Reversible Photochromic Reactions of Bacteriorhodopsin from Halobacterium salinarum at Femto- and Picosecond Times

Abstract

The operation of bacteriorhodopsin (BR) from the archaeon Halobacterium salinarum is based on the photochromic reaction of isomerization of the chromophore group (the retinal protonated Schiff base, RPSB) from the all-trans to the 13-cis form. The ultrafast dynamics of the reverse 13-cis → all-trans photoreaction was studied using femtosecond transient absorption spectroscopy in comparison with the forward photoreaction. The forward photoreaction was initiated by photoexcitation of BR by pulse I (540 nm). The reverse photoreaction was initiated by photoexcitation of the product K₅₉₀ at an early stage of its formation (5 ps) by pulse II (660 nm). The conversion of the excited K₅₉₀ to the ground state proceeds at times of 0.19, 1.1, and 16 ps with the relative contributions of ~20/60/20, respectively. All these decay channels lead to the formation of the initial state of BR as a product with a quantum yield of ~1. This state is preceded by vibrationally excited intermediates, the relaxation of which occurs in the 16 ps time range. Likely, the heterogeneity of the excited state of K₅₉₀ is determined by the heterogeneity of its chromophore center. The forward photoreaction includes two components—0.52 and 3.5 ps, with the relative contributions of 91/9, respectively. The reverse photoreaction initiated from K₅₉₀ proceeds more efficiently in the conical intersection (CI) region but on the whole at a lower rate compared to the forward photoreaction, due to significant heterogeneity of the potential energy surface.

1. Introduction

Bacteriorhodopsin (BR) is a transmembrane protein of the halophilic archaeon Halobacterium salinarum, the first to be discovered [1] and the best-studied type 1 (microbial) rhodopsin. BR performs a photoenergetic function through an active light-dependent proton transport across the cell membrane and is often used as a model system to study the molecular mechanisms of light energy conversion in biological systems. BR function is based on the photochemical reaction of isomerization of the chromophore group, the retinal protonated Schiff base (RPSB), from the all-trans to the 13-cis form [2,3,4]. The photoreaction is accompanied by a series of transformations of the BR molecule closed in a photocycle. At different stages of the photocycle in the time range from femto- to milliseconds, the excited state I₄₆₀ and intermediate products J₆₂₅, K₅₉₀, L₅₅₀, M^I₄₁₂, M^II₄₁₂, N₅₆₀, and O₆₄₀ are formed (Figure 1a) [5,6,7]. The result of the photocycle is proton transport from the cytoplasm to the external environment, including the main stages: (i) deprotonation of RPSB and protonation of the primary acceptor Asp85 at the stage of M^I₄₁₂ formation; (ii) release of a proton into the external environment at the stage of M^II₄₁₂ formation; (iii) protonation of RPSB at the stage of N₅₆₀ formation; and (iv) proton capture from the cytoplasm at the stage of O₆₄₀ formation. During the N₅₆₀ → O₆₄₀ transition, RPSB undergoes thermal isomerization into the initial all-trans form.

The photocycle is initiated only from the all-trans form of RPSB, the content of which reaches 90–95% in the light-adapted state of BR (BR₅₆₈), while 5–10% of the molecules contain RPSB in the 13-cis form [10,11], the proportion of which in the dark-adapted state of BR reaches 50–60% due to thermal isomerization of RPSB.

The BR photoreaction occurs in the femto- and early picosecond time range, starting from the Franck–Condon state (FC) and ending with the formation of the K₅₉₀ product, the lifetime of which is in the microsecond range [12,13,14,15,16,17,18,19,20,21]; further processes of the photocycle are dark (Figure 1a). The photoisomerization of RPSB occurs in the excited I₄₆₀ state in the coherent regime and can be described as the evolution of a set of coherent excited vibrational states (wave packet) first along the S₁ and then along the S₀ potential energy surfaces (PESs) in accordance with the reaction coordinate (Figure 1b). The S₁ → S₀ conversion occurs through the multidimensional conical intersection (CI) region of S₁/S₀ PESs [22] with a quantum yield of J₆₂₅ formation as high as 0.64 [23].

The initial dynamics of the wave packet are determined by the relaxation of RPSB along the totally symmetric (C–C and C=C) vibrational modes, resulting in the formation of I₄₆₀ from the FC state in 0.1–0.15 ps [24,25,26]. Thus, I₄₆₀ still contains RPSB in the all-trans configuration but with inverted C-C and C=C bonds, which has been confirmed both experimentally [27] and theoretically [24]. The reaction dynamics of S₁ → S₀ conversion are strongly influenced by the presence of a small barrier to the decay of the excited state of S₁ due to the interaction with the S₂ PES, which is reflected by the three-state model (S₀, S₁, and S₂) [3,14,21,24,28,29] (Figure 1b). Then the wave packet begins to move along the reaction vibrational modes—hydrogen out-of-plane (HOOP), and torsional vibrations [17,21,26,30]. During this movement, the wave packet overcomes the barrier at the S₁ PES in 0.45–0.5 ps, reaches the CI region, and after dividing into two subpackets, passes to the S₀ PES of the primary reaction product J₆₂₅, containing RPSB in the 13-cis form, or to the S₀ PES of the BR₅₆₈ initial state [12,13,16,27,31,32]. The structure of RPSB in the product J₆₂₅ was identified by time-resolved resonance Raman spectroscopy [33] and ultrafast spectroscopy [27]. The product J₆₂₅ is converted with a characteristic time of 2–3 ps into the next product K₅₉₀ with a more relaxed 13-cis RPSB [33]. The formation of the product K₅₉₀ completes the process of converting the energy of a quantum of light into chemical energy in the form of conformational changes in the protein, which are subsequently used for proton transfer.

BR, as well as other type 1 rhodopsins and RPSB in solution, is characterized by an additional non-reactive excited-state decay channel with a picosecond lifetime [34,35]. This is associated with branching of the reaction pathway in the FC state [36,37,38] or with the initial heterogeneity of the protein and/or chromophore [14,15,18,37,39]. The latter assumption was confirmed for a number of type 1 rhodopsins [39,40], including BR [18].

Rhodopsins are known to have photochromic properties [8,9,23,38,41,42,43,44,45,46,47,48,49,50,51]. The absorption of the second quantum of light by the intermediate of the photocycle can initiate the reverse 13-cis → all-trans photoisomerization of RPSB, which in many cases proceeds with the formation of the initial state of BR₅₆₈ (Figure 1a) [8]. The ability to photochromism is used in nature in a number of rhodopsins to perform certain physiological functions. For example, sensory rhodopsin of the cyanobacterium Anabaena sp. (ASR) regulates the transcription of genes of the photosynthetic apparatus [52], sensory rhodopsin I of H. salinarum (SRI) and channel rhodopsin of the unicellular green alga Chlamydomonas reinhardtii (ChR2) carry out negative phototaxis [53,54,55], and bistable rhodopsins of type 2 (animal rhodopsins) perform visual and non-visual photoreceptor functions [56].

The study of photochromic reactions initiated from different stages of photoconversion is one of the experimental approaches to studying the mechanism of photochemical reaction and subsequent processes of dark relaxation of rhodopsins. The examination of the reverse photochromic reaction from the primary intermediate state can provide new knowledge about ultrafast photoisomerization of retinal chromophores in different protein environments. The reverse phototransition K₅₉₀ → BR₅₆₈ initiated at the early stages of the photocycle, when large-scale changes in the protein part of the molecule have not yet occurred, is of interest. This phototransition was studied using low-temperature spectrophotometry [8,46,57,58,59,60,61], time-resolved photoelectrometry [62], and time-resolved spectroscopy upon excitation of K₅₉₀ in the pico- [44,45,50,63] and nanosecond [15,23,47] time range. The K₅₉₀ → BR₅₆₈ phototransition was shown to occur with a high quantum yield of 0.8–1 [8,23,44,47,60] without the formation of detectable intermediate products. However, it remains unclear whether the protein state observed upon relaxation of the system in the time interval of 0.1–10 ns is identical to the “hot” K₅₉₀ state that appears immediately after excitation. The differences may be in both the conformation of the RPSB and the protein. Measuring the quantum yield of the reverse photoreaction initiated immediately after the all-trans → 13-cis transition is an important complement to the measurements already performed.

In this work, we investigated the dynamics of the K₅₉₀ → BR₅₆₈ reverse phototransition at the early stage of K₅₉₀ formation 5 ps after the initiation of the forward photoreaction. The work was carried out using the pump-probe and pump-pump-probe methods of femtosecond transient absorption spectroscopy with a time resolution of 25 fs and probing in the spectral range of 400–740 nm. It was shown that the dynamics of the reverse photoreaction of BR is nonexponential with the slow component of S₁ → S₀ conversion completing only at ~16 ps after excitation. This most likely indicates a strong heterogeneity of the chromophore center of the K₅₉₀ product, in contrast to the chromophore center of the initial state of BR₅₆₈. The kinetics of reverse BR photoreaction observed in this work are similar to those measured at a delay time of 60 ps in [45]. A new method of data analysis allowed us to identify an unknown intermediate of the reverse photoreaction converting to BR₅₆₈ at ~16 ps. This method can be applied to study the dynamics of reverse photoreactions of other rhodopsins at the earliest stages of their photoconversion.

2. Results

2.1. Forward Photoreaction

The forward photoreaction was initiated by pumping BR₅₆₈ with a pulse I peaking at 540 nm. The BR photoinduced absorption ΔA^I(λ, t) results were recorded at time delays of up to 11 ps and at a time delay of 50 ps. Figure 2a shows the difference spectra ΔA^I(λ, t) that characterize the forward photoreaction of BR and have already become classical [13,35,46,64]. At a time delay of 0.12 ps, short-wavelength (ESA1_I) and long-wavelength (ESA2_I) absorption and stimulated emission (SE_I) signals from the excited state I₄₆₀ appear in the spectral regions of 400–550 nm (ESA1_I) and >640 nm (ESA2_I and SE_I) (Figure 2a, red curve). Over the next 1–1.5 ps, these signals are replaced by an absorption band in the 600–740 nm region (PA_J) (Figure 2a, yellow curve), which reflects the S₁ → S₀ transition from I₄₆₀ to the primary product J₆₂₅, which contains isomerized RPSB in the 13-cis form. In the picosecond time range, the absorption band of J₆₂₅ in the difference spectra shifts to the short-wavelength region and becomes less intense, which characterizes the formation of the next product K₅₉₀ (PA_K) as a result of vibrational and conformational relaxation (Figure 2a, light blue and blue curves).

In the range of 500–650 nm, a negative signal is observed, associated with the ground state bleaching of BR₅₆₈ (GSB_BR) (Figure 2a). This band coincides in shape with the inverted absorption spectrum of BR₅₆₈. At a time delay of 0.12 ps, the intensity of the GSB_BR band in the difference spectrum is a maximum, and at a 5 ps delay, when the photoreaction is complete, the intensity of this band drops significantly. This is due to factors: (i) the formation of the products J₆₂₅ and K₅₉₀, absorption of which occurs in the same spectral region as the GSB_BR band, and (ii) the return of some of the excited molecules to the initial state of BR₅₆₈ during the photoreaction. The kinetic curves ΔA^I(470 nm, t) (Figure 2b, red curve) and ΔA^I(635 nm, t) (Figure 2c, red curve) reflect the processes described above.

Decomposition of the spectral-temporal matrix ΔA^I(λ, t) at delays up to 50 ps into a linear combination of discrete exponential functions in accordance with Equation (1) (see Section 4) made it possible to determine the times τ₀–τ₂ characterizing the forward photoreaction (

Table 1. Comparison of parameters of the DADS and EADS obtained for the forward and reverse BR photoreactions. Lifetimes (τ_n) and corresponding excited state absorption intensities (ESA1) obtained by decomposing the EADS into Gaussian components.

BR568 → K590	τ0, ps	τ1, ps	τ2, ps
	0.08	0.52	3.5
	ESA1I(474 nm), %
		91	9
K590 → BR568		τ1′, ps	τ2′, ps	τ3′, ps
		0.19	1.1	16
	ESA1K*(460 nm), %
		20	60	20

). Exponential decay-associated difference spectra (DADS) and the relevant evolution-associated difference spectra (EADS) of the successively evolving intermediates of the sequential kinetic model (Scheme 1) are presented in Figure 3.

Calculated lifetimes τ₀ = 0.08 ps, τ₁ = 0.52 ps, and τ₂ = 3.5 ps (Table 1) are in good agreement with the data obtained previously [12,14,16,18,19,20,31,65]. The time τ₀ reflects the dynamics of the Stokes shift in the course of the formation of I₄₆₀ from the FC state. As can be seen from Figure 3a (red curve), with this characteristic time, the ESA1_I and ESA2_I bands shift to the short-wavelength region, and the SE_I band shifts to the long-wavelength region, which reflects the motion of the wave packet along the S₁ PES and the accompanying process of vibrational relaxation. The time τ₁ characterizes the I₄₆₀ decay along the reactive pathway (Figure 1b). The DADS of the respective absorption changes (Figure 3a, green curve) demonstrates the almost complete disappearance of the ESA1_I band in the region of 400–550 nm and an increase in PA_J (600–700 nm) and BR₅₆₈ absorption (560–600 nm). The slow characteristic time τ₂ reflects a minor residual disappearance of the ESA1_I band, a drop in the PA_J, and an increase in the PA_K and BR₅₆₈ absorption (Figure 3a, blue curve), which indicates both the non-reactive path of the I₄₆₀ → BR₅₆₈ transition [18,31] and the J₆₂₅ → K₅₉₀ transition. Most likely, a vibrationally excited BR′ state is formed during the photoreaction, and the relaxation of this state takes several picoseconds, as in the case of the J₆₂₅ → K₅₉₀ transition.

Figure 3b shows the respective EADS calculated by the sequential kinetic Scheme 1, which reflect signals from the FC state, I₄₆₀, J₆₂₅, and K₅₉₀, on which the GSB_BR band is superimposed. The decomposition of EADS into Gaussians and the GSB_BR band (see Supplementary Materials, Figure S1) made it possible to obtain the absorption spectra of these states (Figure 3c). This also allowed us to estimate the contributions of the reactive and non-reactive pathways to the overall dynamics of the excited state decay based on the drop in the ESA1 signal (see Supplementary Materials, Figure S1a,b). The contributions of the reactive and non-reactive pathways were 91% and 9%, respectively (Table 1). The slow component of the excited state decay in BR was observed earlier both from transient absorption [14,18,19,20,27,65] and fluorescence [16] signals.

2.2. Reverse Photoreaction

The reverse photoreaction was initiated by pulse II centered at 660 nm by pumping the K₅₉₀ product at an early stage of its formation, 5 ps after the action of pulse I. It is worth noting that, since the J₆₂₅ → K₅₉₀ transition is not completed at this time delay, the reverse photoreaction is partially initiated from the J₆₂₅ product. The ΔA^I+II(λ, t) signals were recorded at time delays of up to 11 ps (Figure 2b,c, blue curves) and at a time delay of 50 ps (Figure 4a, orange curve). Figure 4b shows the absorption spectra of BR₅₆₈ (red curve) and the K₅₉₀ product with an admixture of the J₆₂₅ product at a time delay of 5 ps (blue curve) normalized in accordance with the extinction coefficients. The absorption spectrum of K₅₉₀ + J₆₂₅ was calculated by the difference spectrum ΔA^I(λ, 5 ps) (Figure 2a, green curve) using the GSB_BR band (see Supplementary Materials, Figure S1b,c). It is characterized by a maximum at 583 nm, a width of 1.4 times greater than the width of the BR₅₆₈ absorption spectrum, and an extinction that is only 0.74 of the BR₅₆₈ extinction.

Pulse II was centered at 660 nm for optimal excitation of K₅₉₀ and minimal excitation of BR₅₆₈. However, pulse II also excites a small fraction of BR₅₆₈ molecules, initiating the forward photoreaction. To account for this process, the ΔA^II(λ, 50 ps) spectrum was recorded under the action of only pulse II (Figure 4a, green curve).

Comparison of the kinetic curves ΔA^I(λ, t) and ΔA^I+II(λ, t), presented in Figure 2b,c, showed that at the time delays before the action of pulse II, these curves practically repeat each other. At later times, changes in the difference signal are observed. Comparison of the signals ΔA^I(λ, 50 ps), ΔA^I+II(λ, 50 ps), and ΔA^II(λ, 50 ps) (Figure 4a) allowed us to track the changes in the BR photoinduced absorption at the time delays, when all primary processes have already been completed and the difference spectra consist only of the positive PA_K and the negative GSB_BR bands. The action of pulse II leads to a slight drop in the PA_K band (Figure 4a, orange curve).

The absorption difference spectra ΔA^I+II(λ, t) after the action of pulse II reflect the signals from three BR ensembles: (1) BR₅₆₈ molecules excited by pulse I but not affected by pulse II; (2) BR₅₆₈ molecules excited only by pulse II; (3) K₅₉₀ molecules (and partially J₆₂₅) excited by pulse II. The time evolution of ensembles (1) and (2) is determined by the dynamics of the forward photoreaction with time delays t and t—t₁ relative to pulse I, respectively, where t₁ = 5 ps, and the evolution of ensemble (3) is determined by the dynamics of the reverse photoreaction K₅₉₀ → BR₅₆₈ with a time delay t—t₁ relative to pulse II. The absorption changes of the three BR ensembles are described by Equations (S3), (S5), and (S6) (see Supplementary Materials). The absorption dynamics of the third ensemble, ΔA₃(λ, t—t₁), characterizes the reverse photoreaction (Figure 5).

Decomposition of the spectral-temporal matrix ΔA₃(λ, t—t₁) into a linear combination of discrete exponential functions in accordance with Equation (1) (see Section 4) made it possible to determine the times characterizing the reverse photoreaction of BR (Table 1). The exponential decay-associated difference spectra (DADS) (Figure 6a) and the difference spectra A_k(λ) of intermediate products (EADS) (Figure 6b) of the sequential kinetic model (Scheme 1) were also calculated.

In the dynamics of the reverse BR photoreaction, three transitions with characteristic times τ′₁ = 0.19 ps, τ′₂ = 1.1 ps, and τ′₃ = 16 ps were revealed (Table 1). The corresponding DADS and EADS together with the final spectrum ΔA₃(λ, 45 ps) are shown in Figure 6a and b, respectively. The EADS of the fastest intermediate resolved for delays shorter than τ′₁ (Figure 6b, red curve) reflects the spectrum of relaxed excited state of K₅₉₀ (K₅₉₀*)—an analogue of the excited state I₄₆₀—relative to the GSB_BR band. This spectrum, similar to the spectrum of I_460, contains an intense ESA1_K* band and a small ESA2_K* band, which are typical for the excited state of RPSB in rhodopsins. The FC state could not be resolved in these measurements. The EADS of two following intermediates evolving with the characteristic times τ′₂ and τ′₃ also contain the absorption band of K₅₉₀*, which indicates the heterogeneity of the excited state. The complete disappearance of the absorption band in the 460 nm region, characterizing the excited state S₁, is observed at the characteristic time τ′₃ synchronously with the disappearance of the absorption band in the 620–700 nm region, related to the vibrationally excited state of the intermediate product BR′. The relative distribution of the intramolecular S₁ → S₀ conversion through the timescales τ′₁, τ′₂, and τ′₃ was estimated from the ESA1_K* signal by decomposing the EADS into Gaussian components (see Supplementary Materials, Figure S2) and was found to be 20/60/20, respectively (Table 1).

The decomposition of EADS into Gaussians also allowed us to characterize the spectra of the different states involved in the reverse photoreaction: K₅₉₀* and the intermediate products BR′₁ and BR′₂ (Figure 6c). The absorption spectrum of K₅₉₀* (Figure 6c, red curve) acquired from EADS (0.19 ps) includes a significant contribution from the SE signal, which manifests itself as a broad negative band in the 600–660 nm region. At longer delays, an unknown quantity of the ground state BR₅₆₈ was produced via the S₁ → S₀ conversion in the course of the reverse photoreaction. For this reason, the spectra of the two subsequent kinetic intermediates, BR′₁ and BR′₂, were obtained by decomposing the respective EADS into Gaussian components (see Supplementary Materials, Figure S2b,c). These spectra include a contribution of the K₅₉₀* spectrum (Figure 6c, green and blue curves). The absorption changes ΔA₃(620–700 nm, t) (Figure 5) reflect both the stimulated emission of the K₅₉₀* excited state and the absorption of the vibrationally excited product BR′. Quantitative analysis in the 660 nm region is also hampered by the light scattering of the pulse II. For this reason, the available data do not allow a reliable determination to what extent the kinetic intermediates BR′₁ and BR′₂ correspond to different electronic states of the product BR′. It can be assumed that the intermediate state BR′ is an ensemble of several vibrationally excited precursors of BR₅₆₈, analogs of the J₆₂₅ state in the forward photoreaction. The character of the DADS curves in the long-wavelength spectral region indicates that the final vibrational relaxation BR′ → BR₅₆₈ occurs with a characteristic time τ′₃.

The spectrum ΔA₃(λ, 45 ps) at the final delay (Figure 5, blue curve; Figure 6a,b, dashed lines) with experimental accuracy is a zero line, which indicates the photoconversion K₅₉₀* → BR₅₆₈ with a quantum yield close to 1. The obtained value of the quantum yield refines the one (0.8) we calculated earlier in work [44]. Thus, for the reverse photoreaction initiated from the K₅₉₀ product, as well as for the forward photoreaction, the presence of several pathways of the excited state decay in the femto- and early picosecond time ranges is characteristic, and all these pathways are reactive.

3. Discussion

In this work, the transient absorption dynamics of the BR reverse photoreaction initiated from the K₅₉₀ product at an early stage of its formation was investigated. The decomposition of the spectral-temporal matrices in the 400–740 nm region into discrete exponential functions (see Section 4, Equation (1)) made it possible to identify model-independent DADS of the three transitions with characteristic times of 0.19, 1.1, and 16 ps (Figure 6a, Table 1). Assuming that the absorption dynamics can be approximated by a sequential kinetic model (Scheme 1), we calculated the EADS of three kinetic intermediates (Figure 6b). All intermediates demonstrated a positive absorption at 460 nm, which is a characteristic feature of the excited state of rhodopsins. Decomposition of EADS into Gaussian functions, together with the linear spectrum of GSB_BR (see Supplementary Materials, Figure S2), allowed us to estimate absorption spectra of the intermediates (Figure 6c).

The spectrum of excited state K₅₉₀* resolved at time delays < 0.19 ps (Figure 6c, red curve) differs from the spectrum of I₄₆₀ (Figure 3c, green curve) in several aspects: the main band of K₅₉₀* is blue-shifted to 460 nm relative to the maximum at 474 nm of the I₄₆₀ band in the difference spectra; the satellite band at 520 nm is not pronounced; and there is a large negative SE signal at 620 nm, whereas the SE of the I₄₆₀ state is observed in the far-red region > 720 nm.

The S₁ → S₀ conversion of the K₅₉₀* excited state is kinetically heterogeneous. The fastest transition at τ₁′ = 0.19 ps results in a decrease of the K₅₉₀* absorption at 460 nm by ~20% (Table 1, Figure S2a) and to an appearance of the primary vibrationally excited product BR′ with the band maximum at 690 nm (Figure 6c, green curve). The next transition at τ₂′ = 1.1 ps is accompanied by a further decrease of the K₅₉₀* absorption by ~60% (Figure S2b) and enhancing the product BR′ absorption with a maximum at about 660 nm (Figure 6c, blue curve). Still, there remains some residual K₅₉₀* absorption with a relative amplitude of ~20% (Figure S2c). The slowest transition at τ₃′ = 16 ps leads both to the complete decay of K₅₉₀* absorption and to the evolution of BR′ to the all-trans BR₅₆₈ ground state (Figure 6b, dashed curve).

The mechanism of the S₁/S₀ surfaces crossing in photochemical reactions of various rhodopsins is a matter of long discussion [66,67]. One of the controversial issues is whether the motion along the PES in the CI region is diffusive (overdamped) or inertial. In the case of a diffusive mechanism, the quantum yields of 13-cis and all-trans products do not depend on whether the reaction proceeds in the forward or reverse direction. If we designate the quantum yield of the 13-cis state for the trans → cis transition (the forward BR reaction) as Y₁, and the quantum yield of the trans state for the 13-cis → all-trans transition (the reverse BR reaction) as Y₂, then in the case of the diffusion mechanism, the relation Y₁ + Y₂ = 1 is fulfilled [68]. In the alternative case of an inertial mechanism, the quantum yields of 13-cis and all-trans products depend on the direction of the reaction. The reason for this is that when passing through the thin CI region by the inertial mechanism, the torsional momentum of the nuclear motion is preserved, and this determines the direction of the system’s motion along the reaction coordinate [68,69,70,71]. In a simplified one-dimensional model of the CI region, the system can move along any of the two diabatic terms (thin solid lines in Figure 1b) forming either the product J₆₂₅ or remaining on the excited PES (arrows branching in Figure 1b). A comeback to the ground all-trans state (BR₅₆₈) is possible via movement along the excited PES in the backward direction. Within the framework of this crossing model, equality of quantum yields of the forward and reverse photoreactions is expected: Y₁ ≈ Y₂ [69]. To elucidate the mechanism of S₁ → S₀ conversion in the CI region, it is important to measure the quantum yield of the BR reverse photoreaction.

The zero transient absorption at 45 ps after pulse II (Figure 5) means that the 13-cis → all-trans transition of the reverse BR photoreaction has the same quantum yield Y₂ = 1 as was measured at a nanosecond time scale [8,23,47] and differs substantially from the quantum yield Y₁ = 0.65 of the forward photoreaction. Since the reverse photoreaction was initiated from the product K₅₉₀ immediately after its formation, the motion through the CI region during the reverse photoreaction follows via phase space trajectories that differ significantly from the trajectories of the forward reaction (Figure 7). The differences in the reaction pathways of the forward and reverse reactions may be caused by a multifaceted topology of the CI region. Even for the simplest molecule of AlH₂ consisting of three atoms, the conical intersection represents three points that are not connected to each other [72]. The author concludes that in complex systems, additional intersection regions may appear in unexpected areas of nuclear coordinate space.

The high quantum yield of the reverse photoreaction means the absence of considerable branching and justifies the usage of the sequential kinetic model (Scheme 1) for the derivation of the difference spectra of intermediates. The reverse photoreaction of BR is unexpectedly slow. The characteristic times τ₁′, τ₂′, and τ₃′ are in a good agreement with the data obtained in [45] upon initiation of the reverse photoreaction from the K₅₉₀ product at a time delay of 60 ps (0.3, 1.7, and 11 ps). Our data fully confirm the conclusion of [45] that the excited state K₅₉₀* is long-lived, finally decaying with a time of > 10 ps. However, our data demonstrate that the primary product of the S₁ → S₀ conversion differs significantly from the BR₅₆₈ state: the transient spectra in Figure 5 at delays of 1–6 ps contain a significant positive absorption band in the region of 620–700 nm, whereas similar spectra in Figure 6b of ref. [45] are represented in this region by a bleaching band with a minimum at ~620 nm. The differences may be caused, firstly, by the fact that when calculating the number of BR₅₆₈ molecules excited by pulse I and then by pulse II, we were able to determine the probabilities of these events (parameters α and β) quite accurately (see Supplementary Materials, Section S1.2); and secondly, by the fact that the number of molecules of product K₅₉₀, not excited by pulse II and contributing to the ΔA^I+II(λ, t) signal (the second term of Equation (S6)), was taken into account.

One of the reasons for the presence of several excited states with different decay dynamics and product formation efficiencies in rhodopsins during the forward photoreaction may be variations in the structure of their chromophore centers. The main factors are the conformation of RPSB [19,73] and its interaction with charged amino acid residues, primarily with the complex counterion [18,28,39,40,74,75,76,77,78,79,80], in the case of BR consisting of the Asp85 (primary counterion/proton acceptor), Asp212, and three water molecules [81]. Disruption of the hydrogen bond system that mediates this interaction can lead to a significant slowdown in the photoreaction and a decrease in its efficiency [28]. For BR [18,65,79], proteorhodopsin (GPR) [18], Krokinobacter eikastus sodium pump rhodopsin (KR2) [39], and Chlamydomonas reinhardtii channelrhodopsin (ChR2) [80], an initial heterogeneity of the chromophore center was revealed, associated with partial protonation of the primary counterion or disruption of the hydrogen bond between the counterion and RPSB. In the case of BR, over a wide pH range, the proportion of molecules with protonated Asp85 is extremely small [18], but most likely it determines the presence of a time component τ₂ = 3.5 ps, characterizing the non-reactive excited state decay. It can be assumed that in the case of the reverse photoreaction of BR, the presence of three decay times of the K₅₉₀* excited state is determined by the heterogeneity of the chromophore center of this product, which may also be indicated by the wide absorption spectrum of K₅₉₀ at time delay of 5 ps (Figure 4b, blue curve). Using FTIR spectroscopy and X-ray structural analysis, it was shown that the formation of the K₅₉₀ product weakens or disrupts the hydrogen bond between the RPSB proton and the W402 water molecule, which is part of the complex counterion, and through it with Asp85 and Asp212 [82,83,84,85,86]. Violation of the stable RPSB-counterion system can cause variations in the interaction of the RPSB proton with charged and polar amino acid residues, which will entail a change in the dynamics of the reverse photoreaction. The heterogeneity of the chromophore center of K₅₉₀ associated with the protonation of Asp212 was shown using theoretical calculations [45]. Another reason for this heterogeneity may be the difference in the structure of the chromophore center of the products J₆₂₅ and K₅₉₀, the ratio of which at a time delay of 5 ps was estimated as 30/70. Another suggestion is that the heterogeneity of the excited state may be related to the nature of the population of different vibrational modes during excitation in different molecular ensembles. Photoexcitation of the structurally unrelaxed, twisted 13-cis chromophore most likely results in excitation of both reactive and non-reactive vibrational modes. Since the photoreaction of rhodopsins occurs in a coherent regime, the population of some non-reactive vibrational modes may contribute to the loss of coherence of reactive vibrational modes and thereby slow down the reverse photoreaction.

Photoisomerization of RPSB from cis to trans form in the same environment usually occurs faster than the trans → cis phototransition [3,19,73]. The τ₁′ time obtained in the present work is in good agreement with this pattern. It can be assumed that in about 20% of K₅₉₀ molecules, the interaction of RPSB with the complex counterion is not significantly disturbed, while in 80% of the molecules, significant changes have occurred in this interaction. Based on the obtained data, the following scheme of PESs of the reverse photoreaction of BR can be presented (Figure 7). The photoreaction is initiated in three fractions of molecules. The initial dynamics of the wave packet, as a result of which the K₅₉₀* excited state is formed, most likely does not differ in these fractions. The time of the subsequent S₁ → S₀ transition strongly depends on the interaction of RPSB with the protein environment, which can affect both the shape of the PES of the S₁ electron level and the structure of CI. Because the gas phase cis → trans photoisomerization of RPSB occurs in 0.4 ps [87], it can be concluded that the protein environment can not only accelerate, as evidenced by the time component of 0.19 ps, but also slow down this process. In 80% of K₅₉₀ molecules, the reverse photoreaction is significantly slower (1–16 ps) compared to the gas phase. The vibrational relaxation processes during the formation of the products of the reverse photoreaction take much longer than in the forward photoreaction (16 ps compared to 3.5 ps).

4. Materials and Methods

Reagents were purchased from Sigma, Panreac (Barcelona, Spain) and Anatrace (Maumee, OH, USA).

4.1. Preparation of BR Samples

Purple membranes were obtained from H. salinarum ET1001 cells and kindly provided by the Central Research Technological Institute “Tekhnomash”. A suspension of purple membranes in Na-phosphate buffer (25 mM, pH 7.0) was sonicated at 90 W for three minutes to reduce light scattering. In samples prepared for femtosecond spectroscopy experiments, the concentration of BR was 1.8 mg/mL, the purity factor (A₂₈₀/A₅₆₈) was 1.78, and the absorption at the maximum of the α-band was 4.4 OD units/1 cm optical length. Light adaptation was achieved by illuminating with a halogen lamp (KGM24-250, 24 V, 250 W, Ufa Electric Lamp Plant, Ufa, Republic of Bashkortostan, Russia) for three minutes.

4.2. Stationary Spectroscopy

Stationary absorption spectra of BR were recorded using a UV 1700 spectrophotometer (Shimadzu Corporation, Kyoto, Japan) and quartz cuvettes with an optical length of 1 cm. For this purpose, BR samples prepared for femtosecond experiments were diluted 10 times. This consisted of a sonicated suspension of purple membranes in a Na-phosphate buffer (25 mM, pH 7.0) containing BR at a concentration of 0.18 mg/mL and an absorption at the maximum of the α-band of 0.44 OD units/1 cm optical length.

4.3. Femtosecond Transient Absorption Spectroscopy

The photoinduced absorption signals of BR (∆A(λ, t)) were recorded on a femtosecond setup using the pump-probe [88] and pump-pump-probe [44] methods. The forward photoreaction of BR was initiated by pulse I with a wavelength of 540 nm, a duration of 20 fs, a diameter in the sample of 300 μm, and an energy of 200 nJ (Figure 4b, black curve). The reverse photoreaction of BR was initiated by pulse II with a wavelength of 660 nm, a duration of 25 fs, a diameter in the sample of 180 μm, and an energy of 200 nJ (Figure 4b, grey curve). Excitation of BR by pulse II occurred at a time delay of t₁ = 5 ps after pulse I; excitation by pulse II without preliminary excitation by pulse I was also used for control. Pulses I and II were linearly polarized parallel to each other, and their density was no more than 3·10¹⁵ photon/cm², which corresponded to the linear regime with absorption of less than one photon by BR₅₆₈ and K₅₉₀ molecules. For probing, we used a supercontinuum pulse with an energy of 10 nJ, a diameter in the sample of 100 μm, a time delay relative to pulse I of up to 12 ps, and linear polarization at a “magic” angle of 54.7° relative to pulses I and II. The experiments were carried out at a temperature of 21 °C in a flow optical cell with an optical path length of 0.5 mm. The circulation rate in the flow cell was 9 mL/min, which excluded multiple excitations of the same sample volume at the used excitation frequency of 60 Hz. The spectra were corrected by group delay dispersion as described previously [89]. Accounting for the coherent artifact and deconvolution of the hardware function in the region of t = 0 were carried out in accordance with the method described in [90,91]. The difference spectra of BR absorption ΔA^I(λ, t) and ΔA^I+II(λ, t), recorded after the action of pulses I and I + II, respectively, were obtained by accumulating 50 signals. Additionally, the spectra ΔA^I(λ, t), ΔA^I+II(λ, t), and ΔA^II(λ, t) were recorded at a time delay of t₂ = 50 ps with an accumulation of 5000 signals. Based on the obtained data, the spectral-temporal matrix ΔA₃(λ, t—t₁) was calculated, characterizing the dynamics of the reverse photoreaction K₅₉₀ → BR₅₆₈, where t—t₁ was the time delay relative to pulse II (see Supplementary Materials, Equations (S1)–(S7)). The Matlab application package https://www.mathworks.com/products/matlab.html (accessed on 01 August 2024) was used to process the data.

4.4. Mathematical Analysis of Absorption Dynamics

The absorption dynamics of the forward and reverse BR photoreactions was analyzed by decomposing the spectral-temporal matrices ΔA^I(λ, t) and ΔA₃(λ, t—t₁) into a linear combination of n discrete exponential functions:

$$\mathsf{\Delta }A\left(\mathsf{\lambda },t\right)={\sum }_{k=1}^n{D}_k(\mathsf{\lambda })·e^{-t/{\tau }_k}+A_{n+1}(\mathsf{\lambda }),$$

(1)

under the assumption that the characteristic times {τ_k} can be considered as “global” parameters, and the wavelength-dependent pre-exponential amplitudes D_k(λ) represent the spectra associated with exponential decay (decay-associated difference spectra, DADS) [92]. The times {τ_k} were found by a nonlinear minimization procedure of the normalized sum of squared residuals, the amplitudes D_k(λ), and the final spectrum A_n+1(λ), were calculated using the standard linear regression method [93].

If the spectral dynamics can be approximated by a system of n linear differential equations describing transitions between n + 1 electronic states, then the solution of such a kinetic model will be a linear combination of n exponential components, with the decay times τ_i being defined as the roots of the characteristic polynomial of the system of linear differential equations. In most cases, quantitative evaluation of the number n, the amplitudes D_k(λ), and the decay times τ_k of the decomposition (1) are mathematically reliable [94]. However, it is impossible to determine, in a common case, the kinetic model and the respective matrix of transition rates from the experimental data without additional assumptions, since any rotation of the state vector by an orthogonal transformation does not change the characteristic roots [95]. In other words, a single set of DADS in Equation (1) corresponds to an infinite number of different kinetic models, the choice between which can be made only on the basis of additional information [96].

In the simplest case considered here, the DADS components were enumerated in accordance with increasing decay times and considered formally as n sequential kinetic transitions (Scheme 1).

After determining the characteristic times {τ_k}, the difference spectra A_k(λ) of the intermediate products (which are also called evolution-associated difference spectra, or EADS, in the sequential kinetic model [92]) were calculated by the inverse of the transition rate matrix. If the decay times differ significantly, τ₁ << τ₂ <<…<< τ_n, the EADS of the intermediates are expressed through the DADS components in simple terms:

$$A_k\left(\mathsf{\lambda }\right)={\sum }_{i=k}^n{D}_i(\mathsf{\lambda })+A_{n+1}(\mathsf{\lambda }).$$

(2)

Although structural and kinetic heterogeneities, including the trajectory branching in the CI region [97], are inherent for the photochemistry of BR, its kinetic transitions can be analyzed in the first approximation within the framework of a linear sequential model [19].

5. Conclusions

In this work, the dynamics of the reverse photoreaction of BR initiated from the product K₅₉₀ at an early stage of its formation was characterized. It was shown that the reverse photoisomerization of the RPSB chromophore occurs through an excited state with times of 0.19, 1.1, and 16 ps with a quantum yield of ~1. BR_568, as the final product of the reverse photoreaction, is formed from intermediate states undergoing vibrational relaxation. The presence of three times of the excited state decay can be determined by the presence of different potential barriers on the potential surface of the excited state, which control the rate of intramolecular S₁ → S₀ conversion of the K₅₉₀* excited state to the primary vibrationally excited product BR′. Comparison with the dynamics of the forward photoreaction showed that the reverse photoreaction proceeds, as a whole, more slowly due to a significant increase in the proportion of picosecond components of the excited state decay. At the same time, the reverse dynamics are faster and more efficient in the region of CI: the lifetime of the fastest component of S₁ → S₀ conversion is 0.19 vs. 0.52 ps, and the quantum yield is 1 vs. 0.64. Thus, the obtained results may indicate that the interaction of the chromophore with the protein environment in BR during the forward photoreaction at the stage of the K₅₉₀ product becomes heterogeneous.