Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria

Conventional implementations of two-dimensional electronic spectroscopy typically spatially average over ~1010 chromophores spread over ~104 micron square area, limiting their ability to characterize spatially heterogeneous samples. Here we present a variation of two-dimensional electronic spectroscopy that is capable of mapping spatially varying differences in excitonic structure, with sensitivity orders of magnitude better than conventional spatially-averaged electronic spectroscopies. The approach performs fluorescence-detection-based fully collinear two-dimensional electronic spectroscopy in a microscope, combining femtosecond time-resolution, sub-micron spatial resolution, and the sensitivity of fluorescence detection. We demonstrate the approach on a mixture of photosynthetic bacteria that are known to exhibit variations in electronic structure with growth conditions. Spatial variations in the constitution of mixed bacterial colonies manifests as spatially varying peak intensities in the measured two-dimensional contour maps, which exhibit distinct diagonal and cross-peaks that reflect differences in the excitonic structure of the bacterial proteins.


Supplementary Note 1 -Details of Experimental Setup
The experimental layout is based on the original design by Marcus and co-workers 1 . The output from a commercial broadband 83 MHz Ti:Sapphire oscillator (Venteon One) was sent into a SLM based pulse shaper (MIIPS 640P, Biophotonic Solutions) for dispersion pre-compensation. Laser pulses from the pulse shaper of ~20 fs FWHM pulse duration are split by a 50:50 beamsplitter (Newport, 10B20BS.2), and each portion is routed into two Mach-Zehnder (MZ) interferometers.
Within each of the two MZs, the pulse is further split using 50:50 beamsplitters (BS), and each arm is tagged with a unique phase which is modulated at radio frequency using an acousto-optic modulator (AOM, Isomet M1142-SF80L). The phase modulation frequencies for the four arms are denoted as 14   , such that when the split pulses are recombined at BS3 and BS5, within MZ1 and 5 MZ2 respectively, the pulse amplitude modulates at the difference frequencies of the AOMs, that is, 12  and 34  for MZ1 and MZ2, respectively. One output port from BS3 and BS5 is routed to a monochromator (Optometrics, MC1-04) to generate the reference frequencies, 1 R  and 2 R  for MZ1 and MZ2 respectively, which modulate at 12  and 34  difference frequencies, respectively.
The references for all the SF-2DES experiments were set at 826 nm using a high-resolution spectrometer (Ocean Optics HR4000, 0.1 nm resolution). The FWHM of the reference spectra after the monochromators was 0.5 nm. Beams from the other two output ports (one from each of the two MZs) are each passed through a polarizer P (ThorLabs, GTH10M-B) and waveplate WP (ThorLabs, AHWP05M-980) combination, and are recombined at BS6. The train of 4 phasemodulated pulses generated by the two MZs is then routed through a spatial-filter with two 5 cm lenses, and a 25 m pinhole in order to generate a TEM00 Gaussian spatially-filtered beam mode.
Spatial filtering also helps to minimize any residual spatial chirp. The polarizations of the beams after the spatial filter is set to S to greater than 1300:1 extinction ratios for both MZs.
The resulting beam from the above SF-2DES Setup (Fig. 1, main text) passes through a OD4 875 SP filter (Edmund Optics), and is routed into a confocal microscope (Olympus 1X51).
The microscope is set up in the epi-detection geometry. A 875 nm dichroic mirror (Semrock) inside the microscope transmits the pulse train towards the water objective (Olympus PlanApo 60x, NA1.2). The sample is drop-dried under Nitrogen on a 0.17 mm coverslip, which is sealed on a glass slide using double sided sticky tape followed by sealing the outside surface with Scotch tape.
The objective collar is set to 0. 17 experiments on immobilized and circulating samples, the spectra were collected with a total power of 7.5uW/pulse, corresponding to a total fluence of 12-16 J/cm 2 /pulse. At 83 MHz repetition rate, the total pulse energies for these fluences is ~ 0.09 pJ/pulse, such that the excitation probability at the center of the pulse is less than 0.1%. Low excitation probability is chosen so as to minimize multiple excitations on the molecule by the same pulse.
The references generated from MZs 1 and 2, which modulate at 12  and 34  AOM difference frequencies, respectively, are used for phase-sensitive lock-in detection, while the second port of MZ1 and MZ2 is recombined at BS6. The time delays between the all collinear train of 4 pulses after BS2 are controlled by translational stages (Newport M-VP25XL for t1 and t3 time delays, and ILS150 for t2 time delay) within each arm of the MZs, resulting in an allcollinear train of 4 pulses separated by time delays t1 between the first two pulses, t3 between pulses 3 and 4, and t2 between the 2 nd and 3 rd pulses in the sequence. t1 and t3 delays are scanned from 0 to 90 fs in steps of 5 fs. The t2 delay is scannable from 0 to 800 ps, but is fixed at t2 = 0 fs for the experiment.
The four-wave mixing signal generated by the sample oscillates at the difference rephasing 2D signals. The oscillating signal is demodulated using a lock-in amplifier (Zurich Instruments, HF2LI). Physical undersampling of the oscillating signal, as well as phase-sensitive detection is achieved by signal detection relative to a reference frequency generated by passing MZ 1-2 outputs through monochromators 1-2. The reference signals from monochromators 1 and 2 modulate at 12  and 34  difference frequencies, respectively. The references are detected by amplified photodiodes PD1,2 (ThorLabs PDA36A) and mixed in a 24 bit digital signal processor (Analog Devices, ADAU1761) to generate the reference signals modulating at frequencies The 2D spectra obtained from desired XY locations on the fluorescence image were fit as a linear combination of the basis 2D spectra in Fig. 2. Two of the three coefficients of the linear combination were constrained to lie between 0 and 1, and the sum of the coefficients was constrained to 1. These coefficients correspond to the HL and LL contributions, and the third coefficient was an offset which was constant across a given 2D data, but was free to float across different data sets. In order to solve the constrained linear least-squares fitting, the MATLAB routine lsqlin was used with interior-point convex optimization algorithm.

Supplementary Note 2 -Faster Data Acquisition Using Physical Undersampling in SF-2DES
The number of data points required to obtain the full information content of a two-dimensional interferogram is significantly reduced in SF-2DES 1 . The monochromator settings determine the reduced frequencies at which the signals (rephasing and nonrephasing) oscillate. For the data reported here, the monochromator output light was centered at 826 nm (ωref ~ 2.28 rad/fs). The characteristic excitons in photosynthetic bacteria at 800 nm (ω800 ~ 2.35 rad/fs) and 850 nm (ω850 ~ 2.22 rad/fs) are downshifted in frequency, ω800 -ωref ~ 0.07 rad/fs and ω850 -ωref ~ -0.06 rad/fs, due to physical undersampling 1 in SF-2DES. Taking a step size of 10 fs in t1 and t3 corresponds to the Nyquist limit of ~0.31 rad/fs which is ~5x above the Nyquist limit necessary to resolve these excitonic transitions. Therefore, the physical undersampling inherent in SF-2DES allows shorter experimental time and laser exposure in samples susceptible to rapid photodegradation.
Supplementary Figure 6 shows that if the data shown in the left panel was collected in 10 fs steps (instead of 5 fs), the data acquisition time will go down proportionally to the number of time points collected, to ~12 seconds, without affecting the locations or relative amplitudes of the 2D peaks.
However, "discretization noise" introduced in the data, which is proportional to the 1/N 1/2 , where N is the number of sampled data points 2 , will also affect the noise floor of the data after a certain step size. Hence, faster acquisition times while having an optimum number of sampled data points is key, the choice of which becomes sample-dependent.
Supplementary Figure 6. Normalized t2 = 0 fs absorptive 2D spectra collected at the green solid dot location shown on the fluorescence image in Fig 3a. Data points for the 2D spectrum on the left were collected every 5 fs from 0 to 90 fs in t1 and t3. The spectrum on the right was calculated using the data set on the left, but ignoring every other data point, such that the effective step size 12 in t1 and t3 is 10 fs. The spectral features, their relative amplitudes and locations are not affected across 5 fs or 10 fs step data sets. The data collection time with 5 fs steps is ~45 secs compared to ~12 seconds which would be needed if the data were collected in 10 fs steps. Contours are drawn at 10-90 % in steps of 10%, with additional contours at 95% and 100% to highlight small differences in maxima. Each spectrum is normalized according to its individual maximum.
13 Supplementary Figure 7. Images depicting sections of two dried drops of a diluted solution. An outline mask of each image after thresholding using Otsu's algorithm in ImageJ. a. Two sections of the dried layer from a given drop. b. Three sections of the dried layer from another drop. The red rectangles correspond to the manually selected region of interest which minimally overlaps with the previous section(s).

Supplementary Note 3 -Estimation of number of cells contributing to the signal
In order to estimate the number of bacteria contributing to the signal we first performed a three steps serial dilution of the original solution amounting to a factor of 10 7 . This is a common first step in numerous cell counting protocols looking to obtain a well separated distribution of cells on a surface. Then, small drops of the diluted solution were deposited on the hydrophobic surface of a cover glass using a syringe and left to dry under a Nitrogen atmosphere. The drop volume was estimated to be about 0.08 L using gravimetric analysis. Drying of a droplet on a hydrophobic surface helps achieve a uniform particle deposition and suppresses ring-like Note that even if the cells did not make a monolayer, as long as the thickness of the layer is within the axial resolution of the FWM PSF (Fig. 4b, main text), the resulting estimate of the number of cells contributing to the signal will be an upper bound. This can be seen as follows: In the case that the monolayer thickness was H, the resulting cell density is - In the above equation, the fit parameters are defined as -z0 is a constant offset, xc and yc define the center of the Gaussian,  defines the rotation angle and w1 and w2 define the widths of the major and minor axis of the ellipse. The non-linear least squares fitting was performed in MATLAB by minimizing the residual sum of squares using the Levenberg-Marquardt algorithm.
Supplementary Figure 9. Theoretically expected diameter from a confocal image of a 0.5 m diameter bead. Calculated diffraction-limited confocal point spread function obtained by convoluting the diffraction-limited confocal point spread function of a point source with a spherical bead of 0.5 m diameter. The peak laser excitation wavelength is 780 nm, and a water objective (60x,NA 1.2) is assumed. The calculation also assumes a large detection pinhole such that Hconf (r,z) ~ Hconv (r,z) (see main text). The lateral and axial FWHM from the above confocal PSF are ~0.52 m and ~0.95 m, respectively. Contours are drawn at 0.1%, 1%, 2%, 5%, 10-90 % in steps of 10%, 95% and 98%. The calculation is based on the equations given in ref. 5 .
Comparing the lateral confocal widths with the experimental measurement in Supplementary  Figure 8 shows that the deviation between the ideal and measured lateral width is 0.83/0.52 ~ 1.6x. 20

Supplementary Note 6 -Comparison of Raw versus Zero-padded 2D spectra
Here we compare raw and processed data and show that the data processing steps only account for symmetric changes in 2D spectrum of 10-15% or less. Supplementary Figure 11 (left panel) shows the raw real absorptive 2D spectrum, and the right panel shows the effect of zero-padding the raw data on the distinct 2D cross-peaks. If N points are collected in the experiment along each time axis (19 points from 0 to 90 fs in 5 fs steps in this case), then due to enforced causality in the Hilbert transform (resulting in Kramer-Kronig relation between the absorptive and dispersive parts of the signal), N more data points have to be added to the collected time series 6 . Padding zeros such that the total points are more than 2N points results in mere interpolation without any increase in resolution as pointed out by Bartholdi and Ernst 6 . The spectrum in the left panel is with 2N points, and the right panels is with 128 points.
Supplementary Figure 11. Real absorptive t2 = 0 2D spectra obtained a circulating sample of HL cells. (Left) Without any additional zero padding beyond 2N points, where N is the number experimentally collected time points (19 points). As pointed out by Bartholdi and Ernst 6 , padding additional N points (total 2N points) is a result of Kramer-Kronig relations and can lead to an increase in resolution, whereas padding zeros beyond 2N results in mere interpolation of the raw data with no increase in spectral resolution along 1,3  . (Right) Zero padding with total 128 points. All figures show a 13 ( , ) ( , ) XY   data point at ~875 nm along the 3  axis, where the laser spectrum is approximately zero. The 'Z' value shows the 2D signal level at that location. Comparison of left and right panels shows that due to zero-padding after 90 fs, the 2D amplitude at ~875 nm increases by ~15%.
Supplementary Figure 11 shows that data processing does not change the resolution of 2D peak shapes, but merely interpolates such that in zero padded data (128 points) the contour levels look continuous. The 2D peak shapes slightly broaden but the overall effect of data processing appears 21 symmetric along both frequency axes. Zero-padding causes the signal level at positions with almost no laser spectrum to be on the order of ~10-15%. Below, we discuss that photo-bleaching related distortions in the 2D spectrum (also shown in Supplementary Figure 1) are the major contributor towards asymmetric 2D peak distortions along 3  axis beyond 2D locations inaccessible the laser spectrum. The sample is circulated for obtaining this spectrum such that any photo-bleaching is negligible. (right) 2D spectrum on the right but with a simulated 60% signal photo-bleaching rate (see description of Supplementary Figure 1 in the SI). The marked location corresponds to ~875 nm on 3  axis where there is no laser spectrum, but the 2D signal shows vertical distortions leading to ~15% signal increase at 875 nm, compared to the spectrum on the left. As described in Supplementary Figure 1, asymmetric vertical distortions occur because the scanning scheme used in the experiment scans 1 t delays first and 3 t delays last.

Supplementary Note 7 -Estimation of fluorescence-detection sensitivity, and low-repetition rate experiments
Mie scattering background from the cells makes in vivo conventional 2DES studies very challenging and susceptible to ghost peaks 8 . In contrast, fluorescence 2D provides facile color filtering of the signal, and therefore an attractive route to in vivo studies. Below we compare our approach to the competing approaches in conventional 2DES which have demonstrated in vivo studies [9][10][11] . Given the differences in focusing, repetition rate, as well as the different detectors and the need for scatter subtraction in conventional 2DES it is very difficult to isolate the effect of fluorescence detection alone. Studying a variety of scattering samples with both methods, keeping as many other factors as equivalent as possible, can be done to address this subject in greater detail.
We performed experiments at lower repetition rates (data shown in Supplementary Figure 13) to rule out artifacts in our spectra that could be caused by the use of high repetition rates. This data, which was not spatially resolved, was acquired with focusing conditions and optical densities closer to those used in a conventional 2DES measurements and enables a rough estimate of the relative sensitivity of fluorescence vs conventional detection. Below we compare some of the relevant experimental parameters of our work and other in vivo 2DES studies 9-11 .
Supplementary Table 1 compares the experimental parameters used in our in vivo 2D studies, both the SF-2DES measurements reported in the main paper text (column 2) and lower repetition rate non-spatially-resolved measurements (F-2DES) shown in Supplementary Figure 13 (column 3). Note that the study by Zigmantas and coworkers in the last column is on green sulfur bacteria, and is performed at 77 K, whereas the other studies have been performed at 300 K on circulating purple bacterial samples. Room temperature studies on circulating samples suffer from significantly higher scattering background and lower signals at 300 K. Therefore, directly comparing the SNR from ref. 9 to SF-2DES or the studies by Engel and co-workers 10,11 will not be a fair comparison. Note that for the approach of Engel and coworkers 10,11 , a given point on the 2D spectra during the scan will be 1, 3 () t  , whereas for SF-2DES it will be 13 ( , ) tt . For both such points, the total number of laser shots required to generate a final absorptive 2D spectrum have been considered. Even though the approach of refs. 10,11 can in principal generate a 2D spectrum per laser shot, the scatter removal process significantly slows down the acquisition time. Ref. 8 11 and co-workers at 300 K and in vivo 2D studies from Zigmantas 9 and co-workers at 77 K. We also include fluorescence-detected 2DES (F-2DES) at lower repetition (500kHz) and focusing conditions closer to those used in conventional 2DES measurements. Refs. 10,11 collect a 2D spectrum per laser shot (without any mechanical scanning), but average finely around each T which is required in order to remove the scatter background. Note that the details in refs. 8,9 were insufficient to confidently estimate the total data acquisition times.
Refs. 8,9 use mechanical wedge pairs in order to scan the t1 and t3 time delays. However, due to amplitude modulation and lock-in detection, fine T scanning is not required to remove the scatter. Hence, the total data collection times required to generate a processed 2D spectrum should be of 24 the order of a few seconds and similar to refs. 10, 11 . Experimental parameters which are the most different between the approaches are highlighted in green.
Comparing Supplementary Figure 13 with Fig. 1 of ref. 11 , we assert that the SNR in Supplementary Figure 13 is comparable if not better than ref. 11 . Based on a comparison of columns . Based on the above assertion, we estimate that the sensitivity of fluorescence detection is at least 1/0.0025 ~ 400x better in the F-2DES case. Note that the above factor does not decouple the effect of scatter from the sensitivity of fluorescence detection and we expect that the relative sensitivity of F-2DES and conventional 2DES will depend strongly on differences in sample scattering as well as fluorescence quantum yield. We note that further improvement could be made for the fluorescence-detection approach here by more efficiently-collecting the signal. For the measurements in Supplementary Figure 13, a numerical aperture of ~0.4 was used for the signal collection. Thus an additional ~3 2 x improvement 12 could be obtained with the use of a 1.2 numerical aperture objective, making the expected improvement ~3600x. Figure 13. (A) 1MHz/500kHz laser spectrum overlaid with the background subtracted HL cells linear absorption spectrum. (B, C) Absorptive t2 = 0 fs F-2DES spectra for 1MHz (B) and 500 kHz (C) laser repetition rates. (D) Diagonal peak (DP) and cross-peak (CP) slices corresponding to 1 MHz (solid) and 500 kHz (hollow). The DP and CP peak positions in nanometers are marked in the figure. Supplementary Figure 13B,C show 2D spectra from circulating HL cells with OD ~0.3, and a ~16 m focal spot size obtained from a 5 cm lens (instead of ~1 m from the microscope objective). The laser fluence incident at the sample is 1.5 J/cm 2 /pulse for 1 MHz and 0.75 J/cm 2 /pulse for 500 kHz repetition rate. Thus, compared to the 2D spectra reported in the manuscript, the measurements shown in Supplementary Figure 13 correspond to a combination of 100x lower repetition rates, 16x bigger focal spot size, and 16.5x lower pump and probe fluences. The spectra represent the lowest fluence for which a respectable signal-to-noise ratio (SNR) was attainable without substantially longer acquisition times compared to before. The distinct cross-peaks at t2 = 0 fs persist even under contrastingly different fluence, repetition rate and focusing conditions. For these repetition rates and fluences, Kohler and coworkers estimate 13 <3% steady state carotenoid triplet population in detergent-isolated LH2 complexes. In the presence of neighboring LH2s and LH1-RC 'sink', the carotenoid triplet fraction is expected [13][14][15] to be even lower in LH2s, and exist predominantly on LH1-RC complexes (see section "Modeling of Repetition Rate Dependent Populations" in the SI). Supplementary Figure  13D shows that the cross-peak (CP) and diagonal peak (DP) slices through the peak maxima for the two repetition rates are in decent agreement. Notice that due the flatter laser spectrum compared to the 83 MHz source used in the main paper, the position of the B800 band is closer to the expected position of 805 nm, in agreement with the linear absorption spectrum. As discussed in response to comment 6, the relative DP and CP peak amplitudes are sensitively dependent on the pump and probe laser intensity at the B800 and B850 bands, and the amount of GSB, ESE and ESA contributions at each peak at t2 = 0 fs. Figure 13 A white light continuum is generated by focusing the 1 MHz (or 500 kHz) 1040 nm output of a tunable repetition rate laser amplifier (Spectra Physics, Spirit 1040-16) into a 4 mm YAG crystal, followed by removing the fundamental with two OD6 630 nm long pass optical filters (Chroma, E630LP). The resulting beam is collimated and routed into the experimental setup reported in the manuscript. The spectrum is further cleaned through OD6 740 long pass (Chroma) and OD4 875 short pass (Edmund) optical filters. Note that the output of the SF-2DES spectrometer is not routed into the microscope objective. Instead, a 5 cm lens focuses the pulses (16 m FWHM spot size, 13 fs FWHM pulse duration) into a 1 mm pathlength flow cell (Starna 584.4-Q-1), through which the sample is recirculated at ~260 ml/min using a peristaltic pump. The fluorescence is collected at 90 degrees with optics possessing a numerical aperture of ~0.4, and isolated using two OD6 887 long pass filters (Semrock).

Supplementary Note 8 -Comparison of SF-2DES with other spatially-resolved 2DES approaches for imaging the entire sample
The fluorescence images shown in the paper are collected with a 5 ms binning time for each X,Y location of the piezo stage. For a ~2 m step size which is comparable to the current resolution of SF-2DES spectrometer (~1m FWHM), the total time for collecting a 100 m x 100 m fluorescence image is ~0.005x2500 ~ 13 seconds.
The 2D spectra reported in the manuscript took ~45 seconds. However, Supplementary   Figure 6 shows that 2D spectra with similar signal to noise and similar 2D peak shape resolution can be collected with 10 fs 1,3 t steps in ~ 12 seconds. Thus, for collecting 2500 successive 2D spectra, the total imaging time required will be ~2500x12secs = 8.3 hours. Previously, we have utilized the SF-2DES spectrometer for collecting 2D on circulating samples for successive waiting times such that the setup exhibits good phase stability over an experimental duration of 4 hours.
Hence, collecting 2D spectra over a period of 8 hours is not unfeasible.
In comparison with spatially-resolved 2DIR approaches, the data acquisition time per 2D seconds for each phase cycle per time step. Hence the 2D spectra collection times in that approach will be considerably slower (~18 mins per 2D spectrum) than the approaches compared here.
We expect that practical applications of our method will likely involve the rapid collection of a fluorescence image for sample evaluation, followed by the acquisition of 2D spectra at selected locations.
Supplementary Note 9 -Absolute calibration of SF-2DES signals to determine number of HL to LL cells contributing to 2D signal from a given spatial location This approach described below could be used in the future experiments to determine the absolute number of cells which contribute to the measured four-wave-mixing signals. Note that this approach is different from the simultaneous determination of concentration and extinction coefficient performed in ref. 16  Additionally, although the presented framework 17 is more general, in order to express the unknown concentration in terms of the measured non-linear signal 16 , simplifying approximations such as a two-level system, Condon approximation, vibrationally relaxed non-linear signal are used, which will fail for LH2 complexes. Alternatively, a simplified two-step calibration approach that can work in SF-2DES experiments is as follows.
Firstly, we would need to calibrate the measured fluorescence-detected 2D signal (in Volts), for a given amount of LL and HL cells through separate measurements on samples with varying amount of cells. All the signal processing settings have to be kept constant between the HL and LL samples, and all measurements for each kind of sample. By calibrating the measured signal for a known absolute number of cells, the HL and LL signal ratios derived from the experiments could be easily calibrated to HL to LL cell ratios. Note that this approach assumes 28 that there are no differences between the cell sizes, number of LH2 complexes within the cells, and fluorescence quantum yields for a given type of cells (HL or LL). Additionally, in the outlined approach, only concentration determination will be possible, not determination of extinction coefficient as was done in ref. 16  Supplementary Note 10 -Effect of structured laser spectrum on growth condition dependent

2D peak amplitudes and positions
Below we analyze the reported growth dependent differences in the 2D spectra in greater detail and show thati) 2D spectra recover growth dependent differences above the error bar of the measurement.
ii) When analyzing the relative differences between HL and LL cases, peak positions are strongly affected by the laser spectrum. We argue that with a laser spectrum that covers the B850 band better, the recovered differences will be similar although determined with better accuracy.
With regard to the cross-peak amplitudes, the effect of the laser spectrum is approximately normalized out as long as the pump and probe laser spectra are identical. However, the diagonal peak amplitudes will be strongly affected by the laser spectrum. Additionally, the 2D peak positions will be a weighted product of the laser amplitude with the sample absorption crosssection. We analyze these in detail below.
In R. palustris, the B800 band is known to be unaffected by growth conditions, and the  Fig. 1 of ref. 19 ). In order to consider the growth dependent differences, and the effect of the laser spectrum on the relative amplitude of diagonal peaks, we first remove the rising Mie scattering background in order to extract the absorption strengths in the B800 and B850 bands using a single exponential function to model the background as shown in Supplementary Figures 15A,B.  Figure 15C), both HL and LL B800 bands peak at 805 nm, with the LL band being slightly broader due to the underlying weak ~810 nm band. In the 2D spectrum (Supplementary Figure 15E), the diagonal peaks for HL and LL, both peak at ~818 nm. The B800 band for the LL case is marginally red-shifted (within the resolution of the measurement), possibly due to the broader B800 band (in Supplementary   Figure 15C). In the linear absorption spectrum, the B850 band for the LL case is also slightly broader and blue shifted by 1-2 nm (Supplementary Figure 15D) and peaks at 863-865nm. In comparison, the red-shoulder in the laser spectrum peaks at ~856 nm. Consequently, the B850 2D diagonal peak is located between 855 nm for HL and 852 nm for LL case (Supplementary Figure   15E).
If the laser spectrum is given by () i  , then, for a vibrationally relaxed 2D spectrum, the 2D absorption strength along the diagonal will be approximately given by a square of the product of laser spectrum and the absorption cross-section, that is, However, a strong gradient in the absorption and laser spectrum, or a zero intensity laser spectrum will affect the experimentally derived ratio and its accuracy. Based on Supplementary Figure 15C (for normalized B800 peak strengths) and the above expression, a ratio of ~3.3 is expected for the B850 diagonal peak strengths derived from a vibrationally relaxed 2D spectrum. From Supplementary Figure 15F, the experimentally measured ratio is 4.2(±0.9) and 3.6(±0.7) at 855 nm and 852 nm, respectively. Since, error bars are proportional to the gradients of the parameters on which they depend, both, the gradient on the red shoulder of the laser spectrum, as well as the gradient in the absorption spectrum at ~855 nm, contribute to large error bars on the ratio. Although within the large error bars, the experimentally derived ratio overshoots the ratio on the red edge of 32 the measured B850 peaks. We note that the ratio of ~3.3 is only expected from a vibrationally relaxed 2D spectrum after ignoring any red-shifted ESE or ESA contributions, whereas we compare the expected ratio to a t2 = 0 fs 2D spectrum. Hence, some deviations are expected.
In the reported measurements, the B850 band which has the most visible growth dependence, but is only partially (<50%) probed by the laser spectrum. The 2D peak amplitudes still recover substantial growth dependent differences with large error bars, although the differences seen between B800 and B850 manifolds (between the HL and LL cases) are still easily above the error bar of the measurement. Based on the above analysis, peak positions are more strongly affected by the laser spectrum than the ratio of 2D peak amplitudes. With a flatter laser spectrum (such as that used in a linear absorption spectrometer), the recovered 2D peak positions are expected to be closer to the positions in the linear absorption spectrum. Additionally, absence of a strong gradient in the laser spectrum with the absorption band of the sample will increase the accuracy of the measured peak amplitude (and the relative ratios).
In Fig. 2b in the manuscript, the HL and LL spectra we normalized differently in order to emphasize the growth-dependent differences. That is, the HL 2D spectrum is normalized relative to the B850 diagonal peak (DP_B850), and the LL 2D spectrum is normalized with respect to the B800 diagonal peak (DP_B800). The different normalization is better seen in Supplementary  Similarly, the DP_B850 amplitude will be ~2 compared to 0.51 for the LL case. In the above discussion, we considered the effect of the laser spectrum on cross-comparisons between the HL and LL 2D spectra. As noted above, the peaks in the 2D spectrum will be proportional to a product of the absorption cross-section weighted by the laser spectrum. For example, for population contribution to 2D peaks are roughly given by - the two cross-peaks, the cross-peaks will be balanced for identical pump and probe spectrum.
However, possible imbalances in the pump and probe intensities at the B800 and B850 locations due to change in experimental conditions can result in relative ratios of CPs as well as DPs to vary accordingly. Thus, cross-comparisons between HL and LL 2D peak amplitudes depend critically on the laser spectrum, and are only valid under identical experimental conditions. For this reason, all 2D spectra reported on immobilized samples ( Fig. 2b and Fig. 3b 21 , can also cause imbalance between the CP amplitudes. Vertical distortions in the 2D spectrum caused by photo-bleaching, as seen in Supplementary Figure 1 in the SI, account for ~5% or less of the imbalance between relative CP peak amplitudes. The 2D measurements on the circulating samples (Fig. 3c in the manuscript) were collected on a different day than the ones on immobilized samples. Consequently, we do not use Fig. 3c for any analysis between HL and LL samples, and only show it for the purpose of contrasting the noticeable vertical distortions seen in the immobilized samples. Both imbalance between pump and probe spectrum, and photo-bleaching will cause the CPs to be 'artificially' imbalanced for both LL and HL cases. However, as suggested by Supplementary Figure 1 in the SI, photobleaching can only account for ~5% of CP imbalance. Thus, imbalances in the pump and probe laser spectrum seems to be the dominant cause for the CP imbalance seen in Fig. 3c. This is also likely because the CPs in both, HL and LL, 2D spectra are imbalanced such that CP21 is stronger than CP12, whereas photo-bleaching distorts the 2D spectrum in the opposite way (CP12 becomes slightly stronger relative to CP21).

t2 = 0 fs cross-peaks
The F-2DES approach offers a complementary method to conventional 2DES spectroscopy for characterizing electronic structure and coupling. The approach has been applied in a small number of studies and there has not yet been much theoretical work to describe fluorescence-detected 2D signals. In conventional 2D spectroscopy, cancellations 22  interactions. The fluorescent population after 4 interactions is denoted as a red arrow. Solid (dashed) arrows can be thought to carry a negative (positive) sign, such that the sign of GSB and ESE becomes the same as ESA_1. This is in contrast to conventional 2D where, GSB and ESE have an opposite sign relative to ESA_1. Thus, ESA_1 signal will add to the ESE and GSB contributions instead of cancelling them. The relative sign of ESA_2 is opposite to that of all other contributions. However, the strength of the ESA_2 contribution depends on the quantum yield of internal conversion of a highly excited BChl a monomer, resulting after exciton-exciton annihilation [26][27][28] , to the lowest excited electronic state of BChl a. The quantum yield of the internal conversion process dictates the fluorescence quantum yield, and therefore the strength of the ESA_2 pathway. Therefore, the total t2 = 0 fs contribution on the cross-peaks will have a GSB character, plus some positive mixture of ESA contributions arising from the difference in fluorescence quantum yields of ESA_1 -ESA_2 pathways.
Based on the analysis of wave-mixing pathways outlined in Supplementary Figure 17 (and accompanying caption), the ESA_1 contributions which is known to give rise to negative 2D peak shapes at t2 = 0 fs is now apriori expected to appear as positive, and add to the ESE and GSB contributions. The ESA_2 contribution will still be negative, such that the overall character of the t2 = 0 fs cross-peaks will be GSB plus an admixture of (ESA_1 -ESA_2) pathways, the difference depending on their relative fluorescence quantum yields, as described in the caption of Supplementary Figure 17. Hence, keeping aside any experimental issues, strong peak shape differences between both 2D approaches are expected, as was also pointed out by Marcus and coworkers 22 . Based on above differences, Marcus and co-workers have simulated a conventional 2D and a fluorescence-detected 2D spectrum for a dimer and fit it to experimental measurements. They report distinct cross-peak in F-2DES which is apparently absent conventional 2DES because of cancellations between negative ESA and positive ESE and GSB signals in conventional 2DES as discussed above.
Very recently, while this paper was in revision, Pullerits and co-workers from Lund University, Sweden, have reported 29 t2 = 0 fs fluorescence-detected 2D spectrum from detergentisolated LH2 complexes, and report distinct positive CPs similar to those reported in our in vivo measurements. They consider different hypotheses to explain why the t2 = 0 fs CPs are wellresolved, as opposed to earlier conventional 2D measurements. In agreement with the work of Marcus and our argument above, they also conclude that the cross-peaks as due to the intrinsic difference between fluorescence-detected and conventional 2D approaches. Assuming near unity quantum yield of internal conversion in highly excited BChl a electronic states after excitonexciton annihilation, they propose near perfect cancellation between the two types of ESA pathways, that is, ESA_1 -ESA_2 ~ 0, such that the t2 = 0 fs cross-peaks are dominantly GSB in character. Recently, Tokmakoff and co-workers 30 have also reported similar differences in the fluorescence encoded 2DIR experiments (compare Fig. 5b,c in ref. 30 ).
In the conventional 2DES measurements, t2 = 0 fs positive GSB cross-peaks between B800-B850 manifolds were masked out by negative ESA signals. Such making effects due to strong ESA signals are also known in other photosynthetic proteins, such as the FMO antenna (for example, some of the early waiting time GSB-like cross-peaks are only revealed through conventional 2DES experiments with a polarization scheme that suppresses strong positive and negative diagonal features in Fig. 2 of ref. 31 ). However, as indicated in our data and in the recent report by Pullerits and co-workers 29 , there are, in fact, strong cross-peaks at t2 = 0 fs predominantly due to GSB signals arising out of a common ground state. This opens up new questions about the interpretation of GSB cross-peaks and the common ground state between B800-B850 rings. It should be noted that t2 ~ 0 fs bleach signals in the B850 band after a narrow band pump excitation in the B800 band has been observed by Hess et al. (Fig. 7B of ref. 32  The best atomistic calculations of 2D spectra of LH2 from Rs. molishianum, which are based on previous 2D measurements, show a lack of t2 = 0 fs cross-peaks (for example, see Fig. 8 of ref. 34 ).
Future work will compare the above simulations of conventional 2DES spectra from Jansen and co-workers, with fluorescence-detected 2D simulations of LH2 in the context of R. Palustris.
Simulations of the effect of growth conditions on the excitonic structure in the B850/B850* manifolds will also be a subject of future investigations. The B800 to B850 energy transfer is known 35 to be as fast as ~300 fs due to mixing between the higher lying B850* exciton manifold with the B800 manifold. In particular, reduction in the number of B850-like sites and conversion of some of them into B810-like sites under low-light growth conditions must affect the higher lying B850* manifold, and its mixing with the B800 manifold. Further, it is also already known that the ~200 fs B850 intra-band relaxation 35 also slows down to ~2 ps for low-light grown R.
palustris 19 . Moulisova et al. 19 also estimate the reduction in coupling between closest B850-like sites in a low-light B850 ring to be down to ~50 cm -1 , a reduction of ~6x compared to the unperturbed B850 ring in a high light grown bacteria. The mixing between the B850 exciton manifold and the ~850 nm optically dark state 23 in the B800 manifold is also expected to change upon reduction in the number of B850-like sites.
Despite substantial changes in the B850 excitonic structure, and expected changes in the B800-B850 mixing, t2 = 0 fs GSB like cross-peaks between B800-B850 manifolds are still present in the SF-2DES measurements from low-light cells. This may also be expected based on the spectrally-resolved pump-probe measurements in Fig. 3B of ref. 19 . Note that the LL cells in the present manuscript are closer to the LL1 cells in Moulisova et al. 19 where the B810-like band is ~ 1/4x weaker than the B850-like band. Hence, any possible intra-B850 ring cross-peaks between B810-B850 manifolds and the B810 diagonal peak is expected to be very weak. Our room temperature measurements do not resolve any cross-peaks or diagonal peaks associated with the B810 band, such that the majority of cross-peak contribution is expected to come from the interring B800-B850 interactions. The connection between the t2 = 0 fs GSB-like cross-peaks, and how 39 much of a B800-B850 correlation is implied by their presence even for low-light cells, are open questions to be addressed.

Strength from 2D peaks
We derive an analytic expression to show that growth conditions affect Coulomb coupling and transition dipole strengths, which in turn affect the 2D peak amplitudes seen in the F-2DES measurements. We will do so by oversimplifying the LH2 complex as a dimer, by assuming the B800 and B850 as 'super-molecules' interacting through Coulomb coupling. Note that the oversimplification also neglects the doubly excited manifold of monomeric BChl a molecules, which has been shown to be necessary to include 36 in order to correctly simulate the experimentally measured excited-state absorption signals. Because of different excitonic structure 37 , the HL and LL type LH2 complexes can be considered as two distinct kinds of dimers. The purpose of this oversimplified dimer model is simply to show how microscopic parameters such as site energy , the hypothesized growth parameter G on which the Coulomb coupling J depends (as described later), are reflected in the various contributions to the 2D peak intensities. Using this dimer model, we will argue thati. Presence of CPs in the reported 2D measurements shows that B800 and B850 excitonic manifolds are coupled through a common ground state.
ii. Spatially-varying constitution of HL and LL types of cells cause spatially-varying Coulomb couplings and exciton transition dipole strengths, which in turn map onto spatially-varying 2D peak amplitudes.
To the best of authors' knowledge no 2D experiments and simulations probing a manifold of excitonic states, such as the B800 and B850 LH2 bands, have reported an analysis of coupling strength directly based on the strength of experimentally measured 2D cross-peaks. Condensed phase 2D measurements at room temperature have broad peak shapes due to electronic dephasing caused by the protein bath and the molecular vibrational degrees of freedom, and ensemble averaging over an inhomogeneous distribution of excited state energy gaps. Thus, without a protein structure based microscopic Hamiltonian, the experimentally measured 2D CPs will only represent an 'effective' coupling strength between the B850 and B800 manifolds. For each LH2 ring in the ensemble, there is a manifold of 9 B800 like and 18 B850 like excitonic states, with certain 40 excitonic states having a mixed B800-B850 character 34 . Here we will represent these excitonic manifolds as having 'effective' absorption strengths, . This simplification will be necessary in order for us to make a tractable estimate of how the Coulomb coupling between any two BChl a pairs between the B800 and B850 rings manifests itself in the 2D CPs. In which give rise to a 2D cross-peak. In vivo interactions between adjacent LH2s will further complicate things and have not been considered so far in such calculations 34 .
We make the above 'simplifying' assumptions and represent the LH2 complex effectively as a dimer. We neglect the ~810 nm which develops for LL cells (Fig. 1D of ref. 19 ) . We also do not consider intramolecular vibrations and therefore neglect any possible vibrational-electronic mixing effects 21 . Supplementary Figure 18 Here G is a growth condition dependent factor which controls the relative strength of B800 and B850 excitonic bands which changes due to changing number of B850-like sites in individual LH2 rings depending on light-stress 37 . 12  and r  are defined in Supplementary Figure 18   Supplementary Figure 18. (Left) Site energy levels for a purely electronic dimer with molecules 'X' and 'Y' coupled through Coulomb interactions between their transition dipoles X  and Y  . The resulting interaction energy is J, and depends on the angles 12  and r  between the transition dipoles. We will assume co-planar transition dipoles such that only two angles are necessary to describe their interaction energy.  is the site energy difference between the molecules. Choice of angles 12  and r  dictates whether a dimer behaves like an H or a J aggregate. For simplicity, for the model presented here, we consider 12  = 90 o and r  = 135 o such that the resulting Coulomb coupling is positive, and the site transition dipoles are perpendicular. the ratio of absorption strengths and the excitonic energy gap, partly constrain the parameters J,  , and G. To calculate these parameters, J can be estimated from the protein structure 34 , and  and G can be inferred. However, given a linear absorption spectrum with two bands, it is not possible to conclude apriori whether the two bands represent a coupled system, or two independent species.
In contrast, a 2D spectrum of a coupled system will show cross-peaks versus no cross-peaks for independent species. In order to calculate the relative strengths of the 2D peaks, the excitonic states  Figure 18. All diagrams have a positive sign and lead to a non-oscillatory signal along the waiting time (time interval between second and third interaction). The diagram notation D3 and D4 is adopted from ref. 7 . Figure 19. (B) Rephasing and Non-rephasing ESE pathways which contribute to the diagonal (DP) and cross-peak (CP) regions in a t2 = 0 fs absorptive 2D spectrum of the dimer in Supplementary Figure 18. All diagrams have a positive sign and lead to a non-oscillatory signal along the waiting time (time interval between second and third interaction). Note that no t2 = 0 fs non-oscillatory ESE pathways contribute to the CP regions. The diagram notation D2 and D1 is adopted from ref. 7 . Figure 19. (C) Rephasing and Non-rephasing ESA_1 pathways which contribute to the diagonal (DP) and cross-peak (CP) regions in a t2 = 0 fs absorptive 2D spectrum of the dimer in Supplementary Figure 18. All diagrams have a positive sign and lead to a non-oscillatory signal along the waiting time (time interval between second and third interaction). Note that no t2 = 0 fs non-oscillatory ESA_1 pathways contribute to the DP regions. The diagram notation D5 and D6 is adopted from ref. 7 , whereas "_1" in the subscript represents the ESA_1 type of F-2DES ESA pathway, as described in SI section "2D peak shape differences in F-2DES versus conventional 2DES, t2 = 0 fs cross-peaks."  Supplementary Figures19 (A-C), all ESA_2 diagrams have a negative sign. As described in SI section "2D peak shape differences in F-2DES versus conventional 2DES, t2 = 0 fs cross-peaks", the signal strength of ESA_2 pathways depends on the quantum yield of internal conversion with a BChl a monomer in the LH2 ring. Similar to the modeling by Lott et al. 22 , relative to the signal strength of ESA_1 pathway, the strength of ESA_2 pathway will be represented by a parameter . Note that no t2 = 0 fs nonoscillatory ESA_2 pathways contribute to the DP regions. The diagram notation D5 and D6 is adopted from ref. 7 , whereas "_2" in the subscript represents the ESA_2 type of F-2DES ESA pathway.

Supplementary
From Supplementary Figures19 (A-D), the 2D peak amplitudes will be given by - As seen from the above equations, strength of each t2 = 0 fs 2D peak is proportional to the exciton transition dipole strength, which in turn directly depends on the microscopic parameters G, J and  . When the Coulomb coupling J changes due to changes in G, this is directly reflected in the 2D peak amplitudes. Note that the dimer model in Supplementary Figure 18

Supplementary Note 13 -Modeling of Repetition Rate Dependent Populations
The triplet yield of chlorophylls and its derivative molecules is >60% in solution 41-43 . Intersystem crossing to triplet electronic states is induced by mixing between orbital and spin angular momentum of an electron. This is a well-studied phenomenon in large planar aromatic molecules, and it is further accentuated in chlorophylls due to a heavy central Magnesium atom 44 . The intersystem crossing times in Bacteriochlorophyll a (BChl a) molecule is ~5-10 ns 13,45 . In the absence of other photo-physical processes, the photophysics for BChl a monomers in solution can be well described using Model A (below). shows the expected populations remaining (on nanosecond timescales or longer) in BChl a singlet or triplet excited states, 1B850* and 3B850*, respectively, after one laser pulse excites the sample.
As expected, the initially created population in 1B850* decays back to the 1B850 ground state, along with a simultaneous rise of long-lived triplet 3B850* states. Supplementary Figure 20 (below, bottom panel, right) considers the additive effect of successive pulses (separated by 83 MHz or ~12 ns), and calculates the steady state population fraction of triplet states to be 100 %.
This is expected because the triplet lifetime is much greater than the pulse repetition rate (10 5 ns versus 12 ns). Thus, after ~200 s, all of the BChl a molecules immobilized under the laser spot will be in an excited triplet state.
Supplementary Figure 20 (top) -A simplified three energy level scheme to analyze the slow photo-physical processes in a BChl a molecule in solution. The time constants have been taken from ref. 43 . (bottom left) Evolution of population after excitation by a single laser pulse. The total ground state population is assumed to be 1, such that excitation probability of 0.1% (as used in the reported experiments) will create 10 -3 excited state 1B850* population at time zero. The total ground state population is assumed to be 1, such that the excitation probability of 0.1% (as used in the reported experiments) will create 10 -3 excited state 1B850* population at time zero. (bottom right) Steady state fraction of BChl a triplets after a 12 ns (83 MHz) pulse train is incident on an immobilized sample.
Using Models B and C described below, we show that the situation in the reported SF-2DES  in the current study (64 x 10 12 photons/cm 2 ) are more than 5x lower than fluences for which singletsinglet annihilation has been reported by Pullerits and co-workers 48 . Hence, singlet-singlet annihilation can be neglected. The present model also neglects singlet-triplet and triplet-triplet annihilation processes. Under high triplet and singlet concentrations, both processes start to dominate and the timescales for both processes is expected to be on the order of a few nanoseconds or shorter 13,15 . By neglecting those triplet decay channels, the triplet concentrations predicted by Model 2 should be an overestimate.
Based on the results of Model 2 shown in Supplementary Figure 21 13 ) possibly due to underestimation of annihilation rates. LH2 rings by a single laser pulse. The total ground state population is assumed to be 1, such that the excitation probability of 0.1% (as used in the reported experiments) will create 10 -3 excited state 1B850* population at time zero. (bottom right) Steady state fraction of Carotenoid triplets after a 12 ns (83 MHz) pulse train is incident on an immobilized sample, and excitation probability per LH2 ring (that is, excitation probability per BChl a x 18 BChl a molecules per B850 LH2 ring) is considered 13  Repetition rate and fluence dependent photo-physics within isolated LH1-RC complexes has been studied extensively by Kohler and co-workers 14 through quantitative modeling based on a global master equations approach. Earlier work from the same group has studied similar effects on isolated LH2 complexes 13 and LH2 complexes in arrays 15 (but without an LH1-RC 'sink').
Here, we have considered a very simplified approach and neglected the singlet-triplet (and triplettriplet) quenching dynamics within the LH1-RC complex. Conclusions about the triplet quenching dynamics within the LH1-RC complex from ref. 14 will further add to the picture derived from Model C. We combine the simplified LH2 photo-physics (derived from Model B) with the presence of a LH1-RC 'sink' which is equilibrated 20 with an LH2 ring. For fluences and repetition rates used in the present study, Kohler and co-workers estimate that >90% of the RC proteins will be in an oxidized P + state (Fig. 9A of ref. 14 ). For oxidized RC proteins, the timescale of energy transfer from LH1 to closed RCs (RC+*) is estimated by ref. 14 to be ~0.3 ns. Relaxation of RC+* to the ground state is estimated to be ~0.1 ns from Table 2 Figure 21) is now reduced to only ~5%, that is, ~1 carotenoid per LH2 B850 ring. Note that inclusion of triplet annihilation processes (~10ns 14 ) will further reduce the estimated ~5% steady state fraction of carotenoid triplets. Kohler and coworkers note that both, singlet-triplet and triplet-triplet, annihilation process dominate under high repetition rates and give rise to discrepancies between experimentally measured and simulated fluorescence quenching rates (for example, see  Table 2 of ref. 13 for isolated LH2 complexes).
With regard to the dynamics within the LH1-RC complexes, once singlet population is transferred from the B850 complex to LH1, estimations of ref. 14 for approximately the same repetition rates and fluences can be directly applied to the present study. Based on measured and 55 simulated fluorescence decays from isolated LH1-RC complexes at repetition rates and fluences similar to those in this study, Kohler and co-workers estimate 14 ~40% steady state fraction of all LH1-RC complexes with at least one carotenoid triplet.
Comparing Models A-C and studies by Kohler and co-workers [13][14][15] , we derive the following qualitative conclusions- i) The scenario of 100 % BChl a population converted to triplets under high repetition rates (Model A), only applies to isolated BChl a molecules immobilized under the laser.
ii) When BChl a molecules are present in vivo inside LH2 and LH1 rings, processes 13-15 such as a.) triplet quenching by carotenoid molecules, b.) singlet-triplet annihilation caused by mobile singlets and immobile triplets, c.) triplet-triplet annihilation between adjacent carotenoid molecules, d.) rapid energy transfer towards LH1-RC complexes, will reduce the amount of BChl a triplets in LH2 to ~zero, and the amount of carotenoid triplets to <5% per LH2 ring.
iii) A majority of population transfer occurs towards LH1 causing ~40% of LH1 complexes to have one more carotenoid triplets. However, we note that the LH1 band is negligibly probed in the present experiment (the LH1 shoulder is present at 883 nm and there is no laser intensity beyond 870 nm).
The above comparisons indicate that the overall effect of steady state BChl a and carotenoid triplet populations will be negligible when probing LH2 complexes in vivo as in the reported measurements. At steady state, most of the LH2 BChl a and Car molecules are expected to be present in their ground electronic state. This conclusion based on modeling is consistent with our experiments on flowing samples and our repetition-rate-dependent experiments.