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\begin{document}
	
	\title{Supporting Information for: \\
 Transient 2D IR spectroscopy and multiscale simulations reveal vibrational couplings in the Cyanobacteriochrome Slr1393-g3}
	
\author{David Buhrke$^{1,2,*}$, Yigal Lahav$^{3,4}$, Aditya Rao$^{3}$, Jeannette Ruf$^{1}$, Igor Schapiro$^{3}$ and Peter Hamm$^{1}$\\
\textit{$^1$Department of Chemistry, University of Zurich, Zurich, Switzerland\\
$^2$current adress: Institute of Biology, Humboldt University Berlin, Germany\\
$^3$Fritz Haber Center for Molecular Dynamics Research Institute of Chemistry, The Hebrew University of Jerusalem, Israel\\
$^4$ MIGAL - Galilee Research Institute, Kiryat Shmona, Israel\\}
$^*$corresponding author: david.buhrke@hu-berlin.de
}

\maketitle

\begin{figure}[htbp]
	\centering
	\includegraphics[width=\linewidth]{S1.png}
	\caption{Displacement vectors of the calculated vibrational modes in the  Pg state (left, green) and the Pr state (right, pink).}
 \label{intro}
\end{figure}

\begin{table}
\caption{Calculated anharmonicity of the overtones (diagonal, defined as the difference between overtone and fundamental transition frequency, $\omega_{1,2}-\omega_{0,1}$) and combination bands (off-diagonal, defined as the difference between combination mode and fundamental transition frequency, $\omega_{01,11}-\omega_{00,10}$), in cm$^{-1}$ of the relevant vibrational modes in the Pg state.}

\begin{tabular}{ |p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|  }
\hline
  & CC$_\mathrm{D}$  & CC$_\mathrm{BC}$ & CC$_\mathrm{CD}$ & CC$_\mathrm{AB}$ & CO$_\mathrm{D}$  &  CO$_\mathrm{A}$ \\
 \hline
CC$_\mathrm{D}$  & -12.04 & -1.28 & -1.94 & -0.27 & -1.67 & 0.02 \\
\hline
CC$_\mathrm{BC}$ &  & -0.85 & -0.17 & -4.78 & -0.35 & -0.64 \\
\hline
CC$_\mathrm{CD}$ &  &  & -11.01 & -0.12 & -1.95 & 0.00 \\
\hline
CC$_\mathrm{AB}$ &  &  &  & -4.50 & -0.19 & -1.00 \\
\hline
CO$_\mathrm{D}$  &  &  &  &  & -17.13 & 0.03 \\
\hline
CO$_\mathrm{A}$  &  &  &  &  &  & -17.23 \\
  \hline
\end{tabular}
\label{TablePg}
\end{table}

\begin{table}
\caption{Calculated anharmonicity of the overtones (diagonal, defined as the difference between overtone and fundamental transition frequency, $\omega_{1,2}-\omega_{0,1}$) and combination bands (off-diagonal, defined as the difference between combination mode and fundamental transition frequency, $\omega_{01,11}-\omega_{00,10}$), in cm$^{-1}$ of the relevant vibrational modes in the Pr state.}

\begin{tabular}{ |p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|  }
\hline
  & CC$_\mathrm{BC}$  & CC$_\mathrm{D}$ & CC$_\mathrm{AB}$ &CC$_\mathrm{CD}$ & CO$_\mathrm{D}$  &  CO$_\mathrm{A}$ \\
 \hline
CC$_\mathrm{BC}$  & 0.46 & -2.14 & -0.56 & -0.63 & -0.57  & -0.37 \\
\hline
CC$_\mathrm{D}$  &  & -7.56 & -1.25 & -3.95 & -1.42 & 0.00 \\
\hline
CC$_\mathrm{AB}$ &  &  & -4.98 & -2.46 & -0.48 & -2.16 \\
\hline
CC$_\mathrm{CD}$ &  &  &  & -6.08 & -0.66 & -0.36 \\
\hline
CO$_\mathrm{D}$  &  &  &  &  & -16.84 & 0.06 \\
\hline
CO$_\mathrm{A}$  &  &  &  &  &  & -15.67 \\
  \hline
\end{tabular}
\label{TablePr}
\end{table}


\date{\today}

\end{document}


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\begin{document}
	
	\title{Transient 2D IR spectroscopy and multiscale simulations reveal vibrational couplings in the Cyanobacteriochrome Slr1393-g3}
	
\author{David Buhrke$^{1,2,*}$, Yigal Lahav$^{3,4}$, Aditya Rao$^{3}$, Jeannette Ruf$^{1}$, Igor Schapiro$^{3}$ and Peter Hamm$^{1}$\\
\textit{$^1$Department of Chemistry, University of Zurich, Zurich, Switzerland\\
$^2$current adress: Institute of Biology, Humboldt University Berlin, Germany\\
$^3$Fritz Haber Center for Molecular Dynamics Research Institute of Chemistry, The Hebrew University of Jerusalem, Israel\\
$^4$ MIGAL - Galilee Research Institute, Kiryat Shmona, Israel\\}
$^*$corresponding author: david.buhrke@hu-berlin.de
}

\date{\today}

\begin{abstract}
Cyanobacteriochromes are bi-stable photoreceptor proteins with desirable photochemical properties for biotechnological applications such as optogenetics or fluorescence microscopy. Here, we investigated Slr1393-g3, a cyanobacteriochrome that reversibly photo-switches between a red-absorbing (Pr) and green-absorbing (Pg) form. We applied advanced IR spectroscopic methods to track the sequence of intermediates during the photocycle over many orders in magnitude in time. In the conversion from Pg to Pr, we have revealed a new intermediate which precedes the Pr formation by using transient IR spectroscopy. In addition, stationary and transient 2D~IR experiments measured the vibrational couplings between different groups of the chromophore and the protein during these intermediate states. Anharmonic QM/MM calculations predict spectra in close-to-quantitative agreement with experimental 2D~IR spectra of the initial and the final state of the photocycle. They facilitate the assignment of the IR spectra and provide an atomistic insight into the coupling mechanism. This serves as a basis for the interpretation of the spectroscopic results and suggests structural changes of the intermediates along the photocycle.
\end{abstract}

\maketitle

\section{Introduction}

\noindent Cyanobacteriochromes (CBCRs) are bi-stable cyanobacterial photoreceptors\cite{Rockwell2010, Fushimi2019} with emerging applications in biotechnology, such as in super resolution microscopy\cite{Oliinyk2019} or optogenetics.\cite{Blain-Hartung2018} CBCRs typically consist of multiple photosensory modules that each incorporate an open-chain tetrapyrrole chromophore such as phycocyanobilin (PCB). In the present study, we investigated Slr1393-g3 (from here on denoted Slr-g3 for simplicity), a photosensory domain from a red/green CBCR that incorporates PCB and converts reversibly between a red-absorbing (Pr) and a green-absorbing (Pg) parent state.\cite{Chen2012, Slavov2015, Xu2014, Xu2020}
Both states are modulated by geometric changes of the PCB chromophore that are stabilized by the protein environment.
Figure \ref{intro} shows the structure of PCB inside the binding pocket of Slr-g3, which adopts a highly distorted geometry in Pg, thereby shortening the effective conjugation length compared to Pr.\cite{Xu2020, Wiebeler2018} The exact course of events that leads to these geometric changes is not fully established, hence a detailed mechanistic understanding of the photocycle reactions in red/green CBCRs is still lacking. Time-resolved spectroscopy studies indicated that these proteins show large shifts in their visible absorption properties on the \textmu\text{s}-ms time scale after photoexcitation\cite{Xu2014, Jenkins2019, Kirpich2018}, but it is up to now largely unclear how exactly PCB changes its structure as a function of time and how this process is driven by the protein environment.

\begin{figure*}[htbp]
	\centering
	\includegraphics[width=0.75\linewidth]{QM_intro.png}
	\caption{The QM/MM partitioning and optimized structures of Slr-g3 in the Pg state (left panel) and Pr state (right panel). The chromophore is comprised of 86 atoms (shown in licorice representation). The pyrrole hydrogens were deuterated (shown in dark gray) and positions of the propionate atoms were fixed (shown in light gray) during the calculation of vibrational frequencies. The nomenclature of the four pyrrole rings \textit{A-D} and localisation of the relevant normal modes are indicated in the right panel. 
 }
 \label{intro}
\end{figure*}

Infrared (IR) spectroscopy is a powerful technique to study exactly such protein reaction dynamics, i.e. the light-induced cycles of photoreceptors or catalytic cycles of enzymes.\cite{Kottke2017,Lorenz-fonfria} One of the most popular observables in the mid-IR is the so-called amide I region between 1600 and 1700~cm$^{-1}$, that is dominated by signals from the peptide bond C=O stretching vibrations (called amide I modes).\cite{Barth2002} Additionally, co-factors such as PCB reveal structure-sensitive vibrational modes in the same spectral region, resulting in small IR signals superimposed on the overwhelming amide I band. In photoreceptors, these are e.g. the C=C, C=O or C=N stretching vibrations of retinal, tetrapyrrole or other co-factors that can be identified in light-dependent difference-IR experiments. The same vibrational modes can be measured in resonance Raman (RR) experiments, where they are resonance enhanced over the amide I background. Thus,  RR and IR can be used for cross-validation and provide assignments for difference-IR experiments.\cite{Buhrke2019a, Lorenz-fonfria} The amide~I region of different proteins was investigated in detail not only by linear (1D) but also two dimensional (2D-)IR spectroscopy, which offers additional information such as spectral diffusion, vibrational couplings or anharmonicities.\cite{GANIM2007} Generally, the analysis of the amide I region is tedious due to a strong coupling of the broad amide I modes, and due to spectral congestion, which makes it extremely difficult to extract local information even for small proteins and peptides.\cite{Hamm1998, Strasfeld2009, GANIM2007} Due to this obstacle, most applications of 2D~IR spectroscopy on protein samples require carefully designed experimental conditions such as isotope labeling and very small systems,\cite{Bredenbeck2003,Shim2009} or the introduction of IR labels that absorb outside the amide vibrations, typically in the so-called ``transparent window'' between 1800-2300~cm$^{-1}$.\cite{Adhikary2017,Thielges2021} Although 2D~IR spectroscopy has been thoroughly developed over the last two decades, the technique is still non-standard and requires highly specialized labs and on top of that very expensive equipment such as femtosecond laser systems and optical parametric amplifiers. Due to a combination of these challenges, 2D~IR spectroscopy has so far been applied  only sparsely to investigate the light-induced reactions of photoreceptor proteins, e.g. on Bacteriorhodopsin\cite{Andresen2009, Hamm2021}, Photoactive Yellow Protein\cite{Schmidt-Engler2020}, a CBCR\cite{Ruf2021}, and a Phytochrome.\cite{Buhrke2022}

Here, we tracked the IR response of Slr-g3 after excitation of Pg in the \textmu\text{s}-ms time range with transient IR spectroscopy; we will call this rather conventional method transient 1D~IR spectroscopy from now on. Further, we show that the transformation of the chromophore geometry is accompanied by changes in the coupling between certain vibrational normal modes that show up as difference cross-peaks in a stationary difference-2D~IR experiment. We then combined these two approaches and investigated the photorecation with transient 2D~IR spectroscopy in the \textmu\text{s}-ms time range.\cite{Hamm2021} Through the combination of these three related IR methods with quantum mechanics/molecular mechanics (QM/MM) simulations and anharmonic frequency calculations, we were able to develop a solid mechanistic model for the photocycle of Slr-g3.

\section{Materials and Methods}

\subsection{Protein expression and purification}

Slr-g3 was expressed in \textit{E. coli} with an \textit{in vivo} chromophore assembly protocol and purified as described previously.\cite{Buhrke2020b} For all IR experiments, the samples were dissolved in 50~mM Tris, 200~mM NaCl D$_2$O buffer (pD=7.8) and had a concentration of ca. 2~mM as determined by their UV absorption at 280~nm.

\subsection{IR Spectroscopy}

The setup used for all IR experiments was described elsewhere in detail.\cite{Hamm2021} Briefly, a commercial 100~kHz laser system (Amplitude) and optical parameteric amplifier (FastLite) were used to generate fs mid-IR pulses. The IR pulses were split into pump, probe and reference beams, the latter two of which were passed through the sample cuvette separated by roughly 1~mm, and then imaged onto the entrance slit of a spectrograph that was equipped with a 2x32-element MCT array detection and single-shot ADC electronics at 100~kHz.\cite{Farrell2020} In most experiments, the enhanced referencing scheme introduced in Ref.~\onlinecite{Feng2017} has been applied.

For transient 1D~IR spectroscopy, the IR pump pulses were blocked, while green actinic pulses were derived from a Nd:YAG laser (AO-S-532, CNI, Changchun, China, pulse duration ca. 40~ns) that was electronically synchronized to the 100 kHz probe light. Transient 1D~IR spectra were recorded in a vis-pump-IR-multiprobe scheme.\cite{Greetham2016,Hamm2021,Jankovic2021b,Buhrke2021} The green pump pulse energy was 17~\textmu\text{J} and the polarization was set to magic angle relative the probe beam to suppress orientational effects.

For stationary 2D~IR spectroscopy, the actinic pump pulse was blocked, while a pair of IR pump pulses generated in a pulse shaper (PhaseTech) were imaged onto the sample.\cite{Middleton2010} We used 4-state phase cycling to suppress scattering and strong undersampling in a rotating frame to minimize the number of laser shots (down to 168) needed to measure a complete 2D~IR spectrum. The waiting time between pump pulses and probe pulse was set to 200~fs.

Finally, for transient 2D~IR spectroscopy, both the IR-pump pulse pair as well as the actinic pump were imaged onto the sample. We used an interleaved sampling of 2D~IR and actinic pump delays, as introduced in Ref.~\onlinecite{Hamm2021}, which allowed us to generate a sequence of transient 2D~IR  spectra by proper reshuffling the data, each separated by 10~\textmu\text{s}. The transient 2D~IR  spectra were binned on a logarithmic time-scale with 10 time points per decade, rendering the signal-noise ratio at later delay times better than at earlier times since more transient 2D~IR  spectra enter a bin.

For the transient 1D~IR experiment, the repetition rate of the actinic pump laser, which determines the measurable time window, has been 15~Hz. It has been increased to 30~Hz for the transient 2D~IR  measurements, just enough to cover the complete reaction cycle, again in order to minimize the number of laser shots needed to measure a complete sequence of 2D~IR spectra (ca. 600000).

The sample was contained in a closed-cycle flow system consisting of a peristaltic pump and a sample flow cell with solenoid-driven micro valves developed for precise sample exchange synchronized to the laser system.\cite{Buhrke2021} The flow cycle contained an additional cell between the peristaltic pump and the pressure reservoir that allowed to prepare samples in the Pg state by illumination with a red laser diode (HL6750MG, Thorlabs) before entering the measurement cell (path length 50~\textmu\text{m}).


\subsection{QM/MM calculations}

The model preparation based on the crystal structure of Slr1393g3\cite{5dfx} can be found in detail elsewhere.\cite{Wiebeler2019,Wiebeler2019_2,Rao2021} Briefly, the structures of both Pr and Pg forms (PDB IDs: 5DFX and 5M82, respectively) were protonated and embedded in a TIP3P\cite{tip3p} water box, followed by MM optimization keeping the chromophore restrained to its crystal structure geometry. In this work, starting with the MM optimized structures, all solvent atoms distant more than 3.5~$\mathrm{\AA}$ of the chromophore were removed from the structure and a preliminary QM/MM optimization was performed at XTB2\cite{Grimme19}:ff14SB\cite{Simmerling15} level of theory using the ORCA\cite{ORCA} software package. The QM region contains 86 atoms (Fig. \ref{intro}), which includes the chromophore and the side chain of its binding cysteine residue. A hydrogen link atom is used to saturate the truncated bond between the C$_{\alpha}$ and C$_{\beta}$ carbons of the cysteine sidechain. A second QM/MM optimization was carried out at the B3LYP\cite{Becke92}/6-31G*\cite{Pople98}:ff14SB level of theory with Grimme's D3 dispersion correction with Becke-Johnson damping\cite{Grimme11} using the Gaussian16\cite{Gaussian16} software package. During this step, all MM atoms were kept fixed to their spatial positions, and the PCB pyrrole hydrogens were replaced by deuterium atoms. The optimized structures were subject to IR spectra calculation using the harmonic approximation. In this step the propionate groups of the chromophore were fixed. For calculating the 2D IR spectrum we followed the procedure by Mukamel et al.\cite{Mukamel2003,Mukamel2003_2}, focusing on the harmonic modes between 1600 and 1800~cm$^{-1}$. These include the two C=O stretches of rings A and D, the three C=C stretches of the methine bridges, and the C=C stretch inside ring D (right panel of Fig. \ref{intro}). These modes were subject to anharmonic frequencies, overtones and combination bands, calculation using second order perturbation theory\cite{Barone2004,Barone2005}, as implemented in the Gaussian16 package. It was validated by Geva et. al.\cite{Geva09} against full diagonalization of the vibronic Hamiltonian and was within good agreement. The final 2D IR signal was calculated by non-linear response theory\cite{hamm11} using the anharmonic frequencies and the harmonic IR intensities. The homogeneous dephasing time T$_2$ was taken as 1.0~ps. 

\begin{figure*}[htbp]
	\centering
	\includegraphics[width=0.9\linewidth]{2DIR.png}
	\caption{Stationary 1D~IR and 2D~IR spectroscopy of Slr-g3 in the amide I region. (A,B) 1D~IR spectra in the Pg and Pr states, respectively, and (C) the ``Pr-minus-Pg'' difference 1D IR spectrum. The blue line in panel (C) compares the staionary difference spectrum with the late time transient difference spectrum measured 11~ms after excitation. Panels (D)-(F) show the corresponding 2D~IR spectra, where blue colors indicate the negative signal for the 0-1 transition of the corresponding oscillators, and red colors positive signals from the anharmonically shifted 1-2-transitions. Calculated 1D~IR spectra of PCB in the Pg and Pr states, as well as the ``Pr-minus-Pg'' difference spectrum are shown in panels (G)-(I) and the corresponding 2D~IR spectra in panels (J)-(L).}
	\label{2DIR}
\end{figure*}

\section{Results}

\subsection{Stationary difference spectroscopy}

\begin{table*}
\caption{Experimental and calculated anharmonic frequencies and intensities of relevant vibrational modes in the Pg/Pr states.}
\begin{tabular}{ |p{2.5cm}||p{3cm}|p{3.5cm}|p{4cm}|p{6cm}|  }
\hline
Mode & Exp. freq. (cm$^{-1}$)  & Calc. freq. (cm$^{-1}$) & Calc. IR int. (km mol$^{-1}$) \\
 \hline
CO$_\mathrm{A}$   & n.d./1720  &  1762/1724 & 356/310\\
CO$_\mathrm{D}$   & 1700/1675  &  1697/1670 & 714/1117\\
CC$_\mathrm{AB}$  & 1630/1627  &  1635/1619 & 647/846\\
CC$_\mathrm{CD}$  & n.d./n.d.  &  1617/1632 & 203/192\\
CC$_\mathrm{BC}$  & 1603/1600  &  1612/1595 & 2301/1637\\
CC$_\mathrm{D}$  & n.d./n.d.   &  1605/1594 & 12/24 \\
 \hline
\end{tabular}
\label{Table}
\end{table*}

The 1D IR absorption spectrum of Slr-g3 is dominated by amide I vibrations in the form of an asymmetric, broad and unstructured band in the region between 1600 and 1700~cm$^{-1}$. The spectra in the Pg and Pr states appear to be identical because the spectral changes associated with the photoconversion are too small to see them on the scale of Fig.~\ref{2DIR}A and B. The small changes associated with the photoconversion can be extracted by calculating a  ``Pr-minus-Pg'' difference 1D~IR spectrum, see Fig.~\ref{2DIR}C. Here, negative features correspond to loss of absorption due to Pg bleach, while positive bands indicate an absorption gain in Pr.

The 2D~IR spectra of Slr-g3 in the Pr and the Pg states are  indistinguishable as well in the representation of Fig~\ref{2DIR}D and E. All peaks in a 2D~IR spectrum appear as pairs with a negative (blue) lobe at higher probe frequencies and a positive (red) lobe at lower probe frequencies. Due to the quadratic dependence of the 2D~IR signal on the absorption cross section and the resulting increase in spectral resolving power, two peaks at 1628~cm$^{-1}$ and 1645~cm$^{-1}$ can be distinguished on the diagonal that only appear as slight asymmetry in the 1D~IR absorption spectra. These main amide I peaks are tentatively assigned to contributions of $\alpha$-helical and $\beta$-sheet structures of the protein, respectively.\cite{Barth2007}

Similar to the difference 1D~IR spectrum, a ``Pr-minus-Pg'' difference 2D~IR spectrum was calculated, which bears information about light-induced structural changes (Fig. \ref{2DIR}F). All features in the difference 1D~IR spectrum have counterparts on the diagonal of the difference 2D~IR spectrum that correspond to the change in IR absorbance at the respective frequencies caused by the photoconversion of the protein. However, each diagonal peak consist of two contributions, one on the diagonal corresponding to the 0-1-transition of the corresponding vibrational mode and a second one below the diagonal with opposite sign due to the anharmonically shifted 1-2-transition (excited state absorption).\cite{hamm11} Depending on the signs of the various bands in the difference 1D~IR spectrum, the signs of the diagonal peaks vary.

\begin{figure}[ht]
	\centering
	\includegraphics[width=0.75\linewidth]{Raman.png}
	\caption{Vertical cuts through the experimental difference 2D~IR spectrum at 1600~cm$^{-1}$ (magenta) and 1627~cm$^{-1}$ (orange). The respective dotted lines are taken from a separate ``Pg-minus-Pr'' control experiment for reversibility. Red line: RR spectrum of Slr-g3 in the Pr state (reproduced from ref.~\onlinecite{Buhrke2020}).}
	\label{Raman}
\end{figure}

In addition, cross peaks are observed in the difference 2D~IR spectrum, labelled  \textbf{III},  \textbf{IV} and \textbf{V} in Fig. \ref{2DIR}F. The signs of all these cross peaks indicate they originate from Pr. In order to verify these cross peaks despite their small size (they are more than a factor 100 smaller than the 2D-IR spectra of Pg and Pr), the sample was converted back and forth between both states multiple times, and the inverted ``Pg-minus-Pr'' difference spectrum was also calculated. The reversibility and relative size of the cross-peaks can best be judged in vertical cuts at $\omega_{pump}$ at their maxima shown in Fig.~\ref{Raman}.  Here, the solid magenta and orange lines represent cuts through the ``Pr-minus-Pg'' spectrum while dashed lines correspond to an independently measured, reversed ``Pr-minus-Pg'' experiment.

We also compare these cuts in Fig.~\ref{Raman} with the experimental resonance Raman (RR) spectrum of Slr-g3 in the Pr state that we reproduced from Ref.~\onlinecite{Buhrke2020}. The frequencies of the cross- and diagonal peaks completely coincident with the main peaks of the RR spectrum, confirming that these signals originate from the conjugated C=C system. In Fig.~\ref{2DIR}F, the difference cross-peaks are clearly visible only on one side of the main diagonal with  $\omega_{probe}>\omega_{pump}$, while they are masked by the stronger excited state absorption contributions of the diagonal signals on the other side.  Nevertheless, in Fig.~\ref{Raman}, a superimposed cross-peak can be identified as a kink at 1600~cm$^{-1}$ in the vertical cut at 1627~cm$^{-1}$ (orange line, labeled \textbf{III}).


We anticipate that most features in the difference spectra originate from the pronounced geometric changes of the PCB chromophore, while some may also originate from the changes of protein structure that have impact on the amide I spectrum.\cite{Buhrke2020b} These signals generally overlap with each other. To distinguish these contributions, and to facilitate an assignment, we performed anharmonic QM/MM calculations where the protein environment was fixed and only vibrational modes from the chromophore were considered. Six vibrational modes of PCB were found in the investigated frequency window between 1580 and 1750~cm$^{-1}$, the two, mostly localized C=O stretching modes of the ring A and D carbonyls as well as C=C stretching modes of the conjugated system. The latter are  dominated by stretching motions of the three methine bridges (A-B, B-C and C-D), and are denoted accordingly as CC$_\mathrm{XY}$ in the following. One mode inside ring D (CC$_\mathrm{D}$, see Table~\ref{Table}) was identified as well, but its intensity is very weak, hence this mode will not be discussed here. The calculated atomic displacement vectors of all identified modes in Pg and Pr are given in Fig.S1.  

The calculated frequencies and  IR intensities are listed in Table~\ref{Table} for both states Pg/Pr, the calculated anharmonicities are listed in Tables S1 and S2. Fig.~\ref{2DIR}G and H plot the resulting 1D~IR spectra, which are dominated by 3 peaks (i.e., CC$_\mathrm{BC}$ and CC$_\mathrm{AB}$ as well as CO$_\mathrm{D}$). CC$_\mathrm{CD}$ is very weak and visible only in Pr as a shoulder, while CO$_\mathrm{A}$ is outside the spectral window of Fig.~\ref{2DIR}. With the exception of  CC$_\mathrm{CD}$, all modes reveal a frequency downshift upon the Pg-to-Pr transition.

Based on the QM/MM results, and in combination of the Raman spectrum of Pr shown in Fig.~\ref{Raman},\cite{Buhrke2020} we can assign the experimental peaks of the Pr state, see Table~\ref{Table} (we will return to the Pg state later). This assignment is based on the energy ordering and relative intensities of the  various modes. It is interesting to note that among the bridging modes,  CC$_\mathrm{BC}$ has the strongest IR intensities while CC$_\mathrm{AB}$ has the stronger Raman intensity (Fig.~\ref{Raman}). In accordance with the QM/MM results, this implies that both modes are delocalized among each other to a certain degree, with one being more of a symmetric character and the other of a asymmetric character. Based on the results of the calculations, we conclude that CC$_\mathrm{CD}$ is too weak to be identified experimentally.

Each of the calculated resonances in the 1D~IR spectra shows up with the characteristic doublet on the the diagonal of the corresponding 2D~IR spectrum of Pg (Fig.~\ref{2DIR}J). In addition, strong cross peaks \textbf{I} (between CO$_\mathrm{D}$ and the CC modes) and \textbf{II} (between CC$_\mathrm{BC}$ and CC$_\mathrm{AB}$) reveal that the chromophore modes are coupled among each other.

The 2D~IR spectrum of Pr is better resolved (Fig.~\ref{2DIR}K), since the C=C resonances are spread over a wider frequency range. In particular, a cross peak \textbf{III}  can be identified, connecting the strongly coupled CC$_\mathrm{BC}$ and CC$_\mathrm{AB}$ modes. Furthermore,  CO$_\mathrm{D}$ now produces two distinct cross peaks with the CC$_\mathrm{BC}$ (\textbf{IV}) and CC$_\mathrm{AB}$ (\textbf{V}). These spectral changes give rise to a specific fingerprint pattern in the calculated difference spectrum (Fig. \ref{2DIR}L), reproducing the main features of the experimental difference spectrum surprisingly well (Fig. \ref{2DIR}F). This is in particular true for the cross peaks \textbf{III}, \textbf{IV} and \textbf{V} that connect the major signals from the C=C region with  CO$_\mathrm{D}$ in the Pr state. The  cross peak \textbf{I} with opposite sign, origination Pg, is not visible in the experimental spectrum, either because it is too weak or outside the measured frequency window.

One curiosity is the diagonal peak of CC$_\mathrm{BC}$, whose sign is inverted which is indicative for a positive anharmonicity with the 1-2 frequency being larger than the 0-1 frequency (Fig.~\ref{2DIR}K as well as Table SII in SI). A positive anharmonicity appears when the corresponding potential is steeper than harmonic (more particle-in-a-box like). With the exception of a proton vibrating between two heavier partners,\cite{Dahms2017, Fournier2018, Dereka2021} such as in the Zundel ion, a positive anharmonicity has not been observed experimentally. Here, it is the vibration of the bridging carbon between two heavier pyrrole rings that is predicted to have a positive anharmonicity, but only in the more rigid Pr state, and in the middle of the molecule (i.e., only for CC$_\mathrm{BC}$). The signature of a  positive anharmonicity is also visible in the calculated Pr-minus-Pg difference spectrum   (Fig.~\ref{2DIR}L), but it is not obvious in the experimental counterpart (Fig.~\ref{2DIR}F).


\begin{figure}[t]
	\centering
	\includegraphics[width=\linewidth]{T1DIR_V3.png}
	\caption{Transient 1D~IR spectroscopy of the Pg $\rightarrow$ Pr reaction from 10~\textmu\text{s} to 30~ms. (A) Data represented as a contour plot; blue colors indicate negative bands (bleaches) and red colors positive bands. (B) Dynamical content. (C) Three representative kinetic traces with lifetime analysis fits (black lines).}
	\label{T1DIR}
\end{figure}

\subsection{Transient 1D~IR and 2D~IR spectroscopy}

The stationary 1D~IR and 2D~IR difference spectra of Figs.~\ref{2DIR}C and F report on changes in the geometric and electronic structure between the two stable states of the protein. The time-resolved counterparts of these spectroscopies can provide the same information for transient intermediates during the course of the photocycle. In a recent publication,\cite{Buhrke2020b} we presented transient 1D~IR data of Slr-g3 in the ps to \textmu\text{s} time range obtained with a pump-probe setup based on two electronically synchronized femtosecond laser systems.\cite{Bredenbeck2004} Here, we add new data in the \textmu\text{s}-ms regime acquired with a conceptually different vis-pump-IR-multiprobe spectrometer, operating at repetition rates of 15~Hz (vis pump) and 100~kHz (IR probe, see Materials and Methods).\cite{Hamm2021,Jankovic2021b,Buhrke2021}
The new data reveal two further reaction steps that can be identified directly by visual inspection of the contour plot of Fig.~\ref{T1DIR}A, or in the three selected traces shown in Fig.~\ref{T1DIR}C.  Time constants for these processes were obtained by lifetime analysis with a maximum entropy method,\cite{Kumar2001,Lorenz-Fonfria:06} similar to the analysis that was applied for the first part of the data in our recent paper.\cite{Buhrke2020b} The resulting dynamical content $D$ is plotted in Fig.~\ref{T1DIR}B, which reveals two clear maxima at 250~\textmu\text{s} and 2.5~ms associated with the time constants of these processes.
The properly scaled late time (i.e., 11~ms) transient 1D~IR spectrum is overlaid in Fig.~\ref{2DIR}C (blue line) with the stationary 1D~IR difference spectrum (black line). The perfect agreement of both spectra indicates that the photoreaction is completed after that time and Pg is formed.

 The micro-to-milisecond kinetics of Slr-g3 were up to now only studied by transient visible spectroscopy at single wavelengths, which yielded only one time constant of 1.1~ms in this time window.\cite{Xu2014} This indicates that the two processes we see in the IR could not be distinguished in the visible experiment and a mix of the two time constants was observed. The same would be true if only single traces in the IR, e.g. at 1650 or 1725~cm$^{-1}$ were analyzed (see Fig.~\ref{T1DIR}A), where the two processes have the same sign.
 However, other traces, e.g. at 1610~cm$^{-1}$, show two clearly distinguishable processes with opposite sign and an absorption maximum around 1~ms (marked with an asterisk in Fig.~\ref{T1DIR}A and C). We assign this second kinetic signature to an intermediate state that directly precedes the formation of Pr.

\begin{figure*}[t]
	\centering
	\includegraphics[width=\linewidth]{T2DIR.png}
	\caption{Transient 1D~IR (top row) and transient 2D~IR spectra at time-points (50~\textmu\text{s}, 1~ms, and 11~ms) at which the population of certain intermediates is maximized, see Fig.~\ref{T1DIR}C. Transient 1D~IR spectra are taken from the data set of Fig.~\ref{T1DIR}A.}
	\label{FigTransient2DIR}
\end{figure*}

Fig.~\ref{FigTransient2DIR}D, E and F show a series of transient 2D~IR spectra at time points 50~\textmu\text{s}, 1~ms, and 11~ms, at which the populations of certain intermediates are maximized (compare dashed vertical lines in Fig. \ref{T1DIR}), together with the corresponding  transient 1D~IR spectra (Fig.~\ref{FigTransient2DIR} A, B, and C). Just like for transient 1D~IR spectroscopy (Fig.~\ref{2DIR}C, black vs. blue line), the late time transient 2D~IR spectrum at 11~ms is in essence the same as the stationary 2D~IR difference spectrum of Fig.~\ref{2DIR}F. All diagonal peaks of the latter can be identified also on the diagonal of the 11~ms transient 2D~IR  spectrum. In addition, cross peaks are revealed, but since the signal-to-noise of the 11~ms  transient 2D~IR  spectrum is not quite as good as that of the stationary 2D~IR difference spectrum, we focus the discussion here only on the strongest cross peak \textbf{III} between  CC$_\mathrm{AB}$ and CC$_\mathrm{BC}$. While the diagonal peak patterns are very similar in the earlier 1~ms transient 2D~IR  spectrum, that cross peak is not yet prominent. Hence, the coupling  between the corresponding two modes is switched on only during last kinetic step of the transition from Pg to Pr.

The 50~\textmu\text{s} transient 2D~IR  spectrum is very different. It has three diagonal peaks with inverted signs, in agreement with the corresponding bleaches in the transient 1D~IR spectrum at the same delay time (Fig.~\ref{FigTransient2DIR}A). Based on the results of the QM/MM calculations, we assign the two lower-frequency bleaches to the two bridging modes CC$_\mathrm{BC}$ and CC$_\mathrm{AB}$, while CC$_\mathrm{CD}$ is expected to be too weak to significantly contribute. Since the spectrum is mostly a bleach without any overlapping positive contribution, one  can read off the frequencies of the corresponding modes in the Pg state, listed in Table~\ref{Table}.
Furthermore, an inverted cross peak \textbf{II} can  be identified between CC$_\mathrm{BC}$ and CC$_\mathrm{AB}$. That is, as the bands on the diagonal bleach, the corresponding cross peaks bleaches as well. The calculations predict the strongest coupling between the adjacent  CC$_\mathrm{AB}$ and CC$_\mathrm{BC}$ modes (cross peak \textbf{II} in Fig. \ref{2DIR}J), in agreement with the present assignment of the  50~\textmu\text{s} transient   spectra.

Based on the QM/MM results, we also conclude that third negative band at around 1655~cm$^{-1}$ cannot originate from the chromophore, hence it must originate from the protein. Indeed, in our previous study,\cite{Buhrke2020b} we observed that the kinetic process leading to that band on a 40~ns timescales is only observed in the IR transient spectra, and not in the electronic spectra of the chromophore, which lead us to  conclude that it reflects a response of the protein. Cross peak \textbf{VI} indicates the coupling between the chromophore and the protein (Fig.~\ref{FigTransient2DIR}A).


\section{Discussion}

In transient IR spectroscopy of photoactive proteins, signals that originate from the chromophore are often dominant, since its electronic and geometric structure changes significantly more than that of the embedding protein.\cite{Gerwert1990, Ritter2015, Kottke2017, Lorenz-fonfria} Notable exceptions are phytochromes and LOV domains, where a large-scale re- or unfolding of entire secondary structure elements occurs.\cite{Stojkovic2014, Konold2016} The x-ray structures of Slr-g3 shown in Fig.~\ref{intro} reveal that the biggest changes in this protein concern rings A and D of the PCB chromophore. While all four rings are almost coplanar in the Pr state, rings A and D are tilted out of the plane in Pg. These geometries immediately explain the color change between the two states, i.e., their electronic properties: When rings A and D become coplanar with rings B and C, they increase the size of conjugated system of the chromophore, thereby shifting its electronic absorption bands towards the red.\cite{Wiebeler2018} Additionally, some differences in secondary structure have also been identified by x-ray crystallography, such as e.g. the unfolding of a small segment of the so-called a3-helix in the Pr state.\cite{Xu2020}


The kinetic analysis of our time-resolved data indicates two processes in the \textmu\text{s} to ms time range, or in other words, two meta-stable intermediate states that are maximized around 50~\textmu\text{s} and 1~ms, respectively, before Pr is formed. Both of these meta-stable configurations lie within the time resolution of the transient 2D~IR experiment, and thus the connectivity of the dominant modes allows unprecedented insight into the chromophore configuration at this stage of the photocycle.

The 50~\textmu\text{s} intermediate (Fig. \ref{FigTransient2DIR}A and B) only shows bleach bands associated with the conjugated system of PCB and almost completely lacks positive counterparts, indicating that the chemical structure of the PCB chromophore in this species differs significantly form all other intermediates and parent states. One possibility is that the PCB chromophore is extremely disordered, leading to very broad positive bands with weak intensity. Another process that could explain such spectra is transient deprotonation of the conjugated system, which leads to a reduced dipole strength and therefore reduced IR intensities of associated bands. Such a behaviour is well known from retinal model compounds as well as retinal-binding proteins, where protonated (positively charged) Schiff base compounds typically produce 5-10x stronger IR intensities in the C=C stretching region than their deprotonated (neutral) counter parts that have a lower level of charge alternation between the conjugated carbon atoms.\cite{Siebert1980, Braiman1987, Vogel2001} Transient de- and re-protonation events are also typical for the photocycle of phytochromes\cite{VanThor2001,Borucki2005}, and some studies identified such processes in the red/green CBCR AnPixJ.\cite{Escobar2013, Song2015} Interestingly, pH-dependent experiments on the same sample indicated that the protonation state of the chromophore has a large affect on the vibrational spectra, but barely affects the visible absorption properties\cite{Song2015, Altmayer2022}, which might explain why the  250~\textmu\text{s} process could not be resolved in the transient visible experiments.\cite{Xu2014} According to NMR and RR experiments, the PCB chromophore deprotonates either at the ring B or C pyrrole nitrogen, resulting in a tautomeric species where only one proton is shared between these two pyrrole rings.\cite{Song2015, Altmayer2022} In the light of these findings, we assign the 50~\textmu\text{s} intermediate to such a deprotonated PCB species.

The next intermediate is maximized at 1~ms, and shows positive counterparts to the bleach bands, confirming that the 250~\textmu\text{s} process indeed corresponds to PCB reprotonation. Here, the transient visible study suggested that the formation of Pr in the early milliseconds is preceded by an orange-absorbing intermediate state,\cite{Xu2014} and a RR study found that ring D is already in a Pr-like configuration while ring A still retains an out-of-plane tilt similar to Pg.\cite{Buhrke2020} Such a configuration has a conjugated system with an size that is in-between that of Pg and Pr, hence an electronic absorption band between green and red. The transient 1D~IR results of Fig. \ref{T1DIR} validate this hypothesis, because here it can be directly observed that the final difference signal associated with CO$_\mathrm{D}$ at 1674~cm$^{-1}$ is established at an earlier point in time than CO$_\mathrm{A}$ at $>$1700~cm$^{-1}$. Interestingly, The CO$_\mathrm{D}$ bleach signal is not accompanied by a visible positive counterpart until the reprotonation step, which means that the final coordination environment of ring D that defines the C=O frequency is only established during the 250~\textmu\text{s} process.

As ring A becomes coplanar during the last reaction step, the coupling between between CC$_\mathrm{AB}$ and CC$_\mathrm{BC}$ is switched on, as evidenced by cross peak \textbf{III} (Fig.~\ref{FigTransient2DIR}E vs F). No X-ray structures exist currently for any of the intermediates, and hence anharmonic QM/MM calculations as for Pg or Pr are not feasible. On a less rigorous level, it has been argued that the cross anharmonicity that determines the cross peak intensity in a 2D~IR spectrum correlates with the degree to which normal modes are delocalized, since the source of anharmonicity is local, i.e., that of individual chemical bonds.\cite{Woutersen2002,hamm11,Baiz2011} Upon a normal mode transformation, which delocalizes local modes in a harmonic sense, the local anharmonicity delocalizes accordingly. The complementary intensities of CC$_\mathrm{AB}$ and CC$_\mathrm{BC}$ in the Raman (Fig.~\ref{Raman}) vs the IR spectra (Table~\ref{Table}) indicate that the modes are delocalized to a certain extent in Pr. It it reasonable to assume that these modes are more local in a distorted structure with ring A tilted out of the plane, explaining the weaker anharmonic coupling.

\section{Conclusions}

A combination of three advanced IR methodologies allowed us to track the structural changes of the PCB chromophore inside the protein matrix of the red/green CBCR Slr-g3. First, transient 1D~IR spectroscopy was used to establish the time scales of various photocycle events. The higher resolution power of IR spectroscopy, as compared to UV/Vis spectroscopy, revealed an additional intermediate
preceding the formation of Pr, which has not been observed before. In addition, difference cross-peaks in the stationary 2D~IR spectrum guided the assignment of certain signals based on changes in vibrational coupling of the chromophore  modes. Here it is important to note that the discussed vibrational modes overlap with the strongly overwhelming amide I modes from the protein backbone. Nevertheless, the vibratonal modes of the chromophore can be isolated dy difference spectroscopy and validated by the calculations. Finally, the two previous experiments were combined into transient 2D~IR spectroscopy. The 2D~IR difference spectra of various intermediate species were obtained, that allowed us to gain insights into the coupling patterns associated with the later stages after the photoreaction. The combination of these three techniques allowed us to draw consistent conclusions about the reaction mechanism that Slr-g3 undergoes after excitation. For example, reaction steps could be determined during which the PCB chromophore de- and reprotonates and during which ring A rotates into plane to form the Pr state.

The work also demonstrates that a close-to-quantitative agreement between 2D-IR spectra and anharmonic QM/MM calculations  can be obtained for the initial and final forms, Pg and Pr, respectively. The existing X-ray structures of these two forms served as a basis of the QM/MM simulations. Here, we also make suggestions for the structurual changes of the two transient intermediates preceding the formation of final Pr state, based on a combination of  transient 1D and 2D spectroscopy. 

Time-resolved X-ray scattering experiments are nowadays within reach, using upcoming X-ray free-electron laser facilities,\cite{Standfuss2019} which could provide the fundament of rigorous QM/MM calculations also of those intermediates, to test our structural hypotheses. Since Slr-g3 (as well as other CBCRs) are emerging tools in biotechnological applications, such as optogenetics and fluorescence microscopy,\cite{Oliinyk2019,Blain-Hartung2018} it is highly desirable to understand the molecular mechanism of its photoreaction in real time and at full atomistic detail.\\

\noindent \textbf{Acknowledgement:} This work was supported by the Swiss National Science Foundation (SNF) through Grant No. 200020B 188694/1. DB acknowledges a Liebig-Scholarship by the funds of the German chemical industry (Fonds der chemischen Industrie, FCI). I.S. acknowledges support from the Israel Ministry of Science and Technology (Grant 3-16311). I.S. thanks the DFG Collaborative Research Center 1078, project C6 for support.\\

\noindent \textbf{Data availability statement:} The data that support the findings of this study will be deposited on a repository at the proof stage.\\

