Robert Dods

Petra Båth

Dmitry Morozov

Viktor Ahlberg Gagnér

David Arnlund

Ling Hoi

Joachim Luk

Michal Kübel

Adams Maj

Cecilia Vallejos

Hoi Ling Luk

Joachim Kübel

Michał Maj

Adams Vallejos

Cecilia Wickstrand

Robert Bosman

Kenneth R Beyerlein

Garrett Nelson

Mengning Liang

Despina Milathianaki

Joseph Robinson

Rajiv Harimoorthy

Peter Berntsen

Erik Malmerberg

Linda Johansson

Rebecka Andersson

Sergio Carbajo

Elin Claesson

Chelsie E Conrad

Peter Dahl

Greger Hammarin

Mark S Hunter

Chufeng Li

Stella Lisova

Antoine Royant

Cecilia Safari

Amit Sharma

Garth J Williams

Oleksandr Yefanov

Sebastian Westenhoff

Jan Davidsson

Daniel P Deponte

Sébastien Boutet

Anton Barty

Gergely Katona

Gerrit Groenhof

Gisela Brändén

Richard Neutze
email: richard.neutze@gu.se

A B Samples

R B Crystallization

G B Time

Ultrafast structural changes within a photosynthetic reaction centre

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Photosynthetic reaction centres harvest the energy content of sunlight by transporting

electrons across an energy transducing biological membrane. We use time-resolved serial femtosecond crystallography 1 at an X-ray free electron laser [START_REF] Emma | First lasing and operation of an angstrom-wavelength free-electron laser[END_REF] Our biosphere depends upon the electron transfer reactions of photosynthesis as a primary source of energy. Photosystems and photosynthetic reaction centres form a family of integral membrane protein complexes found in plants, algae, cyanobacteria and photosynthetic bacteria that convert the energy of a captured photon into a charge separated state. The photosynthetic reaction centre of the purple non-sulphur bacterium Blastochloris viridis (RC vir ) contains three transmembrane subunits called H, L and M and a periplasmic subunit C. These subunits support four bacteriochlorophyll molecules (BCh), two bacteriopheophytin molecules (BPh), a tightly bound menaquinone (Q A ), a mobile ubiquinone (Q B ), a single nonhaem iron and four haem co-factors (Fig. 1). Electron transfer reactions originate at a special pair (SP) of strongly interacting bacteriochlorophylls which in Bl. viridis have an absorption maximum at 960 nm. Photo-oxidation of the SP liberates an electron which is transferred to the active branch BPh L within a few picoseconds, is transferred to the tightly bound menaquinone (Q A ) in less than a nanosecond, and is transferred to the mobile ubiquinone (Q B ) in microseconds. SP + is reduced by subunit C and a second photo-oxidation event transfers a second electron to Q B -, which is protonated from the cytoplasm and released into the membrane as ubiquinol (H 2 Q). Other proteins participate in a cyclic flow that returns electrons to subunit C and the net effect is that two protons are transported across an energytransducing membrane for every photon absorbed.

Electrons may tunnel between cofactors when they are separated by approximately 10 Å or less. [START_REF] Marcus | Electron transfers in chemistry and biology[END_REF] The primary electron transfer step from SP to BPh L occurs in 2.8 ± 0.2 ps 4 over a distance of 10 Å by means of a two-step hopping mechanism via the monomeric BCh L [START_REF] Chan | Mechanism of the initial charge separation in bacterial photosynthetic reaction centers[END_REF] and is more rapid than conventional Marcus theory. By contrast, the 9 Å electron transfer step from BPh L to Q A has a single exponential decay time of 230 ± 30 ps [START_REF] Holten | Primary photochemical processes in isolated reaction centers of Rhodopseudomonas viridis[END_REF] which is consistent with conventional Marcus theory. Coherent nuclear motions [START_REF] Vos | Visualization of coherent nuclear motion in a membrane protein by femtosecond spectroscopy[END_REF] and protein structural changes [START_REF] Wang | Protein dynamics control the kinetics of initial electron transfer in photosynthesis[END_REF] have been suggested to influence the initial charge-transfer reactions of photosynthesis yet the specific nature of these putative protein motions is unknown. Flash-freeze crystallographic trapping studies, [START_REF] Stowell | Light-induced structural changes in photosynthetic reaction center: implications for mechanism of electron-proton transfer[END_REF] time-resolved Laue diffraction [START_REF] Wöhri | Light-induced structural changes in a photosynthetic reaction center caught by Laue diffraction[END_REF] and time-resolved serial femtosecond crystallography [START_REF] Young | Structure of photosystem II and substrate binding at room temperature[END_REF][START_REF] Suga | Light-induced structural changes and the site of O=O bond formation in PSII caught by XFEL[END_REF][START_REF] Kern | Structures of the intermediates of Kok's photosynthetic water oxidation clock[END_REF][START_REF] Suga | An oxyl/oxo mechanism for oxygen-oxygen coupling in PSII revealed by an x-ray free-electron laser[END_REF] (TR-SFX) have revealed structural changes in bacterial photosynthetic reaction centres [START_REF] Stowell | Light-induced structural changes in photosynthetic reaction center: implications for mechanism of electron-proton transfer[END_REF][START_REF] Wöhri | Light-induced structural changes in a photosynthetic reaction center caught by Laue diffraction[END_REF] and cyanobacterial photosystem II [START_REF] Young | Structure of photosystem II and substrate binding at room temperature[END_REF][START_REF] Suga | Light-induced structural changes and the site of O=O bond formation in PSII caught by XFEL[END_REF][START_REF] Kern | Structures of the intermediates of Kok's photosynthetic water oxidation clock[END_REF][START_REF] Suga | An oxyl/oxo mechanism for oxygen-oxygen coupling in PSII revealed by an x-ray free-electron laser[END_REF] that occur on the late microsecond to millisecond time-scale, yet no time-resolved crystallographic studies on the time-scale of the primary charge separation reactions of photosynthesis have been reported.

Here we apply time-resolved serial femtosecond crystallography 1 at an X-ray free electron laser (XFEL) to probe the ultrafast structural response of RC vir to light. We photo-excited the special pair with 150 fs pulses centred at 960 nm (Extended Data Fig. 1). X-ray pulses 40 fs in duration were generated at the LCLS 2 and were used to record diffraction patterns from tens of thousands of microcrystals for the time points ∆t = 1 ps, 5 ps (two repeats), 20 ps, 300 ps (two repeats) and 8 µs after photoexcitation (Extended Data Table 1). The time point ∆t = 1 ps populates the photo-excited charge transfer state of the SP in which charge rearrangements have occurred within the bacteriochlorophyll dimer but are prior to the primary electron transfer step; ∆t = 5 and 20 ps are after the initial charge-transfer step and SP is oxidized and BPh L is reduced; ∆t = 300 ps is longer than the time constant for electron transfer to Q A and menaquinone is reduced; and ∆t = 8 µs corresponds to a meta-stable charge separated state.

Extended Data Fig. 2 presents overviews of the |F obs | light -|F obs | dark isomorphous difference Fourier electron density maps ("light" corresponds to data collected from photo-activated microcrystals whereas "dark" corresponds to data collected from microcrystals that were not photo-activated) for all time points. Difference electron density features are visible above 4.0 σ (σ is the root mean square electron density of the map) near SP for all time points and strong features associated with Q A are visible for ∆t ≥ 300 ps (Extended Data Table 2). In contradistinction with ultrafast TR-SFX studies of bacteriorhodopsin, [START_REF] Nogly | Retinal isomerization in bacteriorhodopsin captured by a femtosecond x-ray laser[END_REF] photoactive yellow protein, [START_REF] Pande | Femtosecond structural dynamics drives the trans/cis isomerization in photoactive yellow protein[END_REF] rsEGFP 17 and bacterial phytochromes [START_REF] Claesson | The primary structural photoresponse of phytochrome proteins captured by a femtosecond X-ray laser[END_REF] in which ultrafast structural changes are driven by the movements of atoms due to a photo-isomerization event, TR-SFX measurements of RC vir reveal a knock-on effect on protein structure due to the light-induced redistribution of charge. Electric-field induced conformational changes have been observed

when fields of the order 10 8 V/m are applied across a protein-crystal [START_REF] Hekstra | Electric-field-stimulated protein mechanics[END_REF] and this is the same order of magnitude as electric field perturbations due to the movement of an electron within RC vir .

Recurring changes of electron density are visible as positive difference electron density in the region of overlap between the two bacteriochlorophylls SP L and SP M of the special pair, and complementary negative difference electron density features are visible primarily associated with SP M (Fig. 2, Extended Data Fig. 3, Extended Data Table 2, Supplementary Video 1).

Singular value decomposition (SVD) of all seven difference Fourier electron density maps (Fig. 2e) reveals that the strongest positive and several of the strongest negative difference electron density features of the principal SVD component are associated with the SP (Extended Data Table 2). Quantification of electron density changes [START_REF] Wickstrand | A tool for visualizing protein motions in time-resolved crystallography[END_REF] within the RC vir cofactors (Fig. 2f) and statistical tests against control difference Fourier electron density maps (Methods) provides a very high-level of confidence (p-value ≤ 0.001, Extended data Table 3) that these recurring difference electron density features do not arise by chance. Thus photoexcitation causes the bacteriochlorophylls of SP to move closer together and the bending (an out of plane distortion) of SP M could explain these observations. An out of plane distortion was used to model difference electron density features observed as carbon monoxide was photo-dissociated from the haem of myoglobin [START_REF] Barends | Direct observation of ultrafast collective motions in CO myoglobin upon ligand dissociation[END_REF] (Extended Data Fig. 4).

Nonplanar distortions of chlorin and bacteriochlorin rings are observed in photosystem II and RC sph. due to interactions with the surrounding protein 22 and nonplanar porphyrins are also more easily oxidized than planar porphyrins. [START_REF] Shelnutt | Nonplanar porphyrins and their significance in proteins[END_REF][START_REF] Barkigia | Structural and theoretical models of photosynthetic chromophores. Implications for redox, lightabsorption properties and vectorial electron flow[END_REF] This suggests that the distortion of SP in advance of the primary charge separation event (Fig. 2a) could enhance the yield of the primary charge-transfer reaction, which has been optimized by evolution to achieve almost perfect quantum efficiency. [START_REF] Wraight | The absolute quantum efficiency of bacteriochlorophyll photooxidation in reaction centres of Rhodopseudomonas spheroides[END_REF] When the C-subunit is fully reduced, an electron is transferred from haem 3 to SP + in less than a microsecond. [START_REF] Dohse | Electron transfer from the tetraheme cytochrome to the special pair in the Rhodopseudomonas viridis reaction center: effect of mutations of tyrosine L162[END_REF] The above reasoning implies that SP + may be more easily reduced should SP M return to a planar geometry before this electron transfer occurs. This hypothesis is consistent with our experimental observations since the amplitude of the positive difference electron density feature between the SP bacteriochlorophylls increases from ∆t = 1 ps to 20 ps, decreases for ∆t =300 ps and is insignificant for ∆t = 8 µs (Fig. 2, Extended Data Fig. 3, Extended Data Table 2). Moreover, neither TR-SFX studies of the S2→S3 transition of cyanobacteria PSII [START_REF] Kern | Structures of the intermediates of Kok's photosynthetic water oxidation clock[END_REF] (∆t = 150 µs and 400 µs) nor TR-Laue diffraction studies of RC vir 10 (∆t = 3 ms) report a positive difference electron density feature in the region of overlap between the special pair of (bacterio)chlorophylls, implying that this feature has decayed.

Charge rearrangements cause SP + to move up to 0.3 Å towards the M-subunit by ∆t = 300 ps and the side-chains of both His173 L and His200 M adjust to preserve their ligating interactions with the magnesium ions of SP + , as do His168 L and Tyr195 M adjust conformation in order to maintain their H-bond interactions to SP L and SP M respectively. These structural perturbations are revealed by paired negative and positive difference electron density features on the sidechain of His173 L in the principal SVD components calculated from both the early (1ps, 2 × 5ps, 20 ps) and late (2 × 300 ps, 8 µs) sub-sets of TR-SFX data, whereas positive difference electron density features associated with the side-chains of His200 M and Tyr195 M become noticeably stronger for the later sub-set of data (Extended Data Fig. 3i,j; Extended Data Table 2; Supplementary Video 1). These observations suggest that SP L moves towards subunit M slightly in advance of SP M , which may be due to dielectric asymmetry within photosynthetic reaction centres. [START_REF] Steffen | Dielectric asymmetry in the photosynthetic reaction center[END_REF][START_REF] Najdanova | Analysis of the Electronic Structure of the Special Pair of a Bacterial Photosynthetic Reaction Center by (13) C Photochemically Induced Dynamic Nuclear Polarization Magic-Angle Spinning NMR Using a Double-Quantum Axis[END_REF] Dielectric asymmetry is believed to underpin the phenomenon that electron transfer occurs only along the A-branch [START_REF] Steffen | Dielectric asymmetry in the photosynthetic reaction center[END_REF] in purple bacteria RCs and PSII (Fig. 1).

An electron moves from SP to BPh L in 2.8 ± 0.2 ps 4 and from BPh L to Q A in 230 ± 30 ps. [START_REF] Holten | Primary photochemical processes in isolated reaction centers of Rhodopseudomonas viridis[END_REF] The tightly bound menaquinone is therefore neutral for ∆t = 1 ps, 5 ps and 20 ps; threequarters of the photo-activated population are reduced to semiquinone by ∆t = 300 ps; and essentially all photo-activated molecules have Q A reduced at ∆t = 8 µs. Our difference Fourier electron density maps confirm these expectations since the few difference electron density features visible within the Q A binding pocket for ∆t ≤ 20 ps are isolated whereas more continuous paired positive and negative difference electron density features are visible for ∆t ≥ 300 ps (Fig. 3, Extended Data Fig. 5). These recurring features of the later sub-set of TR-SFX data (2 × 300 ps, 8 µs) produce strong difference electron density features in the principal SVD component that are associated with Q A and its H-bond interaction with His217 M (Extended Data Table 2, Fig. 3d, Supplementary Video 2) and statistical tests establish that these recurring changes cannot be ascribed to noise (p-value ≤ 0.0125, Extended Data Table 3). Structural refinement models these observations as due to a twist and translation of the semiquinone that brings the negatively charged head-group approximately 0.2 Å closer to the positive charge of the non-haem Fe 2+ (Fig. 3f) and thereby stabilizes the reduced form of this cofactor. This interpretation receives support from QM/MM calculations that predict that the Q A to His217 M H-bond is shortened by 0.17 Å when Q A is reduced (Extended Data Fig. 6f) and suggest that semiquinone binding is stabilized by approximately 36 kJ.mol -1 due to structural changes (Extended Data Fig. 6g,h, Methods), which is a sizeable fraction of the energy (125 kJ.mol -1 ) of a 960 nm photon. Similar conclusions were drawn from an earlier analysis using a Density Functional Theory (DFT) formalism. [START_REF] Hasegawa | Energetics of the Electron Transfer from Bacteriopheophytin to Ubiquinone in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis: Theoretical Study[END_REF] Light-induced electron density changes were visible for Q A in TR-SFX studies of the S2→S3 transition of cyanobacteria PSII [START_REF] Kern | Structures of the intermediates of Kok's photosynthetic water oxidation clock[END_REF] for the time points 150 µs and 400 µs, light-induced movements of the mobile quinone Q B were also observed in PSII [START_REF] Young | Structure of photosystem II and substrate binding at room temperature[END_REF][START_REF] Suga | Light-induced structural changes and the site of O=O bond formation in PSII caught by XFEL[END_REF][START_REF] Kern | Structures of the intermediates of Kok's photosynthetic water oxidation clock[END_REF][START_REF] Suga | An oxyl/oxo mechanism for oxygen-oxygen coupling in PSII revealed by an x-ray free-electron laser[END_REF] for delays of hundreds of milliseconds, and larger light-induced motions of Q B were reported in freeze-trapping studies of the Rhodobacter sphaeroides photosynthetic reaction centre. [START_REF] Stowell | Light-induced structural changes in photosynthetic reaction center: implications for mechanism of electron-proton transfer[END_REF] For ∆t = 300 ps, paired negative and positive difference electron density features are associated with the cytoplasmic portions of TM helices D M and E M (Fig. 3e) and indicate that RC vir adjusts its structure in response to the movement of the semiquinone within the Q A binding pocket (Fig. 3f). A more quantitative analysis (Methods, Extended Data Fig. 7, Supplementary Video 3) suggests that low-amplitude protein motions begin to arise already by ∆t = 1 ps (Fig. 4a) as observed in TR-SFX studies of bR [START_REF] Nogly | Retinal isomerization in bacteriorhodopsin captured by a femtosecond x-ray laser[END_REF][START_REF] Wickstrand | A tool for visualizing protein motions in time-resolved crystallography[END_REF] and Mb:CO [START_REF] Barends | Direct observation of ultrafast collective motions in CO myoglobin upon ligand dissociation[END_REF] ; the amplitude of these motions increase with time and by ∆t = 5 ps larger displacements are observed near the SP + and BPh L -cofactors (Fig. 4b); and for ∆t = 300 ps protein conformational changes extend throughout the A-branch of the electron transfer pathway from SP + to Q A -(Fig. 4c).

When the same representation is used to depict protein conformational changes predicted from QM/MM calculations (Supplementary Video 4) almost no structural changes are expected for the photo-excited charge transfer state (Fig. 4d); protein movements arise near the charged cofactors in the SP + :BPh L -charge-separated state (Fig. 4e); and structural changes extend throughout the A-branch in the SP + :Q A -charge-separated state (Fig. 4f). These findings demonstrate that RC vir is not a passive scaffold but rather low-amplitude protein motions engage in a choreographed dance with electron movements taking the lead and protein conformational changes following. Conversely, as the protein's structure adjusts to stabilize these charge rearrangements the energetic barriers hindering the reverse electron transfer reaction increase, thereby extending the lifetime of the change separated species and enhancing the overall efficiency of photosynthesis.

In Marcus theory the total potential energy of an electron donor and its surroundings must be equal to that of the electron acceptor and its surroundings if an electron is to tunnel from donor to acceptor. [START_REF] Marcus | Electron transfers in chemistry and biology[END_REF] Fluctuations in the organizational energy around protein cofactors are therefore essential to facilitate electron transfer reactions. Efforts aimed at understanding how protein conformational dynamics control the rates of electron transfer between cofactors [START_REF] Wang | Protein dynamics control the kinetics of initial electron transfer in photosynthesis[END_REF]30 have been hampered by a lack of experimental tools that characterize protein structural changes on the relevant time-scales. Our observations provide an experimental framework for extending the standard description of electron transfer reactions in photosynthesis [START_REF] Marcus | Electron transfers in chemistry and biology[END_REF]

METHODS

Protein production and purification

The expression and purification of photosynthetic reaction centre from Bl. viridis cells was adapted from Wöhri et al. 31 . Cells were disrupted by three rounds of sonication followed by centrifugation in a JA20 rotor at 15000 rpm for 20 minutes to recover the membrane suspensions. Membranes were then purified by ultracentrifugation at 45000 rpm for 45 to seed an additional round of microcrystal growth [START_REF] Dods | From Macrocrystals to Microcrystals: A Strategy for Membrane Protein Serial Crystallography[END_REF] . Micro-crystals were harvested by pipette and concentrated up to three-fold by centrifugation at 1000 g for 1 min followed by removal of supernatant. These crystals were somewhat thicker and, while diffracting to higherresolution, they highlighted the compromise inherent in TR-SFX since a lower excited-state occupancy was usually observed when working with crystals of higher optical density.

Sample injection and data collection

Microcrystals were transferred from Eppendorf tubes to a sample reservoir using a syringe and passing the microcrystal slurries through a stainless steel 20 μm filter (VICI AG International) or a 20µm nylon filter (Sysmex). The reservoir was loaded into a temperature controlled rocking chamber and injected into the XFEL through a GDVN [START_REF] Deponte | Gas dynamic virtual nozzle for generation of microscopic droplet streams[END_REF] using an internal diameter of 75 μm. The microjet used a microcrystal suspension flow rate of 20 μl.min -1 and was focused to a 10 μm diameter using helium gas. The X-ray beam was aligned to interact with the liquid jet as close to the tip of the GDVN as practical and before Rayleigh breakup of the microjet.

Diffraction data were collected at 293 K at the CXI beam line [START_REF] Liang | The Coherent X-ray Imaging instrument at the Linac Coherent Light Source[END_REF]

Laser photoexcitation

An optical Ti:Sa pump laser 150 fs in duration was focused into a spot size of 190 μm FWHM (323 μm 1/e 2 ) and aligned to overlap with the LCLS X-ray pulse. The LCLS timing-tool [START_REF] Harmand | Achieving few-femtosecond time-sorting at hard X-ray freeelectron lasers[END_REF] provided a timing accuracy of ± 200 fs for the time point, ∆t, between the arrival of the optical pump laser and the X-ray probe. A pump-laser wavelength of 960 nm was used to photo-excite RC vir microcrystals, and this wavelength is at the absorption maximum of the special pair (ε 960 ≈ 100 000 M -1 .cm -1 ). The pump laser energy per pulse was 11.8 µJ in April 2015 and 11.0 µJ in June 2016. For an idealized Gaussian beam, 86.5 % of this light will pass through a spot with diameter 1/e 2 and 50 % of this light will pass through a spot with diameter FWHM. Thus the average fluence within the FWHM spot can be estimated as 25 mJ/cm 2 and 23 mJ/cm 2 which equates to a pump-laser power-density of 138 GW/cm 2 for the 2015 experiment and 129 GW/cm 2 for the 2016 experiment. This calculation defines the units used throughout to specify the laser power-density. Both values are above 30 GW/cm 2 to 100 GW/cm 2 that has been recommended as an upper threshold to avoid nonlinear effects in bacteriorhodopsin. [START_REF] Nass Kovacs | Three-dimensional view of ultrafast dynamics in photoexcited bacteriorhodopsin[END_REF]38 Extreme non-linear absorption was observed as ultrafast sample heating in time-resolved Xray scattering studies of RC vir when pumped with 800 nm light. [START_REF] Arnlund | Visualizing a protein quake with time-resolved X-ray scattering at a free-electron laser[END_REF] When using 800 nm to photo-excite RC vir it is the BCh cofactors (rather than the SP) which absorb light (ε 800 ≈ 180 000 M -1 .cm -1 ). The pump-laser fluence used in that study [START_REF] Arnlund | Visualizing a protein quake with time-resolved X-ray scattering at a free-electron laser[END_REF] was 1560 GW/cm 2 . Ultrafast sample heating within a GDVN liquid microjet has also been measured as a function of the 800 nm pump-laser fluence using time-resolved X-ray scattering (Fig. 28 of reference 40 ).

These measurements show that the energy deposited into RC vir samples is proportional to the pump-laser fluence (a linear response) up to 270 GW/cm 2 and that the measured heating then varies quadratically (a non-linear response) above a pump-laser fluence of 355 GW/cm 2 . Thus either an idealized assumptions of a perfectly aligned Gaussian beam may not be realistic, and/or large losses occur as the incoming laser pulse is reflected from the surface of a GVDN liquid microjet, and/or a thresholds [START_REF] Nass Kovacs | Three-dimensional view of ultrafast dynamics in photoexcited bacteriorhodopsin[END_REF]38 of 30 GW/cm 2 to 100 GW/cm 2 do not apply RC vir when photo-excited at 800 nm. When 960 nm light is used to photo-excite the SP of RC vir it is likely more difficult to induce non-linear effects because the photo-excited state SP* has an absorption maximum red-shifted 70 nm relative to the ground state 41 and hole-burning [START_REF] Meech | Role of charge-transfer states in bacterial photosynthesis[END_REF] has been observed in RC vir such that SP* is effectively transparent to the incoming light.

Moreover, the absorbance of RC vir at 960 nm is only 56 % of it absorbance at 800 nm and therefore non-linear effects are likely to arise at higher power densities when using 960 nm rather than 800 nm to photo-excite RC vir . Non-linear ultrafast heating 40 is observed in RC vir delivered using a GDVN liquid microjet and photo-excited at 800 nm only above a powerdensity of 355 GW/cm 2. Therefore the 960 nm pump-laser power-densities of 138 GW/cm 2 and 129 GW/cm 2 used in this work are below where non-linear effects may reasonably be anticipated. These conclusions are supported by time-resolved IR spectroscopy measurements (Extended Data Fig. 1).

Time-resolved infrared spectroscopy

Time-resolved vibrational spectroscopy measurements were performed with a near infrared (NIR) pump and mid-infrared (IR) probe setup using a regenerative amplifier (Spitfire Ace, Spectra Physics) to deliver pulses centred at 800 nm (1.2 mJ, 5 kHz). The amplifier output is used to pump a TOPAS-TWINS (Light Conversion) capable of generating tuneable femtosecond pulses at two different wavelengths. One path was used to generate mid-infrared probe light centred at 6000 nm via difference frequency generation whereas the other path generated 960 nm pump pulses via second harmonic generation of the idler beam. The 960 nm beam was chopped to 2.5 kHz and delayed in time relative to the probe pulses using an optical delay line. Two weak replicas derived from the midIR beam were used as probe and corresponding reference. Both probe and reference were dispersed in a Horiba spectrograph (grating with 75 gr/mm) and detected and integrated on a double-row MCT array with 64 pixels each on a shot-to-shot basis using a commercial detection system (Infrared Systems).

Samples of RC vir were prepared in a customized cell by enclosing ca. 15 uL of solution (RC vir at ca. 0.4 mM in D 2 O buffer) between two 2 mm thick CaF 2 windows separated by a 25 µm spacer. Probe and reference beams were focused at the sample position and collimated using 90° off-axis parabolic mirrors. The pump beam was focused using a 30-cm lens and overlapped with the probe beam at its focus. The sample cell was placed where pump and probe beams meet and translated continuously perpendicular to the beam direction during data acquisition. The focal spot size of the pump beam was determined using knife-edge scans and yielded perpendicular 1/e 2 radii of 57 µm and 56 µm. Different pump fluences were adjusted using reflective neutral density filters (Edmund Optics). For each fluence, twelve repeats over five time points (1000 pump shots per time point and repeat, at delays of -50, 1, 2, 5 and 300 ps) were recorded and less than 5% of shots were rejected during data treatment. Signals were calculated by subtracting consecutive pump-on from pump-off shots followed by application of the noise reduction algorithm. [START_REF] Feng | General noise suppression scheme with reference detection in heterodyne nonlinear spectroscopy[END_REF][START_REF] Feng | Optimized noise reduction scheme for heterodyne spectroscopy using array detectors[END_REF] The spectral resolution is < 5 cm -1 . The results of these measurements are presented in Extended Data Fig. 1.

Data processing

Images containing more than 20 diffraction spots were identified as diffraction hits by Cheetah. [START_REF] Barty | Cheetah: software for high-throughput reduction and analysis of serial femtosecond X-ray diffraction data[END_REF] Cheetah converted the raw detector data into the HDF5 format and data were then processed using the software suite CrystFEL version 0.6.2. [START_REF] White | CrystFEL: a software suite for snapshot serial crystallography[END_REF][START_REF] White | Recent developments in CrystFEL[END_REF] Crystals were indexed using a tetragonal unit cell (a = b = 226.4 Å, c = 113.7 Å, α = β = γ = 90º). Scaling and merging were performed using Monte Carlo methods using the same software. Data from the dark state and photo-excited states were scaled together using the custom dataset splitting option in the CrystFEL partialator module. Structure factors were calculated from merged intensities by the CCP4 module TRUNCATE [START_REF] French | Treatment of Negative Intensity Observations[END_REF] and molecular replacement was performed using the CCP4 module Phaser 49 using the ground-state RC vir structures solved with XFEL radiation (PDB codes 5O4C and 5NJ4) as a search models. Statistics for data collection and refinement are detailed in Extended Data Table 1.

Electron density difference maps

Isomorphous |F obs | light -|F obs | dark difference Fourier electron density maps were calculated using the refined dark state structures for phases with the time-points Δt = 5 ps (data set a) and 300 ps (data set a) calculated against data and coordinates using the pdb entry 5O4C whereas the time point with the time-points Δt = 1 ps, 5 ps (data set b), 20 ps, 300 ps (data set b) and 8 µs were calculated against data and coordinates using the pdb entry 5NJ4. Thus all difference electron density map calculations used only data collected during the same experiment.

Difference Fourier electron density maps represent measured changes in X-ray diffraction intensities as changes in electron density without bias towards the photo-activated state's structural model. The technique is extremely sensitive to small changes in electron density [START_REF] Henderson | The Ditferenee Fourier Technique in Protein Crystallography: Errors and their Treatment[END_REF] and reveals more subtle features than are apparent from 2mF obs -DF calc electron density maps alone (m is the figure of merit and D is estimated from coordinate errors). A Bayesian weighting calculation script 51 using CNS software 52 was also used to analyse the difference Fourier electron density maps. In this procedure structure factor amplitude differences were weighted by the product of the figure of merit of the ground state structure reflections and of a weighting term, w (Equation 14 of reference [START_REF] Ursby | Improved Estimation of Structure-Factor Difference Amplitudesfrom Poorly Accurate Data[END_REF] ), which was calculated using Bayesian statistics developed to improve signal to noise. [START_REF] Ursby | Improved Estimation of Structure-Factor Difference Amplitudesfrom Poorly Accurate Data[END_REF] For six of seven data-sets the recurring difference electron density features were slightly strengthened by this step. The exception was the time-point ∆t = 8 µs which has difference electron density feature that are weaker than for the other maps (Fig. 2f) and appears due to a lower occupancy of the charge separated state in these microcrystals. It is possible that a fraction of the photo-oxidized SP - population is reduced from the C-subunit by ∆t = 8 µs, which is longer than the time-scale of this electron transfer step. [START_REF] Dohse | Electron transfer from the tetraheme cytochrome to the special pair in the Rhodopseudomonas viridis reaction center: effect of mutations of tyrosine L162[END_REF] However, no efforts were made to reduce the C-subunit when preparing microcrystals and a similar occupancy (30% ± 5%) is observed to persist in timeresolved spectroscopy measurements on crystals for up to millisecond delays. [START_REF] Wöhri | Light-induced structural changes in a photosynthetic reaction center caught by Laue diffraction[END_REF] Singular value decomposition SVD analysis of difference Fourier electron density maps was performed using an in-house code written in python that is based upon an approach previously described. [START_REF] Rajagopal | Analysis of experimental time-resolved crystallographic data by singular value decomposition[END_REF] As has been discussed, [START_REF] Schmidt | Application of singular value decomposition to the analysis of time-resolved macromolecular x-ray data[END_REF] SVD may serve as a noise-filter to enhance the signal across a sequence of difference Fourier electron density maps. This step contains the assumption that the overall mechanism is linear and that changes in electron density are similar over the selected time-

Structural refinement of photo-excited states

Isomorphous |F obs | light -|F obs | dark difference Fourier electron density maps were inspected in COOT. Structural refinement was performed using Phenix. [START_REF] Adams | PHENIX: a comprehensive Python-based system for macromolecular structure solution[END_REF] A model was first placed within the unit cell using rigid body refinement followed by multiple rounds of partial-occupancy refinement where the SP, BCh L , BPh L , Q A , portions of TM helices E L , D L , E M and D M , as well as connecting loops, and additional residues near cofactors (L153-178, L190, L230, L236-248, M193-221, M232, M243-253, M257-266) were allowed to adopt a second conformation with 30 % occupancy and the dark-state structure (pdb entry 5O4C) was held fixed. The occupancy of 30 % was chosen by assessing the results from partial occupancy refinement when the occupancy was allowed to vary and was imposed for all structural refinements for consistency. Results from structural refinement were compared against the difference electron densities and some manual adjustments were made using COOT. [START_REF] Emsley | Coot: model-building tools for molecular graphics[END_REF] Refinement statistics are displayed in Extended Data Table 1. Validation of structure geometry was performed using MOLPROBITY [START_REF] Chen | MolProbity: all-atom structure validation for macromolecular crystallography[END_REF] and PROCHECK. [START_REF] Laskowski | PROCHECK: a program to check the stereochemical quality of protein structures[END_REF] Structural changes were also validated by calculating simulated difference Fourier electron density maps from the refined structures [START_REF] Wöhri | Light-induced structural changes in a photosynthetic reaction center caught by Laue diffraction[END_REF][START_REF] Wickstrand | A tool for visualizing protein motions in time-resolved crystallography[END_REF] (Extended Data Figs. 2l and4j).

Structural analysis of large-scale protein motions

The high multiplicity of SFX data was exploited for structural analysis by randomly selecting a sub-set of experimental observations from within each SFX data-set to create 100 separate (but not independent) serial crystallography data-sets for the two resting state data-sets and the seven photo-activated data-sets, amounting to 900 resampled data-sets in total. For each of these resampled data-sets the mean and uncertainty estimates (σ) for every unique Bragg reflection were determined. Structural refinement over a cycle of 100 rigid body and 100 isotropic restrained refinements with all atoms allowed to move and with every atom having 100 % occupancy were then performed against each of these 900 resampled data-sets using pdb entry 5NJ4 as a starting model. R free values ranging from 22.1 % to 23.1% were recovered. Coordinate errors associated with each individual structural refinement are estimated [START_REF] Murshudov | Simplified error estimation a la Cruickshank in macromolecular crystallography[END_REF] to be ≤ 0.2 Å.

The distances between the Cα atoms of the photo-activated and resting RC vir structures were compared pairwise using the miller package of CCTBX. 61 A 100×100 Euclidian distance matrix was then calculated for every Cα atom and every time point according to: Δr ij ∆t,dark = |r i ∆t -r j dark |, where i and j vary from 1 to100 and denote resampled dataset numbers, ∆r i,j depicts the distance separating the Cα coordinates of datasets i and j, and r i ∆t and r j dark are the refined coordinates obtained from the photo-activated or dark structures, respectively. A second order Taylor series expansion was then used to estimate the mean and error associated with the ratio Δr ij ∆t,dark /Δr ij dark,dark arising from coordinate variations within each set of 100 structural refinements. This expansion leads to the expression:

Error weighted mean ratio = <Δr ij state,dark >/<Δr ij dark,dark > -var(Δr ij dark,dark ) × <Δr ij state,dark > / <Δr ij dark,dark > 3 + cov(Δr ij state,dark , Δr ij dark,dark ) / <Δr ij dark,dark > 2

where <X> is the mean of the set X, var(X) is the variance of the set X, and cov(X,Y) is the covariance of two sets X and Y. The resulting error weighted mean ratios are represented in Fig. 4A to 4C and Extended Data Fig. 7 in which movements are coloured from grey (movements ≤ 80 % of the maximum ratio) to red (movements ≥ 95 % of the maximum ratio).

Full occupancy structural refinement avoided systematic bias in this analysis arising from partial occupancy structural refinement with a single dark-conformation held fixed, but at the cost of underestimating the magnitude of light-induced conformational changes. Despite this limitation, this analysis extracted recurring structural motions that evolve with time (Fig. 4a-c and Extended Data Fig. 7, Supplementary Video 3) and in a manner that is both consistent with the known time-scales of the electron transfer reactions (Fig. 1) and theoretical predictions (Fig. 4d-f, Supplementary Video 4).

Tests of the statistical significance of recurring difference electron density features

For each of the seven experimental difference Fourier electron density maps (∆t = 1 ps, 5 ps (data set a), 5 ps (data set b), 20 ps, 300 ps (data set b), 300 ps (data set a), 8 µs) a lowerpedestal of 3.0 σ was applied such that all electron density with an amplitude < 3.0 σ was set to zero. Both positive and negative difference electron densities were then integrated within a 4.5 Å radius sphere about a chosen coordinate (Extended Data Fig. 3j) as described for the analysis of TR-SFX data recorded from bacteriorhodopsin. [START_REF] Wickstrand | A tool for visualizing protein motions in time-resolved crystallography[END_REF] These positive (A+) and negative (A-) integrated difference electron density amplitudes were merged to yield a single amplitude according to: A(r) = ((A+) 2 +(A-) 2 ) ½ about the centre of integration r. The results of this analysis are presented in Fig. 2f where six centres of integration, r, are chosen as: the centre of the BPh M ring; the magnesium atom of BCh M ; the mid-point between the two magnesium atoms of the two SP bacteriochlorophylls; the magnesium atom of BCh L ; the centre of the BPh L ring; and the centre of the ketone containing six-carbon ring of menaquinone Q A .

For tests of statistical significance (Extended Data Table 3), this set was complemented by the addition of amplitudes extracted by integration about the iron atoms of haem 1 , hame 2 , haem 3 and haem 4 to create a set of ten amplitudes for each of the seven time points: 3 and show that, when a threshold of p ≤ 0.001 is applied, the difference electron density amplitudes associated with the SP cannot be ascribed to noise. When a threshold of p ≤ 0.0125 is applied and the last three time-points (∆t = 300 ps (a), 300 ps (b), 8 µs) are examined as a set, the difference electron density amplitudes associated with the SP, BCh L and Q A cannot be ascribed to noise.

[A(BPh M ), A(BCh M ), A(SP), A(BCh L ), A(BPh L ), A(Q A ),A(H 1 ),A(H 2 ),A(H 3 ),A(H 4 )] ∆t
Conversely, the set of difference electron density amplitudes associated with most other cofactors, as well as all sets of difference electron density amplitudes generated from noise-only maps, are indistinguishable from noise according to the results of this two sample t-test (Extended Data Table 3).

QM/MM Geometry optimizations

Initial coordinates were taken from PDB databank entry 5O4C and missing residues and cofactor segments were retrieved from PDB entry 1PRC. [START_REF] Deisenhofer | Crystallographic refinement at 2.3 A resolution and refined model of the photosynthetic reaction centre from Rhodopseudomonas viridis[END_REF] Protonation states of residues were chosen based on their reference pK a values and structural criteria such as hydrogen bond interactions. After the addition of protons to the structure, a 200 step steepest descent geometry optimization was performed with Gromacs 4.5 [START_REF] Pronk | GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit[END_REF] to relax these coordinates. During this optimization the positions of the heavy atoms were constrained to their positions in the xray structure. As in previous work, the interactions were modelled with the Amber03 forcefield. [START_REF] Duan | A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations[END_REF][START_REF] Ceccarelli | An ab initio force field for the cofactors of bacterial photosynthesis[END_REF] Non-bonded Coulomb and Lennard-Jones interactions were evaluated without periodic boundary conditions (PBC) and using infinite cut-offs.

After relaxing hydrogens with molecular mechanics (MM) optimization, we performed several Quantum Mechanics (QM)/MM geometry optimizations of all atoms in the reaction centre, using the interface between the TeraChem quantum chemistry package [START_REF] Ufimtsev | Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics[END_REF][START_REF] Titov | Generating Efficient Quantum Chemistry Codes for Novel Architectures[END_REF] and Gromacs 4.5. [START_REF] Pronk | GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit[END_REF] These optimizations were also performed without PBC and with infinite cutoffs for the Coulomb and Lennard-Jones interactions. The QM subsystems (Extended Data Fig. 6a-c) were modelled with unrestricted DFT. In these DFT calculation we used the PBE0 functional [START_REF] Adamo | Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model[END_REF] in combination with the LANL2DZ basis set. [START_REF] Dunning | Methods of Electronic Structure Theory[END_REF] Empirical corrections to dispersion energies and interactions were introduced with Grimme's DFT-D3 model. 70 The remainder of the protein, including crystal water molecules, was modelled with the Amber03 force-field, [START_REF] Duan | A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations[END_REF][START_REF] Ceccarelli | An ab initio force field for the cofactors of bacterial photosynthesis[END_REF] in combination with the TIP3P water model. [START_REF] Jorgensen | Comparison of simple potential functions for simulating liquid water[END_REF] We searched for minimumenergy geometries in all relevant oxidation states of the system using the limited-memory Broyden-Fletcher-Goldfard-Shannon quasi-Newton optimization algorithm.

The goal of these optimization steps was to characterize the structural relaxation of the protein in response to changes in the electronic states of the cofactors along the A-branch of the photo-induced electron transfer process. We therefore examined the following electronic configurations:

i. All cofactors in their resting states: SP 0 , BPh L 0 , Q A 0 ii. Special pair photo-excited, other cofactors in resting state: SP*, BPh L 0 , Q A 0 iii. Special pair photo-oxidized, BPh L reduced: SP +1 , BPh L -1 , Q A 0 iv. Special pair photo-oxidized, Q A reduced: SP +1 , BPh L 0 , Q A -1

Since including all co-factors into one large QM-region is computationally too demanding, we performed the optimizations with a different QM subsystem for each co-factor, including nearest residues, in all relevant electronic states. The structural response to the change in electronic state (Fig. 4d-f) was obtained by comparing the optimized geometries and potential energies in the various oxidation states.

To quantify the effect of photo-absorption by the special pair (SP, i to ii) we first optimized the resting state with the SP plus nearby residues in the QM region (Extended Data Fig. 6a), described at the PBE0/LANL2DZ level of theory plus D3 dispersion corrections. This structure was used as a reference for the optimized structures in the excited state (SP*, ii) and after photo-oxidation (SP +1 , iii). Using the same QM/MM subdivision, we optimized the system in the first singlet excited state (S 1 ) by switching the QM description to the Timedependent DFT within the Tamm-Dancoff approximation, [START_REF] Hirata | Time-Dependent Density Functional Theory within the Tamm-Dancoff Approximation[END_REF] and in the photo-oxidized state by switching the spin state of the electronic wave function to the lowest energy doublet state (D 0 ). In the QM/MM optimization of the D 0 state of the SP, we modelled the BPh L with point charges representing the reduced state of that co-factor. Only very modest protein structural changes were associated with the optimized geometries with the SP in the S 1 and D 0 relative to the reference structure in the resting state (S 0 ). Likewise, we also optimized the geometry of the protein with the BPh L and nearby residues in the QM region (Extended Data Fig. 6d) in both the lowest energy singlet (S 0 , i) and doublet (D 0 , reduced, iii) states. In the optimization of the D 0 state of BPh L , the partial charges on the SP were changed to reflect its photo-to adding the electron increases the affinity further by 24 kJ.mol -1 , so that the energy difference between the neutral reactant minimum on the one hand and the reduced product minimum is 188.5 kJ.mol -1 (adiabatic electron affinity, AEA) on the other hand. The calculated AEA is in good agreement with results from previous computations, [START_REF] Hasegawa | Energetics of the Electron Transfer from Bacteriopheophytin to Ubiquinone in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis: Theoretical Study[END_REF] but is an overestimation with respect to the experimental value for the related 1,4-naphthoquinone (175 kJ.mol -1 ). [START_REF] Heinis | Electron Affinities of Benzo-, Naphtho-, and Anthraquinones Determined from Gas-Phase Equilibria Measurements[END_REF] Inside the protein environment, the VEA is much higher (258 kJ.mol -1 ), part of which we attribute to the electrostatic interaction between the reduced Q A co-factor with the positively charged Fe 2+ ligand site. Structural relaxation of both the Q A cofactor and the protein environment increases the electron affinity by 60 kJ.mol -1 to yield an AEA of 318 kJ.mol -1 . Thus, the results of the computations suggest that the structural response of the protein adds another 36 kJ.mol -1 to the intrinsic relaxation energy of Q A (24 kJ.mol -1 in vacuum) as concluded in earlier computations. [START_REF] Hasegawa | Energetics of the Electron Transfer from Bacteriopheophytin to Ubiquinone in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis: Theoretical Study[END_REF] We note that in this analysis we focussed only on the effect of the structural response on the affinity of Q A . To estimate the total reaction energy associated with the photo-induced electron transfer process from the SP to Q A , we also need the absolute energies of the neutral, photo-excited and oxidized states of the SP as well as the neutral and reduced states of BPh L . However, since these energies were not computed with identical QM/MM setups, we do not provide an accurate estimate here.

EXTENDED DATA

  to observe lightinduced structural changes in the photosynthetic reaction centre of Blastochloris viridis on a time-scale of picoseconds. Structural perturbations are first centred upon the protein's special pair of chlorophyll molecules that are photo-oxidized by light. Electron transfer to the menaquinone acceptor on the opposite side of the membrane induces a movement of this cofactor in concert with lower amplitude protein rearrangements. These observations reveal how proteins utilize conformational dynamics to stabilize the charge separation steps of electron transfer reactions.

  to explicitly incorporate protein structural changes. Electron transfer reactions are ubiquitous in nature and therefore a more nuanced understanding of the interplay between protein structural dynamics and the movement of electrons has far-reaching biochemical significance. LeBard, D. N., Martin, D. R., Lin, S., Woodbury, N. W. & Matyushov, D. V. Protein dynamics to optimize and control bacterial photosynthesis. Chem. Sci. 4, 4127-4136 (2013).

Figure 1 :

 1 Figure 1: Electron transfer steps of the photosynthetic reaction centre of Bl. viridis. Cartoon representation of the H, L, M and C subunits. Cofactors are shown in black including the special pair of bacteriochlorophylls (SP), two monomeric bacteriochlorophylls (BCh), two bacteriopheophytins (BPh), a tightly bound menaquinone (Q A ), a mobile ubiquinone (Q B ), a non-haem iron (Fe 2+ ) and four haems. The approximate boundaries of the membrane are suggested in blue. The electron transfer pathway: SP  BPh L  Q A is referred to as the Abranch. Approximate timescales for the first two electron transfer events, from SP to BPh L and from BPh L to Q A , are depicted.

Figure 2 :

 2 Figure 2: Light-induced electron density changes in RC vir at the site of photo-oxidation. a, Experimental F obs light -F obs dark difference Fourier electron density map for ∆t = 1 ps. b, Difference Fourier electron density map for ∆t = 5 ps (data set a). c, Difference Fourier electron density map for ∆t = 20 ps. d, Difference Fourier electron density map for ∆t = 300 ps (data set a). e, Principal component from SVD analysis of all seven experimental difference Fourier electron density maps. All maps are contoured at ± 3.2 σ (blue, positive difference electron density; gold, negative difference electron density; σ is the root mean square electron density of the map). f, Relative amplitudes of difference electron density features integrated within a 4.5 Å sphere 20 centred upon the RC vir co-factors (Extended Data Fig. 3j). The colour bars represent: cyan, ∆t = 1 ps; blue, ∆t = 5 ps a and b (in that order); purple, ∆t = 20 ps; red, ∆t = 300 ps b and a (in that order); mustard, ∆t = 8 µs.

Figure 3 :

 3 Figure 3: Light-induced electron density changes in RC vir within the menaquinone binding pocket. a, Experimental F obs light -F obs dark difference Fourier electron density map for ∆t = 5 ps (data set a). b, Difference Fourier electron density map for ∆t = 300 ps (data set a). c, Principal component from SVD analysis of the first four experimental difference Fourier electron density maps (∆t = 1ps, 5 ps (a), 5 ps (b), 20 ps). d, Principal component from SVD analysis of the final three experimental difference Fourier electron density maps (∆t = 300 ps (a), 300 ps (b), 8 µs). All maps are contoured at ± 3.0 σ (blue, positive difference electron density; gold, negative difference electron density). e, Difference Fourier electron density map for ∆t = 300 ps (data set a) showing the protein immediately surrounding Q A and contoured at ± 3.5 σ. f, Superposition of the refined structures for the dark structure (yellow, Q A in black) and ∆t = 300 ps (purple structure).

Figure 4 :

 4 Figure 4: Structural response of RC vir to electron transfer events. a, Recurring movements of Cα atoms for ∆t = 1 ps quantified by full occupancy structural refinement against 100 randomly resampled TR-SFX data sets. b, Recurring movements of Cα atoms for ∆t = 5 ps (a) using the same representation. c, Recurring movements of Cα atoms for ∆t = 300 ps (a) using the same representation. Recurring movements are represented as error weighted mean ratios relative to 100 control structural refinements (Methods) coloured from grey (< 80 % of the maximum error weighted mean ratio) to red (≥ 95 % of the maximum error weighted mean ratio). An identical representation is given for all time points in Extended Data Fig. 7. d, Movements of Cα atoms estimated from QM/MM energy minimization calculations associated with the SP photo-excited and all other cofactors in resting state: SP*:BPh L 0 :Q A 0

  of the LCLS XFEL during beamtime awarded in April 2015 (run a) and June 2016 (run b). Diffraction data were recorded on a Cornell-SLAC Pixel Array detector 35 . The X-ray wavelengths and equivalent pulse energies were 1.89 Å (6.56 keV) in 2015 and 1.31 Å (9.49 keV) in 2016. An X-ray pulse duration of 36 fs was used in 2015 and 45 fs in 2016. The XFEL beam was focused to a 3 μm 2 spot for both experiments. The detector was located 89 mm from the microjet in 2015 and 145 mm from the microjet in 2016. Diffraction data were collected at a repetition rate of 120 Hz from microcrystals that were not exposed to any optical laser pump (dark-state) and for five time points corresponding to Δt = 1ps, 5 ps, 20 ps, 300 ps and 8 µs after photoexcitation. The time points Δt = 5 ps and 300 ps were repeated in both 2015 and 2016 and are referred to as data sets a and b respectively.

  windows. When applying SVD we evaluate the expression [U,Σ,V] = SVD(A), where A is a matrix of n difference Fourier electron density maps containing m elements; U is an n × n unitary matrix; Σ is an n × m rectangular matrix containing n diagonal elements (the singular values) arranged in decreasing order and all other matrix elements are zero; and the first right singular vector (the first row of the matrix V) is referred to as the principal component.Results from SVD analysis of all seven electron density maps are presented in Fig.2eand Extended Data Fig.3l,m. Results from SVD analysis deriving from the first four time-points (∆t = 1 ps, 5 ps a and b, 20 ps) and the last three time-points (∆t = 300 ps a and b, 8 µs) are shown in Fig.3c,d; Extended Data Fig.3h,i; Extended Data Fig.5h,i; Supplementary Videos 1 and 2. This separation of the maps is motivated by the fact that photo-activated RC vir molecules have menaquinone oxidized for the first sub-set of time-points yet most menaquinone molecules of photo-activated RC vir are reduced for the second sub-set of timepoints.

arranged as a 10

 10 × 7 element matrix. Control "noise only" |F obs | dark -|F obs | dark isomorphous difference Fourier electron density maps were calculated by first selecting sixteen resampled data-sets from the set of 100 generated from the 2015 RC vir dark data, and sixteen resampled data-sets from the set of 100 generated from the 2016 RC vir dark data. Eight |F obs | dark -|F obs | darkisomorphous difference Fourier electron density maps were then calculated by pair-wise comparisons between the sixteen resampled data-sets of the 2015 data, and another eight difference Fourier electron density maps were calculated by pairwise-comparisons of the sixteen resampled data-sets of the 2016 data. Seven control difference Fourier electron density maps were then randomly selected from the set of sixteen "noise-only" maps, difference electron density values with an amplitude lower than 3σ were set to zero, and a set of [A(r,dark-dark)] were created by integrating the remaining difference electron density within a 4.5 Å radius sphere centred upon the RC vir cofactors as described above. A two-sample ttest was then performed in MATLAB to determine if the set of seven time-dependent amplitudes [A(r,∆t)] and the set of seven "noise-only" amplitudes [A(r,dark-dark)] were indistinguishable from one another (the null hypothesis). The t-tests were then repeated 1000 times by randomly selecting a different combination of seven control amplitudes [A(r,darkdark)] from the sixteen "noise-only" difference Fourier electron density maps calculated above (of 16!/(9!×7!) = 11440 possible different combinations of the 16 control maps). The results of this analysis are summarized in Extended Data Table

LEGENDS Extended Data Figure 1 : 42 Extended Data Figure 2 :Extended Data Figure 3 :Extended Data Figure 4 :Extended Data Figure 5 :Figure 3 :

 14223453 photo-oxidation. Experimental F obs light -F obs dark isomorphous difference Fourier electron density maps for the time-points: a, ∆t = 1 ps. b, ∆t = 5 ps (data set a); c, ∆t = 5 ps (data set b). d, ∆t = 20 ps; e, ∆t = 300 ps (data set b); f, ∆t = 300 ps (data set a); g, ∆t = 8 µs. h-i, Principal component from SVD analysis of difference Fourier electron density maps for: h, the first four time-points, ∆t = 1ps, 5 ps (data set a), 5 ps (data set b) and 20 ps; i, the final three time-points, ∆t = 300 ps (data set a), 300 ps (data set b) and 8 µs. All maps are contoured at ± 3.2 σ (blue, positive difference electron density; gold, negative difference electron density). Peak heights listed in Table 2 are marked with coloured circles in panels h and i. j, Representation of a sphere of radius 4.5 Å used to integrate difference electron density above a pedestal of 3.0 σ as described in reference 20 . Positive difference density amplitudes (A+) and negative difference density amplitudes (A-) were merged according to ((A+) 2 +(A-) 2 ) ½ and are displayed in Fig. 2f. These integrated difference electron density values are also used in the statistical analyses presented in Extended Data Table 2. k, Simulated difference Fourier electron density maps near the SP calculated from the refined structure for ∆t = 20 ps versus the refined resting state structure. Data are cut at 2.8 Å resolution for comparison with experimental data. The simulated map is contoured at ± 12.0 σ. l, Relative magnitude of the singular values resulting from SVD analysis of the difference Fourier electron density maps for all seven time-points. m, First (blue) and second (red) columns of the unitary matrix U resulting from SVD analysis of all seven time-points weighted according to their corresponding singular values. The first right singular vector (the principal SVD component) makes a significant and positive contribution to all time-points. In

Δt = 5 Figure 4 :

 54 Figure 4: Dods et al.

  2 PO 4 /Na 2 HPO 4 , pH 6.8) set up against a 1 ml reservoir of 2 M ammonium sulphate. Large crystals grew at 4 °C in 3 days. Crystals were harvested by pipette and crushed mechanically to create a seed stock by vortexing with seed beads for approximately 20 min with occasional cooling on ice[START_REF] Dods | From Macrocrystals to Microcrystals: A Strategy for Membrane Protein Serial Crystallography[END_REF] . For the XFEL experiment in April 2015 (run a) new 18.5 µl sitting drop vapour diffusion crystallization drops were set up in order to yield large numbers of micro-crystals. In these experiments the protein concentration was 8.5 mg.ml -1 and a protein:precipitant concentration of 10:7.5 was used in the drops. 1 µl of undiluted crystal seed stock was spiked into the drops for a final v/v concentration of 5.4 %. Crystallization drops were then mixed by pipette and

	min in
	a Ti45 rotor. Membranes were homogenized in 20 mM Tris-HCl, pH 8.5 and diluted to
	OD 1012 = 10. Membranes were then solubilized in 4 % lauryldimehtylamine-N-oxide (LDAO)

for 3 hours at room temperature. Unsolubilized membranes were removed by ultracentrifugation at 45000 rpm for 75 min in a Ti70 rotor. RC vir protein was purified by loading the supernatant onto a 250 ml POROS 50-μm HQ ion-exchange medium equilibrated with wash buffer (20 mM Tris-HCl, pH 8.5, 1% LDAO). The column was washed with 2 l of wash buffer with 5 % elution buffer (20 mM Tris-HCL, pH 8.5, 1 M NaCl, 1 % LDAO) and eluted with an increasing concentration of elution buffer over 20 column volumes. Fractions with an A 280 /A 830 < 3.5 were pooled and concentrated in 100 kDa MW cut off concentration tubes (Vivaspin) to a volume of 10 ml. This was loaded in 5ml batches onto a HiPrep 26/60 Sephacryl S-300 column (GE) equilibrated with SE buffer (20 mM Tris-HCl, pH 8.5, 100 mM NaCl, 0.1 % LDAO) and eluted into 1.8 ml fractions. Fractions with an A 280 /A 830 < 2.6 were pooled and concentrated, followed by a 20-fold dilution in final protein buffer (20mM NaH 2 PO 4 /Na 2 HPO 4 , pH 6.8, 0.1 % LDAO, 10 μM EDTA) and then concentrated again to 20 mg.ml -1 . Samples were flash-frozen in liquid nitrogen and stored at -80 °C.

Protein crystallization 20 µl sitting drops were set up with a 1:1 ratio of protein solution (10 mg.ml -1 ) and precipitant solution (3.6 M ammonium sulphate, 6 % heptane-1,2,3-triol, 20 mM NaH covered with a glass cover slide. Rod-like crystals grew over 5 days at 4 °C and were 10 -20 µm in the longest dimension. Microcrystals for the experiment in June 2016 (run b) were prepared as above, but with an additional round of microseeding using crushed microcrystals

Acknowledgements

Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Parts of the

sample delivery system used at LCLS for this research was funded by the NIH grant P41GM103393, formerly P41RR001209. Complementary studies were performed at BL3 of SACLA with the approval of the Japan Synchrotron Radiation Research Institute (JASRI, proposal number 2018B8068). RN acknowledges funding from the European Commission Marie Curie Training Networks (X-Probe, NanoMem), the European Union's Horizon 2020 research and innovation programme (grant agreement No. 789030) and the Swedish Research Council (grant No. 2015-00560 and 349-2011-6485), the Swedish Foundation for Strategic Research (grant SRL10-0036), and the Knut and Alice Wallenberg Foundation (grant KAW 2012.0284, KAW 2012.0275 and KAW 2014.0275). GB acknowledges funding from the Swedish Research Council (grant 2017-06734) and the Swedish Foundation for Strategic Research (grant ID17-0060). GG and HLL acknowledge funding from the Academy of Finland (grants 290677 and 304455), the BioExcel CoE project funded by the European Union contracts H2020-INFRAEDI-02-2018-823830 and H2020-EINFRA-2015-1-675728, and the CSC-IT centre in Espoo for access to computing resources. R.N. wishes to thank Professors Neal Woodbury for discussions.

Code Availability

Software used for SVD analysis is available at https://github.com/Neutze-lab/SVD. Code written in MATLAB to analyse difference electron density amplitudes is available at Data Availability Atomic coordinates and structure factors have been deposited in the Protein Data Bank, www.pdb.org. PDB ID codes are the following: 5O4C the dark-conformation (a); 5NJ4 the dark conformation (b); 6ZHW the time-point Δt = 1 ps; 6ZI4 the time-point Δt = 5 ps (a); 6ZID the time-point Δt = 5 ps (b); 6ZI6 the time-point Δt = 20 ps; 6ZI5 the time-point Δt = 300 ps (a); 6ZI9 the time-point Δt = 300 ps (b); 6ZIA the time-point Δt =8 µs. Difference Fourier electron density maps and stream files containing X-ray diffraction intensities are deposited at the CXI database (http://www.cxidb.org/) with identification number ID 161.

Extended Data is available for this manuscript.

Supplementary Information is available for this manuscript.

Author Information

These authors contributed equally: Robert Dods, Petra Båth.

Competing Interests

The authors declare no competing interests. oxidized (D 0 , SP +1 ) state. Again the structural response is rather minor, as the geometries are very similar (Extended Data Fig. 6e).

In the next step of the electron transfer process, the electron transfers from BPh L to Q A (iv).

We optimized the protein with Q A plus its immediate environment, including the non-heme Fe 2+ site, in the QM region. The optimized structures in the resting and reduced states are compared in Extended Data Fig. 6f. Reduction of Q A from menaquinone to (deprotonated) semiquinone induces significant structural changes in the Q A binding pocket. In line with the difference densities observed at 300 ps after photo-excitation, the hydrogen bond between the Q A carbonyl and His217 M reduces by 0.17 Å. We suggest that the reduction of this hydrogen bond helps stabilizing the negative charge on the Q A .

To quantify the overall structural response to the electron transfers, we computed the displacements of the atoms in the various states (ii-iv) with respect to the structure of resting state (i) and recorded these displacements as B-factors to the pdb coordinate file of the resting state. Because only one co-factor was included in the QM region of our QM/MM optimizations, we summed up the displacements of both QM/MM optimizations of each redox state. Fig. 4d-f represents these displacements as colours.

Stabilization energies

To estimate the energetic effects of the protein structural changes on the electron transfer process, we computed the adiabatic and vertical electron affinities for Q A in isolation and in the optimized QM/MM protein models. These energies are shown schematically in Extended Data Fig. 6g,h. For the neutral Q A in vacuum, the electron affinity without structural relaxation is 164.5 kJ.mol -1 (vertical electron affinity, VEA). Structural relaxation in response electron affinities (AEA) and relaxation energies E r were computed at the PBE0-D3/LANL2DZ level of DFT for isolated Q A and at the PBE0-D3/LANL2DZ/Amber03 QM/MM level for Q A within the protein.

Extended Data

FOOTNOTES TO EXTENDED DATA TABLES Extended Data Table 1: Crystallographic data and refinement statistics

Footnotes to Extended Data Table 1

Values in parenthesis is those of the highest resolution shell.

£ Ratio of the number of indexed images to the total number of images.

Extended Data Table 2: Difference Fourier electron density peak amplitudes

Footnotes to Extended Data Table 2 *Positive and negative difference electron density peaks are marked on Extended data Figs.

3h, 3i and 5i. Difference electron density values were read out manually in COOT.

Amplitudes < 2.4 σ are not shown.

Extended Data Table 3: Two sample t-tests of integrated electron density amplitudes

Footnotes to Extended Data Table 3 *Mean σ/sphere represents the root-mean-square of the difference electron density above and below a threshold of ± 3.0 σ within a sphere of radius 4.5 Å centred on the Mg 2+ atoms of the BChs; the Fe atoms of the haems; and ring centres of the menaquinone and BPhe cofactors.

All values are scaled relative to a mean value for SP = 1. † The number of elements in each sampled set of the two-sample t-test. ‡ Difference electron density associated with haem 3 gave the lowest mean σ/sphere (0. $ The hypothesis that the two sets of the t-test are indistinguishable is either true (0) or false

(1) at the specified confidence level. § Features identified as distinguishable from noise with a degree of confidence defined by the given p-value.