) 1950–1959
Fitting the modeled a-helices into the density rods
of the EM map
Each of the helices built in the previous step (i.e., for each helical segment of
the subunit and for each shift) was rotated around its main axis in steps of
10? and then flexibly fitted (keeping that rotational degree of freedom fixed)
into the corresponding density rod of the (simulated) map, by minimizing
an energy function that included van der Waals interactions, electrostatic,
hydrogen bonding, torsional, and density correlation terms. By means of this
procedure (built into ICM (10)) the backbone torsions were optimized to
adjust the shape of each shifted and rotated helix to the particular density
rod. Two of these fitted helices (for a particular rotation and shift), cor-
responding to one of the subunits in each of our test cases, are displayed in
panels a–c of Figs. 3–5.
Optimizing the amino-acid side chains for each
For each combination of rotations and shifts of the a-helices that made up a
subunit, an oligomer was built by repeating the subunit according to the
assumed symmetry. (This was the only step in the procedure where sym-
metry was imposed.) Then, a global side-chain prediction was performed by
means of the SCATD algorithm (side-chain assignment via tree decompo-
sition (31)). This algorithm generates the best packing of the side chains based
on a simplified van der Waals potential and gives a score for that packing.
SCATD takes ?3 s to predict the side chains for each backbone arrangement
of KcsA (264 residues) and large-conductance mechanosensitive ion channel
(MscL)(220residues)(substantiallyless forGpA).The outputof the protocol
was a table of scores for all the combinations of rotations and shifts of the
independent helices. Parallel processing made this step quite efficient. For
example,the score table couldbe generated in, at most, 15–20 min using200
processors of the Scripps Linux cluster (64-bit, 3.4 GHz Intel XEON-EMT).
(For our cases of two independent helices, there are (36 3 7)2¼ 63,504
Minimizing the energy of the best conformations
obtained in the previous step
This step required two maps. The first one was the so-called tethering map,
which was used as a restraint to keep the helices from deviating too much
from the experimental map. It was constructed as follows. First a helical
bundle was built by taking one of the fitted helices for each density rod,
modifying all residues to Gly, and extending each helix by the addition of
two glycines at each end. (The latter prevented the final tethering map from
being too short due to the lower density values near the ends of the helices.)
Then, a new map was obtained by convolving this helical bundle with a
Gaussian kernel with s ¼ 4 A˚(emulating 8 A˚resolution). This value of
s was not critical. Finally, we transformed this new map by applying the
fðxÞ ¼ ae
where a ¼ 0.25 smap, and m is a density value such that the isocontour
surfaceofthe newmapat levelmenclosedthe backbonesofthe fittedhelices
with a reasonable leeway for their adjustment during the minimization
process. The value of m should be independent of the particular structure,
and indeed we found an optimal value of m ¼ 11 for the three cases that we
tested. The particular functional form has the property that its derivative at
x ¼ m is, in absolute value, 1, so it can be considered the point at which the
function starts growing quickly. The particular factor 0.25 in the expression
for a was chosen empirically to get a sufficiently high rate of increase of the
function. The transformed map obtained in this way was our tethering map,
which has low values at the helices’ positions and grows quickly away from
them. Isocontour surfaces of this map at level a for each of our test cases are
shown in the b-panels of Figs. 3–5, with two of the previously fitted helices.
The second map needed for the minimization was the solvent-accessi-
bility grid map. This map gave at each position in space a value between
0 and 1, indicating how much a particular atom would be exposed to water.
Thus, electrostatic interactions of atoms with water were computed accord-
ing to the surface-accessibility approximation of the electrostatic solvation
energy (see Discussion). The experimental values of the solvation-energy sur-
face densities reflect the electrostatic energy differences between the dielec-
tric constant of 80 for water and the dielectric constant of ?10 for octanol. In
the construction of this map, the hydrophilic headgroups of the membrane
wereconsideredas water.Thec-panels inFigs. 3–5showisocontoursurfaces
of the accessibility maps for our three test cases at level 0.8. The blank re-
gion in the middle corresponded to the hydrophobic core of the membrane,
for which we tested thicknesses of 22, 26, and 30 A˚. The regions above and
below were the phospholipid headgroups (7 A˚each) and the water itself
(cytoplasm and extracellular regions). This map was built by taking, as for
the tethering map, one of the fitted helices for each density rod and mod-
ifying all residues to Gly. (No extensions were made here. In the KcsA case,
we also added the pore helix, modified to all-Gly.) This helical bundle was
then used to calculate the accessibility map, which ICM performed by using
a fast modification of the algorithm of Shrake and Rupley (32). Finally, the
slab corresponding to the hydrophobic core of the membrane was set to 0
(except the central part that included the cavity and channel).
The energy minimization then proceeded as follows. We considered the
lowest-scoring 20% of the side-chain-optimized conformations obtained in
the previous step. (This cutoff was used because the minimization was sig-
nificantly slower than the side-chain assignment.) Each of these conforma-
tions was first side-chain minimized (i.e., with no backbone motions) to
eliminate possible severe clashes between side chains, which could make the
structure fail to converge during the minimization process. Next, the struc-
tures thus obtained were subjected to a restrained relaxation, by using a
sequence of decreasing harmonic restraints. After this, the final energy mini-
mization was performed. The energy function consisted of van der Waals,
electrostatic, hydrogen bonding, and torsional energy terms, plus a term that
penalized large deviations of the structure from the given EM density map.
This penalty term was calculated by evaluating the tethering map, described
above, at the positions of the backbone atoms of the structure; that is, by
computing the sum of the map values at the positions of the backbone atoms.
The positions of the side-chain atoms were not included, so their locations
would not be perturbed.The minimized energywas thencorrectedby adding
the desolvation energy, which was calculated by applying the solvent-
accessibility map to the minimized conformation (in the same way as just
described for the tethering map, except that in this case all atoms were used).
We have experimented with two options for the minimization: free or
fixed backbone torsion angles. The former was much more computationally
demanding as there were many more variables to optimize. We used this
option for the GpA case. But for larger systems (including KcsA and MscL)
the flexible-backbone minimization is not feasible, due, in some instances,
to an overly slow convergence of the Newton method, or, in other cases, to
oscillations. Hence, for the larger systems we used rigid-backbone mini-
mization. We were strict about convergence, demanding that the norm of
the energy gradient be ,1—a stringent criterion given the large number
of variables—and that the energy change between consecutive steps be
,4 3 10?63 Nreskcal/mol, where Nresis the total number of residues in the
The energy minimization of each conformation took, for the cases pre-
sented here, between 30 and 45 s on a single processor of the type described
above. Again,this step of our protocol was run in parallel to achieveefficient
The output atomic model
The minimization step produced a table of energies for all the combinations
of rotations and shifts of the independent helices. The conformation having
the lowest minimized energy was taken as the output of our prediction pro-
tocol and was visualized using the ICM software package.
1952Kovacs et al.
Biophysical Journal 93(6) 1950–1959
We have validated our methodology, outlined in Fig. 1, on
three test cases: GpA, KcsA, and MscL, obtaining very good
agreement between the predicted atomic models and the
experimental structures (Table 1). For each of the test cases,
we generated a simulated intermediate-resolution map hav-
ing 6 A˚in-plane and 20 A˚vertical resolution, by convolving
(i.e., blurring) the backbone atoms of the experimental
structure with an anisotropic Gaussian kernel (Figs. 3–5 a).
This emulates the typical resolution of three-dimensional
cryo-EM maps derived by merging image data from tilted
two-dimensional crystals (33–35). Resolution is significantly
degraded due to imaging factors such as specimen drift and
charging, crystal imperfections, and the missing-cone artifact
due to the limited tilt angle.
Glycophorin A is a sialoglycoprotein of human erythrocyte
membranes, and forms dimers by noncovalent association
of its membrane-spanning domain. NMR analysis of GpA
dimers in dodecylphosphocholine micelles showed that the
TM domains associate as a right-handed, parallel, a-helical
structure (36). We used this NMR structure (PDB code
1AFO, model 1) for our first test case. However, we should
emphasize that we did not impose any symmetry on the
dimer, not even when constructing each backbone arrange-
ment. In particular, we considered both vertical shifts and
both rotations as independent of one another. In fact, the
NMR structure itself is not symmetric, the deviation from
symmetricity being 1.7 A˚all-atom RMSD (0.9 A˚backbone-
As described in Materials and Methods, the 20% lowest
scoring conformations were energy-minimized, and these
12,700 points are shown in Fig. 2 a. The minimization was
done, for this particular test case, with free backbone torsion
angles, since the small size of this structure allowed full con-
vergence over the whole set of variables. There was excellent
agreement between the NMR structure and the best-energy
prediction, with a backbone RMSD of 0.89 A˚(Fig. 3, d and
e). The second-best prediction (0.77 A˚RMSD) differed in
only 0.01 kcal/mol from the first one. Then there was a jump
to the third best solution (0.76 A˚RMSD) of almost 10 kcal/
mol. Also, the first five solutions belonged to the first energy
basin (meaning, the region around a local minimum) shown
in Fig. 2 a, with RMSDs &1 A˚. The bottom of the secondary
energy basin (solution number 6) is located at ?2.5 A˚
RMSD, with an energy 16 kcal/mol higher than that of the
The KcsA channel is a bacterial homolog of eukaryotic po-
tassium channels, which regulates, with high selectivity, the
transmembrane flux of K1ions. KcsA is a homotetramer,
and an x-ray structure at 1.9 A˚resolution (9) (PDB code
1R3J) showed that each subunit contains two integral TM
TABLE 1 Summary of RMSD values for our test cases
(TM1 / TM2)
(1.17 / 2.21) (1.37 / 3.38) (1.78 / 4.34)
The second row of MscL gives values for each of the two subsets of helices
independently. The higher values for TM2 reflect its screw motion relative
to the x-ray structure.
tions that were energy-minimized during the predictions of (a) GpA, (b)
more detail of the low-energy conformations. In each case, the origin of the
energy scale has been set at 25 kcal/mol lower than the minimum energy.
The numbers indicate the rankings of the indicated solutions (see text). On
the lower right of each plot, the (minimized) energy of each experimental
structure is shown. Due to unresolvable clashes, there are many low-RMSD
conformations that span a wide range of energy values, especially in cases
b and c.
Plots displaying the 20% (12,700) lowest-scoring conforma-
Prediction of Helical TM Proteins1953
Biophysical Journal 93(6) 1950–1959
ionic selectivity. In our predictions, we have not considered
the P-loop, except for the construction of the solvent-acces-
sibility map (see Materials and Methods).
The x-ray structure and our best-energy prediction were in
close agreement, with a backbone RMSD of 1.59 A˚(Figs. 2
b and 4, d and e). Note that on the outside of the complex
(facing the lipid) the predicted side chains differed more
from the experimental coordinates due to lack of constraints
(Fig. 4 g), but the interhelical packing was well reproduced
(Fig. 4 f). There were three solutions belonging to the sec-
ondary energy basin, with RMSDs of between 2.2 and 2.4 A˚
(Fig. 2 b). In this test case the secondary energy basin (false
positives) was 15 kcal/mol higher than the first. We note that
the energy span is much larger than for GpA (Fig. 2 a),
presumably due to the greater complexity of the structure
and because the minimization procedure was done with fixed
backbone torsion angles (see Materials and Methods). This
resulted in stronger interactions with the tethering map for
incorrect backbone geometries. Also, in Fig. 4, d and e, we
density map obtained from the NMR structure. (b) Tether-
ing map, used as a restraint during the minimization stage.
(c) Solvent-accessibility map, contoured at level 0.8. Dis-
played for reference are the two TM helices. (d) Side view
and (e) top view of the dimer. The NMR structure is in
blue, and our prediction (lowest-energy conformation) is in
red. The backbone RMSD of this prediction is 0.89 A˚with
respect to the NMR structure. (f) Closeup of a helix-
packing region near the center, where the fit of side chains
is close to the NMR structure. (g) Closeup of a region
facing the lipid, where, due to lack of packing constraints,
the predicted side chains deviated from the NMR structure.
Panel heights are: first row, 56 A˚; second row, 50 A˚; and
third row, 12 A˚.
GpA. (a) Isocontour surface of the simulated
1954 Kovacs et al.
Biophysical Journal 93(6) 1950–1959
can see that the shorter helix did not bend enough to fit com-
pletely into the corresponding density rod (i.e., to match the
experimental helix). This happened, in this particular case,
because of the presence of density corresponding to the pore
helix, which moved the top part of the helix toward it during
the flexible fitting step. No attempt was made to correct this
at this time, but its correction would certainly decrease the
MscL is a specialized class of membrane proteins that
mediate the sensing of physical forces and stresses on the
membrane by transducing them into electrochemical re-
sponses. An x-ray crystal structure at 3.5 A˚resolution from
Mycobacterium tuberculosis showed that the channel is a
homopentamer with two TM helices per subunit (37) (PDB
code 1MSL). This third test case represented a higher order
oligomeric structure (pentamer versus tetramer for KcsA).
The crystal structure and our best-energy prediction had a
backbone RMSD of 1.88 A˚(Figs. 2 c and 5, d and e), which
is slightly higher than for KcsA and approximately twice
the RMSD for GpA. We note that the second-best solution
(with 1.83 A˚ RMSD) was more then 28 kcal/mol higher
than the first, and then there were several solutions that
proceeded upward in energy while staying at ;1.85 A˚
during the minimization stage. (c) Solvent-accessibility
TM helices of a subunit. (d) Side view of a subunit and (e)
our prediction (lowest-energy conformation) is in red. The
the crystal structure. (f) Closeup of a helix-helix interface
structure. (g) Closeup of a region facing the lipid, where,
due tolack of packingconstraints,the predictedside chains
deviated from the crystal structure. Note that the fourfold
was not imposed. Panel heights are: first row, 80 A˚; second
row, 70 A˚; and third row, 12 A˚.
Prediction of Helical TM Proteins 1955
Biophysical Journal 93(6) 1950–1959
RMSD. The first point of the secondary energy basin was
solution number 8, 46 kcal/mol higher than the best solution,
with an RMSD of 3.5 A˚
phenomenon occurred in this test case: the shorter helix
was rotated and translated (screw motion) relative to the
x-ray crystal structure (thus giving an average of 1.88 A˚
RMSD), in such a way that many of the positions occupied
by the experimental side chains were nearly occupied by side
chains of different amino acids.
(Fig. 2 c). An interesting
DISCUSSION AND CONCLUSIONS
We developed an efficient method for structure prediction
of a-helical membrane proteins when an intermediate-re-
solution EM density map is available. We make use of a
novel and efficient method, SCATD (31), to predict side-
chain conformations for a given backbone geometry. The
SCWRL method (38), which is commonly used for this
purpose, failed in our cases because the annular structure
of the channels produces biconnected components that are
too large, and therefore intractable by SCWRL. However,
SCATD uses an entirely different approach called tree de-
composition, which can solve large structures quickly (,3 s).
After side-chain optimization and scoring, the best-scoring
conformations are minimized using an energy function that
includes van der Waals, electrostatic, hydrogen bonding,
torsional and desolvation components. It has been postulated
that van der Waals interactions are a predominant factor in
TM helix packing (39) and in soluble proteins (38,31), but
we also observed that other energy terms had a substantial
contribution to the total energy and, in many cases, were
comparable to the van der Waals energy. For instance, a
considerable fraction of the stabilization energy was due to
hydrophobic and hydrogen-bonding interactions.
lated density map obtained from the x-ray structure. (b)
Tethering map, used as a restraint during the minimization
stage. (c) Solvent-accessibility map, contoured at level 0.8.
Displayed for reference are two TM helices of a subunit.
(d) Side view of a subunit and (e) top view of the pentamer.
The crystal structure is in blue, and our prediction (lowest-
energy conformation) is in red. The backbone RMSD of
this prediction is 1.88 A˚with respect to the crystal struc-
ture. (f) Closeup of a helix-helix interface where the pre-
dicted side-chain packing is close to the crystal structure.
(g) Closeup of a portion of the shorter helix, for which the
prediction exhibits a screw motion along the backbone rel-
ative to the crystal structure, but in such a way that there is
an approximate substitution of side chains. The fivefold
symmetry of the side chains is nearly perfect. Panel heights
are: first row, 60 A˚; second row, 60 A˚; and third row, 12 A˚.
MscL. (a) Isocontour surface of the simu-
1956 Kovacs et al.
Biophysical Journal 93(6) 1950–1959
Our method also incorporates a penalty term, through a so-
called tethering map, which aids in guiding the minimization
process so that the helices remain close to their experimen-
that would place one or more helices outside of the corre-
sponding density. This restraining map acts only on the back-
bone atoms of the structure, thus avoiding perturbations of
the side chains. Tests that allowed the tethering map to re-
strain side-chain atoms led to wrong results.
Electrostatic interactions are divided into intramolecular
and molecule-solvent interactions. The intramolecular energy
was calculated using a distance-dependent dielectric constant
eint¼ 4R (where R is the distance), whereas protein-solvent
interaction was based on solvent accessibilities of the surface
atoms: E ¼ +AiEi: The energy densities Eiwere derived
from water-octanol transfer energies (using a dielectric con-
stant for water (40) ewater¼ 80). The solvent-accessible areas
Aiof each atom were calculated by taking into account both
the surrounding atoms and a special grid map describing the
membrane and channel geometry. This solvent-accessibility
map indicates how accessible to water an atom at a partic-
ular point in space would be. In generating the solvent-
accessibility map, we initially assumed that the hydrophobic
barrier is 22 A˚thick, and that the polar lipid headgroups are
in the aqueous phase. Since the membrane thickness varies
for different kinds of cells, we also carried out the calcu-
lations using thicknesses of 26 and 30 A˚for the hydrocarbon
core of the lipid bilayer. While these model predictions were
the same as for a thickness of 22 A˚for KcsA and for MscL,
the results (not shown) were different for GpA. We surmise
that this dependence in the GpA case was due to the very
small contact area between both TM helices, resulting in a
relatively large influence of the solvation energy.
The use of the tethering map and our approach for com-
puting the solvation energy yielded a significant increase in
the overall efficiency of our protocol. This represents an in-
termediate approach between, on the one hand, considering
(Poisson-Boltzmann equation)—both of which are compu-
tationally too expensive—and, on the other hand, treating the
molecule as if in vacuo, which ignores the solvation con-
tribution altogether. Besides being computationally efficient,
our approach allows easy modeling of arbitrary solvent ge-
ometries, especially exemplified by the pore regions in the
c-panels of Figs. 4 and 5.
We validated our protocol using three test cases: GpA,
KcsA, and MscL. These three examples have two indepen-
dent helices (i.e., helices not related by symmetry). For each
case, we computed three RMSDs (Table 1): for backbone
atoms only, for all buried heavy atoms, and for all heavy
atoms. In addition, for MscL we give separate values for
the subsets of helices TM1 and TM2. This shows excellent
agreement for TM1 with the crystal structure, but TM2 is off
due to the screw motion mentioned in Results. Although the
stereochemistry of this structure was quite reasonable, we do
not know whether this conformation exists in nature or
whether it may even have functional significance. Note that
in all cases the buried-heavy-atom RMSDs are substantially
lower than the all-heavy-atom RMSDs, confirming that the
largest deviations from the experimental structures occur
away from interhelical interfaces, due to lack of constraints.
We believe that these energetically favorable conformations
for the side chains apposed with the lipids could in fact exist.
Notably, our test calculations did not impose any symmetry
(other than in building the backbone arrangements for KcsA
and MscL), and yet the side-chain conformations of the TM
residues in these two cases were virtually symmetric. The
RMSDs with respect to perfectly symmetric structures were
0.48 A˚for KcsA and 0.57 A˚for MscL. These are all-heavy-
atom static RMSDs; hence, they include backbone asymme-
positive indication that the procedure attains full convergence.
The predicted conformations for GpA, KcsA, and MscL
were close to the experimental structures, with RMSDs
between 0.9 and 1.9 A˚for the backbone atoms, depending on
the size of the complex. At the bottom right of each panel in
Fig. 2 are shown the energy values corresponding to the ex-
perimental structures. We notethat for GpA (Fig. 2 a) and for
MscL (Fig. 2 c) these energy values were higher than the re-
spective best solutions obtained by us. This could presum-
ably be due either to imperfections in the parameters or to the
functional form of the energy function utilized in the calcu-
lations. Another possibility, as suggested by Fleishman and
Ben-Tal (7), is that the conformations that we used as tem-
plates do not represent the actual native-state structures, but
were distorted by crystal packing, detergent interactions, the
nonphysiological conditions used for crystallization, or some
other reason. Another likely factor that may assign higher-
than-minimum energy to the experimental conformation is
the presence of extra elements such as the extracellular and
intracellular loops, whereas our calculations took into con-
sideration only the TM domains.
A strength of our approach is that it allows for backbone
and side-chain flexibility, thereby yielding more realistic re-
sults than methods that treat the helices as rigid bodies.
Backbone flexibility is incorporated by performing a fine
sampling of backbone geometries (every 10?/1.5 A˚), flexibly
fitting each of these into the EM map, and then using these
rigid backbone geometries during the final energy minimi-
zations. This approach is fast and fully convergent, unlike
earlier attempts that performed the minimizations over all
in many cases, failed to converge. An exception was GpA,
whose all-variable minimizations fully converged, due to the
reduced size of thestructure. We expect that all-variablemin-
imizations would be applicable to other membrane proteins
with two dissimilar TM helices such as heterodimeric in-
With current computing power, our protocol can be ap-
plied to the prediction of structures containing up to four
Prediction of Helical TM Proteins1957
Biophysical Journal 93(6) 1950–1959
independent helices. We can expect that further optimization
of the protocol and use of more powerful computers will
expand the complexity of membrane proteins amenable to
our procedure, including systems with more than four inde-
Given the lability of many membrane proteins in deter-
gents, we can expect that EM analysis of two-dimensional
crystals in lipid bilayers will continue to be a valuable strat-
egy for membrane protein structural biology. Due to crystal
imperfections and the difficulty in recording images at high
tilt angles, structures determined by two-dimensional electron
crystallographyare oftenat an intermediate resolution (9–6A˚).
Consequently, the computational methods thatwe have devel-
oped will be particularly useful for fitting atomic-resolution
structures that can be validated using other methods such as
distance constraints provided by, for example, fluorescence
resonance energy transfer (42,43) and electron paramagnetic
resonance spectroscopy (44,45). Given that the majority of
drug targets are membrane proteins, a robust and reliable
structure-prediction protocol would be quite valuable in
combination with virtual ligand screening (46).
This work was supported by National Institutes of Health grants No. R01
HL048908 (M.Y.) and No. R01 GM071872 (R.A.).
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