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Electric-field distribution inside the bacterial photosynthetic reaction center of Rhodopseudomonas viridis
Volume 173, number 2,3
CHEMICAL PHYSICS LETTERS
5 October 1990
Electric-field distribution inside the bacterial photosynthetic reaction center of Rhodopseudomonas viridis Chong Zheng, Malcolm E. Davis and J. Andrew McCammon Department of Chemistry, Universityo,fHowon, Houston, TX 77204-5641, USA Received 16 April 1990; in tinal form 20 June 1990
The electric-field distribution inside the bacterial photosynthetic reaction center of Rhodopseudomonas uiridiswas obtained by solving the linearized Poisson-Boltzmann equation with a grid size of (2 A)‘. The order of potentials induced by the protein medium for the four heme groups in the cytochrome part is Hml: 310 mV, Hm2: 370 mV; Hm4: 380 mV, Hm3: 130 mV. The potential profile is similar along both the L and the M branches, a result of the C, symmetry related environment. In both the L and the M subunits, bacteriochlorophyll has the lowest potential. It is shown that the Poisson-Boltzmann method can also be used to analyze the variation of local fields inside proteins in response to applied fields. For the reaction center, the dielectric response to an applied field is anisotropic. There are significant induced x and y components of the internal field for an applied field along the z direction (the C, axis). Thus the effective dielectric-constant tensor of the protein medium has non-zero offdiagonal elements. Analysis of how the applied field and ionic strength influence the internal field indicates that there is relatively small screening due to free solvent in the complex. The difference between the potentials at various cofactors is due to the sum of small contributions from the protein environment, rather than a few charged residues.
1. Introduction Knowledge of the electric-field distribution inside the bacterial photosynthetic reaction center, and of how it changes with environmental influences such as applied fields and ionic strength, is indispensable for understanding the electron-transfer kinetics and the control of proton diffusion to the secondary quinone. For example, the interpretation of the Starkeffect spectroscopy data and the conclusion thereafter about the involvement of the intermediate L branch bacteriochlorophyll, B, in the electron-transfer process assumed that the internal electric field is linearly proportional to the applied field [ 1-7 1. The quantitative discrepancy between the theoretical prediction and the experimental results of the electric-field effects on the primary charge separation in the reaction center was attributed partly to the lack of detailed information on the internal electric-field distribution and its dependence on applied field [ 81. Theoretical interpretations are needed in order to help understand the results of electrochromism, kinetic and EPR measurements of the relative potentials of the cofactors in the reaction center [9-l 13. 246
Understanding of how the potential is influenced by the ionic strength of the adjacent aqueous medium will also help explain the facts that the primary current, corresponding to the electron transfer from the special pair to the primary quinone QA,is nearly independent of the ionic strength, and that the secondary current, corresponding to the subsequent electron transfer from cytochrome c outside the membrane to the special pair, is influenced strongly by the ionic strength of the medium [ 12,131. Finally, theoretical description of how protons diffuse to the secondary quinone QB requires detailed information on the electric-field distribution along the diffusion channel [ 14-161. Several research groups have calculated the electric-field distribution in the absence of applied fields. Niedermeier and coworkers summed Coulomb point charges calculated from MNDO and INDO methods to obtain the potentials for the cofactors [ 17,181. However, their treatment did not include the solvent effect. Warshel and coworkers developed a method which takes into account the contributions from both the permanent and the induced dipole moments in the protein [ 19-221. Using this method, they have
0009-2614/90/$ 03.50 0 1990 - Elsevier Science Publishers B.V. ( North-Holland )
CHEMICAL PHYSICS LETTERS
Volume 173, number 2,3
calculated the electrostatic free energy of the states along the reaction center. Honig and coworkers used the linearized Poisson-Boltzmann equation to calculate the electrostatic characteristics inside the reaction center [23]. Feher’s research group also calculated the electrostatic potential inside the reaction center by solving the finite-difference form of the Poisson equation [ 241. However, these previous theoretical works did not focus on the effects of the applied field and ionic strength. Our method is also of the linearized Poisson-Boltzmann type, which includes contributions of the permanent and induced dipole moments and the correction due to the finite size of the protein atoms, although implicitly through the use of dielectric constants for excluded atomic volume and solvent space. The method also allows the calculation of the dependence of the internal electric field on the applied field and the ionic strength of the medium. In this work, we will analyze the electric-field distribution inside the bacterial photosynthetic reaction center from Rhodopseudomonas viridis, compare it with experimental results and with other theoretical work, and try to understand the possible biological consequences.
2. Method All calculations were done with the UHBD program developed in this laboratory. The program solves the linearized Poisson-Boltzmann equation using a finite-difference algorithm. The linearized Poisson-Boltzmann equation for polarizable media is
-v.[t(r)V~(r)l+E(r)KZ(r)~(r)=P(r)
9
where c is the permittivity, $ the electrostatic potential, K the Debye-Hilckel screening parameter delined as K*= e2n0jkgTc, e the electron charge, no the ionic concentration, kB the Boltzmann constant, T the temperature and p the charge density [ 2 5 1. When integrated over each small cubic cell where t and @ can be considered constant, -
f s
cd&V@+
I Y
fdI”K’@=
s Y
dVp,
the differential equation becomes a set of coupled
5 October 1990
difference equations that can be solved numerically:
where h is the area of the face of the cubic cell and ej the permittivity of the jth face, j runs over all of the faces of the cell: pi, et, Ki and qi are, respectively, the potential, the permittivity, the Debye-Htckel screening parameter and the charge inside the ith cubic cell [25-271. When a protein is divided into many small cubic cells, a large set of coupled linear equations needs to be solved. Luckily, this system of linear equations is very sparse, which permits a fast algorithm to be applied [ 271. We used a cell size of (2 A l3 for the reaction center of Rhodopseudomonas viridis. The coordinates of the reaction center are from an X-ray diffraction structure at a resolution of 2.3 A [ 28,291. The total number of cells is 863. The size of an atom in the protein was chosen to be its van der Waals sphere. Within this sphere the permittivity is 2, and outside it 78. The protein was immersed in a dielectric medium with a permittivity of 78 in order to model the conditions in which most experiments that we compared with were carried out; no lipid bilayer is present, although this could be included using the methods described here. The charges are from Jorgensen’s OPLS parameters [ 301.
3. Potentials for the cofactors at zero applied field The calculated potentials for the four heme groups in the cytochrome unit of the reaction center are plotted in fig. 1. The potential for each cofactor is the average potential at the atoms in the tt system, since the ILsystem is most likely to be involved in the electron transfer. For reference, the spatial relationship of the cofactors is shown in scheme 1. As can be seen from fig. 1, the potential goes up by about 2 kcal/ mole from Hml to Hm4, then drops at Hm3 by about 6 kcal/mol e. The order of the potentials supports the conclusion from electrochromism studies in C. vinosum that the low-potential heme should be the one that is closest to the special pair [ 91, but is different from the assignment by EPR measurement [ 111, which states that the closest heme should have the highest potential. If the potential is calculated at 241
Volume 173, number 2,3
CHEMICAL PHYSICS LETTERS
Applied
E = 0 (V/cm) X 10’
I
I
I
I
Hml
Hm2
Hm4
Hm3
I
I
I
I
Cofactors Fig. 1. Potential profile for the heme groups. Refer to scheme 1 in the text for the cofactor notation.
Hl
H3
PM. ,
FL
Scheme 1.
the Fe positions only, instead of averaging over the TCsystem, the relative order of the potential agrees qualitatively with the EPR assignment of a low-highlow-high sequence. Thus it seems that the potentials that are to be compared with the EPR experiments should be taken from the Fe positions only, since the EPR measurements are concerned with the iron, or 248
5 October 1990
the Aorbitals localized on the iron. Nevertheless, the calculated potential only reflects the contribution from the protein environment and thus cannot be strictly compared with EPR data, which is also related to the affinity of an electron to the quantummechanical II orbitals of the heme groups. Since one of the axial ligands in Hm3 is methionine, the redox potential can be greatly affected by the orientation of the sulphur lone pair relative to the d orbitals of the iron because of spin-density donation [ 3 1,321. The calculated potential profile is also different from that by Niedermeier and coworkers, who noted that, without taking into account the solvent screening effect, the net negative charges on the H subunit may strongly affect the potential of the adjacent protein medium [ 17,181. The potential gap between Hm4 and Hm3 of about 11 kcal/mol per unit charge, or 477 mV, is to be compared to the value by Niedermeier of around 40 kcal/mol e, or, 1700 mV, which is much larger than the EPR estimate of 480 mV [ 111. Recently, their research group also applied the linearized Poisson-Boltzmann technique with the solvent effect taken into account, and obtained a splitting much closer to the experimental value [ 39 1. Honig and coworkers also took into account the solvent effect, and obtained a profile very close to the experimental estimate [ 23 1. Our calculation of the potentials at the Fe positions agrees qualitatively with theirs, despite the fact that they used a different set of charge parameters. The difference in potentials in these heme groups is not caused by a single nearby residue, but is the result of the sum of small environmental differences around each group. For example, within a 5 A sphere centered at the Fe atom of either Hm2 or Hm3 there is the same number of charged 0, N and S atoms, but in the 5-6 8, shell there are two more charged nitrogen atoms from Arg 264 for Hm3, which contribute a net charge of - 0.1 (proton unit) with the OPLS parameters. Since a - 0.1 charge can produce a potential of more than 20 mV at 10 A in protein media, the small environmental differences around the heme groups can add up to the calculated 240 mV splitting. Fig. 2 shows the potential profile of the cofactors along the L and M branches in the reaction center. There is great similarity between the L branch (solid line), along which the electron transfer actually takes place, and the M branch. This is not surprising, since
5 October 1990
CHEMICAL PHYSICSLETTERS
Volume 173,number 2,3
Applied E = 0 (V/cm) X 10”
No Transmembrane
I
I
I
Helices,
I
E,= 0
I
f
1
y ’ \(g --_.
Cofactors
Cofactors
Fig. 2. Potential profile along the L (solid line) and the M (dashed line) branches. Referto scheme I in the text for the cofactor symbols. Q stands for QA in the L branch and Qe in the M branch. Other symbols are: P for the special pair, B for the bacteriochlorophyll, H for the bacteriopheophytin and Fe for the non-heme iron.
the two branches are related by a quasi C, symmetry axis and thus have similar environments. However, there is a small difference. The potential at the special pair and at the bacteriochlorophyll
L M
is lower along
the M branch than along the L branch about 4 and 1 kcal/mol e, respectively. The lower potential at bactcriochlorophyll may also diminish its involvement in the electron-transfer process. Thus the difference between the L and M branches might be due in part to the different potentials for the bacteriochlorophylls. The same conclusion was reached before by Warshel and Aqvist using a different methodology [ 221, but is opposite to that by Treutlein et al. [IS] who did not take solvent effects into account. On the other hand, the feature in fig. 2 is different from what has been calculated by Feher and coworkers. Their potential profile does not have a dip at the bacteriochlorophyll. The discrepancy might be due to the different charge parameters. Finally, the closeness in potential between QA and QB in fig. 2 indicates that the measured 340 meV or so difference [33,34] should come from the molecular orbitals of the two quinones, rather than from the protein environment. This conclusion is also corroborated by the estimated difference of -0.02 eV in energy, due to the protein medium around QAand QB, from the study of Michel-Beyerle and coworkers [ 35,361.
Fig. 3. Potential profile along the L (solid line) and the M (dashed line) branches as calculated without the presence of the ten rransmembranehelixes.
There is speculation that the dipole moments associated with the ten transmembrane helices facilitate the electron transfer along the L branch [ 28,371. To test this hypothesis, we calculated the potential profile without the presence of the ten transmembrane helices, shown in fig. 3. As can be seen, one of the roles of the transmembrane helices seems to be to lower the potential of the bacteriochlorophyll. This seems to suggest that the presence of the helices should slow down the electron transfer, if bacteriochlorophyll is involved in the electron transfer. However, this might be due to the increase of the solvent volume that was originally occupied by the helices. A realistic calculation should take this fact into account. But even without the presence of the transmembrane helices, there is still some similarity between the L and the M paths. Again, the inequality in potentials between the L and M paths is caused by the sum of many small environmental differences, as has been stated by Michel-Beyerle and coworkers [ 35,361.
4. Influence of the applied field Knowledge of how the internal field in the reaction center depends on the applied field is essential for analyzing Stark-effect spectroscopy data [ l-81. Our calculation, using the linearized Poisson-Boltz249
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CHEMICAL PHYSICS LETTERS
mann equation, will give the dependence only through the linear term. Thus the calculated internal field will vary linearly with the applied field. Fig. 4 shows the dependence of the z component of the internal field at various cofactors along the L branch on the applied field up to the experimental range of 1O6V/cm [ l-61. The applied field is parallel to the C, axis of the reaction center, the z axis is chosen to be parallel to the C, axis, and the x axis points from the M to the L subunit. At zero applied field, the z component of the internal field is stronger at the bacteriochlorophyll than at the special pair, and is antiparallel to that at the bacteriopheophytin. But the internal field at all these three cofactors changes linearly with the applied field in the same manner, i.e. with nearly the same proportionality constant. The proportionality constant for the special pair is slightly larger than that for the bacteriopheophytin. Since the atoms are treated as polarizable spheres with a permittivity of 2, the internal electric field Ei”felt inside the van der Waals spheres of these atoms can be related to the applied field I?, through [ 381
5 October 1990
where CFi,and E, are the dielectric constants inside the spheres and of the medium, respectively. With this model, the slope in fig. 4 gives an effective protein dielectric constant t,= 3.4. The fact that the effective medium dielectric constant is much smaller than the solvent dielectric constant 78 indicates that the free volume for the solvent is very small. This may be one of the reasons that the initial turnover current in a voltage clamp experiment, corresponding to the electron transfer from the special pair to the primary acceptor, is nearly independent of ionic strength, while the secondary current, corresponding to the transfer of electrons from cytochrome c outside the membrane to the reaction center, is strongly affected by salt concentration [ 12,131. Our calculation indicates that the protein medium is not isotropic. Fig. 5 is a plot of the x, y components of the internal field as a function of an external
Internal -41*o -41.2
E
at L Special Pair
I RX
67 ’ 0
I
I
I
1
I
2
4
6
6
10
Applied E (V/cm)
Applied E (V/cm) X 10’ Fig. 4. z component of the internal electric field as a function of an external field exerted along the Cz axis (zaxis) of the reaction center. The top graph is the internal field at the special pair, the middle at the bacteriochlorophyll, and the bottomat thebacteriopheophpin, along the L branch.
250
1
X 10’
Fig. 5. x and y components of the internal electric field as a function of an external field exerted along the Cz axis (z axis) of the reaction center. The x axis points from the M to the L subunit, and the XI plane is defined by the bacteriochlorophyll and the bacteriopheophytin groups in both the L and the M branches. The top graph is the x component and the bottom the y component of the internal electric field at the special pair (L branch).
Volume173,number 2,3
CHEMICALPHYSICSLETTERS
field, applied along the z direction, with z parallel to the C, axis of the protein and x pointing from the M to the L subunit direction. The xz plane cuts through the special pair, the bacteriochlorophylls and the bacteriopheophytins of both branches. As can be seen, there are appreciable induced x, y components in the protein medium. In other words, there are nonzero off-diagonal elements in the dielectric-constant tensor.
5. Dependence of the internal electric field on ionic strength To estimate the solvent volume that can contribute to screening effects due to ionic concentration, we calculated the potential profile in the presence of a monovalent salt at a concentration of 100 mM, the concentration at which many voltage clamp experiments were carried out [ 121. At this concentration the overall shape of the profile remains the same, but the potential gap between the highest and the lowest points is reduced from 28 to 23 kcal/mol e. Since the purpose of the calculation was to estimate the solvent effect inside the reaction center, the membrane was not included in this calculation. The membrane-protein interaction is significant, as has been demonstrated by Yeates et al. [ 241. In fig. 6, the logApplied E = 0 (V/cm) X 10’ I I I I
-
4.9
1
4,8 _---------_,__
P 2 x
-
PM --__
--__
--_
5 October 1990
arithm of the z component of the internal electric field at the special pair for zero applied field is plotted against the square root of the ionic concentration. This can be understood from the simple Debye-Hiickel theory, in which the internal field depends exponentially on the Debye-Htickel screening parameter K= eJ=. Thus the logarithm of the internal field varies linearly with the square root of the ionic concentration no. Fig. 6 shows this linear relationship, but the proportionality constant is much smaller (5 x I 0F3) than would be anticipated from Debye-Hiickel theory ( z 1). This again indicates that the free volume for solvent is very small.
6. Conclusion The electric-field distribution inside the bacterial photosynthetic reaction center from Rhodop,se&monad viridis shows remarkable similarity along the L and the M branches, a result of the C, symmetry related environment. The field produced from the ten transmembrane helices does not seem to favor the L branch at this linearized Poisson-Boltzmann level. The dependence of the internal field on applied and ionic strength indicates that the free volume for solvent that could effectively screen the field is small. The dielectric response of the protein medium to an applied field is anisotropic, with appreciable induced x and y components for an external field applied along the z direction. The discrepancy between the calculated potentials and experimental measurements at various cofactors indicate that a realistic comparison should include the contributions from both the protein medium and the chromophores.
Acknowledgement
0
2
4
6
SQRT [Ionic Concentration
8
10
(mM) ]
Fig. 6. Plot of logarithmof the z componentof the internal electric field at the specialpair as a function of the sq& root of the ionic concentration.
We thank Professor J. Deisenhofer of University of Texas Southwestern Medical Center at Dallas for providing us the 2.3 8, resolution coordinates of the bacterial photosynthetic reaction center Rhodopseudomonas viridis. This work has been supported in part by NSF, NIH, the Robert A. Welch Foundation, the Texas Advanced Research Program, the John von Neumann Center and the San Diego Supercomputer 251
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CHEMICAL PHYSICS LETTERS
Center. JAM is the recipient of the 1987 Hitchings Award from the Burroughs Wellcome Fund.
References [ I] D. deleeuv, M. Malley, G. Buttermann, M.Y. Okamura and G. Feher, Biophys. J. 37 (1982) 11la. [ 2 ] M. L&he, G. Feher and M.Y. Okamura, Proc. Nat]. Acad. Sci. US 84 (1987) 7537. [ 3 ] D.J. Lockhart and S.G. Boxer, Proc. Natl. Acad. Sci. US 85 (1988) 107; Chem. Phys. Letters 144 (1988) 243; Biochemistry 26 ( 1987) 664. [4] D.J. Lockhart, R.F. Goldstein and SC. Boxer, J. Chem. Phys. 89 (1988) 1408. [ 5 ] Z.D. Popovic, G.J. Kovacs, P.S. Vincett, G. Algeriaand P.L. Dutton, Biochim. Biophys. Acta 851 (1986) 38. [6] T.J. DiMagno, E.J. Bylina, A. Angerhofer, DC. Youvan and J.R. Norris, Biochemistry 29 ( 1990) 899. [7] S.H. Lin, C.Y. Yeh and G.Y.C. Wu, Chem. Phys. Letters 166 (1990) 195. [ 81 M. Bixon and J. Jortner, J. Phys. Chem. 92 ( 1988) 7 148. [9] G.D. Case and W.W. Parson, Biochim. Biophys. Acta 325 (1973) 441. [IO] K. Hashimoto, S. Itoh, K. Takamiya and M. Nishimura, J. Biochem.91 (1982) 1111. [ II] W. Nitschke and A.W. Rutherford, Biochemistry 28 ( 1989) 3161. [ 121N.K. Packham, P. Mueller and P.L. Dutton, B&him. Biophys. Acta 933 ( 1988) 70. [ 131H.N. van der Wal, R. van GrondeBe, F. Millett and D.B. Knaff, B&him. Biophys. Acta 893 (1987) 490. [ 141G. Feher, J.P. Allen, M.Y. Okamura and D.C. Rees, Nature 339(1989) 111 [ 15] M.L. Paddock, S.H. Rongey,G. Feherand M.Y.Okamura, Proc. Natl. Acad. Sci. US 86 (1989) 6602. [ 161J.P. Allen, G. Feher, T.G. Yeates, H. Komiya and DC. Rees, Proc. Nat]. Acad. Sci. US 85 (1988) 8487. [ 17] C. Niedermeier, Diploma&it, Technischen Universitat Miinchen ( 1989).
252
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[ 181H. Treutlein, K. Schulten, C. Niedermeier, J. Deisenhofer, H. Michel and D. DeVault, NATO ASI Series A 149 ( 1988) 369. [ 191S. Creighton, J.-K Hwan8 A. Warshel, W.W. Parson and J. Norris, Biochemistry 27 (1988) 774. [20] S.T. Russell and A. Warshel, J. Mol. Biol. 185 (1985) 389. [2 I] A. Warshel, S.T. Russell and AK. Churg, Proc. Natl. Acad. Sci. US 81 ( 1984) 4785. ]22] A. Warshel and J. Aqvist, Chem. Scripta 29A (1989) 75. [23]M.R. Gunner and B. Honig, in: Perspectives in photosynthesis, eds. J. Jortner and B. Pullman (Khtwer, Dordrecht, 1990) p. 53. [241 T.O. Yeates, H. Komiya, DC. Rees, J.P. Allen and G. Feher, Proc. Natl. Acad. Sci. US 84 (1987) 6438. [25] M.E. Davis and J.A. McCammon, Chem. Rev. 90 (1990) 509. [261 K Sharp and 6. Honig, Chem. Scripta 29A ( 1989) 7 I. [27] M.E. Davis and J.A. McCammon, J. Comput. Chem. 10 (1989) 386; 11 (1990) 401. [28] J. Deisenhofer, 0. Epp, K. Miki, R. Huber and H. Michel, Nature318 (1985) 618. [29] J. Deisenhofer and H. Michel, Science 245 (1989) 1463. [30] W.L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Sot. 110 (1988) 1657. [31] H. Senn, R.M. Keller and K. Wtithrich, Biochem. Biophys. Res. Commun. 92 (1980) 1362. [ 321 F.S. Mathews, Progr. Biophys. Mol. Biol. 45 ( 1985) I. [ 331 M.R. Gunner, Y. Liang, D.K. Nagus. R.M. Hochstrasser and D.L. Dutton, Biophys. J. 37 (1982) 226a. [34] A. Gopher, Y. Blatt, M. SchBnfeld, M.Y. Okamura and G. Feher, Biophys. J. 48 (1985) 311. [35] M.E. MichelBeyerle, M. Plato, J. Deisenhofer, H. Michel, M. Bixon and J. Jortner, B&him. Biophys. Acta 932 ( 1988) 52. [36] M. Plato, K. Mobius, M.E. Michel-Beyerle, M. Bixon and J. Jortner, J. Am. Chem. Sot. 110 (1988) 7279. [37] W.G.J. Hol, Progr. Biophys. Mol. Biol. 45 ( 1985) 149. [ 381 J.D. Jackson, Classical electrodynamics, 2nd Ed. (Wiley, NewYork, 1975) p. 151. I391 K. Schulten, private communication.
CHEMICAL PHYSICS LETTERS
5 October 1990
Electric-field distribution inside the bacterial photosynthetic reaction center of Rhodopseudomonas viridis Chong Zheng, Malcolm E. Davis and J. Andrew McCammon Department of Chemistry, Universityo,fHowon, Houston, TX 77204-5641, USA Received 16 April 1990; in tinal form 20 June 1990
The electric-field distribution inside the bacterial photosynthetic reaction center of Rhodopseudomonas uiridiswas obtained by solving the linearized Poisson-Boltzmann equation with a grid size of (2 A)‘. The order of potentials induced by the protein medium for the four heme groups in the cytochrome part is Hml: 310 mV, Hm2: 370 mV; Hm4: 380 mV, Hm3: 130 mV. The potential profile is similar along both the L and the M branches, a result of the C, symmetry related environment. In both the L and the M subunits, bacteriochlorophyll has the lowest potential. It is shown that the Poisson-Boltzmann method can also be used to analyze the variation of local fields inside proteins in response to applied fields. For the reaction center, the dielectric response to an applied field is anisotropic. There are significant induced x and y components of the internal field for an applied field along the z direction (the C, axis). Thus the effective dielectric-constant tensor of the protein medium has non-zero offdiagonal elements. Analysis of how the applied field and ionic strength influence the internal field indicates that there is relatively small screening due to free solvent in the complex. The difference between the potentials at various cofactors is due to the sum of small contributions from the protein environment, rather than a few charged residues.
1. Introduction Knowledge of the electric-field distribution inside the bacterial photosynthetic reaction center, and of how it changes with environmental influences such as applied fields and ionic strength, is indispensable for understanding the electron-transfer kinetics and the control of proton diffusion to the secondary quinone. For example, the interpretation of the Starkeffect spectroscopy data and the conclusion thereafter about the involvement of the intermediate L branch bacteriochlorophyll, B, in the electron-transfer process assumed that the internal electric field is linearly proportional to the applied field [ 1-7 1. The quantitative discrepancy between the theoretical prediction and the experimental results of the electric-field effects on the primary charge separation in the reaction center was attributed partly to the lack of detailed information on the internal electric-field distribution and its dependence on applied field [ 81. Theoretical interpretations are needed in order to help understand the results of electrochromism, kinetic and EPR measurements of the relative potentials of the cofactors in the reaction center [9-l 13. 246
Understanding of how the potential is influenced by the ionic strength of the adjacent aqueous medium will also help explain the facts that the primary current, corresponding to the electron transfer from the special pair to the primary quinone QA,is nearly independent of the ionic strength, and that the secondary current, corresponding to the subsequent electron transfer from cytochrome c outside the membrane to the special pair, is influenced strongly by the ionic strength of the medium [ 12,131. Finally, theoretical description of how protons diffuse to the secondary quinone QB requires detailed information on the electric-field distribution along the diffusion channel [ 14-161. Several research groups have calculated the electric-field distribution in the absence of applied fields. Niedermeier and coworkers summed Coulomb point charges calculated from MNDO and INDO methods to obtain the potentials for the cofactors [ 17,181. However, their treatment did not include the solvent effect. Warshel and coworkers developed a method which takes into account the contributions from both the permanent and the induced dipole moments in the protein [ 19-221. Using this method, they have
0009-2614/90/$ 03.50 0 1990 - Elsevier Science Publishers B.V. ( North-Holland )
CHEMICAL PHYSICS LETTERS
Volume 173, number 2,3
calculated the electrostatic free energy of the states along the reaction center. Honig and coworkers used the linearized Poisson-Boltzmann equation to calculate the electrostatic characteristics inside the reaction center [23]. Feher’s research group also calculated the electrostatic potential inside the reaction center by solving the finite-difference form of the Poisson equation [ 241. However, these previous theoretical works did not focus on the effects of the applied field and ionic strength. Our method is also of the linearized Poisson-Boltzmann type, which includes contributions of the permanent and induced dipole moments and the correction due to the finite size of the protein atoms, although implicitly through the use of dielectric constants for excluded atomic volume and solvent space. The method also allows the calculation of the dependence of the internal electric field on the applied field and the ionic strength of the medium. In this work, we will analyze the electric-field distribution inside the bacterial photosynthetic reaction center from Rhodopseudomonas viridis, compare it with experimental results and with other theoretical work, and try to understand the possible biological consequences.
2. Method All calculations were done with the UHBD program developed in this laboratory. The program solves the linearized Poisson-Boltzmann equation using a finite-difference algorithm. The linearized Poisson-Boltzmann equation for polarizable media is
-v.[t(r)V~(r)l+E(r)KZ(r)~(r)=P(r)
9
where c is the permittivity, $ the electrostatic potential, K the Debye-Hilckel screening parameter delined as K*= e2n0jkgTc, e the electron charge, no the ionic concentration, kB the Boltzmann constant, T the temperature and p the charge density [ 2 5 1. When integrated over each small cubic cell where t and @ can be considered constant, -
f s
cd&V@+
I Y
fdI”K’@=
s Y
dVp,
the differential equation becomes a set of coupled
5 October 1990
difference equations that can be solved numerically:
where h is the area of the face of the cubic cell and ej the permittivity of the jth face, j runs over all of the faces of the cell: pi, et, Ki and qi are, respectively, the potential, the permittivity, the Debye-Htckel screening parameter and the charge inside the ith cubic cell [25-271. When a protein is divided into many small cubic cells, a large set of coupled linear equations needs to be solved. Luckily, this system of linear equations is very sparse, which permits a fast algorithm to be applied [ 271. We used a cell size of (2 A l3 for the reaction center of Rhodopseudomonas viridis. The coordinates of the reaction center are from an X-ray diffraction structure at a resolution of 2.3 A [ 28,291. The total number of cells is 863. The size of an atom in the protein was chosen to be its van der Waals sphere. Within this sphere the permittivity is 2, and outside it 78. The protein was immersed in a dielectric medium with a permittivity of 78 in order to model the conditions in which most experiments that we compared with were carried out; no lipid bilayer is present, although this could be included using the methods described here. The charges are from Jorgensen’s OPLS parameters [ 301.
3. Potentials for the cofactors at zero applied field The calculated potentials for the four heme groups in the cytochrome unit of the reaction center are plotted in fig. 1. The potential for each cofactor is the average potential at the atoms in the tt system, since the ILsystem is most likely to be involved in the electron transfer. For reference, the spatial relationship of the cofactors is shown in scheme 1. As can be seen from fig. 1, the potential goes up by about 2 kcal/ mole from Hml to Hm4, then drops at Hm3 by about 6 kcal/mol e. The order of the potentials supports the conclusion from electrochromism studies in C. vinosum that the low-potential heme should be the one that is closest to the special pair [ 91, but is different from the assignment by EPR measurement [ 111, which states that the closest heme should have the highest potential. If the potential is calculated at 241
Volume 173, number 2,3
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E = 0 (V/cm) X 10’
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I
Hml
Hm2
Hm4
Hm3
I
I
I
I
Cofactors Fig. 1. Potential profile for the heme groups. Refer to scheme 1 in the text for the cofactor notation.
Hl
H3
PM. ,
FL
Scheme 1.
the Fe positions only, instead of averaging over the TCsystem, the relative order of the potential agrees qualitatively with the EPR assignment of a low-highlow-high sequence. Thus it seems that the potentials that are to be compared with the EPR experiments should be taken from the Fe positions only, since the EPR measurements are concerned with the iron, or 248
5 October 1990
the Aorbitals localized on the iron. Nevertheless, the calculated potential only reflects the contribution from the protein environment and thus cannot be strictly compared with EPR data, which is also related to the affinity of an electron to the quantummechanical II orbitals of the heme groups. Since one of the axial ligands in Hm3 is methionine, the redox potential can be greatly affected by the orientation of the sulphur lone pair relative to the d orbitals of the iron because of spin-density donation [ 3 1,321. The calculated potential profile is also different from that by Niedermeier and coworkers, who noted that, without taking into account the solvent screening effect, the net negative charges on the H subunit may strongly affect the potential of the adjacent protein medium [ 17,181. The potential gap between Hm4 and Hm3 of about 11 kcal/mol per unit charge, or 477 mV, is to be compared to the value by Niedermeier of around 40 kcal/mol e, or, 1700 mV, which is much larger than the EPR estimate of 480 mV [ 111. Recently, their research group also applied the linearized Poisson-Boltzmann technique with the solvent effect taken into account, and obtained a splitting much closer to the experimental value [ 39 1. Honig and coworkers also took into account the solvent effect, and obtained a profile very close to the experimental estimate [ 23 1. Our calculation of the potentials at the Fe positions agrees qualitatively with theirs, despite the fact that they used a different set of charge parameters. The difference in potentials in these heme groups is not caused by a single nearby residue, but is the result of the sum of small environmental differences around each group. For example, within a 5 A sphere centered at the Fe atom of either Hm2 or Hm3 there is the same number of charged 0, N and S atoms, but in the 5-6 8, shell there are two more charged nitrogen atoms from Arg 264 for Hm3, which contribute a net charge of - 0.1 (proton unit) with the OPLS parameters. Since a - 0.1 charge can produce a potential of more than 20 mV at 10 A in protein media, the small environmental differences around the heme groups can add up to the calculated 240 mV splitting. Fig. 2 shows the potential profile of the cofactors along the L and M branches in the reaction center. There is great similarity between the L branch (solid line), along which the electron transfer actually takes place, and the M branch. This is not surprising, since
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CHEMICAL PHYSICSLETTERS
Volume 173,number 2,3
Applied E = 0 (V/cm) X 10”
No Transmembrane
I
I
I
Helices,
I
E,= 0
I
f
1
y ’ \(g --_.
Cofactors
Cofactors
Fig. 2. Potential profile along the L (solid line) and the M (dashed line) branches. Referto scheme I in the text for the cofactor symbols. Q stands for QA in the L branch and Qe in the M branch. Other symbols are: P for the special pair, B for the bacteriochlorophyll, H for the bacteriopheophytin and Fe for the non-heme iron.
the two branches are related by a quasi C, symmetry axis and thus have similar environments. However, there is a small difference. The potential at the special pair and at the bacteriochlorophyll
L M
is lower along
the M branch than along the L branch about 4 and 1 kcal/mol e, respectively. The lower potential at bactcriochlorophyll may also diminish its involvement in the electron-transfer process. Thus the difference between the L and M branches might be due in part to the different potentials for the bacteriochlorophylls. The same conclusion was reached before by Warshel and Aqvist using a different methodology [ 221, but is opposite to that by Treutlein et al. [IS] who did not take solvent effects into account. On the other hand, the feature in fig. 2 is different from what has been calculated by Feher and coworkers. Their potential profile does not have a dip at the bacteriochlorophyll. The discrepancy might be due to the different charge parameters. Finally, the closeness in potential between QA and QB in fig. 2 indicates that the measured 340 meV or so difference [33,34] should come from the molecular orbitals of the two quinones, rather than from the protein environment. This conclusion is also corroborated by the estimated difference of -0.02 eV in energy, due to the protein medium around QAand QB, from the study of Michel-Beyerle and coworkers [ 35,361.
Fig. 3. Potential profile along the L (solid line) and the M (dashed line) branches as calculated without the presence of the ten rransmembranehelixes.
There is speculation that the dipole moments associated with the ten transmembrane helices facilitate the electron transfer along the L branch [ 28,371. To test this hypothesis, we calculated the potential profile without the presence of the ten transmembrane helices, shown in fig. 3. As can be seen, one of the roles of the transmembrane helices seems to be to lower the potential of the bacteriochlorophyll. This seems to suggest that the presence of the helices should slow down the electron transfer, if bacteriochlorophyll is involved in the electron transfer. However, this might be due to the increase of the solvent volume that was originally occupied by the helices. A realistic calculation should take this fact into account. But even without the presence of the transmembrane helices, there is still some similarity between the L and the M paths. Again, the inequality in potentials between the L and M paths is caused by the sum of many small environmental differences, as has been stated by Michel-Beyerle and coworkers [ 35,361.
4. Influence of the applied field Knowledge of how the internal field in the reaction center depends on the applied field is essential for analyzing Stark-effect spectroscopy data [ l-81. Our calculation, using the linearized Poisson-Boltz249
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CHEMICAL PHYSICS LETTERS
mann equation, will give the dependence only through the linear term. Thus the calculated internal field will vary linearly with the applied field. Fig. 4 shows the dependence of the z component of the internal field at various cofactors along the L branch on the applied field up to the experimental range of 1O6V/cm [ l-61. The applied field is parallel to the C, axis of the reaction center, the z axis is chosen to be parallel to the C, axis, and the x axis points from the M to the L subunit. At zero applied field, the z component of the internal field is stronger at the bacteriochlorophyll than at the special pair, and is antiparallel to that at the bacteriopheophytin. But the internal field at all these three cofactors changes linearly with the applied field in the same manner, i.e. with nearly the same proportionality constant. The proportionality constant for the special pair is slightly larger than that for the bacteriopheophytin. Since the atoms are treated as polarizable spheres with a permittivity of 2, the internal electric field Ei”felt inside the van der Waals spheres of these atoms can be related to the applied field I?, through [ 381
5 October 1990
where CFi,and E, are the dielectric constants inside the spheres and of the medium, respectively. With this model, the slope in fig. 4 gives an effective protein dielectric constant t,= 3.4. The fact that the effective medium dielectric constant is much smaller than the solvent dielectric constant 78 indicates that the free volume for the solvent is very small. This may be one of the reasons that the initial turnover current in a voltage clamp experiment, corresponding to the electron transfer from the special pair to the primary acceptor, is nearly independent of ionic strength, while the secondary current, corresponding to the transfer of electrons from cytochrome c outside the membrane to the reaction center, is strongly affected by salt concentration [ 12,131. Our calculation indicates that the protein medium is not isotropic. Fig. 5 is a plot of the x, y components of the internal field as a function of an external
Internal -41*o -41.2
E
at L Special Pair
I RX
67 ’ 0
I
I
I
1
I
2
4
6
6
10
Applied E (V/cm)
Applied E (V/cm) X 10’ Fig. 4. z component of the internal electric field as a function of an external field exerted along the Cz axis (zaxis) of the reaction center. The top graph is the internal field at the special pair, the middle at the bacteriochlorophyll, and the bottomat thebacteriopheophpin, along the L branch.
250
1
X 10’
Fig. 5. x and y components of the internal electric field as a function of an external field exerted along the Cz axis (z axis) of the reaction center. The x axis points from the M to the L subunit, and the XI plane is defined by the bacteriochlorophyll and the bacteriopheophytin groups in both the L and the M branches. The top graph is the x component and the bottom the y component of the internal electric field at the special pair (L branch).
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CHEMICALPHYSICSLETTERS
field, applied along the z direction, with z parallel to the C, axis of the protein and x pointing from the M to the L subunit direction. The xz plane cuts through the special pair, the bacteriochlorophylls and the bacteriopheophytins of both branches. As can be seen, there are appreciable induced x, y components in the protein medium. In other words, there are nonzero off-diagonal elements in the dielectric-constant tensor.
5. Dependence of the internal electric field on ionic strength To estimate the solvent volume that can contribute to screening effects due to ionic concentration, we calculated the potential profile in the presence of a monovalent salt at a concentration of 100 mM, the concentration at which many voltage clamp experiments were carried out [ 121. At this concentration the overall shape of the profile remains the same, but the potential gap between the highest and the lowest points is reduced from 28 to 23 kcal/mol e. Since the purpose of the calculation was to estimate the solvent effect inside the reaction center, the membrane was not included in this calculation. The membrane-protein interaction is significant, as has been demonstrated by Yeates et al. [ 241. In fig. 6, the logApplied E = 0 (V/cm) X 10’ I I I I
-
4.9
1
4,8 _---------_,__
P 2 x
-
PM --__
--__
--_
5 October 1990
arithm of the z component of the internal electric field at the special pair for zero applied field is plotted against the square root of the ionic concentration. This can be understood from the simple Debye-Hiickel theory, in which the internal field depends exponentially on the Debye-Htickel screening parameter K= eJ=. Thus the logarithm of the internal field varies linearly with the square root of the ionic concentration no. Fig. 6 shows this linear relationship, but the proportionality constant is much smaller (5 x I 0F3) than would be anticipated from Debye-Hiickel theory ( z 1). This again indicates that the free volume for solvent is very small.
6. Conclusion The electric-field distribution inside the bacterial photosynthetic reaction center from Rhodop,se&monad viridis shows remarkable similarity along the L and the M branches, a result of the C, symmetry related environment. The field produced from the ten transmembrane helices does not seem to favor the L branch at this linearized Poisson-Boltzmann level. The dependence of the internal field on applied and ionic strength indicates that the free volume for solvent that could effectively screen the field is small. The dielectric response of the protein medium to an applied field is anisotropic, with appreciable induced x and y components for an external field applied along the z direction. The discrepancy between the calculated potentials and experimental measurements at various cofactors indicate that a realistic comparison should include the contributions from both the protein medium and the chromophores.
Acknowledgement
0
2
4
6
SQRT [Ionic Concentration
8
10
(mM) ]
Fig. 6. Plot of logarithmof the z componentof the internal electric field at the specialpair as a function of the sq& root of the ionic concentration.
We thank Professor J. Deisenhofer of University of Texas Southwestern Medical Center at Dallas for providing us the 2.3 8, resolution coordinates of the bacterial photosynthetic reaction center Rhodopseudomonas viridis. This work has been supported in part by NSF, NIH, the Robert A. Welch Foundation, the Texas Advanced Research Program, the John von Neumann Center and the San Diego Supercomputer 251
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CHEMICAL PHYSICS LETTERS
Center. JAM is the recipient of the 1987 Hitchings Award from the Burroughs Wellcome Fund.
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[ 181H. Treutlein, K. Schulten, C. Niedermeier, J. Deisenhofer, H. Michel and D. DeVault, NATO ASI Series A 149 ( 1988) 369. [ 191S. Creighton, J.-K Hwan8 A. Warshel, W.W. Parson and J. Norris, Biochemistry 27 (1988) 774. [20] S.T. Russell and A. Warshel, J. Mol. Biol. 185 (1985) 389. [2 I] A. Warshel, S.T. Russell and AK. Churg, Proc. Natl. Acad. Sci. US 81 ( 1984) 4785. ]22] A. Warshel and J. Aqvist, Chem. Scripta 29A (1989) 75. [23]M.R. Gunner and B. Honig, in: Perspectives in photosynthesis, eds. J. Jortner and B. Pullman (Khtwer, Dordrecht, 1990) p. 53. [241 T.O. Yeates, H. Komiya, DC. Rees, J.P. Allen and G. Feher, Proc. Natl. Acad. Sci. US 84 (1987) 6438. [25] M.E. Davis and J.A. McCammon, Chem. Rev. 90 (1990) 509. [261 K Sharp and 6. Honig, Chem. Scripta 29A ( 1989) 7 I. [27] M.E. Davis and J.A. McCammon, J. Comput. Chem. 10 (1989) 386; 11 (1990) 401. [28] J. Deisenhofer, 0. Epp, K. Miki, R. Huber and H. Michel, Nature318 (1985) 618. [29] J. Deisenhofer and H. Michel, Science 245 (1989) 1463. [30] W.L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Sot. 110 (1988) 1657. [31] H. Senn, R.M. Keller and K. Wtithrich, Biochem. Biophys. Res. Commun. 92 (1980) 1362. [ 321 F.S. Mathews, Progr. Biophys. Mol. Biol. 45 ( 1985) I. [ 331 M.R. Gunner, Y. Liang, D.K. Nagus. R.M. Hochstrasser and D.L. Dutton, Biophys. J. 37 (1982) 226a. [34] A. Gopher, Y. Blatt, M. SchBnfeld, M.Y. Okamura and G. Feher, Biophys. J. 48 (1985) 311. [35] M.E. MichelBeyerle, M. Plato, J. Deisenhofer, H. Michel, M. Bixon and J. Jortner, B&him. Biophys. Acta 932 ( 1988) 52. [36] M. Plato, K. Mobius, M.E. Michel-Beyerle, M. Bixon and J. Jortner, J. Am. Chem. Sot. 110 (1988) 7279. [37] W.G.J. Hol, Progr. Biophys. Mol. Biol. 45 ( 1985) 149. [ 381 J.D. Jackson, Classical electrodynamics, 2nd Ed. (Wiley, NewYork, 1975) p. 151. I391 K. Schulten, private communication.