Simulations of Two-dimensional Infrared and Stimulated Resonance Raman Spectra of Photoactive Yellow Protein

Abstract

We present simulations of one and two-dimensional infrared (2DIR) and stimulated resonance Raman (SRR) spectra of the dark state (pG) and early red-shifted intermediate (pR) of photoactive yellow protein (PYP). Shifts in the amide I and Glu46 COOH stretching bands distinguish between pG and pR in the IR absorption and 2DIR spectra. The one-dimensional SRR spectra are similar to the spontaneous RR spectra. The two-dimensional SRR spectra show large changes in cross peaks involving the C=O stretch of the two species and are more sensitive to the chromophore structure than 2DIR spectra.

1. Introduction

The reaction to light in all biological organisms is governed by photoreceptor proteins, which transduce light into a usable chemical signal to initiate light perception in bacteria, plants, and animals [1, 2]. The initial events in photoreceptors often involve a cis-trans isomerization in an embedded chromophore followed by a local relaxation occurring on ns timescales. Characterizing the initial events in photoreceptors is challenging because both high structural resolution and ultrafast time resolution are required [3]. Time-resolved vibrational spectroscopy is an ideal probe beacuase it provides excellent temporal and structural resolution [3, 4].

Predicting local active site motions in photoreceptors through vibrational spectroscopy could help further the understanding of the initial events in a wide range of photoreceptors existing in bacteria, plants, and animals. Photoactive yellow protein (PYP) is a 125 residue, 14 kD, globular protein with an α/β fold that is proposed to initiate the negative phototactic response in Halorhodospira Halophila [3, 2]. p-coumaric acid (pCA), the chromophore within one of PYP’s two hydrophobic cores, is covalently bound to Cys69 by a thioester linkage and is stabilized by a hydrogen bond network with Glu46, Glu42, Thr50, and Cys69 [5, 3, 2].

Upon absorption (λ_max=446 nm), PYP undergoes a complex photocycle that was initially characterized by UV/visible absorption [6], and subsequently by time-resolved X-ray crystallography [7, 8, 9, 10, 11]. In the dark state (pG or I₀), pCA exists in the deprotonated trans form with a hydrogen bond to the amide group of Cys69 [12, 5]. After excitation, the chromophore undergoes a fs trans to cis isomerization via a bicycle pedal mechanism that disrupts the hydrogen bond between pCA and Cys69 [3, 11]. Within several nanoseconds, relaxation around the active site leads to the formation of the red-shifted intermediate (pR or I₁) [13, 8, 10, 11]. The chromophore is then protonated by Glu46 [13, 14], causing a protein quake that partially unfolds it [7, 15] on a millisecond timescale to form its putative signaling state (pB or I₂). Finally, in a subsecond process, the pG state is recovered. This involves the deprotonation of pCA by Glu46, the reisomerization of pCA, and the refolding of the protein [3].

The isomerization follows a “volume-conserving” path because the chromophore is embedded within the densely packed hydrophobic core [13, 8, 11]. The strong hydrogen bonding network and the covalent attachment to Cys69 further constrain the number of such mechanisms [16]. The trans to cis isomerization is achieved via a bicycle pedal mechanism where the rotation about the double bond is concomitant with a rotation about the C-C(=O) bond. This breaks the hydrogen bond between Cys69 and pCA, shifting the pCA carbonyl stretch from 1633 to 1666 cm⁻¹[17]. Following this bicycle pedal mechanism, rotations about the S-C(=O), C^α-C^β, and C^β-S bonds leads to the formation of pR by relieving strain in the active site [13, 8, 16, 10, 11].

Both Infrared (IR) and resonance Raman (RR) spectroscopy detect vibrational resonances, but through a different window. In RR, only those vibrations which are coupled to an excited state are observed, which permits the observation of vibrational dynamics of a chromophore within a host. This site selectivity has been used to study photosensors such as rhodopsins and phytochromes. On the other hand, IR spectroscopy observes all vibrational resonances within the pulse bandwidth. The secondary structure of proteins is observed via the amide transitions. However, if a small number of vibrational resonances are spectrally isolated (e.g. by isotope labeling), IR spectra may also be used to study local dynamics.

In this paper, we report simulations of IR and RR spectra of the pG and pR states of PYP. Details of the quantum chemical and molecular dynamics simulations are given in section II. The simulated IR spectra are presented in section III and compared with experiment. We particularly focus on the IR difference spectrum of the Glu46 COOH stretch. We also present the simulated 2D IR spectra for pG and pR. In section IV, the simulated spontaneous RR spectra are presented and compared with experiment. The simulated one and two-dimensional stimulated RR spectra are presented as well. We finally conclude and discuss future extensions.

2. Methods

2.1. Molecular Dynamics Simulations

Molecular dynamics (MD) simulations of the pG and pR states of PYP were performed using the GROMACS software package [18]. The pG initial structure was taken from PDB 1NWZ [9] and the pR initial structure was taken from PDB 1OT9 [10]. The protein was modeled using the Gromos96 united-atom force field [19] and the parameters for PCA were obtained from a previous study [20].

Each structure was solvated in a cubic box of SPC water [21] with a minimum solvation layer of 0.9 nm. This resulted in a box of length 62.7 Å for pG and 63.4 Å for pR. To neutralize the system, six water molecules were replaced with sodium ions. The systems were minimized for 5000 steps using a steepest descent algorithm. The water, ions, and protein hydrogens were then allowed to relax for 250 ps in the NPT ensemble while non-hydrogen protein atoms were harmonically restrained. The systems were equilibrated in the NPT ensemble for 500 ps at 300K, after which the protein RMSD and total energy remained constant.

All simulations were performed using cubic periodic boundary conditions. Long-range electrostatic interactions were calculated using the particle mesh Ewald method [22, 23] with a short range cuto of 9 Å. Van der Waals interactions were computed using a cuto of 14 Å. For NPT equilbration, the temperature and pressure were controlled via weak coupling to an external bath [24] with a temperature coupling time constant of 1 ps, pressure coupling time constant of 0.5 ps and isothermal compressibility of 4.5× 10⁻⁵ bar⁻¹. The temperature of the NVT simulations was controlled using a Nose-Hoover thermostat [25, 26] with a 0.1 ps damping coefficient. The LINCS [18] and SETTLE algorithms [27] were used to constrain bond lengths, which permitted a 2 fs timestep.

2.2. Electronic Structure Calculations

Electronic structure calculations (section 4) were performed using the Gaussian09 software package [28]. We used the PBE0 functional [29, 30, 31, 32] and the 6-311++G** basis set using a polarizable continuum model with conductor like solvations [33, 34] to simulate the active site within an aqueous environment.

3. IR Spectra

The IR spectra of PYP were simulated using an effective vibrational Hamiltonian which can be recast using the bosonic creation ($b_i^{†}$) and annihilation (b_i) operators [35, 36, 37]:

$$H\left(t\right)=\hslash \sum _i{\omega }_i\left(t\right)b_i^{†}{b}_i+\hslash \sum _{i,j}{J}_{\mathit{ij}}\left(t\right)b_i^{†}{b}_j+\frac{\hslash }{2}\sum _i{\Delta }_i{b}_i^{†}{b}_i^{†}{b}_i{b}_i$$ (1)

ω_i and Δ_i are the fundamental frequency and the anharmonicity of mode i respectively, and J_ij is the coupling between modes i and j. The interaction of the vibrational system with the field is given by:

$$H^{\prime }\left(t\right)=\sum _i{\mu }_i\left(t\right)\cdot \mathit{E}\left(t\right)\left(b_i+b_i^{†}\right)$$ (2)

In the Hamiltonian, we include 126 modes in the carbonyl stretching region: 124 amide I modes, the Glu46 COOH side chain stretching mode, and the pCA C=O stretch. We have used electrostatic DFT maps from the literature to evaluate the fluctuating parameters in H(t) and H’(t) for the amide I and COOH vibrations. For the amide I vibrations, the electrostatic DFT map of [38] was used to evaluate ω(t) while the transition dipole was fixed to the gas phase value [39] and the anharmonicity was fixed to the measured value of −16 cm⁻¹[40]. The Glu46 carboxylic acid vibration was modeled using the electrostatic DFT map in reference [41]. We have further constructed a new electrostatic DFT map for the pCA C=O stretch. Details are given in the supporting information. J_ij was given by the transition-dipole coupling model. The nearest-neighbor coupling between amide I modes was given by the Torii and Tatsumi dihedral angles map [42].

3.1. IR Absorption

All simulations were performed in the inhomogeneous limit by averaging over 2000 configurations taken from 4 ns MD simulations. The field-free frequencies of the amide-I modes and the Glu46 COOH mode were set to 1681 cm⁻¹and 1745 cm⁻¹respectively to match experimental results [43]. Likewise, a shift of −75 cm⁻¹was applied to the cis and trans pCA C=O stretching modes to match experimental results [17]. Note that the same shift was applied to each isomer. The homogeneous vibrational dephasing was fixed to 5.5 cm⁻¹for all transitions.

The simulated spectrum of pG is shown in figure 2. It compares well with experiment. The spectrum is dominated by the amide I band, centered around 1640 cm⁻¹with a full-width half-maximum of 40.6 cm⁻¹. The band below 1600 cm⁻¹in the experimental spectrum is due to absorption of the amide II and carboxylate modes which are not included in the simulations.

Figure 2.

Comparison of the simulated (red) and experimental (blue) [43] IR spectra of pG.

The calculated difference absorption spectrum between the pG and pR states is presented in figure 3. It shows two positive-negative features corresponding to changes in the amide I and Glu46 COOH bands. The dominant feature is caused by the amide I modes while the smaller signal is caused by the Glu46 COOH mode. Minima in the difference spectrum are assigned to pG and maxima are assigned to pR.

Figure 3.

The calculated difference absorption spectrum of pR and pG. The amide I region and Glu46 COOH stretching regions are clearly marked. Four peaks are labeled: (I) pR amide I, (I’) pG amide I, (II) pR Glu46 COOH, and (II’) pG Glu46 COOH

The amide I band shifts from 1665 cm⁻¹in pG (peak I’ in figure 3) to 1633 cm⁻¹(peak I in figure 3) in pR resulting in the amide I shift of 1633-1665=−32 cm⁻¹. Likewise, the Glu46 COOH shifts from 1742 cm⁻¹in pG (peak II’ in figure 3) to 1723 cm⁻¹(peak II in figure 3) in pR resulting in the Glu46 COOH shift of 1723-1742=−19 cm⁻¹. The simulated amide I shift of −32 cm⁻¹compares to the experimental value of −17 cm⁻¹[14, 16] while the simulated Glu46 COOH shift of −17 cm⁻¹compares to the experimental value of −8 cm⁻¹[13, 14, 16]. The simulations overestimate the magnitude of the amide I and Glu46 COOH shifts, however the sign of the shifts are correct. This demonstrates that MD simulations in combination with electrostatic DFT maps can qualitatively predict frequency shifts in the carbonyl stretching region. The shift of the pCA C=O stretch cannot be accurately determined from the difference IR absorption due to its overlap with the amide I band. This may be due to the relatively weak oscillator strength of the pCA C=O stretch. Inclusion of anharmonic coupling of the C=O stretch to other vibrational modes of the chromophore in the electrostatic DFT map could potentially increase its oscillator strength (see Supporting Information). The shift of the pCA C=O stretch is easily determined from RR spectra where only the chromophore vibrational modes are observed [17]. This shift has also been observed in excited state IR difference spectra of PYP mutants [44]. In that experiment, the protein backbone does not have time to react to the chromophore isomerization due to the short delay between the visible pump and IR probe and the pCA C=O stretch can be clearly observed.

It has been determined in the literature that the shift in the Glu46 COOH band is caused by a change in the distance of Glu46 and pCA [13, 14]. Contributions from nearby bands that are not included in our simulations may make this measurement more complicated in experiments. In pR, Glu46 moves slightly closer to the phenolate anion of pCA to precipitate the proton transfer from Glu46 to pCA. This movement causes a slight red-shift in the Glu46 COOH stretching band [13, 14, 16]. The difference spectrum in the region of the Glu46 COOH stretch was fit to a sum of two Gaussians:

$$\Delta I\left(\omega \right)=\sum _{i=1}^2{A}_i\exp \left[-\frac{{(\omega -{\omega }_i)}^2}{2{\sigma }_i^2}\right]$$ (3)

The results of the fit are presented in table 1.

Table 1.

The central frequencies and full width at half maximum (FWHM) of the Glu46 COOH peaks as estimated from the IR di erence spectrum. The FWHM is defined as ${\sigma }_i\sqrt{2\ln 2}$. The average distance ⟨r⟩ and the standard deviation σ_r of the Glu46(H)-pCA(O⁻) distance (figure 1) are also shown.

	pG	pR
ωi (cm−1)	1741.86	1722.93
FWHM (cm−1)	26.86	18.65
⟨r⟩ (Å)	3.56	1.72
σr (Å)	1.34	0.24

The central frequency of the pG and pR Glu46 COOH stretch is correlated with the average distance between the Glu46 hydrogen atom and the anionic oxygen of pCA. In pR, where Glu46 and pCA have an average distance of less than 2 Å, the central frequency is lower than in pG where the average distance is greater than 3 Å. Our findings confirm the experimental findings of references [13, 14, 16]. It should be noted that IR difference spectra at short delay times (up to ≈800 ps), do not show a frequency red-shift of the Glu46 COOD band following the decay of the excited state. This was first attributed by Groot et al. [45] to an unrelaxed pR state and was later confirmed by Heyne et al. [46].

The linewidths of the Glu46 COOH stretching peaks can similarly be related to the fluctuations in the active site of the protein. In the pG MD simulation, the distance between Glu46 and pCA fluctuates more than in the pR simulation and therefore, this leads to a larger FWHM due to a larger degree of inhomogeneous broadening. The larger structural fluctuations in pG are caused by Glu46 being occasionally forced out of the hydrogen bonding position with pCA. The hydrogen bond is typically replaced by the side chain of Thr50 while Glu46 then forms a hydrogen bond with the amide backbone of Thr50. This conformational mobility of Glu46 in pG has been observed in room temperature liquid state NMR studies [47].

Experimental IR difference spectra of PYP have observed the frequency shift of the Glu46 COOH stretch, however, the differences in the linewidths of the Glu46 COOH peak have not been observed. In the steady-state experiments of Ho et al. [13], the Glu46 COOH difference band was observed to have similar linewidths for pG and pR. This is likely due to the low temperatures (80K) that were used during these experiments. In room temperature species associated difference spectroscopy experiments [45], the linewidths of the Glu46 COOH peak cannot be accurately assessed due to the small number of data points used for fitting in this region.

3.2. 2D-IR

The 2D-IR spectra were calculated in the rephasing direction (k_I = −k₁ + k₂ + k₃) with all pulses colinear and with the same polarization (xxxx). The spectra were calculated using the quasiparticle approach based on the nonlinear exciton equations [48, 49, 50, 35] as implemented in SPECTRON [36]. The real-space excitonic overlap [49] was truncated at a value of 0.5 and t₂ was set to 0 fs. All spectra were normalized to a maximum absolute value of 1.0.

The 2D-IR spectra of pG and pR are shown in figure 4. The region plotted only includes the amide I and pCA C=O stretch. The simulated 2D-IR spectra of pG and pR are nearly identical with a single inhomogeneously broadened peak near ω₁ = ω =1640 cm⁻¹ that is dominated by the amide I modes. The difference 2DIR spectrum (pR-pG) shown in figure 4c reveals the red-shift of the amide I band in pR compared to pG. While the pCA C=O stretch is also included in this band, it cannot be effectively deconvoluted from the amide I modes.

Figure 4.

The complex part of the rephasing 2D IR spectra of (a) pG and (b) pR. The difference 2D IR spectrum (pR-pG) is shown in (c).

The linear absorption spectra can already distinguish between the pG and pR states and the 2DIR does not provide much new information. However, by isotope-labeling certain secondary strutcural elements (e.g. specific α-helices and β strands), it may be possible to gain new information from 2DIR spectra. We further note that the coupling to other modes (e.g. C=C stretches) are not observed in the simulated 2DIR spectra as they are not explicitly included in the Hamiltonian. The coupling of C=O stretching modes with other types of modes could provide additional spectroscopic signatures.

4. Resonance Raman Spectroscopy

In RR spectroscopy, we only consider vibrations which are coupled to a given electronic transition. The electronic Hamiltonian is given by:

$$H=\mid g\rangle H_g\langle g\mid +\mid e\rangle H_e\langle e\mid$$ (4)

where H_g is the ground state vibrational Hamiltonian and H_e is the excited state vibrational Hamiltonian. To describe the ground state and excited state vibrational Hamiltonians, we will assume that the vibrations are modeled as linearly displaced harmonic oscillators. The ground state and excited state vibrational Hamiltonians are:

$$H_g=H_{B,g}+\frac{\hslash }{2}\sum _i^N{\omega }_i(p_i^2+q_i^2)$$ (5a)

$$H_e=\hslash {\omega }_{\mathit{eg}}^0+H_{B,e}+\frac{\hslash }{2}\sum _i^N{\omega }_i(p_i^2+{(q_i+{\delta }_i)}^2)$$ (5b)

where ω_i is the frequency of the i-th normal mode, q_i and p_i are the dimensionless coordinates for vibration i, and δ_i is the dimensionless displacement of vibration i. H_B,g and H_B,e are the bath Hamiltonians.

To make a connection with equation 1, we can rewrite equation 6 using the creation and annihilation operators:

$$H=\mid g\rangle H_g\langle g\mid +\mid e\rangle H_e\langle e\mid$$ (6a)

$$H_g=H_{B,g}+\hslash \sum _i^N{\omega }_i{b}_i^{†}{b}_i$$ (6b)

$$H_e=\hslash {\omega }_{\mathit{eg}}^0+H_{B,e}+\hslash \left[\sum _i^N{\omega }_i{b}_i^{†}{b}_i+\frac{1}{\sqrt[]{2}}\left(b_i^{†}+b_i\right)+\frac{{\delta }_i^2}{2}\right]$$ (6c)

It should also be noted that the ground state Hamiltonian of equation 1 collapses into H_g when J_ij = 0 and Δ_i = 0.

For all further calculations, we will use an extended description of the chromophore which includes the active site residues Glu46, Tyr42, and Cys69 (figure 5). We refer to these structures as the active site fragments of pG and pR. Glu46 is represented by CH₃O₂H and Tyr42 is represented by CH₃OH. In the pG state, Cys69 is represented by H₂O. We do not include Cys69 in the pR state as it does not make a hydrogen bond with the chromphore. The sulfur atom of the chromophore is capped with a methyl group in pG and pR. In the Hamiltonian (equation 6), we include all modes between 400 cm⁻¹and 2000 cm⁻¹(63 modes for pG and 64 modes for pR). We note that the model used for the RR simulations differs from the IR simulations. The RR simulations include only chromophore modes in the range 400-2000 cm⁻¹while the IR simulations consider all C=O stretching modes in the protein. We only consider the low-lying π – π* transition, which is calculated as 24356 cm⁻¹for pG and 25082 cm⁻¹for pR. In our calculations, the nearest excited states occur at 34115 cm⁻¹for pG and 31937 cm⁻¹for pR. The π – π* transition has previously been shown to be isolated from all other transitions [51, 52]. The displacements, δ_i, are calculated using the gradients of the ground and excited state potential energy surfaces [53, 54, 55]:

$${\delta }_i=\frac{1}{\hslash {\omega }_i}\frac{\partial (E_e-E_g)}{{\partial }_{q_i}}$$ (7)

Figure 5.

The optimized ground state structures of the active site fragments of (a) pG and (b) pR used in the resonance Raman calculations.

4.1. Electronic Absorption

To calculate the visible linear absorption spectrum, we will use the cumulant expansion technique [56]. The linear absorption spectrum is given by:

$$\sigma \left(\omega \right)=-\frac{i}{\hslash }{\mu }_{\mathit{ge}}{\mu }_{\mathit{eg}}{\int }_0^{\infty }{\mathit{dte}}^{i\omega t}{e}^{-i{\omega }_{\mathit{eg}}t-{\gamma }_{\mathit{eg}}t-g\left(t\right)}$$ (8)

where ω_eg is the transition frequency from the ground to excited electronic state, μ_ij is the transition dipole from states j and i, and γ_eg is the homogeneous electronic dephasing. The line broadening function g(t) will include the effects of coupling between the electronic transition and intramolecular vibrations as well as the electronic transition and the fluctuations of the protein and solvent.

We have used the Brownian oscillator model to model the coupling of the electronic transition to the fluctuating protein and solvent [56]. The frequency-frequency correlation function was fit to [56]:

$$\langle \delta {\omega }_{\mathit{eg}}\left(t\right)\delta {\omega }_{\mathit{eg}}\left(0\right)\rangle ={\Delta }^2{e}^{-\Lambda t}$$ (9)

where Δ is the amplitude of the fluctuations and Λ⁻¹ is their correlation time. The dimensionless parameter, k = Λ/Δ was evaluated to determine the timescale of the bath. From a 2 ps MD simulation of the solvated protein, snapshots were saved every 8 fs. For each snapshot, the active site fragment was replaced by the PBE0/6-311++G** optimized structure and all surrounding atoms within 20 Åof the active site were replaced by their MM point charges to generate a background charge density. TDDFT calculations were then performed to calculate the low-lying π-π* excitation energy for each snapshot and the frequency-frequency correlation function was calculated 6. The results of the fit are presented in table 2. For both pG and pR, the interaction with the bath is strongly inhomogeneous. The magnitude of the fluctuations induced by the bath agree with a previous QM/MM study [52].

Table 2.

Values of Λ, Δ, and κ obtained from the fit to equation 9 for pG and pR.

	pG	pR
Λ−1 (fs)	94.07	97.32
Δ (cm−1)	491.2	525.5
κ	0.116	0.158

Including the coupling of the electronic system to the intramolecular vibrations and the strongly inhomogeneous bath results in a line-broadening function g(t):

$$g\left(t\right)=\frac{{\Delta }^2}{2}{t}^2+\sum _j\frac{{\delta }_j^2}{2}\left[\right(\text{coth}(\beta \hslash {\omega }_j∕2)\left)\right(1-\cos \left({\omega }_{j}t\right))+i(\sin \left({\omega }_{j}t\right)-{\omega }_{j}t\left)\right]$$ (10)

The simulated visible absorption spectra of pG and pR are shown in figure 7. The simualted spectra have an overall blue shift when compared to experiment as has been observed in previous computational studies [51, 57, 58, 52, 59, 60]. The simulated pR spectrum is blue-shifted from the simulated pG spectrum, which is contrary to the experimental result. Inclusion of a larger number of residues can give more accurate excitation energies [20], however, the computational cost increases greatly. However, the directionality of the frequency shift only changes the relative resonance enhancement of the Raman transitions between the two intermediates. As we will demonstrate in the following section, we believe we have calculated the correct excited state transition for pG and pR based on comparison with the experimental spontaneous-RR spectra.

Figure 7.

Simulated (bottom) and experimental [61] (top) visible absorption spectra of PYP. The pG spectrum is shown in black and the pR spectrum is shown in red.

4.2. Spontaneous Resonance Raman Spectroscopy

The spontaneous RR spectra were calculated using the effective polarizability given in equation A12 of reference [62]. We assume the impulsive limit and the lineshape function, $g_e^{j^{\prime }}\left(t\right)$ includes an additional additive contribution from the fluctuating protein-solvent as in equation 10. The spectra were calculated using an incident frequency (ω_j) which was set to the frequency of maximum absorption of pG (24390 cm⁻¹). We set the homogeneous electronic dephasing γ_eg to 100 cm⁻¹. The simulated spectra for are compared to experiment [17] in figure 8 and mode assignments are given in tables S3 and S4. Our simulations reveal that the C=O stretching mode, shaded in pink in figure 8, shifts from 1689 cm⁻¹in pG to 1714 cm⁻¹in pR due to the breakage of the hydrogen bond to the Cys69 backbone. This peak is also significantly more intense in pR than in pG. This change in intensity is caused by the difference of the value of the displacements for the C=O stretch, δ_C=O, relative to the displacements for the strongest C=C+C=C(ph) stretch, δ_C=C. The strongest C=C+C=C(ph) stretch at 1593 cm⁻¹is dominated by the vinyllic C=C rather than aromatic C=C stretch. In pG, the δ_C=O/δ_C=C = 0.11/0.50 = 0.22 and in pR, δ_C=O/δ_C=C = 0.30/0.35 = 0.86. In the experiment, the C=O stretching mode is nearly silent at 1633 cm⁻¹in pG, however, upon formation of pR, this mode shifts to 1666 cm⁻¹and shows a significant increase in intensity [17].

Figure 8.

Simulated (blue) and experimental [17] (green) spontaneous RR spectra for (a) pG and (b) pR.

4.3. One-dimensional stimulated Resonance Raman Spectra (1D-SRR)

The one-dimensional stimulated resonance Raman (1D-SRR) spectra were calculated using an effective polarizability which is given by equations (A11) and (A14) of reference [62]. The lineshape function, $g_e^{j^{\prime }}\left(t\right)$ includes an additional additive contribution from the fluctuating protein-solvent as in equation 10. We calculate the spectra using a 5 fs pump pulse centered at 22141 cm⁻¹and a 5 fs probe pulse was set to the frequency of maximum absorption (24390 cm⁻¹for pG, 25126 cm⁻¹for pR). The resonance offset is intended to ensure that the excited-state contribution to the signal is small compared to the ground state contribution. We define the parameter:

$$\zeta =\frac{\langle {\psi }_e^{\left(1\right)}\mid {\psi }_e^{\left(1\right)}\rangle }{\sqrt{\langle {\psi }_g^{\left(2\right)}\mid {\psi }_g^{\left(2\right)}\rangle }}$$ (11)

where $\mid {\psi }_e^{\left(1\right)}\rangle$ and $\mid {\psi }_g^{\left(2\right)}\rangle$ are the nuclear wavefunctions on the ground and electronic states which are first and second order in the field respectively. The detunings used here were chosen such that ζ ≤ 0.1. The simulations included a vibrational dephasing of 10 cm⁻¹. The 1D-SRR spectra are shown in figure 9. By comparing the spontaneous RR spectra (figure 8) with the 1D-SRR spectra, it is seen that the 1D-SRR spectra are similar to the spontaneous RR spectra. Both the spontaneous RR and 1D-SRR spectra reveal that the chromophore C=O stretching mode occurs at higher frequency with a higher intensity in pR.

Figure 9.

1D-SRR spectra of pG and pR. The overlap of the pump (blue) and probe (magenta) pulses with the visible absorption spectra is shown in (a) pG and (b) pR. The 1D-SRR spectra are shown in (c) pG and (d) pR.

4.4. Two-dimensional stimulated Resonance Raman (2D-SRR) Spectra

The two-dimensional stimulated resonance Raman (2D-SRR) signals are given by the four loop diagrams in figure 10. The 2D-SRR spectra were calculated using equation (A11) of reference [62] with an effective polarizability given by equations (A14-A22). The lineshape function, $g_e^{j^{\prime }}\left(t\right)$ includes an additional additive contribution from the fluctuating protein-solvent as in equation 10. fs pulses centered at 22141 cm⁻¹for the pump pulses, k₁ and k₂. The probe pulse, k₃ was a 5 fs pulse centered around the frequency of maximum absorption (24390 cm⁻¹for pG, 25126 cm⁻¹for pR). As in the 1D-SRR simulations, the pump pulses are pre-resonant to ensure that the excited-state contribution is small compared to the ground state contribution. We have used a homogeneous vibrational dephasing of 10 cm⁻¹.

Figure 10.

The four loop diagrams used to calculate the 2D-SRR signal.

The absolute value of the 2D-SRR spectra for pG and pR are shown in 11. Spectra were plotted on a non-linear scale arcsinh (cS) where S represents the signal, normalized to a maximum absolute value of 1, and c is a scaling factor which is set to 10. The most dramatic change between the 2D-SRR spectra of pG and pR are the cross peaks associated with the C=O stretch that are absent in pG but present in pR. In pG, these cross peaks, which are extremely weak, are along the horizontal slice ω₂ = 1689 cm⁻¹and along the semi-diagonal slice ω₂ = ω₁ – 1689 cm⁻. In pR, these cross peaks appear along the horizontal slice ω₂ = 1714 cm⁻¹and along the semi-diagonal slice ω₂ = ω₁ – 1714 cm⁻. The appearance of these cross peaks in the pR spectrum provides an additional feature to distinguish between pG and pR.

In figure 12, we present the 2D-SRR spectra in the the region (1500 < ω₁ < 1800, 1500, ω₂ < 1800)to emphasize the difference in the cross peaks associated with the C=O stretch in the pG and pR 2D-SRR spectra. This region of the spectrum only includes contributions from C=O and C=C stretching modes. In the pG spectrum, there are two diagonal transitions which result from the C=C+C=C(ph) stretching mode at (1593 cm⁻¹,1593 cm⁻¹) and the C=C+C=C (ph) stretching mode at (1539 cm⁻¹,1539 cm⁻¹). There are also cross peaks which appear at (1539 cm⁻¹,1593 cm⁻¹) and (1593 cm⁻¹,1539 cm⁻¹). In the pR spectrum, all four of these peaks are present, but there are five new peaks which are associated with the C=O stretch. The diagonal C=O stretching peak at (1714 cm⁻¹, 1714 cm⁻¹) appears and there are cross peaks between the C=O stretch and the C=C+C=C(ph) stretch at 1593 cm⁻¹located at (1714 cm⁻¹, 1593 cm⁻¹) and (1593 cm⁻¹, 1714 cm⁻¹). Cross peaks between the C=O stretch and the C=C+C=C(ph) at 1537 cm⁻¹stretch occur at (1714 cm⁻¹, 1537 cm⁻¹) and (1537 cm⁻¹, 1714 cm⁻¹). The difference spectrum (pR-pG) (panel c of figure 12) reveals clear signatures of the new off-diagonal peaks that appear in pR, which can be seen at (1714 cm⁻¹, 1593 cm⁻¹), (1593 cm⁻¹, 1714 cm⁻¹), (1714 cm⁻¹, 1537 cm⁻¹), and (1537 cm⁻¹, 1714 cm⁻¹).

Figure 12.

Absolute value 2D-SRR spectra in the C=C and C=O stretching region for (a) pG and (b) pR. The difference 2D-SRR spectrum is shown in (c). All spectra are normalized to a maximum absolute value of 1 and are plotted on a linear scale.

The cross peaks between the C=O and C=C+C=C(ph) stretching modes in figure 12 arise from diagram (iv) in figure 10 when g’ ≠ g”. According to these diagrams, the peak intensities are proportional to ${\alpha }_{{\mathit{gg}}^{″}}^{\left(3\right)}{\alpha }_{g^{″}{g}^{\prime }}^{\left(2\right)}{\alpha }_{g^{\prime }g}^{\left(1\right)}$. Therefore, these cross peaks contain ‘intermode’ elements of the polarizability, α_g”_g’, which may not be probed by spontaneous or 1D-SRR spectroscopy. These elements are inherently related to the chromophore structure and dynamics as projected onto the vibrational modes g’ and g”.

The diagonal (ω₁ = ω₂) slices of the 2D-SRR spectra are shown in figure 13. As in the spontaneous and 1D-SRR spectra, the C=O stretching diagonal peak is much more intense in pR and occurs at a higher frequency compared to pG.

Figure 13.

The diagonal (ω₁ = ω₂) slices of the 2D-SRR spectra of (A_pG) pG and (A_pR) pR. The C=O stretching peak is shaded in pink. The labels A_pG and A_pR correspond to the labels in figure 11

The slices of the 2D-SRR spectra along ω₂ = 1689 cm⁻¹for pG and ω₂ = 1714 cm⁻¹for pR are plotted in panels B_pG and B_pR of figure 14. The horizontal slice is more intense in pR compared to pG. Additionally, in the pR spectrum, the diagonal C=O stretch, which appears at 1681 cm⁻¹for pG and 1714 cm⁻¹for pR, has a much higher relative intensity compared to the cross peak of the C=O stretch with the C=C+C=C(ph) stretching mode, which appears at 1593 cm⁻¹in pG and pR. In fact, the slice along ω₂ = 1689 cm⁻¹for pG is dominated by this cross peak.

Figure 14.

The horizontal slices of the 2D-SRR spectra of (B_pG) pG and (B_pR) pR and the semi-diagonal slices associated with the pCA C=O stretch of (C_pG) pG and (C_pR) pR. The diagonal C=O stretching peak is shaded in pink in panels B_pG and B_pR. All labels correspond to the labels in figure 11

The slices of the 2D-SRR spectra along the semi-diagonal that are associated with the C=O stretch (ω₂ = ω₁ – 1689 cm⁻¹for pG and ω₂ = ω₁ – 1714 cm⁻¹for pR) are shown in panels C_pG and C_pR of figure 14 for pG and pR respectively. Due to the Lorentzian lineshapes in the current calculations, there are peaks which appear in these slices due to the tails of nearby peaks in the ω₁ direction. We have plotted the stick spectrum with the slices to ensure that no false peaks were analyzed. The intensity of this slice in pG is much weaker than in pR. This is similar to the horizontal slices in B_pG and B_pR where the cross peaks associated with the C=O stretch in pG were much weaker compared to the cross peaks associated with the C=O stretch in pR.

If C=C modes were to be included in the IR simulations (equation 1), the C=C stretching/C=O stretching cross peaks in the 2DIR spectra would probe the coupling of C=C and C=O stretches in the protein. However, due to the high degree of degeneracy of C=O and C=C transitions, only the average coupling of these bands would be observed unless specific modes could be spectrally isolated (e.g. by site-specific isotope labeling). RR spectroscopy only probes vibrational modes coupled to the chromophore excited state transition. We can then clearly assign the cross peaks in the 2D-SRR spectra to two different vibrational modes of the chromophore. This provides a clear view of local structure variations of the chromophore.

5. Conclusions

Simulations of IR and RR spectra of the pG and pR intermediates of PYP provide complementary information in photosensors. The difference linear IR absorption spectrum (pR-pG) reveals an amide I shift and a shift of the Glu46 COOH mode, both of which have been experimentally observed. A careful analysis of the Glu46 COOH difference band revealed that the pR state has a narrower linewidth than the pG state which is caused by the fact that the Glu46(H)-pCA(O-) hydrogen bond is held more tightly in the pR state. The rephasing 2D-IR using the xxxx polarization were also calculated and revealed the shift in the amide I band.

The simulated sponatneous RR spectra agree well with experiment. The spontaneous RR spectra reveal a blue-shift and an increase in intensity of the C=O stretching peak. The simulated 1D-SRR spectra of pG and pR are similar to the sponanteous RR spectra and also reveal the blue-shift and increase in intensity of the C=O stretch. The 2D-SRR spectrum of pR has cross peaks associated with the C=O stretch that do not appear in pG. Due to the novel information contained in the 2D-SRR spectra, we see this as a new method of probing chromophores in hosts, particularly in photosensors.

Highlights.

1. We simulated 2DIR and 2D-SRR spectra of the pG and pR intermediates of PYP

2. 2DIR spectra reveal shift in amide I band

3. 2D-SRR spectra show change in cross peaks associated with chromophore C=O stretch

Figure 1.

Active site structure of PYP in the (a) pG and (b) pR states. Hydrogen bonds are marked in dotted lines and the Glu46(H)-pCA(O-) hydrogen bond is labeled as r. The trans to cis isomerization occurs about the pCA C=C bond and a concomitant rotation about the C-C(=O) bond breaks the hydrogen bond between pCA and Cys69.

Figure 6.

The frequency-frequency correlation functions for the π-π* excitation energy of PYP for (a) pG and (b) pR. The raw data is represented by the black dots and the exponential fit to equation 9 is represented by the blue line.

Figure 11.

Absolute value 2D-SRR spectra of (a) pG and (b) pR. Spectra were plotted on a non-linear scale arcsinh (cS) where S represents the signal, normalized to a maximum absolute value of 1,and c = 10.

Table 3.

Calculated and experimental values of the frequency of maximum absorption of pG and pR in cm⁻¹.

	Calculated	Experiment
pG	24390	22472
pR	25126	21930