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Single-shot submicrosecond mid-infrared spectroscopy on protein reactions with quantum cascade laser frequency combs Jessica Laura Klocke, Markus Mangold, Pitt Allmendinger, Andreas Hugi, Markus Geiser, Pierre Jouy, Jérôme Faist, and Tilman Kottke Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b02531 • Publication Date (Web): 06 Aug 2018 Downloaded from http://pubs.acs.org on August 11, 2018

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Analytical Chemistry

Single-shot submicrosecond mid-infrared spectroscopy on protein reactions with quantum cascade laser frequency combs Jessica L. Klocke,† Markus Mangold,*,‡ Pitt Allmendinger,‡ Andreas Hugi,‡ Markus Geiser,‡ Pierre Jouy,§ Jérôme Faist,§ and Tilman Kottke† †

Physical and Biophysical Chemistry, Department of Chemistry, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, Germany. ‡ IRsweep AG, Laubisruetistrasse 44, 8712 Staefa, Switzerland. § Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland. ABSTRACT: The kinetic analysis of irreversible protein reactions requires an analytical technique that provides access to timedependent infrared spectra in a single shot. Here, we present a spectrometer based on dual frequency comb spectroscopy using midinfrared frequency combs generated by quantum cascade lasers. Attenuation of the intensity of the combs by molecular vibrational resonances results in absorption spectra covering 55 cm-1 in the fingerprint region. The setup has a native resolution of 0.3 cm-1, noise levels in the µOD range, and achieves submicrosecond time resolution. We demonstrate the simultaneous recording of both spectra and transients of the photoactivated proton pump bacteriorhodopsin. More importantly, a single shot, i.e. a single visible light excitation, is sufficient to extract spectral and kinetic characteristics of several intermediates in the bacteriorhodopsin photocycle. This development paves the way for the non-invasive analysis of enzymatic conversions with high time resolution, broad spectral coverage, and minimal sample consumption.

Time-resolved studies of reactions in the condensed phase are of outstanding relevance to chemistry and biology. Important processes whose sub-second kinetics are key for future developments include the fixation of CO2 into fuels,1 water oxidation in photosynthesis,2 or the folding of proteins.3 Understanding of the underlying mechanisms presents scientists with a chance to develop revolutionary means of energy conversion and treatments for diseases such as Alzheimer's or Parkinson’s.4 Infrared and Raman spectroscopy allow for studying minute yet relevant structural changes in an analyte due to their sensitivity to single proton movements or hydrogen bond rearrangements. Time scales from femtoseconds to microseconds are addressed by pump-probe methods,5-7 whereas the important time range from nanoseconds to tens of milliseconds is covered by infrared techniques including step-scan FTIR,8 tuneable laser,9 dispersive infrared,10 and resonance Raman spectroscopy.11 Unfortunately, these techniques require a considerable number of acquisitions to collect a full set of time-dependent spectra. Therefore, natural photo-induced processes that are either thermally reversible within an amenable time (e.g. microbial rhodopsins12) or returnable to their initial state by photons or oxygen13,14 have been studied in detail (Figure 1). However, several highly important natural processes are irreversible such as the responses of visual rhodopsin12 and the B12dependent CarH receptor15 or are non-repeatable such as water splitting by photosynthetic reaction centres.16,17 Others are only slowly repeatable including the recovery of phototropin, which regulates plant growth towards the light.18 In particular, caged compounds are a convenient but irreversible approach

for the fast initiation of enzymatic reactions for time-resolved studies.19 All these processes have in common that their comprehensive analysis requires excessive, often prohibitive amounts of sample for repetitive experiments.

Figure 1. Three types of light-driven protein reactions. Excitation of reactant A produces intermediates represented by B and finally product C. Such reactions may have a thermal (i) or stimulated (ii) back-reaction or may be irreversible (iii) and thereby challenging to analyze. Frequency-comb spectroscopy20-22 has enabled the direct observation of time-resolved broadband spectra since its characteristic minimum acquisition time is linked to intrinsic properties of the frequency combs (see below). Fiber-based frequency combs were employed to achieve submillisecond, high-resolution gas spectroscopy.23-26 Extending these sources into the mid-infrared spectral range remains challenging,27 and the search for more efficient comb generation mechanisms

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such as microresonators28,29 is ongoing. The discovery of an electrically-pumped frequency-comb source that is based on a semiconductor quantum cascade laser30 drastically simplified mid-infrared dual-comb spectroscopy.31,32 The chip-scale nature of the source promises compact sensor devices and also allows for submicrosecond time resolution. The 0.3 cm-1 spacing of the frequency comb modes is ideal for solid or fluid phase measurements and, in particular, for biological matter. Here, we report on a quantum cascade laser dual frequency comb spectrometer that, with its parallel measurement of hundreds of wavelengths with sub-microsecond time resolution, was applied to a single-shot kinetic analysis of a biological photoreaction. EXPERIMENTAL SECTION Sample Preparation. Wild-type bacteriorhodopsin was obtained by homologous expression from Halobacterium salinarum (strain S9). Halobacterium salinarum was grown in 4.3 M NaCl, 80 mM MgSO4, 27 mM KCl, 10 mM sodium citrate, 10 g L-1 peptone medium, pH 6.5, for 8 days and lysed by addition of distilled water. Fragments of purple membrane (PM) containing bacteriorhodopsin were isolated by fractionated centrifugation according to Oesterhelt and Stoeckenius.33 3 or 12 µL of PM suspension with 530 µM bacteriorhodopsin were slowly dried on a BaF2 window and rehydrated to the original volume with 1 M KCl, 50 mM K2HPO4/KH2PO4 buffer, pH 7.2, 9.0 or 6.0, respectively. A second BaF2 window was applied to prevent evaporation of the droplet during 30 min of rehydration. Afterwards, the sample was sealed using vacuum grease and the path length was reduced to 4 or 16 µm to achieve an absorbance of 0.8 or 2.2, respectively, at 1650 cm-1. The temperature of the samples was kept constant at 17 °C by a circulating water bath. After an equilibration time of at least 30 minutes, the sample was light-adapted by exposure to the 532-nm actinic laser. Frequency-Comb Spectroscopy. The experiments were conducted using a table-top dual frequency-comb spectrometer. The emission of two frequency combs is combined using a 50:50 CaF2 beam splitter and attenuated with neutral density filters. One combined beam is focused on a high-bandwidth HgCdTe reference detector (PV-4TE-10.6, Vigo Systems). The other combined beam is transmitted through the sample as a collimated beam with 4 mm beam diameter and is finally detected by a second HgCdTe detector. The analog signal of the detectors is digitized on a 2-channel digitizer with 650MHz analog bandwidth, 1.6 GS/sec sampling rate, and 12 bit resolution per channel (Keysight U5303A). A germanium filter (5% cut-on: 1.65 µm, Laser Components) placed in the beam path after the sample was used to block visible stray light. The samples had a path length of 16 µm and were excited at 532 nm with the second harmonic of a pulsed Nd:YAG laser (Ultra100, Quantel) with a pulse duration of 10 ns at a repetition rate of 2 Hz. The laser beam was expanded to a diameter of 1.5 cm using a bi-concave lens with a focal length of 250 mm resulting in an intensity of 12 mJ/cm2 at the sample. For a time range of 5 ms prior to the laser pulse, dark spectra were recorded, averaged and used as a reference for the calculation of light-induced difference spectra. Subsequently, the response of the sample was monitored for 15 ms. Step-Scan FTIR Spectroscopy. Step-scan measurements were performed on an IFS 66v spectrometer (Bruker) equipped with a DC-coupled photoconductive mercury cadmi-

um telluride (MCT) detector at a spectral resolution of 4.5 cm. An infrared band-pass filter (Laser Components) was used to block stray light and restrict the spectral range to 1974-988 cm-1. For excitation, 532-nm pulses with a duration of 10 ns were generated by an optical parametric oscillator (Opta) pumped by the third harmonic of a Nd:YAG laser (QuantaRay 130-10, Spectra Physics) with an intensity of 5.2 mJ/cm2 at the sample. The 10 Hz repetition rate of the laser was reduced to 2 Hz by an optical shutter (LSTXY, nm Laser Products). 449 mirror positions were recorded with 4 coadditions and 1000 equidistant time slices of 5 µs up to 5 ms. Reference spectra were recorded for 173 µs, before excitation, and used to calculate light-induced difference spectra. Samples had a path length of 4 µm and were exchanged after a maximum of 10776 excitations. For the final spectra, 11 experiments were averaged with 44 coadditions in total corresponding to ~20,000 excitations. Data Analysis. The digitized beating signal was analyzed using MATLAB (Mathworks). The 20 ms time traces were cut into time slices of 4-times the length of the required time resolution, with subsequent time slices overlapping by 75% of their length. This procedure is justified by a “loss” of 75% of the signal information by applying a flattop window to each time slice. In spite of the overlaps, the evaluation led to fully uncorrelated signals of adjacent time slices. After Fourier transformation, the equidistance of the beating signals was used to automatically detect the peak positions of individual beating signals. The amplitude at the peak position of the heterodyne spectrum retrieved from the signal detector was then normalized to the amplitude of the same time slice retrieved from the reference detector. The ratio of signal to reference detector amplitudes was then taken as the instantaneous value of the transmitted laser intensity. The pre-trigger intensity (here first 5ms of each acquisition) was averaged and used as a background measurement. The post-trigger intensities normalized by this background represented the time resolved difference spectra. Further, the time-resolved spectra were analyzed using MATLAB. For the dual-comb spectra, 6, 14, and 25 adjacent lines were averaged and weighted according to their line intensity, resulting in a resolution of 2.0 cm-1, 4.5 cm-1 and 8.0 cm-1, respectively. For the transients, 14 or 31 lines were averaged and weighted according to their line intensity. To increase the signal-to-noise ratio, dual-comb data taken after 130 µs and step-scan data recorded after 125 µs were averaged on a logarithmic time scale. A weighted global fit was applied using a kinetic model of sequential first-order reactions with four intermediates. The weighting factors were calculated from the variance of the reference spectra along the wavenumber dimension. Nonlinear fits were performed with the program SolvOpt for MATLAB (The Mathworks). From the concentration profiles, the species-associated difference spectra (SADS) were calculated via matrix division according to D=AC+ with C+ being the pseudoinverse of C. Further analysis was performed with OriginPro (OriginLab). The crystal structure (PDB ID 1C3W) was visualized using the PyMOL Molecular Graphics System (Schrödinger). 1


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Analytical Chemistry

Figure 2. Setup for dual-comb spectroscopy. (A) Spectrometer with two quantum cascade laser frequency-combs (i), sample chamber with optically excited bacteriorhodopsin sample (ii) and two fast AC-coupled HgCdTe photodetectors (iii). (B) Spectrum of the two frequency combs measured with an FTIR spectrometer (inset) and resulting heterodyne beating signal in the radio-frequency range (main panel). (C) Schematic representation of two interleaved frequency combs with repetition rates frep1 and frep2 (top panel). An absorption feature in the optical range is mapped onto the radio frequency range by beating adjacent comb modes (lower panel). (D) 100% transmission line fluctuations at 10 ms integration time at 0.3 cm-1 and 4.5 cm-1 spectral resolution, respectively. Inset: Allan deviation of a single comb line during a single acquisition and 500 acquisitions of 20 ms duration average. 105. The chip-based QCL frequency combs have much larger frep ~ 1010 Hz. The large frep simultaneously increases the limit RESULTS AND DISCUSSION frep/2 and decreases the number of modes N needed for a given Establishing a Dual-Comb Spectrometer. The dual-comb spectral coverage. Here, frep/2 is so large that the limit for ∆frep system (Figure 2A) contains two free-running quantum casis to accommodate the multi-heterodyne signal within the 800 cade laser (QCL) frequency-combs centered at a wavelength MHz analog bandwidth BW of the detector, i.e. N*∆frep < BW. of ~1220 cm-1 and spanning 70 cm-1 (Figure 2B, inset).34 They For the present measurements, ∆frep was set at ~2 MHz allow-1 -1 overlap in the spectral range from 1185 cm to 1240 cm ing for a time resolution of about 1 µs. resulting in dual-comb absorption spectra covering 55 cm-1. The signal-to-noise ratio of the system is assessed with AlThe continuous wave output power is about 700 mW causing lan deviation plots of a single, high-intensity comb line (Figan average power per comb tooth of >2 mW. The two freure 2D, inset) showing standard deviation as a function of quency comb sources are combined using a 50:50 beam splitintegration time. In a single acquisition, it reaches about 1 ter and attenuated with neutral density filters. One combined mOD at 100 µs time resolution. For a planned experiment that beam is focused on a high-bandwidth HgCdTe reference demeans, a state with 100 µs life time can statistically be obtector. The other combined beam is transmitted through the served if it induces a change in absorbance of more than sample, passed through a germanium visible beam block and 1 mOD. By averaging 500 acquisitions, the standard deviation detected by a second HgCdTe detector. A heterodyne beat of a single line at 100 µs time resolution and the correspondspectrum (Figure 2B) results from the mixing of the two freing minimum detected absorbance change reduces to below 50 quency comb lasers, as schematically shown in the top panel µOD (Figure 2D, inset). The measurement deviation of a of Figure 2C. The short cavity length of QCLs result in large 100% transmitting sample at 10 ms integration time (Figure repetition frequencies of the lasers frep1, frep2. ∆frep = frep1 - frep2 is 2D, open symbols) is well above the standard deviation exthe frequency spacing between beatings of neighboring comb pected from the Allan plots, since it is dominated by weak teeth in the radio frequency range (bottom panel of Figure lines in the multiheterodyne spectrum. Therefore, it can be 2C). The time resolution of the overall instrument is limited by strongly improved by averaging multiple, e.g. 14 neighboring the requirement to resolve neighboring teeth in the beating multiheterodyne lines (full symbols). The resulting spectral spectrum of the combs. Thus, the shortest measurement time resolution is 4.5 cm-1 as commonly used for time-resolved that allows for full spectral evaluation of the beating signal is FTIR spectroscopy. In this case, we observe a peak-to-peak given by Tres=2/∆frep. For high time resolution spectroscopy, a variation on the order of 100 µOD throughout the highlarge ∆frep is thus favorable. In most dual comb systems, ∆frep intensity range of the spectrum, while the noise level is about is limited by the condition N*∆frep < frep/2, with N representing 10 times higher in the low intensity range from 1205 to the number of beatings to be observed. In fiber combs, the 8 1215 cm-1. typical 1 ms time resolution results from frep ~ 10 Hz and N ~



Figure 3. Time-resolved analysis of the bacteriorhodopsin photocycle. (A) Light-induced retinal isomerization in bacteriorhodopsin from all-trans to 13-cis 15-anti and the subsequent deprotonation are fully reversible within milliseconds. (B) Simplified photocycle of bacteriorhodopsin. (C) Light-induced difference spectra obtained with dual-comb experiments after 500 shots with a spectral resolution of 4.5 cm-1 at pH 7.2. (D) Spectra averaged from raw data are representative for KL, L, M and N according to global analysis. (E) Good agreement of spectra from step-scan FTIR spectroscopy with those from dual-comb experiments shown in (D). (F) Identical M spectrum (400-800 µs) obtained after the same FT processing, and increase to 2 cm-1 resolution (dual-comb spectroscopy only). Bands were normalized to the integral. (G) Spectra from single-shot experiment with dual-comb spectroscopy at 8 cm-1. The standard deviation of difference absorbance over 50 shots is shown as error bars at 1200 cm-1 and 1189 cm-1. (H) Data analyzed with a higher time resolution of 320 ns and averaged over 500 shots. The 320-ns spectrum represents the pure KL intermediate at 8 cm-1 resolution in contrast to the 2.2-µs spectrum of a mixture of KL and L at 4.5 cm-1. The inset illustrates the time resolution with a linear time scale. An intermediary spectral region with high noise is omitted in (G) and (H). ing.41 Here, we demonstrate that even a single excitation can elucidate its various photocycle states. Analysis of a Biological Photoreaction. The present research focuses on the well-understood kinetics of the transWe investigated the photocycle of bacteriorhodopsin using a membrane protein bacteriorhodopsin from Halobacterium well-hydrated film embedded in its native environment as salinarum,35 which binds a retinal as chromophore in a sevenpurple membrane patches at pH 7.2, 1 M KCl and 17 °C, close to physiological conditions. After recording 5 ms of reference α-helical fold (Figure 2A). Bacteriorhodopsin acts as a lighttransmission, the photocycle of bacteriorhodopsin was initiatdriven proton pump and undergoes a photocycle starting with ed using a 10 ns laser pulse at 532 nm for excitation with an the isomerization of the retinal (Figure 3A, 3B).36 It has been intensity of 12 mJ/cm2. The spectral evolution was monitored previously extensively characterized regarding its intermedi35 for another 15 ms and absorption difference spectra were ates and the proton-pumping mechanism using time-resolved calculated. The experiment was repeated at 2 Hz and 500 FTIR spectroscopy37-40 among other methods. Bacteriorhodopaverages were performed. In the spectral range accessible by sin is an exceptionally stable protein, which withstands more the dual-comb spectrometer, we detected two marker bands of than 100,000 excitations, thus allowing for extensive averag-


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Analytical Chemistry retinal at 1189 (+) cm-1 and 1200 (-) cm-1 (Figure 3C), which have been assigned previously to changes in the C-C stretches and coupled CCH rocks of the retinal chromophore.42,43 Four intermediates (τ1 = 12 µs, τ2 = 140 µs, τ3 = 3.3 ms, τ4 >12 ms) were resolved between 2.2 µs and 15 ms by performing a spectrally weighted global fit with sequential reactions (Figure S1, Supporting Information). Characteristic changes over time resulted from averaging raw data according to the maximal concentrations of the intermediates from the global fit (Figure 3D). Among others, the transient loss at 1189 cm-1 reflects the deprotonation of the retinal linkage in the M intermediate. Reference measurements were acquired with a step-scan FTIR spectrometer under the same conditions as those of dualcomb spectroscopy, except for a lower excitation intensity of 5.2 mJ/cm2 (Figure 3E and Figure S2, Supporting Information). The resulting species-associated difference spectra (SADS) were assigned to intermediates KL, L, M and N,40,41,43 although KL showed some admixtures by L at 1506 cm-1 (see below). The time constants and SADS were consistent with those from dual-comb spectroscopy (Figure S2, Supporting Information). Averaging of the raw data produced spectra including all the characteristics of KL, L, M, and N in this spectral range (Figure 3E).40,41,43 A direct comparison of the M spectrum between dual-comb and step-scan spectroscopy shows excellent agreement, if the same (Blackman-Harris) windowing is applied (Figure 3F, blue and black trace). The spectrum exemplifies that the quality of the dual-comb recording is as high as that of FTIR spectroscopy after the same data treatment. The dual-comb data was also evaluated using a higher spectral resolution of 2 cm-1 resolving a negative band at 1226 cm-1 in the spectrum of the M intermediate (Figure 3F). This high resolution would require a severe increase in repetitions when using step-scan FTIR spectroscopy (here from 19.756 to 41.492 shots), whereas it is inherent in dualcomb spectroscopy. Typically, such high resolution is not required to resolve the majority of signals in biological samples, but it may provide valuable information. Accordingly, the band at 1226 cm-1 has been observed in high resolution experiments at 220 K,44 but we assert that it has not been resolved previously in time-resolved experiments. Single Shot Spectra and Kinetics. Strikingly, a single shot of the experiment clearly resolved all characteristic profiles of the intermediates without a baseline correction or any other manipulation of the data (Figure 3G). To illustrate that the selection of the single shot was representative, the standard deviation of difference absorbance over 50 single shots was included (Figure 3G and Figure S3, Supporting Information). It is important to note that this time-resolved experiment is the first single-shot analysis of a protein reaction in the mid-IR spectral range. Previous experiments have succeeded in resolving single-shot kinetics at selected wavenumbers.45 Here, we covered a broad spectral range comprising multiple absorption bands. The coverage is only limited by the current status of QCL comb technology. Next, the limits of the time resolution were evaluated. At the expense of lower spectral resolution and higher noise, the time resolution limit Tres = 2/∆frep was overcome and a resolution of 320 ns was achieved. A linear time trace (Figure 3H, inset) shows the decay of the KL intermediate. From the raw data, a spectrum at 320 ns was isolated without performing any global analysis, which represents the pure KL intermediate10,40,41 (Figure 3H). The spectrum clearly differs from the mixture of

KL and L obtained at 2.2 µs. Evidently, even the submicrosecond intermediates of the photocycle can be elucidated with the dual-comb approach with only few repetitions of the experiment. Finally, reaction kinetics at the maxima of the difference bands were evaluated from 2.2 µs to 15 ms covering almost four orders of magnitude in time (Figure 4). A good agreement was obtained with results from step-scan spectroscopy (Figure 4A). The time range of the dual-comb spectrometer can even be extended >15 ms by applying larger memory electronics. An advantage of the considerably higher intensity of the QCL emission as compared to the globar in the FTIR spectrometer is espoused by its capacity to strongly increase the limited path length of below 10 µm in H2O, which facilitates the application of flow systems46 without degrading the sample (Figure S4, Supporting Information). Moreover, we show that identical kinetics but significantly higher signal can be obtained from a sample having four times longer path lengths (Figure S5 and S6, Supporting Information). To demonstrate the sensitivity, the effect of pH on the photocycle was examined (Figure 4B). The increase in pH from 6.0 to 9.0 led to a decrease in rate constants after 100 µs, which was quantitatively analyzed and assigned applying global fits to the average of 500 acquisitions (Figure S7, Supporting Information). Formation and decay of the N intermediate is characterized by an internal reprotonation of the retinal Schiff base linkage and an uptake of a cytoplasmic proton by Asp96, respectively. Therefore, the decrease of rate constants by increase in pH reflects the deceleration of proton transfer at lower external proton concentration in agreement with literature (at higher pH, both M and N are accumulated).35,43 Most importantly, the kinetics was observed even in a single shot (Figure 4C). Application of a global fit to the single shot at pH 6.0 enabled us to successfully identify three out of four time constants (τ2 = 84 µs, τ3 = 1.3 ms, τ4 = 8.5 ms) (Figure S8, Supporting Information). The volume employed for these single shot kinetic experiments was 12 µL at a sample concentration of 530 µM. The volume actually probed by the IR light, however, amounts to only 200 nL as derived from the beam diameter of 4 mm and a path length of 16 µm. Thanks to the single shot performance, very low sample consumption might therefore be achieved in the case of irreversible reactions.



Figure 4. Kinetic analysis of the bacteriorhodopsin photoreaction at different pH. (A) Good agreement of time traces at three selected wavenumbers of dual-comb spectroscopy data averaged over 500 shots with those from step-scan experiments. (B) Kinetics from dual-comb spectroscopy averaged over 500 shots show a decrease in the rate constants after 100 µs with an increase in pH. (C) A single shot averaged over 10 cm-1 is sufficient to extract the characteristic kinetics. The standard deviation of the mean value of difference absorbance over 50 shots is shown as line with error bars. CONCLUSIONS AND OUTLOOK We have presented a QCL-based dual-comb spectrometer that can be used to analyze the kinetics of reactions in a single shot. The experiment delivers full spectra every 320 ns for a duration of 20 ms. While the native spectral resolution of the dual-comb system is well below the linewidth of condensedphase spectra, a lower resolution can be used to improve the signal-to-noise ratio. At native resolution, an RMS measurement noise of 1 mOD at 100 µs time resolution in a single shot and 50 µOD in 500 shots is observed, which reduces to 400 µOD in a single shot and as low as 15 µOD in 500 shots at 4.5 cm-1 resolution. By this, we were able to reproduce all the characteristics of the intermediates KL, L, M and N of the bacteriorhodopsin photocycle in the spectral range 1185-1240 cm-1. The single shot measurement capability makes vibrational spectroscopy of irreversible reactions with sample volumes as low as 200 nL possible. Dual-comb spectroscopy’s application is not limited to photoreceptive systems such as bacteriorhodopsin but can be extended to other reactions triggered by external perturbations such as jumps in electric potential or temperature. Moreover, channel or enzymatic activity can be artificially initiated for time-resolved studies by the modern tools of optogenetics.47 Above all, the high temporal resolution in combination with the broad-band mid-infrared measurement performance opens a plethora of applications where short measurement times are required, such as in-line quality control in a production environment or high-throughput screening in drug development. Given its potential to integrate the light source into an all solid-state solution, the present work represents an important cornerstone for a broadband laser-based lab-on-a-chip device48 enabling smart monitoring solutions in environmental or personalized medicine.

ASSOCIATED CONTENT Supporting Information Global fit of results from dual-comb spectroscopy and step-scan FTIR spectroscopy, representiveness of a single shot, influence of the probe light exposure on the sample, absorption spectra of samples with different path lengths, dual-comb experiments on samples with different path lengths, global fit of results at different pH values, global fit of a single-shot experiment.

The Supporting Information is available free of charge on the ACS Publications website.

AUTHOR INFORMATION Corresponding Author The authors declare no competing financial interests. Correspondence and requests for materials should be addressed to M.M. ([email protected]).

Author Contributions All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT We thank Ina Ehring for the preparation of bacteriorhodopsin. This work was supported by a Heisenberg fellowship (KO3580/42) and DFG grant KO3580/5-1 to T.K. and by the Swiss National Science Foundation, Project no. 200020_178942, to J.F.

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