Aborted double bicycle-pedal isomerization with hydrogen bond ...

Aborted double bicycle-pedal isomerization with hydrogen bond breaking is the primary event of bacteriorhodopsin proton pumping Piero Altoèa,1, Alessandro Cembrana,1,2, Massimo Olivuccib,c,3, and Marco Garavellia,3 a Dipartimento di Chimica “G. Ciamician,” Università di Bologna, via Selmi 2, Bologna, I-40126 Italy; bDipartimento di Chimica, Università di Siena, via De Gasperi 2, Siena, I-53100 Italy; and cChemistry Department, Bowling Green State University, Bowling Green, OH 43403

Edited by Michael Robb, Imperial College, London, United Kingdom, and accepted by the Editorial Board September 22, 2010 (received for review May 20, 2010)

Quantum mechanics/molecular mechanics calculations based on ab initio multiconfigurational second order perturbation theory are employed to construct a computer model of Bacteriorhodopsin that reproduces the observed static and transient electronic spectra, the dipole moment changes, and the energy stored in the photocycle intermediate K. The computed reaction coordinate indicates that the isomerization of the retinal chromophore occurs via a complex motion accounting for three distinct regimes: (i) production of the excited state intermediate I, (ii) evolution of I toward a conical intersection between the excited state and the ground state, and (iii) formation of K. We show that, during stage ii, a space-saving mechanism dominated by an asynchronous double bicycle-pedal deformation of the C10 ═ C11 ─ C12 ═ C13 ─ C14 ═ N moiety of the chromophore dominates the isomerization. On this same stage a N ─ H∕water hydrogen bond is weakened and initiates a breaking process that is completed during stage iii. photoisomerization ∣ quantum mechanics/molecular mechanics (QM/MM) ∣ retinal proteins

T

he light-activated proton pump bacteriorhodopsin (bR) is an Archaea receptor contained in the purple membrane of Halobacterium salinarium. As shown in Scheme 1, upon photoexcitation, the all-trans retinal chromophore (PSBT) bounded to Lys216 via a protonated Schiff base linkage is converted to the 13-cis isomer (PSB13). This event triggers a series of conformational changes that ultimately result in a proton translocation from the cytoplasmic to the extracellular domain (1). The bR protein environment affects both the spectroscopic and photochemical properties of PSBT (2–4). First, the absorption maximum (568 nm) is red-shifted with respect to the one observed in solution (440 nm in methanol). Second, timeresolved spectroscopy reveals a dominant excited state lifetime component of 450 fs (5, 6) almost matching the 500-fs time scale for formation of the vibrationally hot primary photoproduct J (7, 8). In contrast, PSBT in solution features a biexponential decay dynamics with a dominant (ca. 10-fold longer) 2-ps component (9–11). Finally, although bR photoisomerizes stereoselectively (leading exclusively to PSB13) with high (ca. 67%) quantum yield (9, 12), irradiation of PSBT in solution leads to a mixture of different stereoisomers with a smaller (ca. 25%) total quantum yield (9, 13). Low-temperature spectroscopic studies provided evidence for the existence of a tiny (≤1 kcal mol−1 ) energy barrier on the excited state (S1 ) potential energy surface of bR (14, 15). Such a barrier would explain the 450-fs short-lived quasistationary state observed by Ruhman et al. (5) that is assigned to the fluorescent state I (16–18) and precedes decay to the ground state (S0 ). Recent experiments by Léonard et al. (19) have also revealed that the photoinduced changes in the permanent dipole moment of PSBT are mirrored by the absorption of Trp86 up to the first stable (i.e., cryogenically trapped) photoproduct K (7). Relative to bR, K bears 11.7–15.9 kcal mol−1 stored photon energy (20). 20172–20177 ∣ PNAS ∣ November 23, 2010 ∣ vol. 107 ∣ no. 47

9

11

13

9

+ N H

11

h

13

+

Lys216

N H

500fs

PSB13

PSBT

Lys216

Scheme 1.

The investigation of the photoisomerization mechanism of bR is of great interest because this receptor is the archetypal ion pump machine. Its comprehension may open previously undescribed perspectives for the use of bR in nanotechnology or for the design of unique molecular devices (21, 22). In recent years numerous theoretical works, involving various hybrid quantum mechanics/molecular mechanics (QM/MM) approaches, have investigated the tuning of the spectroscopic properties of the retinal chromophore (23–28), the mechanism, stereoselectivity, and dynamics of its photoisomerization (29–32), and the energy storage (33). However, these studies have not yet delivered a coherent mechanistic scenario. For instance, the counterion effects on the spectroscopy of PSBT, as well as the mechanism of the PSBT space-saving photoisomerization, are not resolved. Our recent work on the retinal chromophore in vacuo (34, 35) shows that the CASPT2//CASSCF/6-31G* protocol yields balanced values for geometrical parameters, energy differences, spectroscopic properties, and change in dipole moment. Most important, it delivers an accurate description of the photochemically relevant potential energy surfaces (PESs). The same protocol has been successfully coupled with the AMBER molecular mechanics force field to investigate the photoisomerization of the visual pigment rhodopsin (Rh) (4, 36), returning energies that agree with the experiments. These studies support a two-state model for the retinal chromophore isomerization: the S1 path develops entirely along a charge transfer (i.e., hole-pair 1Bu -like) state and ends into a S1 ∕S0 conical intersection (CI) where the reacting double bond features a ca. −90° twisted structure. Because of its geometrical and electronic structure, this point is consistent with that of a twisted intramolecular charge transfer (TICT) state (34, 37). The analysis of the S1 isomerization coordinate along the minimum energy path reveals that this is sequentially dominated by different, almost uncoupled, modes. First, a stretching mode Author contributions: M.O. and M.G. designed research; P.A. and A.C. performed research; P.A., A.C., M.O., and M.G. analyzed data; and M.O. and M.G. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. M.R. is a guest editor invited by the Editorial Board. 1

P.A. and A.C. contributed equally to this work.

2

Present address: Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431.

3

To whom correspondence may be addressed. E-mail: [email protected], olivucci@ unisi.it, or [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/ doi:10.1073/pnas.1007000107/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1007000107

1.1 Chromophore Structure and Absorption Maximum. The optimized S0 bR structure (see Fig. 1) displays a −160° value of the PBST C12 ─ C13 ─ C14 ─ C15 dihedral angle corresponding to a 20° clockwise twisted C13 ═ C14 double bond. In contrast, the PSBT structure optimized in vacuo is planar (45). The bR C13 ═ C14 pretwist is larger than the one observed for the reactive bond of Rh (4, 36) and bias the photoisomerization in the clockwise direction (as detailed by the computed path; see below). This suggests that the stereoselectivity observed in bR (see, e.g., ref. 31) is decided by the asymmetry of the protein cavity that tilts the S1 PES in order to favor a unidirectional C13 ═ C14 photoisomerization. The computed 53.6 kcal mol−1 (534 nm) required for the vertical π → π
spectroscopically allowed (f ¼ 0.411) S0 → S1 transition in bR compare well with the experimental value of 50.3 kcal mol−1 (568 nm); see Fig. 2. This value is blue-shifted (þ6.9 kcal mol−1 ) as compared to that computed in vacuo (see SI Text for details). This effect agrees with previously reported values by Rajamani and Gao (∼4 kcal mol−1 ) (23), Vreven and Morokuma (2–6 kcal mol−1 ) (30), and Houjou et al. (∼7 kcal mol−1 ), (24, 25) and is due to electrostatic destabilization of the S1 state by the protein (2, 46). The blue-shift effect due to the complex counterion (Asp85, Asp212, Arg82) alone is much higher (þ20.1 kcal mol−1 for the bare chromophore/counterion pair with respect to vacuo; see SI Text), revealing that the protein has a high shielding effect (ca. 65%). This conclusion is consistent with previous computational studies on Rh (4). A consequence of the above results is that the opsin-shift observed when going from solvent (440 nm) to bR (570 nm) (ca. −13 kcal mol−1 ) is mainly due to (i) the binding pocket structure that forces the β-ionone

1.48 (161) 1.43 (163) 1.48 (163)

1.47 (-168) 1.39 (-172) 1.47 (-169)

1.2 Excited State Intermediates and Transient Spectroscopy. The PSBT displacement occurring after photoexcitation leads from the FC region to a shallow S1 minimum displaying bond order inversion and a negligible twisting of the reactive C13 ═ C14 double bond (see Fig. 1). This structure is assigned to the fluorescent state I (5, 6). The corresponding computed and observed transition energies agree within 1–2 kcal mol−1 (see Fig. 2): (i) The ∼740 nm (38.6 kcal mol−1 ) fluorescence maximum observed by Schenkl et al. (16) is matched by the 37.6 kcal mol−1 (761 nm) energy gap computed for the S1 → S0 transition at this point. (ii) Hasson et al. (14) described a transient near-IR absorption peaking at 850 nm (i.e., 33.6 kcal mol−1 ). This band can be attributed to the significantly allowed S1 → S3 transition, which is computed to be 35.9 kcal mol−1 (797 nm). (iii) Finally, the transient absorption in the visible seen by Logunov et al. (47) and peaking at 490 nm (i.e., 58.3 kcal mol−1 ) can be assigned to the S1 → S4 transition, which shows an energy gap of 57.2 kcal mol−1 (500 nm) and a not negligible f . Notice that these properties are also consistent with the results of transient spectroscopic studies of artificial rhodopsins hosting a conformationally locked retinal analog (16–18). 1.3 Photoisomerization, Photoproduct Formation, and Retinal Dipole Moment Changes. The 60%) by the protein. The bR opsin-shift is due to an increased double-bond conjugation (in going from the skewed 6s-cis conformation in solvent to the fully planar 6s-trans in bR) and to an opsin-induced dumping of the counterion electrostatic effect. The bR photoisomerization mechanism involves three stages: (i) a backbone rearrangement leading to an inverted bond order intermediate I on S1 (first stage, ≤50 fs); (ii) the C13 ═ C14 torsion accompanied by concurrent twistings of the adjacent bonds allowing the system to proceed along a space-saving isomerization coordinate reaching the deactivation region; a chromophore-Nζ H∕W402 hydrogen bond breaking is also initiated during this stage (second stage, to ∼450 fs); (iii) the S0 relaxation leading to double-bond reconstitution and Nζ ─ Cε single bond twisting that result in an aborted bicycle-pedal progression and lead to the K state (third stage, till ∼3 ps). This final step is responsible for completing Nζ ─ H∕W402 hydrogen bond breaking that is one of the main contributions to the energy storage. 3. Computational Methods Consistently with previous works (4, 36, 50), the photoisomerization path is computed in terms of a relaxed scan (with the C13 ═ C14 twisting angle fixed at specified values) carried out using our recently developed QM/MM potential [the GAUSSIAN98 (60) and TINKER (61) suite of programs are employed]. The retinal, Schiff base nitrogen and attached ε-carbon atom (see Scheme 1) constitute the QM part of the system, described at the CASSCF/ 6-31G* level (with an active space of 12 π-electrons in 12 π-orbitals), whereas AMBER is used for all MM atoms. All QM atoms and MM atoms comprising the Lys-216 side chain (Cγ H2 , Cδ H2 , and Cβ H2 ) are free to relax, whereas the protein framework [PDB ID code 1C3W (62) is used] is kept fixed: We assumed that this has no time to change (i.e., full thermal equilibration is prevented) during the subpicosecond time scale of the bR primary photoinduced event investigated here, a view that is supported by the similarity recognized between the bR and K crystal structures (see Fig. 5). W402 may be an exception: Although it belongs (and is tightly bound via hydrogen bonding) to the complex counterion (see Fig. 5), possibly limiting its motion, nevertheless it also directly/strongly interacts (via hydrogen bond) with the chromophore and can respond to its changes. Therefore, two sets of computations were employed to compute the path with a locked/ unlocked W402, respectively, which eventually delivered the same mechanistic outcome (see Fig. 4A and SI Text). This validates the fixed W402 model, which the results reported in this work are generally referred to. The employed crystallographic structure is considered as a mean representation of the experimental position of the atoms (although at low temperature), and the computed path portrays a mean static view of the process. This approach to ultrafast photoinduced reactions has been already employed successfully to study the Rh primary event (4, 36, 43, 50). Multiconfigurational second-order perturbation theory computations [carried out with the CASPT2 (63) method using the MOLCAS5 (63) package] are then used to increase the accuracy of the energy profiles. Whenever possible, a single state approach is employed. Otherwise, when root flipping occurs, a state average procedure (by equally weighting the first five singlet roots) is used, together with a multistate approach (MS-CASPT2) (64) when required. Oscillator strengths (f ) are computed using correlated (CASPT2) energies within the RASSI approach (65). See SI Text for further details on computations and protein setup. ACKNOWLEDGMENTS. M.G. is grateful to Prof. Stefan Haacke for useful discussions. M.O. is grateful to the Center for Photochemical Sciences and the College of Arts and Sciences for start-up funding. This research has been sup-

Altoè et al.

1. Oesterhelt D, Stoechenius W (1971) Rhodopsin-like protein from the purple membrane of Halobacterium halobium. Nature New Biol 233:149–152. 2. Cembran A, Bernardi F, Olivucci M, Garavelli M (2004) Counterion controlled photoisomerization of retinal chromophore models: A computational investigation. J Am Chem Soc 126:16018–16037. 3. Coto PB, Strambi A, Ferré N, Olivucci M (2006) The color of rhodopsins at the ab initio multiconfigurational perturbation theory resolution. Proc Natl Acad Sci USA 103:17154–17159. 4. Tomasello G, et al. (2009) Electrostatic control of the photoisomerization efficiency and optical properties in visual pigments: On the role of counterion quenching. J Am Chem Soc 131:5172–5186. 5. Ruhman S, Hou BX, Friedman N, Ottolenghi M, Sheves M (2002) Following evolution of bacteriorhodopsin in its reactive excited state via stimulated emission pumping. J Am Chem Soc 124:8854–8858. 6. Schmidt B, et al. (2005) Excited-state dynamics of bacteriorhodopsin probed by broadband femtosecond fluorescence spectroscopy. Biochim Biophys Acta 1706:165–173. 7. Dobler J, Zinth W, Kaiser W, Oesterhelt D (1988) Excited-state reaction dynamics of bacteriorhodopsin studied by femtosecond spectroscopy. Chem Phys Lett 144:215–220. 8. Mathies RA, Cruz CHB, Pollard WT, Shank CV (1988) Direct observation of the femtosecond excited-state cis-trans isomerization in bacteriorhodopsin. Science 240:777–779. 9. Hamm P, et al. (1996) Femtosecond spectroscopy of the photoisomerisation of the protonated Schiff base of all-trans retinal. Chem Phys Lett 263:613–621. 10. Logunov SL, Song L, El-Sayed MA (1996) Excited-state dynamics of a protonated retinal Schiff base in solution. J Phys Chem 100:18586–18591. 11. Kandori H, Katsuta Y, Ito M, Sasabe H (1995) Femtosecond fluorescence study of the rhodopsin chromophore in solution. J Am Chem Soc 117:2669–2670. 12. Kandori H, et al. (1996) Real-time detection of 60-fs isomerization in a rhodopsin analog containing eight-membered-ring retinal. J Am Chem Soc 118:1002–1005. 13. Freedman KA, Becker RS (1986) Comparative investigation of the photoisomerization of the protonated and unprotonated normal-butylamine Schiff-bases of 9-cis-retinals, 11-cis-retinals, 13-cis-retinals, and all-trans-retinals. J Am Chem Soc 108:1245–1251. 14. Hasson KC, Gai F, Anfinrud PA (1996) The photoisomerization of retinal in bacteriorhodopsin: Experimental evidence for a three-state model. Proc Natl Acad Sci USA 93:15124–15129. 15. Shapiro SL, et al. (1978) Picosecond and steady state, variable intensity and variable temperature emission spectroscopy of bacteriorhodopsin. Biophys J 23:383–393. 16. Schenkl F, et al. (2002) Ultrafast energy relaxation in bacteriorhodopsin studied by time-integrated fluorescence. Phys Chem Chem Phys 4:5020–5024. 17. Ye T, et al. (1999) On the nature of the primary light-induced events in bacteriorhodopsin: Ultrafast spectroscopy of native and C-13 ═ C-14 locked pigments. J Phys Chem B 103:5122–5130. 18. Zhong Q, et al. (1996) Reexamining the primary light-induced events in bacteriorhodopsin using a synthetic C-13 ═ C-14-locked chromophore. J Am Chem Soc 118:12828–12829. 19. Léonard J, et al. (2009) Functional electric field changes in photoactivated proteins revealed by ultrafast Stark spectroscopy of the Trp residues. Proc Natl Acad Sci USA 106:7718–7723. 20. Birge RR, et al. (1989) A spectroscopic, photocalorimetric, and theoretical investigation of the quantum efficiency of the primary event in bacteriorhodopsin. J Am Chem Soc 111:4063–4074. 21. Dugave C, Demange L (2003) Cis-trans isomerization of organic molecules and biomolecules: Implications and applications. Chem Rev 103:2475–2532. 22. Hampp N (2000) Bacteriorhodopsin as a photochromic retinal protein for optical memories. Chem Rev 100:1755–1776. 23. Rajamani R, Gao J (2002) Combined QM/MM study of the opsin shift in bacteriorhodopsin. J Comput Chem 23:96–105. 24. Houjou H, Inoue Y, Sakurai M (2001) Study of the opsin shift of bacteriorhodopsin: Insight from QM/MM calculations with electronic polarization effects of the protein environment. J Phys Chem B 105:867–879. 25. Houjou H, Inoue Y, Sakurai M (1998) Physical origin of the opsin shift of bacteriorhodopsin. Comprehensive analysis based on medium effect theory of absorption spectra. J Am Chem Soc 120:4459–4470. 26. Hayashi S, Ohmine I (2000) Proton transfer in bacteriorhodopsin: Structure, excitation, IR spectra, and potential energy surface analyses by an ab initio QM/MM method. J Phys Chem B 104:10678–10691. 27. Fujimoto K, Hasegawa JY, Hayashi S, Kato S, Nakatsuji H (2005) Mechanism of color tuning in retinal protein: SAC-CI and QM/MM study. Chem Phys Lett 414:239–242. 28. Fujimoto K, Hayashi S, Hasegawa JY, Nakatsuji H (2007) Theoretical studies on the color-tuning mechanism in retinal proteins. J Chem Theor Comput 3:605–618. 29. Vreven T, Morokuma K (2000) The ONIOM (our own N-layered integrated molecular orbital plus molecular mechanics) method for the first singlet excited (S-1) state photoisomerization path of a retinal protonated Schiff base. J Chem Phys 113:2969–2975. 30. Vreven T, Morokuma K (2003) Investigation of the S0 → S1 excitation in bacteriorhodopsin with the ONIOM(MO∶MM) hybrid method. Theor Chem Acc 109:125–132. 31. Hayashi S, Tajkhorshid E, Schulten K (2003) Molecular dynamics simulation of bacteriorhodopsin’s photoisomerization using ab initio forces for the excited chromophore. Biophys J 85:1440–1449. 32. Warshel A, Chu ZT (2001) Nature of the surface crossing process in bacteriorhodopsin: Computer simulations of the quantum dynamics of the primary photochemical event. J Phys Chem B 105:9857–9871.

33. Hayashi S, Tajkhorshid E, Kandori H, Schulten K (2004) Role of hydrogen-bond network in energy storage of bacteriorhodopsin’s light-driven proton pump revealed by ab initio normal-mode analysis. J Am Chem Soc 126:10516–10517. 34. González-Luque R, et al. (2000) Computational evidence in favor of a two-state, two-mode model of the retinal chromophore photoisomerization. Proc Natl Acad Sci USA 97:9379–9384. 35. Cembran A, González-Luque R, Serrano-Andrés L, Merchán M, Garavelli M (2007) About the intrinsic photochemical properties of the 11-cis retinal chromophore: Cmputational clues for a trap state and a lever effect in Rhodopsin catalysis. Theor Chem Acc 118:173–183. 36. Andruniów T, Ferré N, Olivucci M (2004) Structure, initial excited-state relaxation, and energy storage of rhodopsin resolved at the multiconfigurational perturbation theory level. Proc Natl Acad Sci USA 101:17908–17913. 37. Garavelli M, et al. (1998) Photoisomerization path for a realistic retinal chromophore model: The nonatetraeniminium cation. J Am Chem Soc 120:1285–1288. 38. Turro NJ (1991) Modern Molecular Photochemistry (Benjamin-Cummings, Menlo Park, CA). 39. Gilbert A, Baggott J (1991) Essentials of Molecular Photochemistry (Blackwell Science, Oxford UK). 40. Warshel A (1976) Bicycle-pedal model for the first step in the vision process. Nature 260:679–683. 41. Warshel A (1978) Energetics of enzyme catalysis. Proc Natl Acad Sci USA 75:5250–5254. 42. Schapiro I, Weingart O, Buss V (2009) Bicycle-pedal isomerization in a rhodopsin chromophore model. J Am Chem Soc 131:16–17. 43. Polli D, et al. (2010) Conical intersection dynamics of the primary photoisomerization event in vision. Nature 467:440–443. 44. Szymczak JJ, Barbatti M, Lischka H (2009) Is the photoinduced isomerization in retinal protonated Shiff bases a single- or double-torsional process? J Phys Chem A 113:11907–11918. 45. Cembran A, et al. (2005) Structure, spectroscopy, and spectral tuning of the gas-phase retinal chromophore: The beta-ionone “handle” and alkyl group effect. J Phys Chem A 109:6597–6605. 46. Cembran A, Bernardi F, Olivucci M, Garavelli M (2005) The retinal chromophore/ chloride ion pair: Structure of the photo isomerization path and interplay of charge transfer and covalent states. Proc Natl Acad Sci USA 102:6255–6260. 47. Logunov SL, Volkov VV, Braun M, El-Sayed MA (2001) The relaxation dynamics of the excited electronic states of retinal in bacteriorhodopsin by two-pump-probe femtosecond studies. Proc Natl Acad Sci USA 98:8475–8479. 48. Birge RR, Zhang C-F (1990) Two-photon double-resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low-lying 1Ag-like and 1Bu*(-)-like π,π* states. J Chem Phys 92:7178–7195. 49. Nielsen IB, Lammich L, Andersen LH (2006) S1 and S2 excited states of gas-phase Schiff-base retinal chromophores. Phys Rev Lett 96:018304. 50. Migani A, et al. (2004) Structure of the intersection space associated with Z/E photoisomerization of retinal in rhodopsin proteins. Faraday Discuss 127:179–191. 51. Schenkl F, et al. (2006) Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption. Proc Natl Acad Sci USA 103:4101–4106. 52. Liu RSH, Asato AE (1985) The primary process of vision and the structure of bathorhodopsin: Amechanism for photoisomerization of polyenes. Proc Natl Acad Sci USA 82:259–263. 53. Saltiel JPD, et al. (2009) Photoisomerization of all-cis-1,6-diphenyl-1,3,5-hexatriene in the solid state and in solution: Asimultaneous three-bond twist process. Angew Chem Int Edit 48:8082–8085. 54. Terentis AC, Ujj L, Abramczyk H, Atkinson GH (2005) Primary events in the bacteriorhodopsin photocycle: Torsional vibrational dephasing in the first excited electronic state. Chem Phys 313:51–62. 55. Hayashi S, Tajkhorshid E, Schulten K (2002) Structural changes during the formation of early intermediates in the bacteriorhodopsin photocycle. Biophys J 83:1281–1297. 56. Lanyi JK, Schobert B (2003) Mechanism of proton transport in bacteriorhodopsin from crystallographic structures of the K, L, M1 , M2 , and M2 0 intermediates of the photocycle. J Mol Biol 328:439–450. 57. Logunov SL, El-Sayed MA, Song L (1996) Photoisomerization quantum yield and apparent energy content of the K intermediate in the photocycles of bacteriorhodopsin, its mutants D85N, R82Q, and D212N, and deionized blue bacteriorhodopsin. J Phys Chem 100:2391–2398. 58. Birge RR, Cooper TM (1983) Energy storage in the primary step of the photocycle of bacteriorhodopsin. Biophys J 42:61–69. 59. Schulten K, Tavan P (1978) A mechanism for the light-driven proton pump of Halobacterium halobium. Nature 272:85–86. 60. Frisch MJ, et al. (1998) Gaussian98-Revision A.6 (Gaussian Inc.,, Pittsburgh, PA). 61. Ponder JW, Richards FM (1987) An efficient Newton-like method for molecular mechanics energy minimization of large molecules. J Comput Chem 8:1016–1024. 62. Luecke H, Schobert B, Richter H-T, Cartailler JP, Lanyi JK (1999) Structure of bacteriorhodopsin at 1.55 angstrom resolution. J Mol Biol 291:899–911. 63. Andersson K, et al. (1999) MOLCAS 5.0 (Lund University, Lund). 64. Malmqvist PA, Roos BO, Serrano-Andres L (1998) The multi-state CASPT2 method. Chem Phys Lett 288:299–306. 65. Malmqvist P-Å, Roos BO (1989) The CASSCF state interaction method. Chem Phys Lett 155:189–194.

Altoè et al.

PNAS ∣ November 23, 2010 ∣

vol. 107 ∣

no. 47 ∣

20177

CHEMISTRY

ultrafast photoinduced intra- and inter-molecular processes in natural and artificial photosensors,” project 2008JKBBK4).

BIOPHYSICS AND COMPUTATIONAL BIOLOGY

ported by Ministero della Pubblica Istruzione, Università, Ricerca Scientifica e Tecnologica - Progetti di Rilevante Interesse Nazionale 2008 (“Tracking