1 Department of Biotechnology, Tokyo University of Agriculture and Technology, Nakacho, Koganei, Tokyo 184-8588, 2 Ryoka System Inc., Computational Science and Technology Division, Irifune, Urayasu,Chiba Prefecture 279-0012 and 3 Helix Research Institute, Inc.,15323 Yana, Kisarazu-shi, Chiba 292, Japan
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Abstract |
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Keywords: bacteriorhodopsin/lattice model/membrane protein/polar interactions/structure prediction/transmembrane helix
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Introduction |
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Several theoretical methods using various algorithms have been proposed with which to analyze and predict the structures of membrane proteins with seven transmembrane helices (Jähnig, 1992; Baldwin, 1993
, 1997; Cronet et al., 1993
; Donnelly et al., 1993
; Du and Alkorta, 1994
; Taylor et al., 1994
; Tuffery et al., 1994
; Herzyk and Hubbard, 1995
; Suwa et al., 1995
; Bowie, 1999
; Koshi and Bruno, 1999
; Pilpel et al, 1999
). Among these, the method proposed by Taylor et al. (1994) is very convenient because a single amino acid sequence is a sufficient basis upon which to reconstruct the three-dimensional (3D) structure of a membrane protein. They adopted a lattice model as the structural template of the arrangement of transmembrane helices. The configuration of seven transmembrane helices is determined according to the basic premise that the sides of helices with more hydrophobic and variable residues face the lipid bilayer phase. Bowie (1999) estimated the number of folds of membrane proteins, including seven-helix-type membrane proteins. The folds may serve for extending the lattice models to more general templates. A novel index of amino acids was developed by Pilpel et al. (1999) for predicting the orientation of transmembrane helices, which may improve the performance of 3D structure prediction of membrane proteins.
However, their procedure may not address structural change during the functioning process, for example the photocycle of bacteriorhodopsin, because a unique index value is allocated to each amino acid irrespective of its protonation state. Studies of bacteriorhodopsin photointermediates have revealed that the structure change of bacteriorhodopsin is coupled with the protonation and deprotonation of essential residues in transmembrane helices. The Schiff base of Lys216 with retinal is protonated in the ground state and deprotonated in the photointermediate states of M and N. Comparisons between the various states of bacteriorhodopsin show that the later photointermediates have a different 3D structure to the ground state (Subramaniam et al., 1993, 1999
; Kamikubo et al., 1996
; Spudich and Lanyi, 1996
; Kamikubo et al., 1997
; Sass et al., 1997
, 1998
; Oka et al., 1999
). Sass et al. (1997, 1998) explicitly stated that these structural changes are caused by the altered charge distribution in the protein.
Suwa et al. (1995) proposed a method with which to predict the structure of membrane proteins based on the assumption that polar interactions are essential for stability of the tertiary structure. They developed a probe helix method with which to characterize the polar interaction field around a transmembrane helix. The polar interaction energy between a transmembrane helix and a probe helix consisting of serinealanine block copolymer was calculated, in which the copolymer spans the alternative halves of a transmembrane helix (Suwa et al., 1992). The energy value was used as the index of helix surface polarity, which corresponds to the serine stretch of the probe helix. Suwa et al. (1995) evaluated the polar interaction energy of the seven-helix system of bacteriorhodopsin, assuming the experimental position of transmembrane helices. The best arrangement of seven helices obtained from the calculated polar interaction energy was the same as that of the experimental structure and the orientation of helices was also very similar to the experimental helix configuration. This method may address the structural change of a membrane protein such as bacteriorhodopsin in the functioning processes, because the algorithm is based on the charge distribution in the protein, which changes owing to the protonation states of polar residues.
This study extends the method of Suwa et al. (1995) by adopting the lattice models of seven helices to survey a wider structural space. The predicted and experimental structures were very similar, strongly suggesting that the algorithm adopted in this work reflects the essential part of the interactions by which the 3D structure of bacteriorhodopsin is stabilized. Furthermore, the 100 optimal structures of bacteriorhodopsin in the triangle lattice indicated a preference for a triangle consisting of helices C, F and G.
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Methods |
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We assumed that the tertiary structure of a membrane protein is stabilized mainly by polar interactions between transmembrane helices. Binding specificity arises from the difference in the polar area on the sides of helices. Figure 1a shows schematically the mechanism of specific binding. For example, when helices A and C have polar areas only in their upper and lower halves, respectively, they do not effectively bind each other. However, when helix B has two polar areas on opposite sides in the upper and lower halves, then helices A and C will be connected through helix B. In this way, the configuration of helices may be determined as a jigsaw puzzle, in which the indentation of pieces consists of polar sides of helices. We therefore call this method the polar jigsaw puzzle (PJP) (Suwa et al., 1995
).
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The PJP assumes that the total interaction energy E between a pair of transmembrane helices has two terms, the polar interactions of the Ehelix at the hydrophobic region and the rubber elasticity Eloop at the region linking two neighboring helices:
![]() | (1) |
Here, the pair polar interaction between two transmembrane helices Ehelix is approximately expressed by the following equation:
![]() | (2) |
The latter term of total energy is the effective interaction energy, arising from the structure of loop segments. We assumed a rubber elastic potential function for this term:
![]() | (3) |
Simplified expression of polar interactions between helices
In the PJP framework, the polar interaction energy Ehelix between transmembrane helices is simplified using the polar index of a helix (Suwa et al., 1995), which expresses the strength of polarity of a helix, by dividing its surface into vertical and angular directions, as shown in Figure 1b
. The values of the polar index were estimated by calculating the interaction energy of a transmembrane helix using N-probe (NAla2Ser11Ala10Ala2C) and C-probe helices (NAla2Ala10Ser11Ala2C). These probes characterized the distribution of polar residues in each half of the transmembrane helices, as shown in Figure 1c
. The value of the polar index varies according to the number and the polarity of residues that face the serine block of the probe helix. Rotating a transmembrane helix by 15°, this method generates 24 values for the polar index per probe helix. Therefore, 48 values of the polar index were obtained for each transmembrane helix, which expressed the vertical and angular distribution of the polar residues.
The angular function of the interaction energy B(ij,
ji) can then be described in terms of the polar index P(
).
![]() | (4) |
Although this expression for the polar interaction energy is very simple, it agrees well with the pair energy calculation of various model helices (Suwa et al., 1995). The coefficient A is the factor used to adjust the simplified energy function to the direct calculation. When the interacting helices have the same type of charge, the factor A is 0.02 (kcal/mol)1 and otherwise the value is 0.14 (kcal/mol)1.
We applied the probe helix method in the present study using CHARMm-QUANTA (Molecular Simulation) on an Indy (Silicon Graphics) (Brooks et al.,1983). The dielectric constant of the system used for the probe helix method was set at 2.0. The configuration of the two helices was antiparallel and the standard distance between helices was 1.2 nm. The cut-off parameters were 0.8 nm for non-bonded interaction and 120° for hydrogen bonding.
Lattice models of seven transmembrane helices
The total energy in the PJP framework decreases upon contact of the polar surface of helices. Therefore, the lower energy of a multi-helix system should be realized for the structures with more nearest neighbor pairs of helices. Figure 2 shows six structures of a seven-helix system in the triangle lattice, in which the number of the nearest neighbor pairs is 12 (L12) and 11 (L11A, L11B, L11Bm, L11C and L11Cm). The structures L12 and L11A are symmetric, whereas the structures L11Bm and L11Cm are the mirror images of L11B and L11C, respectively. The position of transmembrane helices in the real structure of bacteriorhodopsin, for example, is not identical with any of the six models. However, the lattice model may be used as the initial basis for a more realistic structure prediction of membrane protein structure. This will be reported elsewhere.
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Bacteriorhodopsin
We applied the present method to the seven transmembrane helices of bacteriorhodopsin, because this protein has many polar residues in the hydrophobic regions and is therefore suitable for analysis using PJP. Seven transmembrane regions of bacteriorhodopsin were taken from the structure defined by Grigorieff et al. (1996): A, 931; B, 3862; C, 77100; D, 105127; E, 134157; F, 166191; G, 202226. Table I shows the amino acid sequences of the seven transmembrane regions together with the ratio of polar residues in those regions. The average ratio of polar residues was about 30% when all residues with polar groups such as Tyr and Trp were classified as polar residues. This value is large enough to determine structures by their polar interactions.
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Results |
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Figure 3 shows the polar interaction energy profile of seven TM helices in bacteriorhodopsin as a function of their orientational angles. The open and filled circles indicate the polar interaction energies of upper (external) and lower (cytoplasmic) halves of TM helices, respectively, that are obtained from the calculated energy between a TM helix and one of N- and C-probe helices. The values of the polar interaction energy are used as the polar indices in Equation 4
. Namely, the polar interaction energy with a probe helix was assumed to represent the strength of polarity of the helix surface.
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The interhelix binding energy Ehelix of pairs of helices was calculated using Equation (4). Each diagram in Figure 4
shows the energy landscape in orientational angle space of two helices. The vertical and horizontal axes represent rotational angles of a pair of TM helices. A gray scale represents the intensity of binding energy with darker spots indicating higher binding energy. The numbers above the interaction map represent the length of linking segments between TM helices. Polar interactions of pairs containing helices C, F and G were significantly stronger than those of other helix pairs. Therefore, helices C, F and G will be closely packed in energetically preferable structures.
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Discussion |
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This method has the following advantages. First, the helix configuration is determined based upon polar interactions between helices in the present study. In the framework of this method, the predicted structure depends not only on the amino acid sequences but also on the protonation states of charged residues. This algorithm has the potential advantage of predicting the structural change of a membrane protein during the functioning process, because function is usually coupled with the protonation and deprotonation of polar residues at an active site (Oka et al., 1999; Subramaniam et al., 1993
, 1999
; Kamikubo et al., 1996
, 1997
; Spudich and Lanyi, 1996
; Sass et al., 1997
, 1998
). Second, the optimal structure and important triangles of transmembrane helices can be revealed by this method. Information about an active site arising from analyses of an important helix triangle will be useful for molecular biologists, who investigate functionally important amino acids. Third, the method is not associated with structural frustration, which is a serious problem in the molecular simulation of proteins. A helix is assumed to be a rigid rod, having a polar interaction field of smooth angular dependence. Therefore, the energy landscape of the total system becomes smooth and the determination of the grand energy minimum is guaranteed in the framework of this method. Fourth, the structure of a membrane protein with seven transmembrane helices may be automatically predicted. Therefore, predictive ambiguity, arising from manual handling of structures during the processes of molecular modeling, is avoided.
However, this method also has disadvantages and limitations. The physical interaction dominant for the structure formation is assumed to be the polar interaction in the central region of transmembrane helices. In general, polar interaction is significant in a non-polar environment because of a low dielectric constant. Therefore, polar interaction in the hydrophobic region of a membrane should be an important factor for binding between transmembrane helices. In fact, the seven helices of bacteriorhodopsin have a considerably large proportion of polar residues, as seen from Table 1, which is a prerequisite of the PJP. The importance of polar interactions for interhelix binding in bacteriorhodopsin was previously proven by alcohol denaturation experiments (Mitaku et al., 1988
, 1995
; Kukita and Mitaku, 1993
; Mukai et al., 1999
). However, the present method is not applicable to membrane proteins containing transmembrane helices without polar residues because such helices cannot bind with other helices in the framework of the PJP. The packing (Fleming et al., 1997
; MacKenzie et al., 1997
) of transmembrane helices may be the binding mechanism of such helices. A statistical index of amino acids such as kPROT (Pilpel et al., 1999
) may be useful for solving the problem of 3D structure predictions of membrane proteins with only a few polar residues.
Another limitation is that of the size of the protein being analyzed. The present prediction system focuses on membrane proteins with seven transmembrane helices. This type of membrane proteins is also very important, because many are G-protein coupled receptors, which constitute the major factor by which a cell communicates with the environment and with other cells. However, the types of membrane proteins are highly diverse. For example, many channels and pumps have more than 10 transmembrane helices. When the number of transmembrane helices increases, the number of templates of lattice points also increases, but very rapidly. The combination of helices and lattice points also increases greatly, rendering prediction very difficult. The method of sampling of structural templates proposed by Bowie (1999) will serve for surveying the structure of membrane proteins with more transmembrane helices.
Despite these limitations, this automated method may be used for several purposes. The structure predicted by the present method may be used as the initial basis upon which to determine a more detailed structure. The next steps of structure prediction will be to refine the positioning of helices, to remove the restriction of lattice points and to determine the tilting of helices with respect to the normal membrane. Such refinements are promising when applied to bacteriorhodopsin not only in the native state but also in the functional intermediate states and will be reported elsewhere. Making this prediction system internationally available through the Internet will help molecular biologists. Important triangles of transmembrane helices are provided by this system, even if many energetically preferable structures are not similar to the true structure. Therefore, the number of possible sites of mutation that can be used for studying functionally important residues will be greatly reduced. The mode of structural change of a membrane protein such as bacteriorhodopsin during its functioning process can be discussed according to the prediction, since stabilization of the helix configuration by polar interaction is assumed.
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Notes |
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Acknowledgments |
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References |
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Received February 23, 2000; revised July 7, 2000; accepted August 23, 2000.