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PROTEINS: Structure, Function, and Genetics 26146-156 (1996)
Modeling of Halorhodopsin and Rhodopsin
Based on Bacteriorhodopsin
Martin Neumiiller and Fritz Jiihnig
Max-Planck-Institut fur Biologie, Abteilung Membranbiochemie, Tubingen, Germany
ABSTRACT
Bacteriorhodopsin (BR),halorhodopsin (HR), and rhodopsin (Rh) all belong
to the class of seven-helix membrane proteins.
For BR, a structural model at atomic resolution
is available; for HR, diffraction data are available only down to a resolution of 6 A in the
membrane plane, and for Rh, down to 9 A. BR
and HR are closely related proteins with a sequence homology of 34%, while Rh does not
share any sequence homology with BR. An
atomic model for HR is derived that is based on
sequence alignment and the atomic model for
BR and is improved by molecular dynamics
simulations. The model structure obtained accounts well for the experimentally observed difference between HR and BR in the projection
map, where HR exhibits a higher density in the
region between helices D and E. The reason for
this difference lies partially in the different side
chains and partially in slightly different helix
tilts. The scattering amplitudes and phases of
the model structure are calculated and agree
with the experimental data down to a resolution of about 8 A. If the helix positions are
adopted from the projection map for HR and
used as input in the model, this number improves to 7 A.Analogously, an atomic model for
Rh is derived based on the atomic model for BR
and subjected to molecular dynamics simulations. Optimal agreement with the experimental
projection map for Rh is obtained when the entire model structure is rotated slightly about
two axes in the membrane plane. The agreement with the experimental projection map is
not as satisfactory as for HR, but the results
indicate that even for a nonhomologous, but
structurally related, protein such as Rh, a n acceptable model structure can be derived from
the structure of BR. o 1996 Wiley-Liss, Inc.
Key words: membrane proteins, seven-helix
proteins, G-protein-coupled receptors, R factor, phase error
tion contained in the known structures in order to
predict still unknown structures. Membrane proteins are especially reluctant to crystallize so that
structure predictions for them are all the more desired. Steps in this direction have been undertaken,
the best example being the class of seven-helix proteins with G-protein-coupled receptors modeled on
the basis of bacteriorhodopsin, for which an atomic
model is available (reviewed in refs. 1 and 2).
The drawback of these attempts is the lack of any
control: The predicted structures of the receptors
cannot be tested because their experimental structures are not known, hence it is not clear how reliable these studies are. To improve this situation, we
have modeled the structures of halorhodopsin (HR)
and rhodopsin (Rh) on the basis of the structure of
bacteriorhodopsin (BR). For BR, an atomic model
for the structure has been derived by Henderson
and collegues (1990) from electron cryomicroscopy
(ECM) data? Projection maps of the structure and
helix tilts of HR and Rh have recently been reand these data were used to test the
model structures.
HR and BR are closely related proteins (reviewed
in ref. 8). To create a model of the structure of HR,
the sequences of HR and BR were aligned and the
polypeptide chain of HR was put onto the structure
of BR according to this alignment (model I). Because
the experimental structure of BR3 contains only the
seven membrane-spanning helices and not the peripheral loops, only the membrane-spanning helices
of HR were obtained in this way; the connecting
loops were added by a simple modeling procedure.
This initial structure was subjected to a molecular
dynamics (MD) simulation in order to relax the
strains contained in the structure, and the resulting
MD structure was considered as the model structure
for HR. A projection map of this structure was determined and compared with the experimental
map.* The goodness of the structure was quantified
by calculating two-dimensional R factors and phase
errors. In addition, helix tilt angles were determined
and compared with experimental data.5
INTRODUCTION
It is well known that many more protein sequences are available than protein structures. One
way to improve this situation is to crystallize more
proteins, and another way is to exploit the informa0 1996 WILEY-LISS. INC.
Received November 17, 1995; accepted April 22, 1996.
Address correspondence and reprint requests to Martin Neumuller, Max-Plank-Institut fur Biologie, Abteilung Membranbiochemie, Corrensstrasse 38, D-72076 Tiibingen, Germany.
MODELING OF HALORHODOPSIN AND RHODOPSIN
Two alternatives were considered for the initial
structures: (1)to preserve the homology to BR and
use experimental data on HR as additional input for
modeling (model 11),or (2) to release the homology to
BR and use exclusively experimental data on HR as
input (model 111).
Rh lacks any sequence homology to BR. Hence the
membrane-spanning helices were predicted on the
basis of their hydrophobicity' and then put onto the
helices of BR. The initial model structure was again
subjected t o a n MD simulation, and the model structures were tested against the experimental data6 by
comparing the projection maps and calculating twodimensional R factors and phase errors.
METHODS
Construction of Initial Structures
for Halorhodopsin
Model I: Homology modeling of H R
based on B R
The amino acid sequences of HR and BR have
been determined by Blanck and Oesterhelt" and
Dunn and colleagues," respectively, and were
taken from GenBank. The mature proteins of HR
and BR comprise 251 and 248 residues, respectively.
For modeling, the last 14 residues of HR were cut
off. The sequences were aligned using the GAP utility of GCGUW (Genetics Computer Group, University of Wisconsin, Madison, WI). With the default
parameters, a gap in helix A of HR was obtained,
which could be eliminated by increasing the parameter for gap penalty. In the final alignment without
gap, 37% of the helical residues and 34% of all residues were identical.
The ECM structure of BR was taken from the
Brookhaven Data Bank (entry 1BRD). It contains
164 residues of 1369 atoms representing the seven
membrane-spanning helices. The polypeptide chain
of HR was put onto this structure according to the
above alignment by adopting the backbone coordinates of all residues in the helices as well as the side
chain coordinates of identical residues in the helices.
The side chain conformations of nonidentical residues were considered as regular and were modeled
by using a utility of SYBYL (Tripos Associates,
Munchen, Germany). The N-terminal, C-terminal,
and loop regions were constructed by a data bank
search, also by using a SYBYL utility.
Model II: Homology modeling using
a d d i t i o n a l data on H R
The helices of HR were the same as in model I, but
their positions were taken from the experimental
two-dimensional density map of HR. In the first approach (model IIa), the centers of mass of the helices
were read off from the map as presented by Havelka
and coworkers: and the helices of model I moved to
these positions without altering their orientations.
147
In the second approach (model IIb), the helices of
model I were translated and rotated as rigid bodies
in small steps until the two-dimensional scattering
phases and amplitudes became optimal, as expressed by a minimal R factor (see below). In both
approaches, the N-terminal, C-terminal, and loop
regions were modeled as for model I.
Model 111: Modeling of H R using exclusively
data on H R
The procedure follows closely the work of Jahnig
and Edholm'' on BR. The seven membrane-spanning helices were predicted on the sequence according to their hydrophobicity.' Moreover, their most
hydrophobic sides were predicted due to amphipathy, and marker residues in the middle of these sides
were specified. Seven regular helices comprising the
membrane-spanning helices and parts of the intervening loops were constructed. These were oriented
along the membrane normal in z direction and positioned in z direction such that the marker residues
were located in the middle of the membrane (z = 0).
Their positions in the membrane plane were taken
from the two-dimensional density map for HR4 as in
the case of model IIa, and their orientations about
the helix axes were chosen so that the marker residues pointed to the outside of the kidney. The chromophore retinal was added in all-trans conformation and oriented to pack optimally.
Construction of an Initial Structure
for Rhodopsin
The sequence of Rh has been determined by several groups and was taken from GenBank. It comprises 349 residues. For modeling, the N and C termini were cut off, and only the region from residues
33 t o 314 was used. Because of the lack of any sequence homology between Rh and BR, the membrane-spanning helices of Rh were predicted on the
basis of their hydrophobicity, in analogy to model I11
for HR. The prediction was in good agreement with
that by Alkorta and Du13 from a sequence divergence analysis of G-protein-coupled receptors
(GPCRs).The Rh and BR sequences were aligned on
the basis of helical regions and amphipathy, and the
polypeptide chain of Rh was put onto the ECM structure of BR according to this alignment. Actually,
this procedure leads to the same assignment of predicted helices to maxima in the density map as proposed by Baldwin14 from a comparative study of a
large number of GPCRs. The chromophore retinal
was modeled in 11-cis conformation and oriented to
pack optimally. The connecting loops were constructed as in model I for HR, implementing an S-S
bridge between CysllO and Cys187.
Molecular Dynamics Simulations
The MD simulations were performed using the
GROMOS package (BIOMOS B.V., University of
148
M. NEUMULLER AND F. JAHNIG
Groningen, Groningen, Netherlands). The initial
structures constructed for the three models of HR
and the model of Rh were first subjected to extensive
energy minimization. Then MD runs were started
comprising a heating run of 10 ps to reach a temperature of 300 K and a production run of 100 ps.
During the heating period, the system was coupled
to a heat bath with a relaxation time of 10 fs, and
during the production run the relaxation time was
increased to 100 fs. The time step used in the simulations was 2 fs. The nonbonded interactions were
cut off a t 10 A and a neighbor list technique was
used with updates every 10 steps. A dielectric constant of 1 was used throughout, and all side chains
had a net charge of zero. For each model, three MD
runs with different initial velocities were performed.
Scattering Factors
The two-dimensional lattice of HR is cubic, with a
lattice constant of a = 102 A and two centrosymmetric tetramers in the unit cell? The structure factors are derived using the expression
where ri denotes atom positions and G h k reciprocal
lattice vectors; ui and ui are the components in the
membrane plane of the positions of the N atoms of
one monomer relative to the center of the tetramer
at (d2,O). The scattering factors f , are given by the
atomic form factors Fiand the Debye-Waller factors
as
f i = Fiexp {-[<(Aui)2>(G!k)2
+ <(A~~)~>(Gik)~]/2}
(2)
where <(AuJ2> and <(Auil2> denote the meansquare positional fluctuations of the atoms. Writing
Fhk = IFhkJexp ( i a h k ) defines the scattering amplitudes p h k l and the scattering phases @hk. The expression for the structure factors indicates that they
are real, that is, the phases can adopt only the values 0" and 180".
The MD structures for HR were tested against the
two-dimensional scattering data of Havelka and colleagues4 by determining the R factor and the phase
error A@.* These data contain m = 101 structure
factors extending down to a resolution of 6 A. Using
only those with a figure of merit above 0.95, m reduces to 66.The R factor is given by
*The amplitudes presented in Table I of Havelka et a1.4 are
slightly in error. Corrected data were provided by R. Henderson (personal communication).
=
c
hk
phk -
mpI/cImp''
(3)
hk
The MD structure factors have to be scaled so that
the sum of the experimental amplitudes agrees with
the s u m of the MD amplitudes. In contrast to the R
factor used in x-ray crystallography, the R factor
used here accounts for errors in amplitudes and
phases. The phase error is given by
(4)
It is important to note that before calculating R
factors and phase errors, the monomers in the unit
cell were translated and rotated as rigid bodies to
minimize the R factor.
The mean R factor and phase error may also be
split up into R factors R , and phase errors A@, of
groups of reflections specified by the resolution d =
down to which they extend." Typically, 20 reflections were gathered in a group yielding five groups specified by the d values 14.5, 10.0,
8.0, 7.0, and 6.0 A.
To get an impression of typical R factors and phase
errors, we considered an arbitrary MD structure as
the reference structure, positioned it in the HR unit
cell, and determined its scattering amplitudes and
phases. Then the positions of all atoms in this structure were altered randomly, beginning with small
displacements and increasing them stepwise. For
each step, the rms distance to the reference structure on the one hand, and the mean R factor and
phase error on the other, were calculated. The related pairs of R factor versus rms distance and phase
error versus rms distance are plotted in Figure 1.
For example, an rms distance of 3 A corresponds
roughly to R = 45%and A@ = 40".
The two-dimensional structure factors of the Rh
lattice were calculated analogously. The Rh unit cell
is orthorhombic-cz = 43 A and b = 140 A-and
contains four monomers in centrosymmetric positioxm6 Therefore, the phases can adopt only the values 0" and 180". The experimental two-dimensional
structure factors were provided by G. Schertler (personal communication). They extend down to a resolution of 7 A, but are reliable only down to about 9
A, including m = 60 structure factors.+
Projection Maps
Projection maps of the model structures were obtained by calculating the two-dimensional structure
+Inthis paper, the structure of bovine Rh is modeled. Recently, experimental data on frog Rh were reported with a
The differences between
resolution extending down to 6
bovine and frog Rh are minor, much smaller than the differences between Rh and BR.
MODELING OF HALORHODOPSIN AND RHODOPSIN
1
I
I
I
100
80
80
60
60
n
=
0
a,
'$ 40
40
20
0
20
LLLL-L,
0
Fig. 1. R factor (0)
and phase error A@ (0)as a function of the rms distance between a
reference structure and a structure obtained from the reference structure by stepwise randomization of the atom coordinates. One of the model structures for HR was used as the reference
structure.
factors and using them as input for the standard
crystallographic programs of the CCP4 package
(Daresbury, UK). Because the loops are missing in
the BR model structure, they were also omitted in
the HR and Rh model structures when projection
maps were prepared. For HR and Rh, the experimental structure factors extend down to resolutions
of 6 A and 9 A in the membrane plane, respectively,
and therefore in constructing projection maps for the
model structures only the structure factors extending to 6 A or 9 A were used.
For comparison, projection maps based on the experimental two-dimensional structure factors for
BR, HR, and Rh were constructed. They are identical to the maps reported by Hawelka and associates4
for BR and HR and by Schertler and colleagues6for
Rh. For BR, the experimental two-dimensional
structure factors were taken from the Brookhaven
Data Bank (entry RlBRDSF).
Extension and Orientation of Helices
Helical regions were specified by determining the
backbone dihedrals @ and and imposing the condition that both angles lie within a range of r 2 0 "
around their regular values -57" and -4T, respectively. The axes of the helices were determined by
averaging the positions of seven Ca atoms a t each
end of a helix, the connecting line between the average positions representing the helix axis.15 The
orientation of the axes was specified by the polar
angle 6 between the axes and the membrane normal
and the azimuth angle cp between the projection of
the helix axes onto the membrane plane and an axis
roughly parallel to a vector joining helices B and D.5
For HR, the angles 6 and cp were compared with the
angles determined experimentally by Havelka and
~olleagues.~
RESULTS
Initial and Final Structures for Halorhodopsin
In model I, an initial structure for HR was obtained by homology modeling based on the partially
known structure of BR. The initial structure was
energy-minimized and subjected to an MD simulation, comprising a heating run of 10 ps and a production run of 100 ps. During this procedure, the
structure moved away from the initial structure, as
shown for model I in Figure 2. Taking for the final
150
M. NEUMULLER AND F. JAHNIG
C
B
D
*
A
E
G
F
Fig. 2. Movements of the helix centers in the membrane plane during heating and production
run for model I. The initial positions are marked by a dot. The notation A-G of the helices follows
their order on the sequence.
helix positions the average over the last 60 ps of the
MD run, the helices moved on the average by 1 A,
with helix C moving the largest distance and helix F
the smallest. These changes in structure may be
quantified in terms of the rms distance of the C a
atoms between the initial and the instantaneous
structure, plotted as a function of time in Figure 3A.
The rms distance increases rapidly during the heating run and stays essentially constant during the
production run. A typical value is 3.5 A, which reduces to 2.5
when only the helical regions are
considered. Because the energy still decreases during the first 40 ps of the production run, as shown in
Figure 3B, the mean MD structure was determined
by averaging over the last 60 ps.
In Figure 3A, the rms distances between the initial and the instantaneous structure are shown for
three MD runs that differed in the initial velocities
of the atoms. The temporal behavior is roughly the
same in all three cases; however, this does not imply
that the structures moved in the same direction. Actually, the three final structures differ among each
other by about 3 A (considering only the C a atoms).
Such behavior has been observed in MD simulations
of BR16 (and of bovine pancreatic trypsin inhibitor'?) and led to the construction of a time- and ensemble-averaged structure. This averaged structure
is not free of strain: because of the ensemble-averaging, the bond lengths and bond angles are not in
equilibrium. Therefore, the averaged structure was
subjected to 20 steps of energy-minimization in order to relax the bond lengths and bond angles, and
the energy-minimized structure thus obtained was
considered as the final MD structure.
The initial structures of the two other models
were treated in the same way and showed a similar
behavior. For model 111, the difference between the
structures obtained from the three runs with different initial velocities was most pronounced, namely,
about 5 A.
The final energies of the three models-listed in
Table I-were obtained as the mean values of the
potential energies over the last 10 ps of the production runs and over the three runs with different initial velocities. From these data, one would predict
that model IIa leads to the best model structure for
HR, but the energy differences between the model
structures are not very pronounced.
Projection Maps for Halorhodopsin
Projection maps of the initial and final MD structure for model I are shown in Figure 4c,d, together
with the map derived from the experimental twodimensional scattering data for HR (Fig. 4e). For
comparison, the projection map of the model structure for BR derived by Henderson and coworkers:
and the map derived from the experimental two-dimensional scattering data for BR are included (Fig.
151
MODELING OF HALORHODOPSIN AND RHODOPSIN
5.0
4.0
3.0
O S .
5:
E
2.0
1
1.o
0.0
,
L
L
,
Bl
r
g
h
-5.5
3
Y
-k
0
Y
v
B
-6.0
w”
em
-6.5
0
50
time (ps)
100
Fig. 3. A: Time course of the rms distance of the MD structure
from the initial structure. B: The total potential energy for model I.
The simulation started with an energy minimization (em) followed
by a heating run (hr) of 10 ps and a productionrun (pr) of 100 ps.
The rms distance of the CU atoms is shown for three runs with
different initial velocities (Fig. A), the energy for the first of these
runs (Fig. 6).
4a,b). The latter two maps differ slightly, the reason
lying partially in the neglect of the loops and the
lipids in the model structure for BR and partially in
errors in the model structure itself. By analogy, the
map of the model structure we derived for HR deviates somewhat from the map derived from the scattering data.
Havelka and colleagues4 have pointed out that
the main difference in the projection maps of HR and
BR resides in the region between helices D and E,
the two helices being more connected in density for
HR than for BR (Fig. 4b,e). This difference is reflected also in the maps of the model structures for
the two proteins (Fig. 4a,d), implying that the model
structure for HR is realistic in this respect. The reason for this difference can be found in the map of the
initial structure for HR (Fig. 4c), which exhibits a
connection in density of helices D and E. Because
the initial structure was constructed to coincide
with the model structure of BR, except for the side
chains being replaced by those of HR, part of the
higher density between helices D and E arises simply from the different side chains of HR compared to
BR. The increase in density becomes more pronounced on passing from the initial to the final
structure of HR (Fig. 4d). The reason for this additional effect lies in slight changes in the tilt of helices D and E on going from BR to HR. Hence the
main difference between HR and BR, the density
between helices D and E, is a consequence of different side chains and of slightly different helix tilts.
The latter is discussed in more detail in the section
“Helix Tilt for Halorhodopsin” below.
Amplitude and Phase Errors
for Halorhodopsin
For a quantitative test of the model structures,
their two-dimensional structure factors were calculated and R factors and phase errors determined relative to the experimental amplitudes and phases4
For this purpose, the final MD structures were positioned and oriented in the unit cell of the HR lat-
152
M. NEUMULLER AND F. J m N I G
TABLE I. Energies, Phase Errors and R Factors of the Model
Structures for HR and Rh*
Structure
HR
Model I
E,,+(kJ/mol)
-6130590
Model IIa
-6400k90
Model IIb
-6100+100
Model I11
Rh
-6080k100
-8590 k 100
A@ (deg)
initial
final
41
(24)
39
(30)
37
(19)
48
(27)
36
39
(19)
25
(8)
34
(27)
46
(19)
48
R(%)
initial
final
65
(52)
62
(56)
58
65
(57)
62
(50)
74
(63)
82
(55)
72
(68)
74
(62)
110
*The phase errors and R factors represent deviations between the two-dimensional
structure factors calculated for the MD structures and the experimental structure factors. For HR, 101 experimental structure factors extending down to a resolution of 6 A
were used! The numbers in brackets represent the results when only the 66 structure
factors with a figure of merit above 0.95 were used. For Rh, 60 experimental structure
factors were used extending down to a resolution of 9 A.6
BR
HR
Rh
Fig. 4. Projection maps for BR (left), HR (middle), and Rh
(right). For BR: a: map of the model structure derived by Henderson et aL3 and b: experimental density map. For HR: c: map of
the initial structure of model I; d: map of the final structure of
model I; and e: experimental density map? For Rh: f: map of the
initial model structure; g: map of the final model structure; and h:
experimental density map.6 The x and y axes indicated in Fig. a
are parallel to those of the BR model structure of Henderson et
a1.3
tice to yield minimal R factors, and for this position
and orientation the mean phase errors A@ were calculated. The rms fluctuations of the atoms entering
the structure factors were determined as time- and
ensemble-averaged fluctuations relative to the final
MD structure (the fluctuations in the helices were
smaller than in the loops, typical rms values for the
Ca atoms being 1.1h; and 2.2 A, respectively). "he
MODELING OF HALORHODOPSIN AND RHODOPSIN
minimal R factors and phase errors of the initial and
final structures for the three models are listed in
Table I.
In all cases, the phase error decreases on going
from the initial to the final structure. For the final
structure of model I, the phase error is A@ = 39".
The smallest phase error is obtained for the final
structure of model IIa, A@ = 25". Because the
phases for the HR lattice can have only two values,
0" or 180",this value implies that 14 phases of 101
used in the analysis are wrong. Model I11 is the
worst case; the phase error is large and improves
only slightly from A@ = 48"for the initial structure
to A@ = 46" for the final structure. When only the
66 structure factors with a figure of merit above 0.95
are taken into account, the phase error of models I
and I11 decreases to A@ = 19" and of model IIa to A@
= 8", corresponding to 7 and 3 wrong phases out of
66, respectively. It is worth to be noted that the
phase errors would be larger by about lo", if ensemble-averaging in deriving the final MD structure
would be omitted.
The R factors remain constant on passing from the
initial to the final structure, except for model IIb. In
the latter case, however, the initial structure was
constructed by minimizing the R factor, and a low
initial R factor was obtained, which increased during the MD simulation.
R factors and phase errors were also determined
for groups of reflections specified by the resolution
down to which they extend. They are plotted in Figure 5 as a function of resolution. Both the group R
factor and the group phase error remain small down
to 8 A for model I and down to 7 A for model IIa, and
increase a t higher resolution. The increase of both
quantities a t lower resolution, that is, at 14.5 A,
may be caused by the neglect of lipids in the model
structure as well as by inaccuracies in the experimental data at low scattering angles. In any case,
the data of Figure 5 indicate that the model structures are good down to 8 A for model I and down to
7 A for model IIa.
A mean phase error of A@ = 39" as obtained for
model I is roughly equivalent to an rms distance
between the model structure and the correct but unknown structure of HR of about 3 A, as indicated by
Figure 1.Considering the R factor of 65%,one would
obtain a slightly higher rms value of about 4 A.
However, the large R factor may partially arise from
uncertainties in the experimental scattering amplitudes at low resolution. It indeed decreases to 58%if
only the reflections between 14.5 A and 6 A are
taken into account. This lower R factor would be
equivalent to an rms distance of about 3.5 A. Furthermore, a certain rms distance between two structures is equivalent to agreement in the structure
factors down to a resolution roughly three times as
large, that is, in this case to a resolution of about 10
A. By the same argument, the phase error of 25"for
153
model IIa is roughly equivalent to an rms distance of
about 2 A and an agreement in structure factors
down to about 6 A. These numbers are close to those
obtained above from group R factors and phase errors.
Helix Tilt for Halorhodopsin
In a last step, the MD structures were tested
against experimental data available for the threedimensional structure of HR, namely, the tilt of the
he lice^.^ For this purpose, the extensions of the helices had first to be determined. This was done by
calculating the backbone dihedrals @ and 9 and imposing the condition that their values lie within
k20" of the values for regular helices, -57" and
-47", respectively. The resulting extensions of the
helices for model I are listed in Table 11. On the
average, the helices are 24 residues long and thus
have about the same length as those of BR. Next, the
helix axes were specified by determining the midpoints of 7 Ca atoms a t both ends of each helix and
connecting the two midpoints by a line. The orientation of the helix axes was described by the polar
angle 6 between the axes and the membrane normal
and the azimuth angle cp between the projection of
the helix axes onto the membrane plane and an axis
roughly parallel to a vector joining helices B and D.5
The values of 8 and cp for the initial and final structure of model I are included in Table 11, together
with the experimental data of Havelka and colleagues5 and the difference angle A between the helix axes in the model structure and the experimental
structure. Due to the construction of model I, the tilt
of the helices in the initial structure is identical to
the tilt in the model structure of BR.3 The average of
A over all helices is 6",for the initial as well as for
the final structure of model I. For the final structure
of model IIa, this average value reduces to 4", while
for model I11 it increases to lo".
When helices D and E are considered in more detail, it is obvious that helix E is more strongly tilted
than helix D. Furthermore, the azimuth angle cp of
helix E varies strongly on going from the initial to
the final structure, the change from -153" to 165"
indicating a rotation of helix E toward helix D. This
rotation is too large because in the experimental
structure the angle cp is -167". In any case, this
rotation of helix E toward helix D is one of the reasons for the higher density in the region between
helices D and E in the projection map of HR as compared to BR (Fig. 4).
Results for Rhodopsin
An initial structure for Rh was constructed based
on a hydrophobicity analysis and the structure of
BR. Energy minimization and MD simulations were
performed in the same way as for HR. Again three
production runs with different initial velocities extending over 100 ps were started and the final struc-
154
M. NEUMULLER AND F. JAHNIG
150
I
I
I
I
A
100
h
s?
v
rr"
50
I
I
0
5
I
I
t--
+
B
0,
80
g) 60
h
s?.
eU'
40
,,
20
....-
0
L - . I L _ _ - - - - l - L -
7
5
9
I
I
11
13
I
15
resolution d (A)
Fig. 5. A: R factors R, and B: phase errors A@, for groups of reflections specified by the
resolution d down to which they extend for model I (0)
and model Ila (0).
TABLE 11. Extension and Tilt of the Helices in the Initial and Final MD Structure
of Model I for HR and in the Experimental Structure*
Helix
A
B
C
D
E
F
G
Extension
final
8-28
37-69
84- 100
112-130
138-159
172-200
208-235
I?
23
4
5
10
18
15
16
c
p
(deg)
initial
122
40
-37
61
-153
172
140
A
7
4
4
7
6
5
8
B
21
9
2
10
12
13
18
c
p
(deg)
final
155
-83
21
82
165
159
166
A
B
9
11
3
6
6
4
7
(deg)
exP
26
136
2
111
2
-68
5
112
13
-167
10
169
23
153
cp
*The tilt of the helices is specified by the polar angle 6 of the helix axes relative to the membrane normal
and by the azimuth angle cp of the projection of the helix axes onto the membrane plane relative to an axis
roughly parallel to a vector joining helices B and D.5 The experimental data are taken from Havelka et
aL5The angle A is the angle between the helix axes in the MD structures and the experimental structure.
ture was determined by time-averaging over the last
60 ps and ensemble-averaging over the three runs.
During the simulations, the energy and the rms distance of the MD structure from the initial structure
behaved roughly in the same way as for HR, the
final energy being -8591 kJlmol and the final rms
distance being 5.1 h;, considering only Ca atoms.
This rms distance is 1.8 h; larger than for HR,
MODELING OF HALORHODOPSIN AND RHODOPSIN
mainly due to the longer loops between the helices,
which provide more flexibility to the Rh structure. If
only the helices are considered, the final rms distance is 2.6 A, which is similar to the case of HR.
Projection maps of the initial and final model
structure together with the map derived from the
experimental two-dimensional scattering data for
Rh6 are included in Figure 4.The experimental twodimensional density of Rh (Fig. 4h) may be described as consisting of two helices oriented perpendicular to the membrane (F, G) and surrounded by
an arc of three tilted helices (A, B, C ) with two separate perpendicular helices attached (D, E). The assignment of the predicted helices on the sequence to
those on the density map is not known; however, it
has been proposed to correspond to that of BR'' and
as such is indicated in Figure 4h. The initial model
structure (Fig. 4f) reflects some features of the experimental density, which, however, become less evident in the final model structure (Fig. 4g). It is important to note that this partial agreement between
initial model structure and experimental data is
mainly a consequence of an altered orientation of
the entire Rh molecule in the unit cell found by minimizing the R factor. Actually, the entire Rh molecule was rotated by -16" about the z axis and 11"
about they axis relative to the orientation of the BR
molecule in the BR lattice. This altered orientation
leads to an altered tilt of the helices causing the
changes in the density map. Especially, helices E, F,
G are oriented roughly perpendicular to the membrane and well resolved, while helices A, B, C are
more tilted and exhibit a tendency to become connected in the density. However, they do not yet form
an arc, and helix D is not yet separated from helix C
as in the experimental density.
The two-dimensional structure factors of the
model structure were calculated and tested against
the experimental structure factors.6 The R factors
are 82%and 110%and the phase errors 36" and 48"
for the initial and final model structure, respectively
(Table I). These values are higher than those obtained for HR, indicating that the model structure
for Rh is not as good as the model structure for HR.
DISCUSSION
An initial model structure for HR was derived
based on the sequence homology to BR and the
known structure of BR (model I). The initial model
structure was equilibrated by MD simulations yielding the final model structure. The goodness of the
model structure was tested by comparison with experimental data on HR available in the form of twodimensional scattering amplitudes and phases4 and
tilt angles of the he lice^.^ Comparison with the scattering data was performed by visual inspection of
projection maps and by calculating R factors and
phase errors.
The experimental projection maps of BR and HR
155
agree to a large extent and exhibit only a small difference in the region between helices D and E. In the
case of BR, the densities of the two helices are well
separated, and in the case of HR they are more connected. This feature is reflected in the projection
map of the initial model structure for HR and becomes more pronounced in the final model structure,
which implies that the main difference between the
structures of BR and HR is caused partially by different side chains and partially by different helix
tilts. The mean deviation of the helix tilt angles in
the final model structure from the experimental values is 6".
The final model structure for HR has a mean R
factor of 65%and a mean phase error of 39". When
the reflections are split up into groups differing in
resolution, the agreement between model structure
and experimental data extends down to about 8 A.
This number implies that the model structure has
an estimated rms distance from the unknown structure of HR of roughly 3 8.When R factor and phase
error are determined by considering only the experimental structure factors with a figure of merit
above 0.95, the phase error reduces to 19".
The goodness of the model structure for HR is improved considerably, when experimental data on HR
are incorporated in the model. When the positions of
the helices are adopted from experiment (model II),
the phase error decreases to 25"and the R factor to
62%. Considering again only the structure factors
with a figure of merit above 0.95, the phase error
becomes 8" equivalent to 3 wrong phases out of 66.
Because a structure is more sensitive to phases than
to amplitudes, this indicates that the structure essentially agrees with the experimental data. This is
also expressed by a mean deviation in the helix tilt
angles between the model and the experimental
structure, which is not more than 4".
Both the phase error and the R factor increase,
when only the positions of the helices of HR are
taken from experiment and the homology to BR is
neglected (model 111).The phase error becomes 46"
and the R factor 74%. When only the structure factors with a figure of merit above 0.95 are considered,
the phase error reduces to 19". This value is the
same as for model I, which is remarkable in view of
the fact that model I11 was constructed by adopting
the positions of the helices from the projection map
of HR and making no use of the known structure of
BR.
A model structure for Rh was derived based on the
structure of BR. Homology modeling could not be
applied in this case because Rh and BR do not share
any sequence homology. Therefore, the helices on
the sequence were predicted on the basis of their
hydrophobicity. The goodness of the model structure
was again tested by comparison with the experimental two-dimensional scattering data.6
The experimental projection maps of BR and Rh
156
M. NEUMULLER AND F. JAHNIG
exhibit larger differences than those of BR and HR.
BR and HR are both kidney-shaped, with the inner
helices B, C, D perpendicular to the membrane and
the outer helices E, F, G, A slightly tilted. By contrast, in the projection map of Rh helices A, B, C
form an arc around helix G and are tilted, while
helices D, E, F, G are roughly perpendicular to the
membrane. These features are reflected to a considerable extent in the initial model structure for Rh
and are largely preserved in the final model structure. The point is that all the Rh molecules of the
model structures (which are based on the structure
of BR) were rotated about two axes in the membrane
plane to obtain optimal agreement with the experimental scattering data for Rh. Hence the large difference between the two-dimensional densities of
BR and Rh are caused to a considerable extent by
different orientations of the two molecules in their
crystal lattice and, less significantly, by differences
in the internal structure of the molecules. This theory is supported by Hoflack and colleagues," who
question the proposal of others'' that Rh and other
GPCRs form a structural class distinct from the
structural class of BR and HR.
The R factor and phase error of the model structure for Rh are both relatively large, 110% and 48",
respectively, indicating that the agreement of the
model structure with experiment is poorer than in
the case of HR. Further improvement in modeling
Rh may be achieved by taking into account that proline residues are located in different helices in BR
and Rh.
In conclusion, the results on HR demonstrate that
modeling of a protein based on a closely related
one-in this case BR-leads to a reliable model
structure. Simple homology modeling provides a
good model structure, but an ensuing MD simulation does not lead to a remarkable improvement.
The results on Rh demonstrate that even in the case
of a nonhomologous, but structurally related, protein an acceptable model structure is obtained.
ACKNOWLEDGMENTS
We thank 0. Berger for many helpful discussions,
R. Henderson for providing corrected scattering amplitudes for HR, and G. Schertler for providing scattering amplitudes and phases for Rh.
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