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. REFERENCES 1. Donnelly, D., Findlay, J.B.C. Seven-helix receptors: Structure and modelling. Curr. Opin. Struct. Biol. 4582-589, 1994. 2. Vriend, G. Molecular modeling of GPCRs. 7'" 3:l-10, 1993 (available from EMBL, Meyerhofstrasse 1, D-69117 Heidelberg). 3. Henderson, R., Baldwin, J.M., Ceska, T., Zemlin, F., Beckmann, E., Downing, K.H. A model for the structure of bacteriorhodopsin based on high resolution electron cryo-microscopy. J. Mol. Biol. 213:899-929, 1990. 4. Havelka, W.A., Henderson, R., Heymann, J.A.W., Oesterhelt, D. Projection structure of halorhodopsin at 6 A resolution obtained by electron cryo-microscopy. J . Mol. Biol. 234837-846,1993. 5. Havelka, W.A., Henderson, R., Oesterhelt, D. Three-dimensional structure of halorhodopsin at 7 A resolution. J. Mol. 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