Letter pubs.acs.org/JPCL
Two-Dimensional Electronic Spectroscopy Reveals Ultrafast Downhill Energy Transfer in Photosystem I Trimers of the Cyanobacterium Thermosynechococcus elongatus Jessica M. Anna,† Evgeny E. Ostroumov,† Karim Maghlaoui,‡ James Barber,‡ and Gregory D. Scholes*,† †
Department of Chemistry, Institute for Optical Sciences and Centre for Quantum Information and Quantum Control, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada ‡ Division of Molecular Bioscience, Department of Life Sciences, Imperial College London, Sir Ernst Chain Building - Wolfson Laboratories, South Kensington Campus, London, SW7 2AZ, United Kingdom ABSTRACT: Two-dimensional electronic spectroscopy (2DES) was used to investigate the ultrafast energy-transfer dynamics of trimeric photosystem I of the cyanobacterium Thermosynechococcus elongatus. We demonstrate the ability of 2DES to resolve dynamics in a large pigment−protein complex containing ∼300 chromophores with both high frequency and time resolution. Monitoring the waiting-time-dependent changes of the line shape of the inhomogeneously broadened Qy(0−0) transition, we directly observe downhill energy equilibration on the 50 fs time scale.
SECTION: Spectroscopy, Photochemistry, and Excited States
P
specifically pump−probe and transient absorption spectroscopy, have elucidated energy-transfer time scales characteristic of PSI.2,9,11−18 In a typical transient absorption measurement, a narrow band pump-pulse excites a subensemble of molecules to a population, and the evolution of this population is monitored with a broad-band probe pulse. In heterogeneous samples, such as pigment−protein complexes, it is desirable to be able to link dynamic aspects of the system to a specific subensemble of the heterogeneous chromophores. Using pump−probe techniques, one is limited in this respect and is required to choose between either high-frequency resolution or high time resolution; that is, there is a trade-off between frequency resolution and time resolution defined by the time-bandwidth product. To gain more direct insight into the ultrafast dynamics of PSI, Fourier transform 2DES can be applied. Fourier transform 2DES is a third-order nonlinear optical spectroscopy that circumvents the above-described issues by spreading the information contained in a 1-D pump−probe spectrum over two frequency axes. That allows elucidation of a frequency−frequency correlation map where each excitation frequency is correlated to each detection frequency for a given waiting time, t2.19,20 To obtain this frequency−frequency correlation map, three incoming optical fields (E1, E2, and E3) interact with the sample, leading to the emission of the signal, which is characterized
hotosynthesis is the process by which sunlight is converted to chemical energy. The first step of this process is the harvesting of solar energy, which is accomplished via pigment− protein complexes. Two large membrane bound pigment− protein complexes that are primarily responsible for the conversion of solar energy to chemical energy in plants, cyanobacteria, and algae are photosystem I (PSI) and photosystem II (PSII).1 Under physiological conditions, PSI uses the energy of an absorbed photon to drive a transmembrane electron-transfer reaction resulting in an electrochemical gradient across the thylakoid membrane − converting a photon into electromotive force − which is closely associated with CO2 reduction.2,3 The first step in this process is absorption of a photon by a chlorophyll antenna. Understanding these initial photophysical events − how the energy of an absorbed photon is funneled to the reaction center − will provide insight into biotechnology and bioengineering4,5 and may inspire the design and construction of more efficient solar cells and technologies to generate solar fuels.4,6,7 A particular challenge is to ascertain how excitation energy diffuses on longdistance scales through complex and energetically disordered multichromophore assemblies. Here we show how 2DES provides surprisingly incisive information on ultrafast downhill energy migration in cyanobacterial PSI, a particularly large light-harvesting complex. Optical spectroscopy has proved to be a valuable tool for understanding electronic structure, energy transfer, and dynamics of PSI.8−10 Third-order optical spectroscopies, © 2012 American Chemical Society
Received: November 5, 2012 Accepted: November 23, 2012 Published: November 23, 2012 3677
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Figure 1. (a) 2.5 Å resolution crystal structure of the PSI trimer and monomer from T. elongatus (PDB code 1JB0)31 are shown. The chlorin rings of the chlorophyll molecules are shown in green, the carotenoids in orange, the phylloquinones in purple, and the iron−sulfur clusters in yellow. (b) Linear absorption spectrum of PSI trimers from T. elongatus in the Qy spectral region is shown in green along with the normalized intensity of the incoming laser pulse, which has a temporal fwhm of 12 fs.
Figure 2. Two-dimensional electronic spectra of PSI trimers at three different waiting times, t2 = 60, 100, and 240 fs, are shown. (a) Twodimensional spectra over the entire spectral bandwidth of the incoming laser pulse are shown. (b) Two-dimensional spectra zooming in on the Qy(0−0) spectral regions are shown.
through spectral interferometry with a fourth pulse, ELO, so that both amplitude and phase information are obtained. The arrival of the first pulse creates a coherence between the ground and excited state, effectively tagging the chromophores and marking the beginning of the coherence period, t1. The t1 time period ends with the arrival of the second pulse, which creates either a population or another coherence and marks the beginning of the waiting time, t2, where the system is free to evolve. The arrival of the third pulse marks the end of the waiting time and the beginning of the coherence time, t3, effectively reading out the current state of the previously labeled chromophores. Fourier transformation along t1 and t3 yields the excitation (ω1 or λ1) and detection (ω3 or λ3) frequency axes and the resulting 2D spectrum, where ω signifies angular frequency and λ wavelength. Previous 2DES studies have proved to be promising in studying energy transfer in photosynthetic pigment−protein complexes,19 including FMO,21−23 LHCII,24,25 phycobiliproteins,26,27 LH2,28 LH3,29 and the reaction center of PSII.30 Of these systems, the LHCII trimer contains the most chromophores, having ∼45 chlorophylls in the pigment− protein complex. We have extended these studies to the much
larger photosynthetic pigment−protein complex, trimeric PSI, having a mass of 387 kDa and containing ∼300 chlorophylls.31 Another interesting aspect of PSI, setting it apart from the previously studies on pigment−protein complexes is that PSI contains both the reaction center chlorophylls and the lightharvesting antenna chlorophylls. Applying 2DES to investigate energy migration in PSI trimers at ambient temperature, we observe ultrafast downhill energy transfer on the 50 fs time scale in the Qy spectral region. The 2.5 Å resolution crystal structure of the PSI trimer and monomer from T. elongatus is shown in Figure 1.31 The chlorin rings of the chlorophyll molecules are shown in green, the carotenoids in orange, the phylloquinones in purple, and the iron−sulfur clusters in yellow. In cyanobacteria, the PSI trimers lack the LHCI subunits that are associated with the monomeric PSI complex of plants. The six chlorin rings belonging to the three pairs of chlorophyll molecules of the reaction center lie in the center of the monomer. These reaction center chlorophylls are separated from the antenna chlorophylls by ∼18 Å, excluding the two so-called “linker chlorophylls”.31 The antenna chlorophyll molecules are arranged in a nonsymmetrical bowl-like structure around the reaction center with the 3678
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Figure 3. Waiting-time-dependent traces (left) of the diagonal and off-diagonal points indicated on the 2D spectrum (right) are shown. After the first 50 fs, we observe a decay of the diagonal peaks and a growth of the off-diagonal peaks.
Mg2+−Mg2+ distance between the chlorophyll molecules ranging from 7 to 16 Å.31 The antenna chlorophylls mainly function to absorb energy and funnel this energy to the reaction center chlorophylls, where the primary charge separation occurs. The experiments we report here were performed on the trimeric form and probe the Qy and Qx electronic transitions of the chlorophyll molecules, not the transitions associated with the Soret band or carotenoid molecules. Figure 1b shows the linear absorption spectrum of trimeric PSI from T. elongatus at room temperature in the Qy spectral region along with the spectrum of the incoming laser pulse. In the spectral region of interest there are three resolvable peaks, the Qy(0−0) centered at 678 nm, the Qy(0−1) vibronic transition centered at 626 nm, and the Qx transition at 587 nm. In this manuscript, we focus on the Qy(0−0) band. Taking the second derivative of the linear absorption spectrum, we resolve four transitions in this region at 667, 678, 685, and 708 nm. These values are in agreement with low-temperature (5 K) absorption and CD measurements.32,33 We note that those low-temperature measurements also find transitions at 673 and 696 nm, which are not revealed in the room-temperature absorption spectrum. The absorptive 2D spectra of the PSI trimers for three different waiting times are displayed in Figure 2. Figure 2a shows the 2D spectra over the entire spectral region spanned by the incoming laser pulse. The peaks lying along the diagonal correspond to the peaks in the linear spectrum with the Qy(0−0) absorption band peaking at 678 nm. We do not clearly observe the Qy(0−1) transition on the diagonal owing to a combination of the transition having a weaker transition dipole moment, the spectral tuning of the incoming laser pulse, and overlap with excited-state absorption in this spectral region. However, a crosspeak at the frequencies corresponding to the frequencies of the Qy(0−0) and Qy(0−1) transitions is clearly seen below the diagonal. This peak arises because the two transitions have a common ground state and lie within the bandwidth of the incoming laser pulse. This demonstrates one of the powerful aspects of 2D spectroscopy: a crosspeak having corresponding weak and strong diagonal peaks can be used to gain information on the coupling and frequency of the weaker transition.34−38 We note that the conjugate crosspeak above the diagonal is not clearly observed, and this is attributed to spectral overlap with excited-state absorption. For the work reported here, we focus on the Qy(0−0) diagonal peak, which comprises the inhomogeneous distribution of absorption bands of ∼300 chlorophylls per PSI trimer. Figure 2b plots the 2D spectra shown in Figure 2a zoomed in on the Qy(0−0) spectral region. At early waiting times, after the
nonresonant solvent response has fully decayed, the Qy(0−0) band appears elongated along the diagonal. As the waiting time increases, the line shape of the peak changes. We emphasize that in the analysis of the line shape we have found it is important to have carefully phased spectra, and a detailed description of our new phasing procedure is given in the Methods section. There is an asymmetric aspect to the line shape evolution, with the bottom right part of the peak growing in as the waiting time increases, indicating downhill energy transfer. 2DES therefore gives rather direct information on the ultrafast redistribution of excitation energy in the PSI antenna, which is predominately from higher to lower Qy(0−0) energies within the inhomogeneous distribution. We note here that this information is in principle contained in a pump−probe spectrum. In fact, the projection of the 2D electronic spectrum onto the ω3 axis yields the broad-band pump−probe spectrum. The line shape evolution observed here demonstrates how more direct information on energy redistribution in heterogeneously broadened samples can be obtained from the 2D electronic spectra when compared with pump−probe spectra. Monitoring the amplitude changes of the Qy(0−0) transition as a function of waiting time gives further insight into the time scale of this downhill energy transfer among the antenna chlorophylls. Figure 3 plots the waiting-time-dependent traces, where the amplitude for a given excitation and detection frequency is plotted as a function of waiting time. We note that data during the first 50 fs (indicated by a shaded gray box) are not analyzed due to the contributions from the nonresonant solvent response. Because the Qy(0−0) band is congested, we rely on our linear absorption spectra and previous low-temperature studies performed on trimers of PSI of T. elongatus to determine the points of interest in the 2D spectra. The monitored points are indicated on the 2D spectrum shown in Figure 3. From the plots of the traces we see that the two points on the diagonal at λ1 = λ3 = 678 nm (blue) and λ1 = λ3 = 696 nm (green) both decay but at different rates, with the higher energy transition decaying faster. The amplitude of the off diagonal points at λ1 = 678 nm, λ3= 696 nm (cyan) and λ1 = 668 nm, λ3= 696 nm (red) grow in amplitude and appear to reach a maximum by t2 = 150 fs, indicating a growth on the ∼50 fs time scale. Energy transfer has been previously observed in PSI, with time scales ranging from 160 to 180 fs assigned to site-to-site hopping times, 300 fs to 1 ps assigned to bulk chlorophyll equilibration, 1 to 10 ps assigned to energy transfer between the bulk and “red” shifted chlorophyll, and longer time scales 3679
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hopping between different multichromophoric units occurs on a faster time scale than the 350 fs uphill energy transfer component, precluding the uphill energy transfer between the excitonic states comprising a multichromophoric unit. One of the main goals of using electronic spectroscopy to study biological complexes is to map the spectroscopic signatures to the structural aspects of the system. For PSI, this can be a daunting task with ∼300 chlorophyll antenna contributing to the heterogeneously broadened Q y(0−0) transition. Despite this, progress has been made in applying models to PSI to understand energy-transfer and spectroscopic signatures.46,51,52,57−60 Although some of these studies have observed sub-100 fs components that were assigned to energy equilibration among the bulk antenna chlorophyll,46,52 most of the theoretical studies tended to focus more on processes being explored experimentally, such as the energy equilibration among the bulk and “red” chlorophyll molecules and trapping dynamics. The direct observation of the ∼50 fs time scale energy equilibration reported here may further facilitate the theoretical exploration of dynamics on the sub-100 fs time scales in PSI. Further theoretical studies may help to explore whether the observed 50 fs growth can be described solely by downhill energy transfer between different excitonic states. More specifically, theoretical studies may aid in understanding the role molecular vibrations may play in the downhill energy equilibration in the Qy(0−0) transition. In large complex condensed phased systems, such as PSI, the observed experimental signatures may have contributions from multiple processes. Because the resulting 2DES signal is an ensemble average, the same chromophore in different photosystem I complexes being probed in the experiment may lie in slightly different environments, leading to an overall heterogeneous system. For coherences (whether vibrational and/or electronic) created during the waiting time, this heterogeneity can effectively act as another dephasing mechanism, leading to a faster dephasing time when compared to the dephasing time of a single system.61,62 In other words, the measured response can be thought of as the sum of the signals from many complexes. Thinking of the resulting signal in this manner, slight differences in the phase of the oscillatory components resulting from the heterogeneity of the system will lead to destructive interference. The net result may be that oscillatory components associated with vibrational or electronic coherences created during t2 are not observed experimentally. In PSI, we see a decay of the diagonal traces and a corresponding growth of the off diagonal traces indicating that the dominant contribution to the observed 50 fs growth is energy transfer. This conclusion is further supported by the assignment of the sub-100 fs component in other light-harvesting pigment−protein complexes21,25,29,30 and theoretical studies.46,51,52 In conclusion, by applying 2DES to trimeric PSI, we are able to directly observe an ultrafast 50 fs time scale energy-transfer component. We attribute this 50 fs energy transfer component to downhill energy equilibration between neighboring excitonically coupled chlorophyll molecules that is facilitated by the spatial overlap of the excitonic wave functions. This component precedes the time scale associated with site-to-site hopping, indicating that in PSI the first step to energy equilibration is downhill energy transfer among excitonically coupled chlorophyll molecules. This observation may further facilitate theoretical studies exploring ultrafast energy equilibration, which may in turn provide further insight into the design of
ranging from 20 to 70 ps assigned to trapping of the energy by the reaction center.2,11−13,15−18,39−45 Previous fluorescence upconversion44 and photon echo peak shift43 studies on PSI have observed evidence of a sub-100 fs energy-transfer component in addition to longer time scale energy-transfer components; although due to the instrument response functions of 100 fs 39 and 280 fs, 44 the fluorescence upconversion measurements may have lacked the time resolution to observe the ∼50 fs component observed in this study.46 In this letter, we focus on the ultrafast sub-100 fs energy-transfer component only. Full characterization of the processes occurring on longer range time scales will require measurements over longer waiting times and will be the objective of future work. Previous 2DES studies on photosynthetic complexes including chlorosome,47 trimeric LHCII,25 the FMO complex,21 LH3,29 and the D1-D2-cyt-b559 reaction center of PSII30 have observed ultrafast downhill energy equilibration on the 50−150 fs time scale. In the molecular aggregate chlorosome complex this ultrafast component was attributed to exciton diffusion,47 whereas in the pigment−protein complexes this ultrafast energy transfer component is attributed to relaxation among different excitonic states.21,25,29,30 In PSI trimers, where the Qy transition includes contributions from both the reaction center and light-harvesting antenna chlorophylls, we assign the 50 fs component to ultrafast downhill energy equilibration among neighboring excitonically coupled antenna chlorophyll, in accord with the previous studies on pigment−protein complexes.21,25,29,30 The ∼50 fs downhill spectral equilibration component observed here precedes the ∼100 fs site-to-site hopping component previously observed,39 indicating that the first step after light absorption is not diffusive site-to-site energy hops but a local downhill energy equilibration within the heterogeneously broadened chlorophyll antenna. In PSI, the antenna chlorophyll molecules lie within different local protein environments, which can lead to neighboring chlorophyll molecules having slightly different site frequencies. These neighboring chlorophyll molecules may also be strongly coupled, leading to the formation of excitons, multichromophoric units consisting of 2 to 4 chromophores having excitonic wave functions that are delocalized over the coupled chromophores. The spatial overlap of these excitonic wave functions can facilitate ultrafast energy transfer between the excitonic states with the time scales being directly proportional to the extent of the spatial overlap of the excitonic wave functions.48−50 We attribute the 50 fs growth observed in PSI to energy transfer from higher energetic excitonic states to lower energetic excitonic states comprising a multichromophoric unit, which is consistent with previous theoretical studies.46,51,52 According to detailed balance, the time scale for the uphill transfer of energy is 350 fs for excitonic states separated by ∼400 cm−1 (e.g., a higher lying state at 670 nm and the lower lying state at 690 nm). Putting this into the context of previous experiments explains the asymmetry of the line shape. Previous experimental studies have observed energy equilibration among the bulk chlorophyll antenna on the 200− 500 fs time scales attributing this to multiple hops between sites.45,53 In accord with our experimental observations, we suggest that these processes may be better described as single and multiple hops among the excitonically coupled multichromophoric units,54−56 which results in the diffusive energy equilibration among the bulk chlorophyll antenna. The diffusive 3680
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Figure 4. Two 2D spectra of PSI trimers at t2 = 200 fs are shown. The spectrum on top was phased according to our previous method of phasing while the spectrum on the bottom was phased according to our new method of phasing described here. Plotted on the right are the corresponding projections of the absorptive spectra onto the ω3 axis (blue) along with pump−probe spectra at a waiting time of 200 fs (green).
analyzing absolute value rephasing and nonrephasing spectra, the removal of the phase distortions is not required. We have found that phasing precision is much more important than we previously realized. The removal of these distortions is referred to as “phasing”. Typical phasing procedures call for the multiplication of the rephasing (nonrephasing) signal by a phase exp(iϕ), where ϕ(ω1,ω3) = +ω1Δt1 − ω3Δt3 − θ (ϕ(ω1,ω3) = −ω1Δt1 − ω3Δt3 − θ).25,64−67 The two linear phase terms account for errors in knowing the precise time origins of t1 and t3, and the constant phase term, θ, results from performing spectral interferometry to detect the signal that results from scanning two independent wedge pairs. We note that for the pump− probe geometry of 2DES, or when the phases of the pulses are known, this phasing procedure is not necessary.68−71 A spectrum is considered to be properly phased when the projection of the absorptive 2D spectrum onto the ω3 axis reproduces the pump−probe spectrum collected under the same experimental conditions that the 2D spectra were collected.64,72 Previous phasing procedures have also found it necessary to constrain the spectra along ω1, adding another constraint where transition frequencies of the projected absolute value of the rephasing, nonrephasing, and absorptive spectra onto the ω1 axis are not altered by the phase terms.67,73 Using these constraints along the ω1 and ω3 axes, we employ an unconstrained nonlinear optimization procedure to determine the three phasing parameters, Δt1,R, Δt1,NR, and θ. We experimentally determine the t3 time origin through spectral interferometry of the ELO and the nonresonant solvent response of methanol, allowing for the −ω3Δt3 term to be neglected. The phasing procedure consists of taking the real part of the sum of SR(ω1,t2,ω3)exp(iω1Δt1,R − iθ) and SNR(ω1,t2,ω3)exp(−iω1Δt1,NR − iθ), which we denote S(ω1,t2,ω3). The optimization procedure converges when a fitness function f is minimized. There are two components to the fitness function
artificial light-harvesting antenna. Future work will explore the polarization-dependent 2D electronic spectra, and longer waiting times will also be obtained to further the insight into the electronic structure, energy transfer pathways, and excitonic couplings.
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METHODS Obtaining Absorptive Spectra. The 2DES experimental setup has been described in detail elsewhere.63 We perform the background free method of 2DES, where the incoming beams are arranged in a box geometry so that the signal is emitted in the background free direction. The signal is detected through spectral interferometry so that both real and imaginary components are obtained. There are two phase-matching conditions relevant for 2DES: ks = −k1 + k2 + k3, referred to as rephasing, and ks = +k1 − k2 + k3, referred to as nonrephasing. In the background-free geometry of 2DES, the rephasing and nonrephasing spectra are collected independently, and the absorptive spectrum is obtained by taking the real part of the sum of these spectra (eq 1).64,65
∫0
∞
S(ω1 , t 2 , ω3) = Re[ +
∫0
dt1
∞
dt1
eiω1t1eiω3t3]
∫0
∫0
∞
dt3 SR (t1 , t 2 , t3)e−iω1t1eiω3t3
∞
dt3 S NR (t1 , t 2 , t3) (1)
In the above equation, SR is the rephasing spectrum and SNR is the nonrephasing spectrum, ω1 and ω3 are the excitation and detection frequency axes, t1 is the time delay between the first and second pulse, and t3 is the time delay after the third pulse. Errors in the precise origin of the t1 and t3 time delays can lead to a mixing of real and imaginary components of the signal, leading to an absorptive spectrum with dispersive distortions. To extract meaningful results from absorptive 2D spectra, it is imperative that the spectra be properly phased; however, when 3681
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using a 50 to 100 mM MgSO4 gradient, and the purity was assessed by gel filtration analysis.74
that are defined as follows: (1) the sum of the squared difference between the normalized projection of S(ω1,t2,ω3) onto the ω3 axis and the normalized pump−probe spectrum and (2) the sum of the squared difference between the projection of the absolute value of SR(ω1,t2,ω3) and S(ω1,t2,ω3) onto the ω1 axis and the sum of the squared difference between the projection of the absolute value of SNR(ω1,t2,ω3) and S(ω1,t2,ω3) onto the ω1 axis. In Figure 4 we demonstrate the results of the phasing procedure on PSI data for a given waiting time, t2 = 200 fs. The spectrum on the top was obtained using our previous method of phasing,63 where it was assumed that the time origins of t1 and t3 are precisely known and that the phase difference between the local oscillator and emitted signal is 0. The spectrum on the bottom was obtained using our new method of phasing where the difference in the time origins was determined to be Δt1,R = −0.6 and Δt1,NR = 2.6 fs and the constant phase of θ = 5.2 was determined. Comparing the projection of the 2D spectra onto the ω3 axis with the pump− probe spectrum confirms that the spectrum on the bottom is properly phased according to the projection slice theorem. For the phased data, differences in the pump−probe spectrum and the projection are attributed to the fact that within the current experimental setup the pump−probe spectrum cannot be obtained under exactly the same conditions that the 2D spectrum was obtained. We see obvious differences between the two 2D spectra. For the data phased according to the previous method, the diagonal peak is shifted from the diagonal by ∼10 nm and the peak amplitudes and shapes are also different. We also note that the waiting-time-dependent amplitudes of the peaks differ when the two data sets are compared. This figure demonstrates the necessity of having properly phased data when one is interested in extracting information from the real component of the signal. Along with using this procedure to obtain the absorptive spectra for PSI, we have tested this phasing method on 2D electronic spectra recorded for the laser dye Rhodamine 800 in methanol, with data taken on different days with different tunings of the incoming pulses. Here we summarize our findings. The phase parameters obtained from the unconstrained nonlinear optimization are consistent with phasing parameters obtained from a genetic algorithm. Because of the high phase stability of the apparatus, we have found the phase parameters determined from properly phasing a 2D spectrum at a given t2 can be applied to all spectra in a given t2 scan and that the phase parameters determined from the 2D spectra of the laser dye can be used to phase the spectra of PSI, demonstrating that the phase parameters are sampleindependent. Finally, we have also observed that the linear phase terms can be approximated as constant phase terms for small Δt1.64 When making this comparison, we have also compared the waiting-time-dependent amplitudes of the peaks in the spectrum and found that they are consistent. The benefits of approximating the linear phase terms as constant phase terms include a decrease in errors of the fitting process and a reduction in the time required to phase the spectra. The data presented in this work were phased using two linear phase terms and a constant phase term that were determined from applying the described procedure to the 2D spectra of PSI at 150 fs. Sample Preparation. Trimeric PSI was purified by anion exchange chromatography (AEC) as described by Kern et al.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Dr. Alison Telfer for helpful discussions and advice on the sample preparation and Dr. James Murray for providing Figure 1a. This work was supported by DARPA under the QuBE program, the United States Air Force Office of Scientific Research (FA9550-10-1-0260) and the Natural Sciences and Engineering Research Council of Canada (G.D.S.) and the Biotechnology and Biological Sciences Research Council, U.K. (J.B. and K.M.).
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REFERENCES
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