Progress of Theoretical Physics Supplement No. 138, 2000 107 A molecular-dynamics study of the rhodopsin chromophore using ultrasoft pseudopotentials Minoru Sugihara, 1 ) Peter Entel, 1 Hendrik Meyer, 2 Volker Buss, 3 Frank Terstegen, 4 and Jürgen Hafner 5 1 Theoretical Physics, University of Duisburg, 47048 Duisburg, Germany 2 Max-Planck Institute for Polymer Science, 55128 Mainz, Germany 3 Theoretical Chemistry, University of Duisburg, 47048 Duisburg, Germany 4 Theoretical Chemistry, University of Zürich, 8057 Zürich, Switzerland 5 Materials Physics Institute, University of Vienna, 1090 Vienna, Austria (Received October 11, 1999) We investigate the effect of different environments on the chromophore of the protein rhodopsin by using the Vienna ab initio simulation package which is based on Density Functional Theory with a plane wave basis set and the implementation of Vanderbilt s ultrasoft pseudopotentials. We have calculated the energy dependence of 11-cis-retinal on the - double bond twist angle in the ground state and our results show that the isomerization in the ground state of the retinal chromophore is more difficult in the presence of the counter ion than without it. 1. Introduction Rhodopsin is a membrane protein, which is responsible for black and white vision in the vertebrate eye. 1) It consists mainly of seven so-called transmembrane helices which form a pocket. It was established that the visual pigment rhodopsin contains as chromophore 11-cis-retinal protonated Schiff base 2) and the visual process is initiated by the photochemical isomerization of 11-cis to all-trans. The isomerization eventually leads to the chemical signal of a nerve impulse sent to the brain which enables us to see. Of all double bonds in the molecule which can theoretically undergo cis-trans isomerization, only the - double bond is affected by the action of light: When rhodopsin absorbs light of 500 nm the chromophore makes a Franck-Condon transition into the first excited singlet state where it isomerizes to the all-trans isomer bathorhodopsin, a process which is complete within 200 fs. On the other hand, the dark-isomerization of the chromophore occurs in the ground state. The isomerization of this thermally activated event requires activation energies in the range of 0.99 ev/molecule (23 kcal/mol) to 1.17 ev/molecule (27 kcal/mol), which is significantly less than the energy of 1.95 ev/molecule (45 kcal/mol) required for the photoisomerization. 3), 4) In this work we have addressed the question whether the dark-isomerization of 11-cis-retinal Schiff base is easier in the protonated or in the deprotonated form. We have calculated the energy dependence of the molecule on the - double bond twist angle in the ground state, and we have also investigated the effect of the environment on the - bond of ) E-mail address: minoru@thp.uni-duisburg.de typeset using PTPTEX.sty <ver.1.0>
108 M. Sugihara, P. Entel, H. Meyer, V. Buss, F. Terstegen, and J. Hafner the chromophore. We have used thevienna ab initio simulation package (VASP) which is a program designed for molecular-dynamics (MD) simulations based on Density Functional Theory. It uses a plane wave basis set and Vanderbilt s ultrasoft pseudopotentials. All calculations are performed for a periodic supercell and the details are described in the publication of its authors. 5) 2. Simulation of 11-cis-retinal Figure 1 shows the structure of the 11-cis-retinal protonated Schiff base. The chromophore of rhodopsin is connected via amino acid Lys-296 to the protein. The nitrogen atom is protonated, and thus the chromophore has a net positive charge. In the simulation we assume for simplicity a uniform background charge of -e per unit cell to achieve charge neutrality. Figure 2 shows the structure of the 11-cis-retinal protonated Schiff base with a counter ion HCOO and one water molecule. The counter ion models part of the amino acid Glu-113. This is the simplest structure where the proton can move from the nitrogen via the water molecule to a negatively charged counter ion HCOO. The whole structure is electrically neutral. Both the protonated Schiff base and the base with HCOO and H 2 O have been optimized by the restricted Hartree-Fock method (Gaussian 98). 6), 7) + N Fig. 1. 11-cis-retinal protonated Schiff base. N + Fig. 2. 11-cis-retinal protonated Schiff base with counter ion HCOO and H 2O. Figure 3 shows the total energy change of these structures as the retinal molecule is twisted about the - bond. The calculation has been done in a 22 12 12 Å 3 simulation box and one k-point (Γ -point only). The cut-off energy was 260 ev. Because of the many atoms which constitute the chromophore, the system
A molecular-dynamics study of the rhodopsin chromophore 109 Energy (ev/molecule) 0.05 0.04 0.03 0.02 0.01 0.0 0 5 10 15 - twist angle Fig. 3. With VASP calculated relative energies of 11-cis-retinal protonated Schiff base without (dotted lines) and with (solid lines) couter ion HCOO and a water molecule as a function of the - cis-double bond twist angle. Squares correspond to the protonated species, circles to the deprotonated species, where the proton is attached to the water molecule. 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Energy (kcal/mol) has many meta-stable structures. In order to obtain the optimized conformation of the molecule, MD simulations with a time step of 0.5 fs have been done for all arrangements (with and without counter ion and also for the case when the twist angle has been fixed) and for a efficiently long time ( 600 fs) at temperature of 2 K. Considering the isolated molecule first, the calculations show that the protonated Schiff base twists around the - bond more easily than the de-protonated Schiff base. This is a consequence of the protonation of the nitrogen atom and the fact that the double bond character of the - bond is decreased compared to the deprotonated form. When the counter ion and the water molecule are added to the chromophore, the character of the - bond is changed. Figure 3 shows that there is no energy difference between the protonated and the de-protonated Schiff bases. The counter ion seems to give back charge to the chromophore. The calculated results by Gaussian 98 also show the same effect of the counter ion and a water molecule. 8) 3. Discussion: HOMO and LUMO analysis Figures 4 and 5 show the electron charge density distribution of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the 11-cis-retinal protonated Schiff base. The charge in the HOMO is mainly localized on the double bonds, except for the - bond, a consequence of the protonation of the nitrogen atom. On the other hand, the charge in the LUMO resides mainly on the single bonds. Figures 6 and 7 show the corresponding charge distribution for the 11-cis-retinal protonated Schiff base with counter ion HCOO and H 2 O. When the counter ion and
110 M. Sugihara, P. Entel, H. Meyer, V. Buss, F. Terstegen, and J. Hafner Fig. 4. HOMO electron charge density distribution of 11-cis-retinal protonated Schiff base. Fig. 5. LUMO electron charge density distribution of 11-cis-retinal protonated Schiff base. Fig. 6. HOMO electron charge density distribution of 11-cis-retinal protonated Schiff base with counter ion HCOO and H 2O.
A molecular-dynamics study of the rhodopsin chromophore 111 Fig. 7. LUMO electron charge density distribution of 11-cis-retinal protonated Schiff base with counter ion HCOO and H 2O. Fig. 8. HOMO electron charge density distribution of 11-cis-retinal de-protonated Schiff base. Fig. 9. HOMO electron charge density distribution of 11-cis-retinal de-protonated Schiff base with counter ion HCOO and H 2O. the water molecule are added to the chromophore, significant changes are observed. In particular the - bond in the HOMO acquires significant charge density becoming more like a double-bond. On the other hand, the LUMO charge densities don t change significantly and remain concentrated mainly on the single bonds. This means that the counter ion gives back negative charge to the chromophore and that
112 M. Sugihara, P. Entel, H. Meyer, V. Buss, F. Terstegen, and J. Hafner the isomerization of the chromophore in the ground state becomes more difficult. H. de Groot and co-workers have simulated the 11-cis to all-trans isomerization with a Car-Parrinello ab initio MD. 9) In their simulation, the counter ion is a chloride ion (Cl ) instead of the more realistic counter ion HCOO and H 2 O. As consequence, the - bond of their HOMO electron charge distribution is still single-bond like and very similar to the HOMO electron charge distribution of isolated 11-cisretinal. 10) We conclude that the ground state isomerization of protonated Schiff base is more difficult in the presence of a counter ion: As a consequence the environment of the chromophore has to be taken into account when studying the isomerization process. Fig. 8 and 9 show the corresponding charge distribution for the 11-cis-retinal deprotonated Schiff base without and with couter ion HCOO and H 2 O. The change in the HOMO of - of the de-protonated Schiff base is double-bond like. There is no significant effect of the counter ion and the water molecule in the de-protonated case. In this work the ground state properties of 11-cis-retinal have been studied by ab initio MD. We have investigated the effect of the environment on the - bond of 11-cis-retinal Schiff base. Our results show the significance of the counter ion on the - bond, rendering the isomerization of the retinal chromophore in the ground state more difficult. The calculated HOMO and LUMO electron charge density distributions support our conclusion. Acknowledgements This work has been supported by the Graduate College Structure and Dynamics of Heterogeneous Systems and by the Sonderforschungsbereich 445 on Nanoparticles from the Gas Phase: Nucleation, Characterization and Properties. References 1) R. R. Birge, Biochem. Biophys. Acta 293 (1990), 1016. 2) G. Wald, Science 162 (1968), 230. 3) R. R. Birge, Biochem. Biophys. Acta 1016 (1990), 293. 4) R. B. Barlow, R. R. Birge, E. Kapian, and J. R, Tallent, Nature 366 (1993), 64. 5) G. Kresse and J. Furthmüller, Phys. Rew. B 54 (1996), 11 169. 6) F. Terstegen and V. Buss, J. Mol. Struct. (Theochem) 369 (1996), 53. 7) F. Terstegen and V. Buss, unpublished. 8) F. Terstegen, private communication. 9) F. Buda, H. J. M. de Groot, and A. Bifone, Phys. Rev. Lett. 77 (1996), 4474. 10) A. Bifone, H. J. M. degroot, andf. Buda, J. Phys. Chem. B101 (1997), 2954.