Ground-state heterogeneity and vibrational energy redistribution in bacterial phytochrome observed with femtosecond 2D IR spectroscopy

Phytochromes belong to a group of photoreceptor proteins containing a covalently bound biliverdin chromophore that inter-converts between two isomeric forms upon photoexcitation. The existence and stability of the photocycle products are largely determined by the protein sequence and the presence of conserved hydrogen-bonding interactions in the vicinity of the chromophore. The vibrational signatures of biliverdin, however, are often weak and obscured under more intense protein bands, limiting spectroscopic studies of its non-transient signals. In this study, we apply isotope-labeling techniques to isolate the vibrational bands from the protein-bound chromophore of the bacterial phytochrome from Deinococcus radiodurans . We elucidate the structure and ultrafast dynamics of the chromophore with 2D infra-red (IR) spectroscopy and molecular dynamics simulations. The carbonyl stretch vibrations of the pyrrole rings show the heterogeneous distribution of hydrogen-bonding structures, which exhibit distinct ultrafast relaxation dynamics. More-over, we resolve a previously undetected 1678 cm − 1 band that is strongly coupled to the A-and D-ring of biliverdin and demonstrate the presence of complex vibrational redistribution pathways between the biliverdin modes with relaxation-assisted measurements of 2D IR cross peaks. In summary, we expect 2D IR spectroscopy to be useful in explaining how point mutations in the protein sequence affect the hydrogen-bonding structure around the chromophore and consequently its ability to photoisomerize to the light-activated states.


I. INTRODUCTION
2][3][4][5][6] Phytochromes contain a covalently bound bilin chromophore, which absorbs red light.In bacterial phytochromes, the biliverdin (BV) chromophore is almost exclusively used.The photoactivated chromophore initiates a cascade of signaling pathways that control bacterial growth and development. 7,8The signaling domains in bacterial phytochromes comprise PAS (Per-Arnt-Sim) and GAF (cGMP phosphodiesterase, adenylyl cyclase, FhlA) domains, which are versatile signaling domains that accommodate the chromophore. 9Structurally, BV is located at the interface of the GAF and PHY domains.The domains are linked to a phytochrome-specific (PHY) domain. 10The extension of the PHY domain into the chromophore region is commonly referred to as the "tongue" and has been shown to convert from an antiparallel β-sheet to an α-helix upon photoisomerization of the chromophore. 11,12This structural transition has been postulated to be responsible for the activation of downstream signaling in phytochromes.
BV is a tetrapyrrole chromophore of the bilin family.It consists of the four substituted pyrrole rings (A-D) that are connected with each other via methine bridges.BV can be seen as a breakdown product of protoporphyrin IX, with which it shares many structural similarities, such as vinyl and propionate substituents.Rings A and D contain oxygen atoms directly connected to the ring structure, forming carbonyl groups that are excellent hydrogen (H)bond acceptors, whereas the propionate groups are connected to rings B and C. The structure of the protein-bound chromophore along the residues capable of H-bonding to the D-ring is depicted in Fig. 1.
The absorption of light by BV induces a transition from the resting (Pr) state to the light-activated (Pfr) state. 13,14The transition involves a photoreaction containing multiple intermediate states, which form due to concerted structural rearrangements of the chromophore and the surrounding protein. 15,168][19] The ability of certain protein residues to form H-bonding interactions with the chromophore is critical for the existence and stability of the transient photo products. 20,21This is confirmed by a large number of mutation studies, in which a conserved amino acid is mutated to one that can no longer form H-bonds through its side chains. 22Mutating Tyr263 to phenylalanine drastically reduces the photoproduct quantum yield, making the photocycle extremely unlikely to happen. 23Similarly, almost all mutations of the Asp207 result in locking the protein in the Pr state, completely inhibiting its photoactivity. 24The His260Ala mutation makes the protein unable to bind the chromophore, while some mutations of the Gln36 destabilize the protein entirely, making it unable to fold into a stable and soluble conformation. 6,248][29][30][31][32] Recently, time-resolved femtosec-FIG.1.The structure of the biliverdin chromophore covalently attached to the phytochrome.The tetrapyrrole rings that make up the chromophore are labeled accordingly.Residues critical for the photochemical properties of BV are included.The closest environment around the D-ring carbonyl shows the presence of His290 residue and two water molecules that stabilize a network with the nearby propionate group of ring C. ond x-ray crystallography has been used to visualize early molecular events upon photoexcitation with atomic resolution, which involves a counter-clockwise rotation of the BV's D-ring and a photodissociation of water molecules that tie the H-bonding network together in the vicinity of the chromophore. 31,32The findings were consistent with the spectroscopic data measured in solution. 18Nevertheless, crystal packing may lock the protein in a specific conformation, and information on heterogeneity and solvation dynamics is often lost. 335][36] Structural information is obtained by analyzing the emergence and time-dependent evolution of cross-peaks between vibrational modes.In most cases, cross peaks in 2D IR spectra appear either due to vibrational coupling between modes or due to dynamic processes, such as energy transfer or chemical exchange.Recently, the first application of 2D IR to study phytochromes has been demonstrated by Buhrke et al., in which complex cross-peak patterns between the chromophore and the protein signals were elucidated for the bacteriophytochrome 1 from Agrobacterium tumefaciens. 37An interesting approach was proposed by Ruf et al. for isolating phycocyanobilin chromophore signals in the 2D IR spectra of a cyanobacteriochrome. 38 The method is based on incorporating isotope unlabeled chromophore into 13 C 15 N-labeled protein structure.This way, the unique signatures of the phycocyanobilin chromophore become separated from more intense protein vibrations.By applying this approach, the solvation dynamics of the resting and light-activated states could be studied with 2D IR spectroscopy.
In this work, we apply such a selective isotope-labeling approach to investigate the structure and dynamics of a bacterial phytochrome from Deinococcus radiodurans with 2D IR spectroscopy.We unravel a heterogeneous distribution of structures around the chromophore, which is manifested by four distinct absorption bands.The ultrafast dynamics are then quantified by the time-resolved evolution of both diagonal and cross-peak features in the 2D IR spectra.

A. Expression and purification of isotopically labeled PAS-GAF-PHY DrBhP phytochrome
The DrBhP bacterial phytochrome was expressed in Escherichia coli strain BL21 (DE3) using the established protocols. 9,11,24,43,45The biliverdin chromophore was incorporated in the protein lysate by incubating overnight on ice.The apoprotein was also isolated to aid peak assignments.The uniformly isotope-labeled protein was expressed in a minimal medium supplemented with 13 C-enriched glucose and 15 NH 4 Cl.The proteins first underwent Ni-NTA affinity purification (HisTrap HP 5 ml, GE Healthcare), followed by size exclusion chromatography (Superdex 200, GE Healthcare) using Äkta pure protein purification system (GE Healthcare).The purified proteins were eluted in 30 mM Tris-HCl (pH 8), concentrated to 10 mg ml −1 , and flash frozen.All purifications were carried out in the dark.

B. Femtosecond 2D IR spectroscopy
The output from a Ti:Sa amplifier operating at 5 kHz (Spectra Physics Spitfire Ace) is first used to pump a commercial optical

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scitation.org/journal/jcpparametric amplifier (TOPAS-Twins, Light Conversion) and generate a tunable signal and idler beams.The fs mid-IR laser pulses are then produced using difference-frequency generation (DFG) of the signal and idler beams by focusing them on a 0.5 mm AgGaS 2 crystal.2][43] Two replicas serving as probe and corresponding reference beam are created using a BaF 2 wedge (each <5% of the total intensity).The remaining portion of the beam is sent to a germanium acousto-optic modulator (Ge-AOM) based pulse shaper (PhaseTech), which generates a pair of pulses with variable time delay.The beams are focused at the sample spot and recollimated using off-axis parabolics of 10 and 15 cm focal length, respectively.After the sample, probe and reference are imaged onto the front slit of a spectrograph as part of a commercial detection system (Horiba i320 spectrograph, dual row MCT array with 64 pixels each; Infrared Systems).The sample was continuously illuminated with a diode laser to ensure that all molecules are in the resting Pr state during 2D IR measurements.The data were collected with a time step of 20 fs with an overall interferogram length of 3200 fs.All measurements were carried out in perpendicular polarization.A more detailed description of the experimental setup has been published elsewhere. 44The sample was placed between a pair of CaF 2 windows with a 56 μm thick spacer for FTIR and 100 μm thick for 2D IR measurements.

C. Quantum mechanics/molecular mechanics (QM/MM) calculations
In a previous study, 45 a 4.5μs-long molecular mechanicsmolecular dynamics (MM-MD) simulation in the NPT ensemble was used to investigate the Pr state of DrBph phytochrome starting from the 4Q0J entry 46 of the Protein Data Bank (PDB).The AMBER ff14SB force field 47 was used for the protein, TIP3P for water molecules, 48 while the general Amber force field (GAFF) 49 was used for biliverdin IXα (BV).From such a sampling, 117 structures were extracted and cut by keeping only one monomer and a shell of water molecules centered on the chromophore.Then, the resulting system was subjected to quantum mechanics (QM)/MM optimizations with BV, the side chain of Cys24, His290, and the closest water molecules with 3.2 Å of D-ring carbonyl and amidic nitrogen as QM subsystem described at B3LYP+D3/6-311G(d, p) level of theory.The complete pipeline followed is reported in a recent study. 20o further understand how a putative protonation of the C-ring propionate may affect the local environment, and consequently, how the stretching frequency of the C-ring propionate shifts, we have here performed a MM MD simulation of the dimeric system by protonating such a chemical group.Specifically, we have carried out 4 replicas of 500 ns, each starting from an equilibrated frame of the "deprotonated" MM MD.The system was first subjected to two minimization cycles gradually releasing the constraints placed on the BV and protein backbone.Multiple heating/equilibration steps were performed in NVT and NPT ensembles, with a stepwise release of the restraints placed on the BV and key protein residues.We have used the same force fields as in the "deprotonated" case.We have recomputed the partial charges of BV using the restrained electrostatic potential atomic partial charges (RESP) protocol 50 on top of a B3LYP/6-311G(d, p) electrostatic potential calculation.We have used the last 400 ns of each replica to sample 328 geometries to compute the frequencies of the A-and D-rings carbonyl groups and the B-and C-rings propionate groups.BV, the side chain of Cys24, and the water molecules within 3.2 Å to the protonated C-ring propionic group were included in the QM subsystem described at the same level of theory as the "deprotonated" case.All the calculated frequencies were scaled by 0.967 to account for anharmonic effects. 51ore information on the MD approach and ab initio frequency calculations used in this study has been described elsewhere. 20,45ll the QM/MM calculations were run with the Gaussian 16 suite of programs, 52 while the MM MD simulations with AMBER18. 53

A. FTIR spectroscopy
The linear FT IR spectra of the 13 C 15 N-labeled phytochrome are presented in Fig. 2. When isotope labels are introduced into the protein backbone, the protein Amide bands become red-shifted by ∼60 cm −1 .As expected, the most intense Amide I band is then centered at 1600 cm −1 , but its tail extends far up to 1660 cm −1 .The chromophore signatures appear as very weak peaks on top of an intense background signal of the Amide I band and D 2 O.

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The signals originating from BV are at least 3 orders of magnitude weaker compared to the Amide I vibrations.Thus, the lack of isotope labeling would make it extremely difficult to extract them.The background-subtracted spectra in the chromophore region are shown in Fig. 2(b).All the peaks observed in the FTIR spectra are successfully detected in 2D IR experiments with identical relative intensities without the need for subtracting the background.For that reason, the vibrational spectra of BV bands are further discussed in detail in the section below.

B. 2D IR spectroscopy and population relaxation of diagonal peaks
Time-resolved 2D IR spectra in the chromophore region are presented in Fig. 3.The spectra were collected for waiting times (Tw) from 0.2 to 4.0 ps.The positive diagonal peaks of the 0-1 transition are depicted in red, whereas the corresponding negative 1-2 transition signals, shifted due to anharmonicity, are given in blue.
The 2D IR spectrum shows four distinct peaks that can be attributed to the internal structure of the chromophore.Following the previous assignments, we attribute the peaks at 1700 and 1710 cm −1 to the carbonyl vibrations of the D-ring. 54The low frequency peak is approximately two times stronger than its high frequency counterpart.Consistent with the previous observations, the vibrational band of the A-ring carbonyl is located at about 1730 cm −1 and is the weakest of all bands but still detectable in 2D IR spectra.The strongest of all peaks is located at around 1678 cm −1 .To the best of our knowledge, the peak has not been assigned before.Its signatures in the time-resolved IR spectra following the excitation with visible pulses are weak, possibly due to destructive interference with the signals originating from the photoproducts. 30The data supporting the assignment of this peak to the chromophore are given in the discussion section.
Population relaxation dynamics of individual peaks are estimated by fitting the diagonal traces of Tw-dependent 2D IR spectra with Gaussian functions and extracting the integrated areas.The fit to one time point and the time-dependent relaxation decay curves are presented in Fig. 4. The most intense peak at 1678 cm −1 decays exponentially with a single time constant of τ = 1.1 ps.Distinct relaxation dynamics are observed for the D-ring carbonyl stretch vibrations at 1700 and 1710 cm −1 .The high frequency peak decays with a single exponential time constant τ = 1.0 ps, whereas the low frequency peak exhibits bi-exponential decay with time constants of τ 1 = 1.5 ps (90%) and τ 2 = 2.5 ps (10%).Constant offset was applied to the fits to account for thermal effects due to the vibrational relaxation process.
The spectral diffusion dynamics of the carbonyls are quantified using center slope (CLS) analysis. 55Spectral diffusion analysis allows us to determine the extent of homogeneous and inhomogeneous contributions to the lineshape and quantify the timescales of the environmental fluctuations that lead to the broadening effects.Slices are taken along the probe axis to avoid interference from the overlapping 1-2 transitions.The intensity of the 2D IR signal of the A-ring carbonyl is too low for accurate time-dependent analyses, and because of that, the CLS estimation is focused on the peaks at 1678, 1700, and 1710 cm −1 .An example of the slices taken for the analysis along the estimated CLS curves is presented in Fig. 5.The 2D IR peaks are elongated along the diagonal, which is indicative of a lineshape that is inhomogeneously broadened.It is often the case FIG. 3. Tw-dependent 2D IR spectra of the DrBhP phytochrome in the chromophore region.The diagonal peaks show absorption bands at 1678 cm −1 and an asymmetric band consisting of two components absorbing at 1700 and 1710 cm −1 , respectively.The region above 1730 cm −1 , where A-ring vibrations are located, is plotted with a 6× intensity scaling factor due to relatively weaker intensity compared to other bands.In addition to the diagonal peaks, a number of cross peaks appear between the signals, which increase in intensity with increasing Tw.The peak at 1678 cm −1 and the A-ring bands are coupled with all other vibrations.The doublet corresponding to the subpopulations of the D-ring mode does not show cross peaks.Vertical slices through the A-ring peak that highlights the discrete nature of cross peaks formed between this band are given in Fig. S2 in the supplementary material.in 2D IR experiments that such correlation is to a large extent lost with increasing Tw because the system is capable of equilibrating within the first several picoseconds.In the case of carbonyl modes of the BV chromophore, the lineshapes remain elongated within the whole experimental window, and the homogeneous component is similar for all the studied vibrations, with a slightly smaller CLS observed for the low frequency component of the D-ring carbonyl stretch.

C. Vibrational coupling and dynamic cross peaks in 2D IR spectra
To gain more insights into the structural dynamics of the protein-bound chromophore, we also take a close look at cross peaks in the 2D IR spectra.The ability to separate cross peaks from diagonal peaks is one of the biggest advantages of 2D IR over conventional IR techniques.The analysis is presented in detail in Fig. 6.The newly detected 1678 cm −1 peak appears to be intrinsically coupled to all carbonyl stretch vibrations in the chromophore, which is manifested by the presence of cross peaks at early waiting times.Interestingly, the vibration is coupled to both the D-and A-ring modes, which are substantially far apart from each other.Nevertheless, the D-and A-ring vibrations appear to be coupled with each other as well, indicating that strong through-bond coupling effects occur in the chromophore.The individual peaks comprising the By increasing the waiting time between the pulses, it is possible to track the emergence of dynamic cross peaks that may occur due to chemical exchange or vibrational energy transfer processes.The averaged Tw-dependent slices along the probe axis for ωpu = 1677-1679 cm −1 are presented in Fig. 6(b).The slices were normalized by the intensities of the diagonal peaks so that the population changes of the cross peaks with respect to their diagonal counterparts can be extracted.The cross peaks rise with increasing Tw but also decay with the population relaxation lifetime as seen in Fig. 6(c).Identical growth/decay pattern has been observed for vibrational energy transfers before. 56The cross peak growth is extremely fast because the modes are inherently coupled.This observation is characteristic of the relaxation-assisted (RA) cross peak intensity enhancement. 57Notably, there is no intensity growth observed between the D-ring peaks at 1700 and 1710 cm −1 .This is understandable in case the two peaks originate from distinct conformations that do not interconvert with each other within the experimental time window.

A. Structural assignment of the IR signals
The biliverdin chromophore exhibits a great number of distinct vibrational modes, which, besides the studied carbonyl stretches, include characteristic, highly delocalized bands originating from the C=C stretch of the methine bridges as well as carboxylic acid signatures of the propionate groups attached to the rings B and C. 58 It has also been shown that BV can be found in different protonation states. 59,60The complexity of the vibrational spectra of BV increases as the chromophore becomes bound to the protein.This is due to the fact that BV becomes part of an extensive H-bonding network connecting protein residues, chromophores, and the surrounding water.
A great deal of information can be obtained from Vis-pump IR-probe experiments as the bleach signals at early time delays are mostly concerned with vibrations associated with the chromophore.This helped assign the high frequency signals to carbonyl stretches of the terminal BV rings. 30The D-ring of BV is the first to significantly change its conformation, and thus, the signals at 1700 cm −1 (in D 2 O) are the strongest in the transient spectra.If structural changes upon photoexcitation are small in other parts of the chromophore and the resulting peaks overlap with peaks originating from the photoproducts, the information that can be taken from the transient spectra is limited.This may explain why the 1678 cm −1 peak has not yet been assigned to any specific vibration.Interestingly, in cyanobacteriochromes, similar peaks are sometimes seen in the resonance Raman spectra and have been assigned to the methine bridge vibrations of rings A and B of phycocyanobilin. 61The significant difference in substituents and the location of double bonds in the A-ring of biliverdin, as compared to phycocyanobilin, makes such an assignment unlikely for the phytochrome studied in this work.

Conformational heterogeneity of the D-ring carbonyl
The D-ring moiety is possibly the most appreciated part of the BV chromophore.It undergoes dynamic rearrangements on a broad range of timescales after light excitation and possesses a carbonyl group that is an excellent sensor that allows tracking those changes with vibrational spectroscopy.The mechanism and rates of the photoisomerization of BV around the D-ring are affected by the presence of H-bonding interactions in its vicinity.Two distinct isoforms of BV have been identified thanks to the high sensitivity of the carbonyl stretch to the local electrostatic environment.This observation has been supported by crystallography and theoretical studies.It has been shown that His290 is at the closest distance to the D-ring carbonyl and interacts with it through an H-bonding network that also involves water molecules and the propionate group of the C-ring. 27Interestingly, by mutating His290 to Thr, the overall distance between the D-ring and the interacting side chain is increased, allowing water molecules to fully solvate the D-ring carbonyl and shifting the vibrational frequency to 1691 cm −1 .This is consistent with the fact that stronger H-bonding interactions red-shift the vibrational frequency of carbonyls. 20,62The two peaks observed in our experimental data are thus assigned to different H-bonding patterns involving the His290 residue and a nearby water molecule around the D-ring.A recent QM/MM simulation study 20 has given important insights into this phenomenon, where a clear bimodal distribution of distances was found between the D-ring carbonyl oxygen atom and a nearby water molecule as well as the nitrogen atom of the His290 residue.In the latter case, the bimodal distribution is seen in QM/MM simulation replicas and a long classical MD simulation alike. 20In the case of the nearby water molecule, we find the same bimodal distribution for both the long MM MD (Fig. S3) and the QM/MM MDs. 20Both of them show a water molecule predominantly at a distance of ∼3.5 Å from the D-ring carbonyl.
Density functional theory (DFT) calculations of the C=O stretching mode as a function of the intermolecular distance from the water molecule predicted a frequency difference of 10 cm −1 , which is consistent with our experimental data.However, the magnitude of the vibrational frequency shift upon H-bonding to the histidine has not been established.Here, we present the results of the QM/MM calculations, which identify the key interactions that give rise to a sub-population of structures around the D-ring carbonyl in the DrBphP phytochrome and link different molecular orientations to the vibrational frequencies observed in the IR spectra (Fig. 7).Overall, we have optimized 117 structures at the DFT level computing the vibrational frequencies of the D-ring carbonyl stretching modes.More details about the methodology are reported in Sec.II.The predicted vibrational frequencies are in excellent agreement with the experimental data.The results show that the chromophore is typically found to be H-bonded to either His290 or a water molecule or does not form an H-bond with either.However, structures in which the D-ring binds to both were also identified, although they occurred extremely rarely.These results suggest that the observed blue shift in the experimental data may be caused by either type of H-bonding interactions, and it is not possible to separate the population of water-bound and Hisbound chromophore signals.As a result, the low-frequency peak at 1700 cm −1 is assigned to the sub-population of structures in which the D-ring does not participate in H-bonding, while the 1710 cm −1 peak is assigned to structures with H-bonded D-ring carbonyls.The ability to resolve these two sub-populations of structures offers a unique opportunity to quantify the effects of H-bonding .The region between 1690 and 1710 cm −1 is due to a single hydrogen bond between carbonyl and either water or His290 (structures B).The frequency region larger than 1710 cm −1 is due to the absence of any hydrogen bond (structures C).Finally, structure A represents a rare case of carbonyl H-bonded to both water and His290.

The Journal of Chemical Physics
interactions on the ultrafast structural dynamics of BV using 2D IR spectroscopy.

1678 cm −1 peak
To prove that the 1678 cm −1 peak can be assigned to the chromophore vibrations, we collected 2D IR spectra of the corresponding apoprotein, which lacks the chromophore in its structure.We then subtracted the 2D IR spectrum of the apoprotein from the spectrum of the wild-type phytochrome.The difference spectrum, presented in Fig. S1, shows an identical peak to the one observed for the isotope-labeled protein.Peaks in that frequency range are often assigned to the side chain vibrations of arginine residues.This is, however, only true in H 2 O, and all our experiments were carried out in D 2 O.We have also ensured that all the hydrogens are properly exchanged by carrying out multiple H-D exchange processes and incubating the sample until other typical signatures of incomplete exchange are completely missing from the spectra.It must also be noted that it would be highly unlikely to see strong 2D IR cross peaks from vibrational coupling as well as fast energy transfer if the vibrational mode was not a part of the internal structure of the chromophore.For the same reason, the vibration cannot be assigned to sub-populations of rings A and D becoming exposed to different electrostatic environments.However, the peak appears to possess many features of a carbonyl vibration such as an apparently large transition dipole moment and short vibrational lifetime.Since the propionate vibrations were not resolved in the experiment, it is possible that the peak originates from the carboxylic ends of the propionate chains attached to rings B and C. The distance between the carboxylate of ring C and the oxygen atom of the D-ring carbonyl is in the range of 6-7 Å, which makes it possible to observe cross peaks when two strong oscillators become coupled.However, it appears a little low in frequency if the propionates are fully protonated and too high for fully deprotonated forms.According to our QM/MM calculations, indeed, deprotonated propionate has the C=O stretching frequency far from the target zone [Fig.8(b)].The dissociation constants of propionic acid in biliverdin and bilirubin are still a matter of dispute, with reported pKa values spanning 4 orders of magnitude, ranging from as low as pKa = 4 to abnormally high pKa = 9. 63 It is generally known that BV is embedded in an acidic pocket and is surrounded by many protein residues.Thus, the vibrational frequencies may deviate substantially from those reported for fully solvated carboxylates.However, it must be noted that identical propionic acid groups are found in most hemoproteins, for which an extremely broad range of absorption frequencies has been reported.For instance, the protonated propionates in the heme structure of cytochrome aa 3 oxygen reductase absorb exactly at 1678 cm −1 . 64Frequencies as low as 1670 cm −1 have been reported in YddV diguanylate cyclase. 65Interestingly, the protonation state of propionate side chains is not simply controlled by the pH of the solution as the Pfr state in Agp2 phytochromes is found protonated even at relatively high pH values. 66o further investigate the implications of a putative propionate protonation, we have performed four 500 ns-long MM MD simulations by protonating the C-ring propionate.Protonation of the propionate of ring B is rather unlikely, as it would completely destabilize the salt bridge that keeps the chromophore structure stable in the binding pocket.The residues around the C-ring propionate have enhanced mobility and interact less frequently with it (Fig. S4).This dynamic behavior (especially of His260) also weakens the interaction between Tyr263 and Asp207.Finally, the close-by residues to B-ring propionate, the OD⋅ ⋅ ⋅His290, and Arg466⋅ ⋅ ⋅Asp207 interactions are not affected by protonation.
To gain more insights into how this different local environment affects the frequency range of carbonyls (A-and D-rings) and propionates (B-and C-rings) groups, we have extracted 328 frames from the MM MDs and optimized them at the DFT level.More details can be found in Sec.II.The results of the calculations are presented in Fig. 8 in comparison with the deprotonated case.The results are consistent with experimental data and suggest that protonated C-ring propionate may contribute to the low-frequency signal in the 2D-IR spectra.The calculated frequencies show that the C=O stretching mode of the C-ring propionates may take a very broad range of values when the group is protonated.The overall band exhibits a bimodal distribution with the high frequencies appearing in the range normally expected for carboxylates and the low-frequency values overlapping closely with the frequencies of the carbonyl stretch of the D-ring.The low-frequency component shows a significant fraction of frequencies below 1700 cm −1 , which puts it relatively close to the observed peak at 1678 cm −1 in view of what frequencies are commonly expected from protonated carboxylic acids.Further experiments are required to definitively determine if the propionates can be protonated in the Pr state and to assess the impact of protonation on the overall stability of phytochrome.

Population relaxation and solvation dynamics
The rate of population relaxation dynamics depends on the internal structure of the vibrationally excited molecule as well as intermolecular interactions that modulate the energy levels and the magnitudes of the anharmonic couplings between modes.Therefore, the vibrational relaxation time constant can often be related to the presence of specific intermolecular interactions, although relating the two becomes more difficult for complex molecular systems, which primarily decay through the intramolecular vibrational redistribution (IVR) process.
The measured population relaxation lifetimes are within the range of what is normally observed for C=O stretch modes, i.e., ∼1 ps.The most interesting from the perspective of the studied system is the observation of a slower relaxation rate and bi-exponential decay of the 1700 cm −1 peak.Considering the fact that both D-ring peaks are strongly coupled to the low frequency peak at 1678 cm −1 , it may be argued that the energy should be redistributed more efficiently from the 1700 cm −1 peak due to a smaller energy gap between the modes.Thus, the results imply that the relaxation pathway involves different, lower-lying vibrational modes, which are characterized by large anharmonic coupling constants.In such a case, the presence of H-bonding interactions with the D-ring carbonyl has a direct effect on the vibrational energy landscape of the chromophore and, as a result, activates alternative vibrational relaxation pathways for its carbonyl stretches.
Normalized center line slope is directly proportional to the frequency-frequency correlation function (FFCF).Therefore, it provides more direct information on the fluctuations in the local electric field than the relaxation time constants.The CLS results show that the inhomogeneous broadening is dominated by rather slow dynamics because the slope does not decay within the entire experimental window.The results are consistent with the CLS curves measured for the carbonyl stretch of phycocyanobilin. 38The CLS values observed here are similar for all vibrations and are in the range of 0.7-0.8.The low frequency component of the D-ring carbonyl stretch appears to have the smallest CLS, indicating a relatively more homogeneous lineshape.It is not clear how the presence of H-bonding interactions may result in a decrease in CLS.Nevertheless, the flat CLS curves suggest that the chromophore itself is rigid on the time scale of 2.5 ps, despite the presence of flexible water and His290 around the stationary D-ring carbonyl.

Vibrational couplings in dynamic cross peaks
2D IR spectra of BV exhibit numerous off-diagonal features, which arise from both vibrational coupling and energy redistribution processes.It was shown before that cross peaks also appear between BV and the Amide I vibrations of the protein backbone. 37he Journal of Chemical Physics

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Coupling between the A-ring and the protein bands is also observed in our data but the analysis of cross-peaks in our study is limited to vibrational modes of the chromophore.The origin of all the cross peaks in 2D IR spectra of bacterial phytochromes remains to be elucidated.Strong vibrational coupling signatures observed in our data between the carbonyl stretches and the peak at 1678 cm −1 allowed us to provide another evidence that the newly detected low frequency peak originates from the internal structure of BV.Interestingly, the peak is coupled to both the D-and A-ring carbonyls.The possible explanation is that it either lies in close proximity to both rings or that the vibrational motions of the BV structure are intrinsically coupled across the entire length of the molecule.This may enable efficient through-bond energy transfer across all rings A to D. The cross peak between the peak at 1678 cm −1 and the high frequency sub-population of the D-ring carbonyl vibration appears weaker in intensity, which may indicate that the peak is coupled more strongly to the D-ring in the presence of H-bonding interactions.
A weak cross peak at early waiting times is also seen between the A-ring carbonyl at 1730 cm −1 and the D-ring carbonyl.The average distance between the carbonyl oxygen atoms was estimated from the crystal structure to be ∼9.4Å, for which one may not expect very intense cross peaks.However, it must be noted that the peak is extremely weak at early Tw s and becomes significantly more pronounced for longer delays.Such time-dependent growth of cross peaks is also found for other vibrational couplings in our 2D IR spectra.Here, it is important to briefly discuss the origin of this phenomenon.The growth of the cross peaks in the studied system cannot be assigned to the through-space vibrational energy transfer process, which is usually much slower and is characterized by r −6 distance dependence that would make energy transfer between distant parts of the molecule extremely unlikely.Nevertheless, all the vibrational modes under study are expected to be characterized by strong anharmonic coupling with other internal modes of BV.It must be noted that the carbonyl groups are fused into the ring structure so that C=O stretch modes become, to a significant extent, delocalized.BV itself is a large molecule with a high density of modes to which the system can relax through IVR.IVR process, thus, populates highly delocalized internal modes, allowing the energy to travel fast and efficiently across long distances in a molecule and, as a consequence, enhance the intensity of cross peaks in 2D IR spectra.Taking advantage of such an effect was introduced under the name of relaxation-assisted (RA) 2D IR spectroscopy and was proposed as a powerful method of enhancing off-diagonal peaks in 2D IR spectra. 57RA 2D IR was shown to allow for measurements of vibrational couplings between bonds, which are separated by distances as high as 10-15 Å. 67 To the best of our knowledge, this phenomenon has not been explored for protein-bound molecules, such as BV.
In the current study, the analysis of cross peaks delivers important information about the molecular system.First, it shows how the presence or absence of cross peaks may help assign peaks to subpopulation of conformations and differentiate them from inherently coupled modes of the same molecular species.The cross peaks at early delays help identify molecular groups that are in close proximity, filtering out the most direct and strongest interactions.As the relaxation process takes place, the intensity growth of cross peaks as a function of Tw gives information on the through-bond coupling and the directions of the intramolecular energy transfer within the molecule.

V. CONCLUSIONS
In this study, we have applied a selective isotope-labeling strategy to isolate the vibrational signals of the protein-bound BV chromophore in a bacterial phytochrome from Deinococcus radiodurans.Shifting the protein signals away from the carbonyl bands of the chromophore has enabled the study of the structure and ultrafast dynamics of BV with 2D IR spectroscopy.The 2D IR spectra identified four major BV-specific vibrations, which were assigned to carbonyl stretch modes of rings A and D, and a major 1678 cm −1 band that is likely to originate from the propionates, but additional experiments are needed for the definitive assignment.The carbonyl stretch of the D-ring shows heterogeneity of H-bonding structures evidenced by the presence of two distinct peaks in the IR spectra.Relaxation dynamics and environmental fluctuations were quantified by analyzing the time-dependent changes in intensity and linewidth of the diagonal peaks.The results indicated that the structure of the chromophore is so rigid that it does not undergo spectral diffusion within the time-window determined by the vibrational lifetimes.The dynamics of the D-ring carbonyl stretch interacting through H-bonding are to some extent different, showing a slower population relaxation rate.2D IR spectra show multiple cross peak features from the vibrational coupling between modes.Tw-dependent analysis of cross peaks reveals significant growth in cross peak intensity, which, based on the observed timescales, is indicative of the relaxation-assisted coupling through internal modes of the chromophore.
In the near future, we plan to continue investigating residuelevel structural dynamics of phytochromes with 2D IR spectroscopy.We believe that 2D IR is an excellent technique for studying the effects of point mutations in the protein sequence on the H-bonding environment around the chromophore.To connect the spectroscopic observables with molecular structure, we are working toward developing BV-specific models of solvatochromism.The results presented here take important steps toward more advanced transient 2D IR measurements on phytochromes.Nevertheless, the techniques used in this study are broadly applicable to studying many other exciting protein-bound molecular complexes.Thus, we expect 2D IR spectroscopy to aid discoveries in many areas of life sciences, where photoactive proteins play an important role.

SUPPLEMENTARY MATERIAL
See the supplementary material for the difference in 2D IR spectra between the WT phytochrome and the corresponding apoprotein, vertical slices through the A-ring cross peaks, and MD analyses of the distribution of intermolecular distances involving key residues in the chromophore binding pocket.

FIG. 2 .
FIG. 2. (a) Raw FTIR spectrum of the 13 C 15 N-labeled DrBhP phytochrome plotted along the D 2 O background of the buffer.The amide vibrations become red-shifted upon isotope-labeling, with the most intense Amide I band appearing slightly below 1600 cm −1 .(b) Background-subtracted FTIR spectra of the biliverdin chromophore in the high frequency region with the most characteristic carbonyl vibrations highlighted.

FIG. 4 .
FIG. 4. (top) Deconvolution of the diagonal trace of the 2D IR spectrum measured at Tw = 0.2 ps.The asymmetric peak corresponding to the D-ring vibration is fitted with two Gaussian functions.Identical fits were carried out for each Tw to extract the population changes of each peak.(bottom) Population relaxation lifetimes of all peaks extracted from the fitting procedure.The peak at 1678 cm −1 decays with a single time constant τ = 1.1 ps.The peak at 1700 cm −1 exhibits slower bi-exponential relaxation dynamics with τ 1 = 1.5 ps (90%) and τ 2 = 2.5 ps (10%).The high frequency component of the D-ring band decays with a single exponential time constant τ = 1.0 ps.

FIG. 5 .
FIG. 5. 2D IR spectrum depicting frequency regions taken for the analysis of the center line slopes (CLS).CLS decays for each peak are shown in the inset.All peaks are highly inhomogeneous throughout the whole experimental time window.

FIG. 6 .
FIG. 6.(a) 2D IR spectrum at Tw = 3.0 ps showing the location of cross peaks between studied vibrations.Cross peaks between the peak at 1678 cm −1 and the D-ring vibrations at 1700 and 1710 cm −1 are labeled with 1 and 2, respectively.The cross peak between the 1678 cm −1 peak and the A-ring vibration at 1730 cm −1 is labeled with 3. The projection along the pump frequency axis is given on top of the spectrum.(b) Normalized Tw-dependent frequency slices were taken through the 1678 cm −1 peak along the probe frequency axis.Vibrational coupling signatures are seen at early time delays and their intensities grow with increasing Tw due to relaxation-assisted intensity enhancement.(c) The analysis of Tw-dependent growth in cross-peak intensities normalized to the corresponding diagonal signals.

FIG. 7 .
FIG. 7.Scatter plots of the D-ring carbonyl stretching (CO D ) frequency as a function of the H-bonding distance between its oxygen atom and the hydrogen of the closest water molecule as well as the distance to His290.The data points in the two plots are colored according to the distance between D-ring oxygen (O D ) and the hydrogen of the His290 residue (left plot) and the hydrogen bond angle spanned by O D -H(His290)-N(His290) atoms (right plot).The region between 1690 and 1710 cm −1 is due to a single hydrogen bond between carbonyl and either water or His290 (structures B).The frequency region larger than 1710 cm −1 is due to the absence of any hydrogen bond (structures C).Finally, structure A represents a rare case of carbonyl H-bonded to both water and His290.