- Email: [email protected]
Chromophore vibrations during isomerization of photoactive yellow protein: analysis of normal modes and energy transfer
Chemical Physics Letters 391 (2004) 181–186 www.elsevier.com/locate/cplett
Chromophore vibrations during isomerization of photoactive yellow protein: analysis of normal modes and energy transfer Xin Yu, David M. Leitner
*
Department of Chemistry and Chemical Physics Program, University of Nevada, Mail Stop 216, Reno, NV 89557, USA Received 25 March 2004; in final form 21 April 2004 Available online 18 May 2004
Abstract Ultrafast studies of fluorescence decay of photoactive yellow protein (PYP) and several mutants by Mataga et al. [Chem. Phys. Lett. 352 (2002) 220] reveal coherent oscillations of about 140 cm1 , attributed to largely chromophore motions, and 50 cm1 , corresponding more to protein matrix vibrations. We identify these vibrations by normal mode analysis. Vibrational modes near 130 cm1 are relatively localized to the chromophore, consistent with interpretation of the ultrafast data. Dynamical coupling between the chromophore and protein matrix enhances twisting of the thioester group near 130 cm1 compared to the isolated chromophore. We also compute rates of vibrational energy transfer rates in PYP and discuss its influence on the photoisomerization kinetics. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Ultrafast experiments and simulations on photoisomerization of proteins on the subpicosecond and picosecond time scales, such as bacteriorhodopsin [1,2] and photoactive yellow protein (PYP) [3–16], have explored the role of dynamic interactions between the chromophore and protein environment in assisting and guiding the reaction. Reorganization dynamics of the protein following the sizable charge redistribution in the chromophore upon photoexcitation of bacteriorhodopsin appears to occur by many local, small-amplitude motions of charged groups and dipoles throughout the protein [1,2]. During the brief period between photoexcitation and isomerization of the chromophore the protein does not have time for significant conformational change, and protein motions responding to charge redistribution of the chromophore are largely vibrational. Some of these collective oscillations are dynamically coupled to, and in effect become part of, the reaction coordinate. Such dynamic coupling may appear as oscillations in fluorescence decay as the wave packet recrosses the transition state *
Corresponding author. Fax: +17757846804. E-mail address: [email protected] (D.M. Leitner).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.04.100
[17] during the course of conformational isomerization. The reorganization energy in such collective vibrations is redistributed elsewhere in the protein and solvent on the picosecond time scale. Recent ultrafast studies by Mataga and coworkers [3–5] on PYP and a number of mutants reveal a similar picture, in this case coherent oscillations with at least two characteristic frequencies. In this Letter, we analyze the vibrations of PYP and energy transfer among them to characterize these oscillations and dynamical coupling between the chromophore and surrounding protein matrix. PYP is a small water-soluble protein of a halophilic photosynthetic bacterium, Ectothiorhodospira halophila, which functions as a photoreceptor for negative phototaxis, specifically avoidance of blue light [6–8]. PYP belongs to a family of blue-light receptor proteins, Xanthopsins [6–8], which contain as their light-sensitive chromophore trans-p-coumaric acid, in PYP a deprotonated coumaric acid thioester (Fig. 1). The chromophore is positioned in PYP by hydrogen bonding at the head part, O -phenyl-, and by covalent bonding at the tail part, –CO–S–, which undergoes ultrafast twisting by flipping the thioester bond following photoexcitation [3–5,16]. This twisting motion is coupled to vibrations of the protein matrix. Coherent oscillations appearing in
182
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
Tyr42 Glu46
O
OH O
HO
_
C1
C6
enhanced by coupling to the protein matrix, and that the energy transfer time from this vibration is comparable to the time for decoherence and on the same time scale as fluorescence decay. The rate of conformational change thus appears to be mediated by the rate of transfer of excess vibrational energy from modes closely associated with conformational change. In the following section, we summarize the computational methods. In Section 3, we present results of our normal mode analysis on PYP in the S1 state, as well as results for the vibrational lifetimes, and compare these results for wt-PYP and two mutants with the ultrafast measurements [3].
C2 C5
2. Computational methods
C3
C4 C7
C8 O
C9 S C10
(Protein)
Pro68
Cys69
Thr70
Fig. 1. PYP chromophore and nearby surroundings.
fluorescence decay curves provide information about the frequencies and the nature of these coupled vibrations [3–5]. A number of simulations [11–14] and ab initio studies [15,16] on PYP have described PYP dynamics when the chromophore is in its cis and trans conformation, and how the protein aids in stabilizing the transition state. This work aims to identify and characterize by analysis of normal modes and their lifetimes the specific vibrations of wild type (wt)-PYP and two mutants that appear as oscillations in fluorescence decay measurements [3–5]. Mataga and collaborators [3–5] identified coherent oscillations in the fluorescence decay of wt-PYP and a number of mutants of roughly 50 and 140 cm1 . Sitedirected mutations of the protein can shift the frequency and amplitude of the oscillation as well as the decay rate itself, and correspondingly the rate of conformational change of the chromophore. The amplitude of the lower frequency oscillation appears more sensitive to changes in protein environment, though both disappear when PYP is denatured [3,4]. Mataga et al. [3] suggest that the 140 cm1 is more localized to the chromophore, which our analysis corroborates. Recent ab initio calculations on the isolated chromophore by Mataga and coworkers [5] provide an assignment of the 140 cm1 mode. We shall see that the twisting motion of the chromophore is
The structure of PYP is available from the Protein Data Bank. We adopt the force fields contained in the program MO I L [18] for the protein apart from the chromophore. The all-atom model for the PYP chromophore in the S1 state has been set up with the partial charges reported in [13], which accounts for the charge redistribution in the chromophore upon photoexcitation with a dipole transition of 8.74 D. Other force field parameters were adopted from MO I L , with some modification of parameters to fit normal modes of the isolated chromophore to ab initio DFT calculations (B3LYP/6-31G*) in the S1 state, specifically for the isolated chromophore terminated with an ethyl group attached to the sulfur. Values of all the force field parameters that we use to model the S1 state of the PYP chromophore will be presented elsewhere [19]. on The protein was then placed in a cubic box, 50 A each side, which was filled with water molecules and heated to 300 K over 10 ps. Five structures where then saved at each subsequent picosecond, and the waters removed for normal mode analysis. Results reported here use the first structure; all were found to give similar results and the same conclusions were reached for each. Projections onto the PYP chromophore include all chromophore atoms through C10 displayed in Fig. 1, and projections onto the thioester group include C8, C9, S and O. We also examine the lifetimes of the normal modes up to 200 cm1 . We compute the vibrational energy transfer rate from mode a, Wa , with the golden rule as we have carried out for other peptides and proteins [20,21]. We consider here only cubic anharmonic terms in the potential energy written as the sum of terms that can be described as decay and collision, the former typically larger except at low frequency where both terms are comparable. Truncation at cubic terms is valid at low temperatures, and gives a first estimate for mode lifetimes under other conditions. Since in this study we address fairly low frequency at 300 K, results that we obtain should be taken as a rough approximation to the
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
vibrational energy transfer rate, which may well be different due both to neglected higher-order anharmonicity as well as to interactions with solvent. The anharmonic decay rate of vibrational mode a is then the sum of these two terms given by [22],
183
(a)
0.03
0.02
Wadecay
p X jUabc j2 h ¼ ð1 þ nb þ nc Þdðxa xb xc Þ; 8xa b;c xb xc
0.01
ð1aÞ 2 hp X jUabc j ðnb nc Þdðxa þ xb xc Þ; 4xa b;c xb xc
(b)
ð1bÞ
where na is the occupation number ofhxmode a, which at a temperature T we take to be na ¼ ðekB T 1Þ1 . The numerically computed Uabc appear as the coefficients of the cubic terms in the expansion of the interatomic potential in normal coordinates [20,21]. Analysis of vibrational lifetimes and pathways provide estimates for the cooling time of the chromophore following photoexcitation.
Projections
Wacoll ¼
0.03
0.02
0.01
(c)
0.03
3. Results and discussion 0.02
To address dynamic interactions between the chromophore and protein matrix, we turn first to the projection of vibrational modes of PYP onto the chromophore, plotted in Fig. 2. The projections plotted in Fig. 2 are a running average over 24 modes to more easily observe trends in how they vary with mode frequency. Fig. 2a shows results for the wild type. We observe there a sizable projection of modes of PYP onto the chromophore at frequencies that correspond quite well to the normal mode frequencies of the isolated chromophore. If we focus instead on only the thioester group (we include in this group the atoms S, C8, C9, and O in Fig. 1), we find significant projection for wt-PYP normal modes near 135 cm1 , not far from the 125.26 cm1 mode of the isolated chromophore. The projection of this mode onto the thioester group of about 0.017 is more than three times higher than what it would be, 0.005, if the vibration were uniformly distributed over the protein. It also makes a relatively large contribution to the projection onto the whole chromophore, which is 0.028, or about 60% of the projection onto the whole chromophore. This can be compared to the projection of the nearby 125.26 cm1 mode of the isolated chromophore onto the thioester group of only 19%. The vibrations of atoms involved in conformational change are thus of larger amplitude, relative to the vibrational amplitude of all the chromophore atoms, when the chromophore is embedded in the protein as opposed to isolated. The direction of the displacements of the atoms in the vibrational modes near 135 cm1 is also consistent with
0.01
50
100
ω (cm-1)
150
200
Fig. 2. Projection of normal modes of S1 PYP onto chromophore (black curve), thioester group (gray curve), and amino acid in position 68 (either Pro68 or Ala68) (dashed curve) for: (a) wild type PYP; (b) P68A mutant; (c) W119G mutant. Vibrational frequencies of the isolated chromophore are indicated (asterisks).
this mode being at least one of the ‘isomerization modes’. In Fig. 3 we plot the direction of the displacements of chromophore atoms in PYP for the 135 cm1 mode and for the 125 cm1 mode of the isolated chromophore. The relative magnitude of displacement of the thioester group compared to the rest of the chromophore is enhanced when the chromophore is embedded in PYP. This is particularly so for the hindered rotation of O, which moves in a direction opposite to that of S, with the overall twisting motion in the direction of conformational change. In contrast, we see for the isolated chromophore significantly more rotation of the phenyl group, which is less pronounced when the chromophore is embedded in the protein due to anchoring by hydrogen bonds at the anion. Returning to Fig. 2a, we notice small peaks in the projection of the vibrational modes near 130 cm1 onto Pro68, indicating dynamical coupling between this
184
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
Fig. 3. The direction of atomic displacements of the PYP chromophore for a vibrational mode of PYP near 130 cm1 is shown. The minimized structure is in black and the displaced structure is in gray. Twisting of the S–C bond of the thioester group is significantly greater than that of the corresponding mode of the isolated chromophore at 125 cm1 , also shown. The latter involves instead twisting of the phenyl ring, which moves less when the chromophore is embedded in the protein. The isolated chromophore is terminated by – SCH2 CH3 (terminal methyl group not shown in figure).
proline and the chromophore. Dynamic interactions between the chromophore and protein environment may be influenced if we substitute, say, an alanine for this proline. Results for the P68A mutant are shown in Fig. 2b. We see again significant overlap with the thioester group and the whole chromophore near 125 cm1 , somewhat red-shifted from the same region for wt-PYP. Projections of these modes onto the thioester group are smaller than for wt-PYP in this region, 0.011 rather than 0.017, but still larger than for other vibrations below 200 cm1 . We also consider vibrations of a second mutant studied by Mataga et al. [3], W119G, which does not affect the region near the binding site of the chromophore. Projection of the normal modes of PYP up to 200 cm1 onto the chromophore, the thioester group, and Pro68 are plotted in Fig. 2c. The positions of the peaks of the respective projections are similar to the positions for wt-PYP, though the values are in many cases different. Still, a sizable projection onto the chromophore is again seen near 130 cm1 , in essentially the same location as that for wt-PYP, due to a large extent to projection onto the thioester group, in this case 0.014. The projection onto the thioester group is somewhat smaller than for wt-PYP, but larger than for P68A. Just as for wt-PYP, the vibrations of the proline and thioester group are coupled.
The vibrational modes near 130 cm1 appear to correspond to the 140 cm1 oscillations observed in the fluorescence decay curves of PYP. As suggested by Mataga et al. [3–5], the modes giving rise to the 140 cm1 appear to be relatively localized to the chromophore, which we find for the vibrations of PYP near 130 cm1 , whose projection onto the atoms of the thioester group is particularly large. The coherence time for this mode was measured to be 700 fs, which we shall see below is reasonably close to the lifetime we calculate for the vibrational modes near 130 cm1 . Mataga et al. [3] also studied the P68A mutant, finding again an oscillation close to 140 cm1 , with a similar coherence time of 740 fs. The fluorescence decay time of the P68A mutant was found to be 4.9 ps, compared to 3.1 ps for wild type PYP, indicating that for the former conformational change of the PYP chromophore takes more than 50% longer [3]. We turn now to the lifetimes of PYP vibrational modes. The vibrational energy transfer rates computed for wt-PYP and the P68A and W119G mutants are plotted in Fig. 4 at a temperature of 300 K for frequencies up to 200 cm1 . The results plotted are running averages over 8 modes to make more visible trends in the energy transfer rate with frequency. The energy transfer rates in all three molecules are similar over this range of frequency, typically somewhat faster in wtPYP. We see that the computed lifetimes range from about 400 fs to about 2 ps for the mutants and about 400 fs to about 1 ps for wt-PYP. The lifetimes of the computed 130 cm1 vibrational modes are similar for wt-PYP and the W119G mutant, about 400 fs, and shorter than the lifetimes we computed for the P68A mutant, which we find to be 500 fs. Though the lifetime is not the only contribution to decoherence, we note that
3
2
W (ps-1 )
1
0 0
50
100
150
200
ω (cm-1)
Fig. 4. Energy transfer rate from normal modes of wild type PYP (black curve), P68A mutant (gray curve), and W119G mutant (dashed curve).
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
this trend is consistent with the reasonably similar decoherence times reported by Mataga et al. [3], which are 700 fs for both wt-PYP and the W119G mutant, and 740 fs for the P68A mutant. Excess energy in a vibrational mode of, say, 130 cm1 may transfer via anharmonic coupling to other modes that largely overlap the thioester group, thus keeping much of the energy in this part of the protein. The energy may also be redistributed to modes that overlap the thioester group much less. The latter case leads to cooling of the chromophore via transfer of energy to the protein matrix. There is of course no sharp distinction between a vibrational mode of PYP that is a chromophore mode or not. Nevertheless, taking the peaks in projections in Fig. 2 to represent bands of chromophore modes, we attempt to identify how much of the energy flows to modes within these peaks and how much flows elsewhere. We find, e.g., that the rate of energy transfer from the ‘chromophore’ modes near 130 cm1 to protein modes outside this band (and outside other bands of ‘chromophore’ modes), amounts to about half of the total energy transfer rate from the 130 cm1 modes computed with all accepting modes. The rest of the energy flows largely to other modes in the 130 cm1 band and into a very low-frequency mode corresponding to translation of the chromophore within the protein. The time for energy to flow out of the chromophore is about half the lifetime of any vibrational mode in the 130 cm1 band, so roughly 1 ps. Mataga et al. [3] also observed a second coherent oscillation in their fluorescence decay measurement. The second oscillation has a frequency of 40, 49 and 76 cm1 for wt-PYP, and the W119G and P68A mutants, respectively. The shift in frequency upon mutation is considerably greater than that found for the 140 cm1 mode, which lies within 2 cm1 of this value for wt-PYP and the two mutants. Mataga et al. [3] argue that this mode is more a protein matrix vibration than the mode near 140 cm1 , since the damping of this oscillation appears to be more strongly affected by mutation than the oscillation near 140 cm1 . Normal mode analysis reveals that this oscillation is indeed less localized on the chromophore than is the 140 cm1 oscillation. We see in Fig. 2 that projections onto the chromophore for modes in the range 40–80 cm1 are smaller than the
185
projections around 130 cm1 . It is also not as easy to identify a particular oscillation that might correspond to the values reported in Ref. [3]; several peaks in the projection appear for wt-PYP and the two mutants that roughly correspond to the isolated chromophore vibrations near 40, 50, 80 and 90 cm1 . One possibility could be the vibrations near 60 cm1 for wt-PYP and the mutants, which correspond roughly to the 52.52 cm1 mode of the isolated chromophore. Still, the observed oscillation in the range 40–80 cm1 may in fact correspond to different sets of vibrations. This interpretation is consistent with that of recent experiments on PYP and ab initio calculations on the isolated chromophore by Mataga and coworkers [5]. They found that the lower frequency oscillation was difficult to characterize by a single mode of the chromophore, but suggested that it might correspond to an out-of-plane mode near 55 cm1 [5]. Our computed results and comparison with observations of Mataga et al. [3] are summarized in Table 1. In summary, we have examined dynamical coupling between the chromophore and surrounding protein matrix of S1 PYP and its role in guiding the twisting of the thioester group by analysis of normal modes and energy transfer among them. Experimental and computational studies of fast photochemical reactions in proteins, in particular ultrafast studies and simulations on bacteriorhodopsin [1,2], reveal that a large charge redistribution in the chromophore upon photoexcitation is followed by a large number of local, small-amplitude motions of charges and dipoles. Charge rearrangement in the chromophore, like loading springs, sets in motion collective oscillations of the protein, some of which couple to, and are thus part of, the reaction coordinate. Such a picture also describes the photoisomerization of PYP. The collective dielectric response of the protein appears to be coupled to coherent wave packet motion on the chromophore, which has been observed to occur with at least two characteristic frequencies in PYP and several mutants by Mataga et al. [3–5]. Our vibrational analysis on wild type PYP and two mutants provides information about the dynamical coupling that underlies the observed oscillations in the fluorescence decay. We find that modes with frequencies near 130 cm1 project significantly onto the chromophore and in particular onto the thioester group where conformational
Table 1 Computed values for projection of vibrational modes of wt-PYP and two mutants, P68A and W119G, onto the thioester group of chromophore, with frequencies near m1 of 130 cm1 (P1 ) and m2 of 60 cm1 (P2 ) Protein
P1
P2
m1 (cm1 )
m2 (cm1 )
s1 (fs)
s2 (fs)
wt-PYP P68A W119G
0.017 0.011 0.014
0.004 0.004 0.008
135 (140) 120 (142) 130 (139)
60 (40) 60 (76) 60 (49)
400 (700) 500 (740) 400 (700)
570 (500) 500 (347) 600 (470)
The lifetimes of the modes, s1 and s2 , respectively, are also listed and compared with the experimental decoherence times. (All experimental results in parenthesis from [3].)
186
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
change largely occurs. This vibration appears to correspond to the oscillation observed near 140 cm1 for wild type PYP and several mutants by Mataga et al. [3–5], which they argued substantially overlaps the chromophore. The vibrational modes near 130 cm1 computed for PYP project more onto the thioester group than does the nearby 125 cm1 mode of the isolated chromophore. This is the same assignment as given recently by Mataga and coworkers [5]. They found by ab initio calculations on the isolated chromophore a 147 cm1 mode that they suggested effectively triggers isomerization in the protein. We find, in fact, enhancement of the twisting motion of the thioester group for the 130 cm1 modes of the protein (Fig. 3), revealing the significance of dynamical coupling between the chromophore and protein scaffolding in guiding isomerization. This significance is further revealed by analysis of the P68A mutant, for which the overlap of modes near 130 cm1 onto the thioester group is smaller, consistent with the observed [3] slower fluorescence decay of P68A. We have also computed the time for energy to flow out of the vibrational modes near 130 cm1 . Vibrational energy flow mediates rates of photoisomerization [23] and PYP is no exception. The faster component of fluorescence decay has a time constant of 238 fs [3], corresponding to about 130 cm1 . If there is a small barrier, excess vibrational energy that the ‘isomerization’ modes near 130 cm1 may have following photoexcitation can assist reaction before deactivation by vibrational energy redistribution. The 3.1 ps component [3] of the fluorescence decay of PYP is on the same scale as the computed time of about 1 ps for vibrational energy transfer to and from modes near 130 cm1 , the difference due to the presence of a perhaps 1 kcal/mol barrier.
Acknowledgements This work was supported by the National Science Foundation (NSF CHE-0112631), a New Faculty Award from the Camille and Henry Dreyfus Founda-
tion and by a Research Innovation Award from the Research Corporation.
References [1] J.T.M. Kennis, D.S. Larsen, K. Ohta, M.T. Facciotti, R.M. Glaesser, G.R. Fleming, J. Phys. Chem. B 106 (2002) 6067. [2] D. Xu, C.H. Martin, K. Shulten, Biophys. J. 70 (1996) 453. [3] N. Mataga, H. Chosrowjan, Y. Shibata, Y. Imamoto, M. Kataoka, F. Tokunaga, Chem. Phys. Lett. 352 (2002) 220. [4] N. Mataga, H. Chosrowjan, S. Taniguchi, N. Hamada, F. Tokunaga, Y. Imamoto, M. Kataoka, Phys. Chem. Chem. Phys. 5 (2003) 2454. [5] H. Chosrowjan, S. Taniguchi, M. Mataga, M. Unno, S. Yamauchi, M. Hamada, M. Kumauchi, F. Tokunaga, J. Phys. Chem. B 108 (2004) 2686. [6] K.J. Hellingwerf, J. Hendriks, T. Gensch, J. Phys. Chem. A 107 (2003) 1082. [7] M.A. Cusanovich, T.E. Meyer, Biochemistry 42 (2003) 4759. [8] M.A. van der Horst, K.J. Hellingwerf, Acc. Chem. Res. 37 (2004) 13. [9] N. Mataga, H. Chosrowjan, Y. Shibata, Y. Imamoto, F. Tokunaga, J. Phys. Chem. B 104 (2000) 5191. [10] D.S. Larsen, M. Vengris, I.H.M. van Stokkum, M.A. van der Horst, R.A. Cordfunke, K.J. Hellingwerf, R. van Grondelle, Chem. Phys. Lett. 369 (2003) 563. [11] D.M.F. van Aalten, W.D. Hoff, J.B.C. Findlay, W. Crielaard, K.J. Hellingwerf, Prot. Eng. 11 (1998) 873. [12] I. Antes, W. Thiel, W.F. van Gunsteren, Eur. Biophys. J. 31 (2002) 504. [13] G. Groenhof, M.F. Lensink, H.J.C. Berendsen, J.G. Snijders, A.E. Mark, Proteins: Structure, Function, and Genetics 48 (2002) 202. [14] G. Groenhof, M.F. Lensink, H.J.C. Berendsen, A.E. Mark, Proteins: Struct. Funct. Genet. 48 (2002) 212. [15] M.J. Thompson, D. Bashford, L. Noodleman, E.D. Getzoff, J. Am. Chem. Soc. 125 (2003) 8186. [16] C. Ko, B. Levine, A. Toniolo, L. Manohar, S. Olsen, H.-J. Werner, T.J. Martinez, J. Am. Chem. Soc. 125 (2003) 12 710. [17] J.N. Onuchic, P.G. Wolynes, J. Phys. Chem. 92 (1988) 6495. [18] R. Elber et al., Comput. Phys. Commun. 91 (1995) 159. [19] X. Yu, D.M. Leitner (to be published). [20] D.M. Leitner, J. Phys. Chem. A 106 (2002) 10 870. [21] X. Yu, D.M. Leitner, J. Phys. Chem. B 107 (2003) 1698. [22] A.A. Maradudin, A.E. Fein, Phys. Rev. 128 (1962) 2589. [23] D.M. Leitner, B. Levine, J. Quenneville, T.J. Martinez, P.G. Wolynes, J. Phys. Chem. A 107 (2003) 10 706.
Chromophore vibrations during isomerization of photoactive yellow protein: analysis of normal modes and energy transfer Xin Yu, David M. Leitner
*
Department of Chemistry and Chemical Physics Program, University of Nevada, Mail Stop 216, Reno, NV 89557, USA Received 25 March 2004; in final form 21 April 2004 Available online 18 May 2004
Abstract Ultrafast studies of fluorescence decay of photoactive yellow protein (PYP) and several mutants by Mataga et al. [Chem. Phys. Lett. 352 (2002) 220] reveal coherent oscillations of about 140 cm1 , attributed to largely chromophore motions, and 50 cm1 , corresponding more to protein matrix vibrations. We identify these vibrations by normal mode analysis. Vibrational modes near 130 cm1 are relatively localized to the chromophore, consistent with interpretation of the ultrafast data. Dynamical coupling between the chromophore and protein matrix enhances twisting of the thioester group near 130 cm1 compared to the isolated chromophore. We also compute rates of vibrational energy transfer rates in PYP and discuss its influence on the photoisomerization kinetics. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Ultrafast experiments and simulations on photoisomerization of proteins on the subpicosecond and picosecond time scales, such as bacteriorhodopsin [1,2] and photoactive yellow protein (PYP) [3–16], have explored the role of dynamic interactions between the chromophore and protein environment in assisting and guiding the reaction. Reorganization dynamics of the protein following the sizable charge redistribution in the chromophore upon photoexcitation of bacteriorhodopsin appears to occur by many local, small-amplitude motions of charged groups and dipoles throughout the protein [1,2]. During the brief period between photoexcitation and isomerization of the chromophore the protein does not have time for significant conformational change, and protein motions responding to charge redistribution of the chromophore are largely vibrational. Some of these collective oscillations are dynamically coupled to, and in effect become part of, the reaction coordinate. Such dynamic coupling may appear as oscillations in fluorescence decay as the wave packet recrosses the transition state *
Corresponding author. Fax: +17757846804. E-mail address: [email protected] (D.M. Leitner).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.04.100
[17] during the course of conformational isomerization. The reorganization energy in such collective vibrations is redistributed elsewhere in the protein and solvent on the picosecond time scale. Recent ultrafast studies by Mataga and coworkers [3–5] on PYP and a number of mutants reveal a similar picture, in this case coherent oscillations with at least two characteristic frequencies. In this Letter, we analyze the vibrations of PYP and energy transfer among them to characterize these oscillations and dynamical coupling between the chromophore and surrounding protein matrix. PYP is a small water-soluble protein of a halophilic photosynthetic bacterium, Ectothiorhodospira halophila, which functions as a photoreceptor for negative phototaxis, specifically avoidance of blue light [6–8]. PYP belongs to a family of blue-light receptor proteins, Xanthopsins [6–8], which contain as their light-sensitive chromophore trans-p-coumaric acid, in PYP a deprotonated coumaric acid thioester (Fig. 1). The chromophore is positioned in PYP by hydrogen bonding at the head part, O -phenyl-, and by covalent bonding at the tail part, –CO–S–, which undergoes ultrafast twisting by flipping the thioester bond following photoexcitation [3–5,16]. This twisting motion is coupled to vibrations of the protein matrix. Coherent oscillations appearing in
182
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
Tyr42 Glu46
O
OH O
HO
_
C1
C6
enhanced by coupling to the protein matrix, and that the energy transfer time from this vibration is comparable to the time for decoherence and on the same time scale as fluorescence decay. The rate of conformational change thus appears to be mediated by the rate of transfer of excess vibrational energy from modes closely associated with conformational change. In the following section, we summarize the computational methods. In Section 3, we present results of our normal mode analysis on PYP in the S1 state, as well as results for the vibrational lifetimes, and compare these results for wt-PYP and two mutants with the ultrafast measurements [3].
C2 C5
2. Computational methods
C3
C4 C7
C8 O
C9 S C10
(Protein)
Pro68
Cys69
Thr70
Fig. 1. PYP chromophore and nearby surroundings.
fluorescence decay curves provide information about the frequencies and the nature of these coupled vibrations [3–5]. A number of simulations [11–14] and ab initio studies [15,16] on PYP have described PYP dynamics when the chromophore is in its cis and trans conformation, and how the protein aids in stabilizing the transition state. This work aims to identify and characterize by analysis of normal modes and their lifetimes the specific vibrations of wild type (wt)-PYP and two mutants that appear as oscillations in fluorescence decay measurements [3–5]. Mataga and collaborators [3–5] identified coherent oscillations in the fluorescence decay of wt-PYP and a number of mutants of roughly 50 and 140 cm1 . Sitedirected mutations of the protein can shift the frequency and amplitude of the oscillation as well as the decay rate itself, and correspondingly the rate of conformational change of the chromophore. The amplitude of the lower frequency oscillation appears more sensitive to changes in protein environment, though both disappear when PYP is denatured [3,4]. Mataga et al. [3] suggest that the 140 cm1 is more localized to the chromophore, which our analysis corroborates. Recent ab initio calculations on the isolated chromophore by Mataga and coworkers [5] provide an assignment of the 140 cm1 mode. We shall see that the twisting motion of the chromophore is
The structure of PYP is available from the Protein Data Bank. We adopt the force fields contained in the program MO I L [18] for the protein apart from the chromophore. The all-atom model for the PYP chromophore in the S1 state has been set up with the partial charges reported in [13], which accounts for the charge redistribution in the chromophore upon photoexcitation with a dipole transition of 8.74 D. Other force field parameters were adopted from MO I L , with some modification of parameters to fit normal modes of the isolated chromophore to ab initio DFT calculations (B3LYP/6-31G*) in the S1 state, specifically for the isolated chromophore terminated with an ethyl group attached to the sulfur. Values of all the force field parameters that we use to model the S1 state of the PYP chromophore will be presented elsewhere [19]. on The protein was then placed in a cubic box, 50 A each side, which was filled with water molecules and heated to 300 K over 10 ps. Five structures where then saved at each subsequent picosecond, and the waters removed for normal mode analysis. Results reported here use the first structure; all were found to give similar results and the same conclusions were reached for each. Projections onto the PYP chromophore include all chromophore atoms through C10 displayed in Fig. 1, and projections onto the thioester group include C8, C9, S and O. We also examine the lifetimes of the normal modes up to 200 cm1 . We compute the vibrational energy transfer rate from mode a, Wa , with the golden rule as we have carried out for other peptides and proteins [20,21]. We consider here only cubic anharmonic terms in the potential energy written as the sum of terms that can be described as decay and collision, the former typically larger except at low frequency where both terms are comparable. Truncation at cubic terms is valid at low temperatures, and gives a first estimate for mode lifetimes under other conditions. Since in this study we address fairly low frequency at 300 K, results that we obtain should be taken as a rough approximation to the
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
vibrational energy transfer rate, which may well be different due both to neglected higher-order anharmonicity as well as to interactions with solvent. The anharmonic decay rate of vibrational mode a is then the sum of these two terms given by [22],
183
(a)
0.03
0.02
Wadecay
p X jUabc j2 h ¼ ð1 þ nb þ nc Þdðxa xb xc Þ; 8xa b;c xb xc
0.01
ð1aÞ 2 hp X jUabc j ðnb nc Þdðxa þ xb xc Þ; 4xa b;c xb xc
(b)
ð1bÞ
where na is the occupation number ofhxmode a, which at a temperature T we take to be na ¼ ðekB T 1Þ1 . The numerically computed Uabc appear as the coefficients of the cubic terms in the expansion of the interatomic potential in normal coordinates [20,21]. Analysis of vibrational lifetimes and pathways provide estimates for the cooling time of the chromophore following photoexcitation.
Projections
Wacoll ¼
0.03
0.02
0.01
(c)
0.03
3. Results and discussion 0.02
To address dynamic interactions between the chromophore and protein matrix, we turn first to the projection of vibrational modes of PYP onto the chromophore, plotted in Fig. 2. The projections plotted in Fig. 2 are a running average over 24 modes to more easily observe trends in how they vary with mode frequency. Fig. 2a shows results for the wild type. We observe there a sizable projection of modes of PYP onto the chromophore at frequencies that correspond quite well to the normal mode frequencies of the isolated chromophore. If we focus instead on only the thioester group (we include in this group the atoms S, C8, C9, and O in Fig. 1), we find significant projection for wt-PYP normal modes near 135 cm1 , not far from the 125.26 cm1 mode of the isolated chromophore. The projection of this mode onto the thioester group of about 0.017 is more than three times higher than what it would be, 0.005, if the vibration were uniformly distributed over the protein. It also makes a relatively large contribution to the projection onto the whole chromophore, which is 0.028, or about 60% of the projection onto the whole chromophore. This can be compared to the projection of the nearby 125.26 cm1 mode of the isolated chromophore onto the thioester group of only 19%. The vibrations of atoms involved in conformational change are thus of larger amplitude, relative to the vibrational amplitude of all the chromophore atoms, when the chromophore is embedded in the protein as opposed to isolated. The direction of the displacements of the atoms in the vibrational modes near 135 cm1 is also consistent with
0.01
50
100
ω (cm-1)
150
200
Fig. 2. Projection of normal modes of S1 PYP onto chromophore (black curve), thioester group (gray curve), and amino acid in position 68 (either Pro68 or Ala68) (dashed curve) for: (a) wild type PYP; (b) P68A mutant; (c) W119G mutant. Vibrational frequencies of the isolated chromophore are indicated (asterisks).
this mode being at least one of the ‘isomerization modes’. In Fig. 3 we plot the direction of the displacements of chromophore atoms in PYP for the 135 cm1 mode and for the 125 cm1 mode of the isolated chromophore. The relative magnitude of displacement of the thioester group compared to the rest of the chromophore is enhanced when the chromophore is embedded in PYP. This is particularly so for the hindered rotation of O, which moves in a direction opposite to that of S, with the overall twisting motion in the direction of conformational change. In contrast, we see for the isolated chromophore significantly more rotation of the phenyl group, which is less pronounced when the chromophore is embedded in the protein due to anchoring by hydrogen bonds at the anion. Returning to Fig. 2a, we notice small peaks in the projection of the vibrational modes near 130 cm1 onto Pro68, indicating dynamical coupling between this
184
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
Fig. 3. The direction of atomic displacements of the PYP chromophore for a vibrational mode of PYP near 130 cm1 is shown. The minimized structure is in black and the displaced structure is in gray. Twisting of the S–C bond of the thioester group is significantly greater than that of the corresponding mode of the isolated chromophore at 125 cm1 , also shown. The latter involves instead twisting of the phenyl ring, which moves less when the chromophore is embedded in the protein. The isolated chromophore is terminated by – SCH2 CH3 (terminal methyl group not shown in figure).
proline and the chromophore. Dynamic interactions between the chromophore and protein environment may be influenced if we substitute, say, an alanine for this proline. Results for the P68A mutant are shown in Fig. 2b. We see again significant overlap with the thioester group and the whole chromophore near 125 cm1 , somewhat red-shifted from the same region for wt-PYP. Projections of these modes onto the thioester group are smaller than for wt-PYP in this region, 0.011 rather than 0.017, but still larger than for other vibrations below 200 cm1 . We also consider vibrations of a second mutant studied by Mataga et al. [3], W119G, which does not affect the region near the binding site of the chromophore. Projection of the normal modes of PYP up to 200 cm1 onto the chromophore, the thioester group, and Pro68 are plotted in Fig. 2c. The positions of the peaks of the respective projections are similar to the positions for wt-PYP, though the values are in many cases different. Still, a sizable projection onto the chromophore is again seen near 130 cm1 , in essentially the same location as that for wt-PYP, due to a large extent to projection onto the thioester group, in this case 0.014. The projection onto the thioester group is somewhat smaller than for wt-PYP, but larger than for P68A. Just as for wt-PYP, the vibrations of the proline and thioester group are coupled.
The vibrational modes near 130 cm1 appear to correspond to the 140 cm1 oscillations observed in the fluorescence decay curves of PYP. As suggested by Mataga et al. [3–5], the modes giving rise to the 140 cm1 appear to be relatively localized to the chromophore, which we find for the vibrations of PYP near 130 cm1 , whose projection onto the atoms of the thioester group is particularly large. The coherence time for this mode was measured to be 700 fs, which we shall see below is reasonably close to the lifetime we calculate for the vibrational modes near 130 cm1 . Mataga et al. [3] also studied the P68A mutant, finding again an oscillation close to 140 cm1 , with a similar coherence time of 740 fs. The fluorescence decay time of the P68A mutant was found to be 4.9 ps, compared to 3.1 ps for wild type PYP, indicating that for the former conformational change of the PYP chromophore takes more than 50% longer [3]. We turn now to the lifetimes of PYP vibrational modes. The vibrational energy transfer rates computed for wt-PYP and the P68A and W119G mutants are plotted in Fig. 4 at a temperature of 300 K for frequencies up to 200 cm1 . The results plotted are running averages over 8 modes to make more visible trends in the energy transfer rate with frequency. The energy transfer rates in all three molecules are similar over this range of frequency, typically somewhat faster in wtPYP. We see that the computed lifetimes range from about 400 fs to about 2 ps for the mutants and about 400 fs to about 1 ps for wt-PYP. The lifetimes of the computed 130 cm1 vibrational modes are similar for wt-PYP and the W119G mutant, about 400 fs, and shorter than the lifetimes we computed for the P68A mutant, which we find to be 500 fs. Though the lifetime is not the only contribution to decoherence, we note that
3
2
W (ps-1 )
1
0 0
50
100
150
200
ω (cm-1)
Fig. 4. Energy transfer rate from normal modes of wild type PYP (black curve), P68A mutant (gray curve), and W119G mutant (dashed curve).
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
this trend is consistent with the reasonably similar decoherence times reported by Mataga et al. [3], which are 700 fs for both wt-PYP and the W119G mutant, and 740 fs for the P68A mutant. Excess energy in a vibrational mode of, say, 130 cm1 may transfer via anharmonic coupling to other modes that largely overlap the thioester group, thus keeping much of the energy in this part of the protein. The energy may also be redistributed to modes that overlap the thioester group much less. The latter case leads to cooling of the chromophore via transfer of energy to the protein matrix. There is of course no sharp distinction between a vibrational mode of PYP that is a chromophore mode or not. Nevertheless, taking the peaks in projections in Fig. 2 to represent bands of chromophore modes, we attempt to identify how much of the energy flows to modes within these peaks and how much flows elsewhere. We find, e.g., that the rate of energy transfer from the ‘chromophore’ modes near 130 cm1 to protein modes outside this band (and outside other bands of ‘chromophore’ modes), amounts to about half of the total energy transfer rate from the 130 cm1 modes computed with all accepting modes. The rest of the energy flows largely to other modes in the 130 cm1 band and into a very low-frequency mode corresponding to translation of the chromophore within the protein. The time for energy to flow out of the chromophore is about half the lifetime of any vibrational mode in the 130 cm1 band, so roughly 1 ps. Mataga et al. [3] also observed a second coherent oscillation in their fluorescence decay measurement. The second oscillation has a frequency of 40, 49 and 76 cm1 for wt-PYP, and the W119G and P68A mutants, respectively. The shift in frequency upon mutation is considerably greater than that found for the 140 cm1 mode, which lies within 2 cm1 of this value for wt-PYP and the two mutants. Mataga et al. [3] argue that this mode is more a protein matrix vibration than the mode near 140 cm1 , since the damping of this oscillation appears to be more strongly affected by mutation than the oscillation near 140 cm1 . Normal mode analysis reveals that this oscillation is indeed less localized on the chromophore than is the 140 cm1 oscillation. We see in Fig. 2 that projections onto the chromophore for modes in the range 40–80 cm1 are smaller than the
185
projections around 130 cm1 . It is also not as easy to identify a particular oscillation that might correspond to the values reported in Ref. [3]; several peaks in the projection appear for wt-PYP and the two mutants that roughly correspond to the isolated chromophore vibrations near 40, 50, 80 and 90 cm1 . One possibility could be the vibrations near 60 cm1 for wt-PYP and the mutants, which correspond roughly to the 52.52 cm1 mode of the isolated chromophore. Still, the observed oscillation in the range 40–80 cm1 may in fact correspond to different sets of vibrations. This interpretation is consistent with that of recent experiments on PYP and ab initio calculations on the isolated chromophore by Mataga and coworkers [5]. They found that the lower frequency oscillation was difficult to characterize by a single mode of the chromophore, but suggested that it might correspond to an out-of-plane mode near 55 cm1 [5]. Our computed results and comparison with observations of Mataga et al. [3] are summarized in Table 1. In summary, we have examined dynamical coupling between the chromophore and surrounding protein matrix of S1 PYP and its role in guiding the twisting of the thioester group by analysis of normal modes and energy transfer among them. Experimental and computational studies of fast photochemical reactions in proteins, in particular ultrafast studies and simulations on bacteriorhodopsin [1,2], reveal that a large charge redistribution in the chromophore upon photoexcitation is followed by a large number of local, small-amplitude motions of charges and dipoles. Charge rearrangement in the chromophore, like loading springs, sets in motion collective oscillations of the protein, some of which couple to, and are thus part of, the reaction coordinate. Such a picture also describes the photoisomerization of PYP. The collective dielectric response of the protein appears to be coupled to coherent wave packet motion on the chromophore, which has been observed to occur with at least two characteristic frequencies in PYP and several mutants by Mataga et al. [3–5]. Our vibrational analysis on wild type PYP and two mutants provides information about the dynamical coupling that underlies the observed oscillations in the fluorescence decay. We find that modes with frequencies near 130 cm1 project significantly onto the chromophore and in particular onto the thioester group where conformational
Table 1 Computed values for projection of vibrational modes of wt-PYP and two mutants, P68A and W119G, onto the thioester group of chromophore, with frequencies near m1 of 130 cm1 (P1 ) and m2 of 60 cm1 (P2 ) Protein
P1
P2
m1 (cm1 )
m2 (cm1 )
s1 (fs)
s2 (fs)
wt-PYP P68A W119G
0.017 0.011 0.014
0.004 0.004 0.008
135 (140) 120 (142) 130 (139)
60 (40) 60 (76) 60 (49)
400 (700) 500 (740) 400 (700)
570 (500) 500 (347) 600 (470)
The lifetimes of the modes, s1 and s2 , respectively, are also listed and compared with the experimental decoherence times. (All experimental results in parenthesis from [3].)
186
X. Yu, D.M. Leitner / Chemical Physics Letters 391 (2004) 181–186
change largely occurs. This vibration appears to correspond to the oscillation observed near 140 cm1 for wild type PYP and several mutants by Mataga et al. [3–5], which they argued substantially overlaps the chromophore. The vibrational modes near 130 cm1 computed for PYP project more onto the thioester group than does the nearby 125 cm1 mode of the isolated chromophore. This is the same assignment as given recently by Mataga and coworkers [5]. They found by ab initio calculations on the isolated chromophore a 147 cm1 mode that they suggested effectively triggers isomerization in the protein. We find, in fact, enhancement of the twisting motion of the thioester group for the 130 cm1 modes of the protein (Fig. 3), revealing the significance of dynamical coupling between the chromophore and protein scaffolding in guiding isomerization. This significance is further revealed by analysis of the P68A mutant, for which the overlap of modes near 130 cm1 onto the thioester group is smaller, consistent with the observed [3] slower fluorescence decay of P68A. We have also computed the time for energy to flow out of the vibrational modes near 130 cm1 . Vibrational energy flow mediates rates of photoisomerization [23] and PYP is no exception. The faster component of fluorescence decay has a time constant of 238 fs [3], corresponding to about 130 cm1 . If there is a small barrier, excess vibrational energy that the ‘isomerization’ modes near 130 cm1 may have following photoexcitation can assist reaction before deactivation by vibrational energy redistribution. The 3.1 ps component [3] of the fluorescence decay of PYP is on the same scale as the computed time of about 1 ps for vibrational energy transfer to and from modes near 130 cm1 , the difference due to the presence of a perhaps 1 kcal/mol barrier.
Acknowledgements This work was supported by the National Science Foundation (NSF CHE-0112631), a New Faculty Award from the Camille and Henry Dreyfus Founda-
tion and by a Research Innovation Award from the Research Corporation.
References [1] J.T.M. Kennis, D.S. Larsen, K. Ohta, M.T. Facciotti, R.M. Glaesser, G.R. Fleming, J. Phys. Chem. B 106 (2002) 6067. [2] D. Xu, C.H. Martin, K. Shulten, Biophys. J. 70 (1996) 453. [3] N. Mataga, H. Chosrowjan, Y. Shibata, Y. Imamoto, M. Kataoka, F. Tokunaga, Chem. Phys. Lett. 352 (2002) 220. [4] N. Mataga, H. Chosrowjan, S. Taniguchi, N. Hamada, F. Tokunaga, Y. Imamoto, M. Kataoka, Phys. Chem. Chem. Phys. 5 (2003) 2454. [5] H. Chosrowjan, S. Taniguchi, M. Mataga, M. Unno, S. Yamauchi, M. Hamada, M. Kumauchi, F. Tokunaga, J. Phys. Chem. B 108 (2004) 2686. [6] K.J. Hellingwerf, J. Hendriks, T. Gensch, J. Phys. Chem. A 107 (2003) 1082. [7] M.A. Cusanovich, T.E. Meyer, Biochemistry 42 (2003) 4759. [8] M.A. van der Horst, K.J. Hellingwerf, Acc. Chem. Res. 37 (2004) 13. [9] N. Mataga, H. Chosrowjan, Y. Shibata, Y. Imamoto, F. Tokunaga, J. Phys. Chem. B 104 (2000) 5191. [10] D.S. Larsen, M. Vengris, I.H.M. van Stokkum, M.A. van der Horst, R.A. Cordfunke, K.J. Hellingwerf, R. van Grondelle, Chem. Phys. Lett. 369 (2003) 563. [11] D.M.F. van Aalten, W.D. Hoff, J.B.C. Findlay, W. Crielaard, K.J. Hellingwerf, Prot. Eng. 11 (1998) 873. [12] I. Antes, W. Thiel, W.F. van Gunsteren, Eur. Biophys. J. 31 (2002) 504. [13] G. Groenhof, M.F. Lensink, H.J.C. Berendsen, J.G. Snijders, A.E. Mark, Proteins: Structure, Function, and Genetics 48 (2002) 202. [14] G. Groenhof, M.F. Lensink, H.J.C. Berendsen, A.E. Mark, Proteins: Struct. Funct. Genet. 48 (2002) 212. [15] M.J. Thompson, D. Bashford, L. Noodleman, E.D. Getzoff, J. Am. Chem. Soc. 125 (2003) 8186. [16] C. Ko, B. Levine, A. Toniolo, L. Manohar, S. Olsen, H.-J. Werner, T.J. Martinez, J. Am. Chem. Soc. 125 (2003) 12 710. [17] J.N. Onuchic, P.G. Wolynes, J. Phys. Chem. 92 (1988) 6495. [18] R. Elber et al., Comput. Phys. Commun. 91 (1995) 159. [19] X. Yu, D.M. Leitner (to be published). [20] D.M. Leitner, J. Phys. Chem. A 106 (2002) 10 870. [21] X. Yu, D.M. Leitner, J. Phys. Chem. B 107 (2003) 1698. [22] A.A. Maradudin, A.E. Fein, Phys. Rev. 128 (1962) 2589. [23] D.M. Leitner, B. Levine, J. Quenneville, T.J. Martinez, P.G. Wolynes, J. Phys. Chem. A 107 (2003) 10 706.