Ultrafast Kβ X-ray emission spectroscopy

The Kβ XES spectrum of 3d transition metal ions is sensitive to the effective 3d spin moment due to the strong exchange interaction between the unpaired 3d electrons and the one unpaired 3p electron in the final state created by the X-ray emission process (Fig. 2a)^24,25. These attributes have been used to follow the femtosecond dynamics of charge transfer and intersystem crossing in transition metal complexes²⁰.

Fig. 2

Time evolution of Fe Kβ X-ray emission difference spectra.

a Area-normalized Kβ X-ray emission spectroscopy (XES) references from Kjaer et al.²⁰. Singlet ([Fe(2,2’-bipyridine)₃]²⁺, blue), doublet ([Fe(2,2′-bipyridine)₃]³⁺, red), triplet (Fe(II)phthalocyanine, orange), quartet (Fe(III)phthalocyanine chloride, purple), quintet ([Fe(phenanthroline)₂(NCS)₂], green)-. b Two-dimensional map of cytochrome c Kβ XES difference signal. c Difference spectra at various time delays. d Time-dependence for Kβ X-ray emission energies indicated by dashed vertical lines in c. Error bars reflect the standard deviation of the signal within a range of 7 detector pixels around these energies.

This Kβ XES study extends the work of Mara et al.⁸ by investigating the potential role of electronic ES populated between the optically generated ¹π−π* state and the quintet metal-centered (⁵MC) state observed for time delays beyond 600 fs. Given the minimal involvement of the Fe electronic structure in the ¹π−π* state, we do not expect an appreciable difference signal. Consequently, the appearance of a time-dependent difference signal distinct from the ⁵MC state provides evidence for additional states involved in the ES relaxation dynamics. Shown in Fig. 2b–d is the difference signal during the first 850 fs after excitation. The spectral shape of the difference signal we observe for the early delay times (Fig. 2c) is clearly distinct from the difference signal at later delay times and strongly indicates the presence of a short-lived ES distinct from the ¹π−π* and ⁵MC ES. As the reference spectra for different spin configurations shown in Fig. 2a demonstrate, the delayed appearance of a negative difference signal at 7054 eV compared to 7058 eV, shown in Fig. 2d, indicates that this intermediate state has either a doublet, triplet or quartet configuration.

Performing a detailed analysis of this observation by using the approaches described in Supplementary Note 1, we confirm the presence of a short-lived intermediate in the relaxation mechanism and assign it to a triplet metal-centered (³MC) state. We then use the reference spectra shown in Fig. 2a to fit the time-resolved XES difference spectra using a rate equation model (Fig. 3). Our Kβ XES measurement does not have a spectroscopic signature for the ¹π−π* ES, so we use the exponential lifetime of 145 ± 5 fs measured by Bräm et al. for the ¹π−π* ES¹³. We use the 5.9 ps exponential lifetime for the ⁵MC state measured by Mara et al.⁸, leaving the lifetime of the intermediate state, the FWHM and time zero of the experimental response function, as well as the excitation yield as the free parameters in the analysis. The best fit gives an instrument response function FWHM of 118 ± 61 fs. The ³MC lifetime is fitted to 87 ± 51 fs and the excitation yield is fitted to 74 ± 2%. Despite the high excitation yield, we have been able to demonstrate the observed dynamics conform to those measured at lower excitation fluences, where a direct comparison can be made. Supplementary Note 2 has a detailed discussion of the power dependence. Fit results are summarized in Supplementary Tables 1–2.

Fig. 3

Population analysis from Fe Kβ X-ray emission spectroscopy.

a Experimental Kβ X-ray emission difference signal. b Best fit using a model with a triplet intermediate state. c Fit residual. d Resulting time-dependent populations for the ¹π−π*, ³MC and ⁵MC states and the ground state (¹GS). The ¹π−π* and ⁵MC lifetimes were fixed to 145 fs and 5.9 ps, respectively. Fitted time constants are 118 ± 61 fs for the instrument response function FWHM and 87 ± 51 fs for the ³MC lifetime.

A variety of potential intermediate electronic ES have been invoked in axial ligand photodissociation mechanisms for heme proteins. Both LMCT and MLCT states have been proposed to be involved. LMCT would produce low-spin Fe(I) and MLCT would produce low-spin Fe(III), both of which would be Fe spin doublets. Franzen et al. have proposed the first electronic ES transition for CO hemoglobin involves electron transfer from the occupied d_π (d_xz, d_yz) orbital to the porphyrin π orbital vacated in the optically generated electronic ES¹¹. This ES should also be energetically accessible in cyt c, but should not initiate dissociation of the Fe–S bond. Bräm et al.¹³ have proposed the ¹π−π* ES decays through an electron transfer from the π* ES to the unoccupied $$ d_{{\mathrm{z}}^2}$$ orbital to create an Fe(I) ion. This orbital has antibonding σ* character consistent with the Fe–S dissociation, but pulse radiolysis measurements show the porphyrin ring will be reduced, rather than the iron atom in ferrous cyt c¹⁵, making ¹π−π* relaxation to a LMCT state energetically inaccessible.

Theoretical studies of the photodissociation mechanism in CO-bound myoglobin also provide useful insight into the potential mechanism for Fe(II)–S photodissociation in cyt c. In computational studies, Waleh and Loew propose that Fe(II)–CO dissociation involves excitation of an electron from the d_π (d_xz, d_yz) orbital to the $$ d_{{\mathrm{z}}^2}$$ orbital²⁶. This study does not make clear the mechanism for populating such a $$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$ configuration but they conclude from their calculated ES energies that the transition can be directly assigned to a ¹[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] (¹MC) state and does not require intersystem crossing to a ³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] (³MC) state²⁶. Similar conclusions have been drawn in the theoretical study by Falahati et al. with the additional complication of significant configuration interaction between the ¹π−π* and the ¹[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] metal-centered ES²⁷.

Using these prior studies of heme protein photodissociation and the constraints imposed by the ultrafast Kβ XES measurement, we conclude that we have observed the involvement of a³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] state in the Fe(II)–S bond dissociation. Since Kβ XES cannot distinguish between the ³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] and ³[$$ d_{\pi }^3{d}_{{\mathrm{x}}^2-{\mathrm{y}}^2}^1$$] states, the choice of the ³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] state and its importance to bond dissociation will be made clearer in the following sections. The XES measurement leaves the ³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] formation mechanism unclear. Most likely, sequential MLCT and LMCT electron transfers, with one involving an intersystem crossing, would result in the formation of the ³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] ES. A Förster energy transfer mechanism dictating the lifetime of the ¹π−π* ES seems unlikely because the ¹[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] metal-centered ES has minimal oscillator strength due to symmetry selection rules.

Ultrafast X-ray solution scattering

Figure 4a shows the transient XSS signal ΔS for scattering vectors Q in the range 0.2–3.3 Å⁻¹ and pump-probe time delays up to 600 fs and Fig. 4b shows ΔS for fixed time delays extending to 15 ps. Our analysis focuses on the structural changes occurring during Fe(II)–S bond dissociation. Figure 4a clearly shows a prominent reduction in scattering between 0.4 and 1.1 Å⁻¹ induced by photoexcitation that develops a characteristic shape and maximum amplitude faster than the rise in the quintet state population (Fig. 4c, blue and red curves) and faster than the 700 fs time constant estimated for the appearance of global protein structural changes based on the 14 Å cyt c radius of gyration²⁸ and strain wave propagation velocity of ~20 Å·ps⁻¹ measured by Levantino et al.²³. As shown in Supplementary Note 3, this difference signal shows negligible time-dependent changes in shape and decays with a 5.2 ± 1.0 ps lifetime, similar to the 5.9 ps time constant for Fe(II)–S bond reformation extracted from the XES measurement⁸. These observations support the assignment of the difference signal in this Q-range primarily to local structural changes associated with Fe-axial coordination, which has informed our structural modeling of the XSS signal.

Fig. 4

Modeling of the X-ray solution scattering difference signal.

a X-ray solution scattering (XSS) difference signal of ferrous cytochrome c. b XSS difference signal at different time delays. Black lines represent structural fits for the 0.1/0.2 ps curves as described in the text and the scaled bulk water heat differential for the 15 ps curve. c Time-dependence at Q-values indicated by dashed lines in b. Black lines represent the ¹π−π* (dashed), ³MC (dotted) and ⁵MC (solid) populations derived from the Kβ X-ray emission spectroscopy measurement (see Fig. 3). All curves are peak normalized for comparison. d Local structural changes are parameterized via Met80 rotation and His18 translation as illustrated by the black arrows. e Time evolution of the Fe–S(Met80) and Fe-N(His18) distances. The width of the time bins has been further increased by a factor of 5 with respect to the data shown in a and c. Errors are estimated for each original time bin assuming 15% uncertainty in sample concentration, 5% uncertainty in the excitation yield and a small discretization error from the fit procedure, then propagated to obtain the errors for the larger time bins. Horizontal dashed lines represent ground state values of the Fe–S(Met80) and Fe-N(His18) bond distances.

Starting with a ferrous cyt c solution structure²⁹, we use a model for the ultrafast nuclear dynamics that only considers specific structural motions focused on changes in the axial ligand positions while neglecting other structural changes at the heme and global protein structural relaxation. Such a model reflects the antibonding nature of the ³[$$ d_{\pi }^3{d}_{{\mathrm{z}}^2}^1$$] ES with respect to the axial ligands and minimizes the number of structural parameters, thus respecting the limited information content of XSS difference scattering curves^30,31. The structural analysis here is constrained to the first 300 fs during which the axial bonding changes significantly, and changes in structure occurring at larger length scales unaddressed by our model will be of lesser importance. Based on previous structural studies of cyt c^8,32, the simulated scattering signal is modeled as a linear combination of the protein signal arising from structural changes at the heme and the water heating signal³⁰. The heme structural changes are parameterized using the positions of Met80 and His18 residues (Fig. 4d). A more detailed discussion of the model implementation and limitations can be found in Supplementary Note 4. Systematic modifications of these structural parameters clearly demonstrate that the negative difference signal seen between 0.4 and 1.1 Å⁻¹ requires significant elongation of both the Fe-Met80 and the Fe-His18 bond lengths. Figure 4b shows a comparison between fits of our model and the measured data at selected time delays. Molecular dynamics (MD) calculations of CO photolysis from myoglobin also show a reduction in scattering intensity in this Q-range directly associated with Fe–CO bond dissociation, supporting our attribution of this reduction in scattering intensity to Fe-Met80 bond dissociation³¹. Within the constraints of our model, we fit a range of Fe-Met80 and Fe-His18 bond lengths (Fig. 4e). For the first 300 fs, our model qualitatively reproduces the observed XSS difference signal of cyt c without the need to invoke heme doming^19,33. This is consistent with the observed delayed appearance of the ⁵MC state that has been suggested as the primary origin of the doming motion due to the antibonding nature of the singly occupied $$ d_{{\mathrm{x}}^2-{\mathrm{y}}^2}$$ orbital with respect to the Fe(II)-N(Por) bonds^27,34,35. We do observe a delayed rise in the positive peak at Q = 1.265 Å⁻¹ strongly correlated with the rise time for quintet state formation (Fig. 4c, green and solid black curves), but attempts to capture this structural feature with heme doming have not been successful and indicate the Q = 1.265 Å⁻¹ signal results from multiple structural changes. The fitted amplitudes of the Fe-Met80 and Fe-His18 structural parameters depend on how accurately the experimental data are rescaled to reflect a single liquid unit cell. A conservative estimate considering uncertainties in sample concentration (±15%) and excitation yield (±5%) dictates the error bars shown in Fig. 4e. When extending the analysis to 600 fs time delays, the Fe(II)-S distance can be reasonably fit with values between 2.5 Å and 2.7 Å, but not with the ≥3 Å found with the XANES analysis presented by Mara et al.⁸. Since a 300–600 fs doming motion would further increase the Fe(II)-S distance, this difference (discussed in Supplementary Note 4) likely reflects the need for a more detailed model of the structural dynamics including the heme doming motion and related global structural changes after 300 fs⁸. These constraints on the analysis do not weaken the conclusion that the formation of a ³MC ES initiates the Fe–S bond dissociation.

The transient signal prevailing beyond 10 ps exhibits the well-known change in the bulk water structure factor resulting from ultrafast energy transfer and equilibration to an elevated solvent temperature^30,36. The observed energy transfer to the solvent accesses the dynamics of energy transfer and equilibration between the protein and solvent. Mara et al.⁸, supported by the rate of local equilibration found in MD simulations of photoexcited heme proteins³⁷, assumed local thermal equilibrium when analyzing the rate of six-coordinate singlet state reformation in ferrous cyt c, an assumption that has been questioned by Benabbas and Champion³⁸. Here we use temperature-dependent changes in the water structure factor to investigate the time scale for local equilibration between protein and solvent. The structure of the difference scattering in the measured range does not show significant variation beyond 1 ps, though the amplitude of the difference signal does show the expected signal decay with a 5–6 ps time constant associated with the ⁵MC decay and a signal rise with a 7 ps time constant associated with the increasing water temperature (see Supplementary Note 3). This ~7 ps time constant agrees with the ~7 ps time constant used for the local heme temperature by Mara et al.⁸ and is consistent with the rate of energy equilibration found in the MD simulation by Zhang and Straub³⁷. These observations support the conclusion that the structural degrees of freedom contributing to the structure factor in the measured Q-range equilibrate to the five-coordinate quintet state prior to relaxation back to the electronic ground state associated with Met80 rebinding and reformation of the Fe(II)–S bond.

Correlation to calculations

We performed Density functional theory (DFT) calculations to ascertain the electronic structures of the triplet and quintet states involved in ligand photodissociation. We optimized the singlet ground state structure (GSS), and generated triplet and quintet equivalents at this singlet GSS. The triplet state at the GSS contains an additional $$ d_{{\mathrm{z}}^2}$$ electron, promoted from a d_π orbital. The quintet state at the GSS is ~5 kcal/mol higher than the triplet species at the GSS, as it now additionally has the $$ d_{{\mathrm{x}}^2-{\mathrm{y}}^2}$$ orbital singly occupied. To investigate where these triplet and quintet surfaces cross, a series of energy calculations were performed at various elongated Fe-axial bond lengths (Supplementary Note 5, Supplementary Fig. 8). For all calculated Fe-axial bond lengths, the quintet surface remains ~4–6 kcal/mol above the triplet surface, indicating that an additional reaction coordinate is required for crossing between these two states. To determine the crossing point, geometry optimizations on the triplet and quintet structures were performed, beginning from the singlet ground state geometry (Supplementary Note 5, Supplementary Fig. 9). These iterative geometry optimizations led to an energy crossing in very few steps, giving triplet and quintet species with similar geometric but different electronic structures, and eventually leading to optimized, low-lying triplet and quintet species with similar energies above the singlet ground state. It should be noted that the triplet state, both at higher energy in the ground geometry and in the relaxed triplet state, has an empty $$ d_{{\mathrm{x}}^2-{\mathrm{y}}^2}$$ orbital, in contrast to the proposal by Benabbas and Champion³⁸. The triplet and quintet structures at the energy crossing are shown in Fig. 5a. The triplet species exhibits asymmetric equatorial elongation due to the alignment of the d_π hole along the equatorially-trans Fe-N(Por) ligands (Fig. 5b). The ramifications of this are discussed below.

Fig. 5

Schematic of the Fe–S bond dissociation and proposed kinetic model for the electronic states involved in bond photolysis of ferrous cytochrome c.

a Structures are shown of the optimized ground state (1, position indicated in b), triplet state at the crossing point (2, indicated in b), and the optimized quintet state (3). Black arrows indicate structural changes with respect to the GSS. b The vertical orange line represents the photoexcitation process and the black line is the proposed trajectory involving the ¹π–π*, ³MC, and ⁵MC states. The dominant motions on the ³MC and ⁵MC surfaces are indicated and defined as separate axes in c. The middle insert shows that the d_π hole of the triplet in the GSS is aligned along an Fe-N(Por) axis, causing equatorial elongation leading to surface crossing. c 3D scheme of the proposed trajectory. The coordinate X₁ represents axial ligand elongation. X₂ comprises heme core expansion and doming. As in b, the vertical orange line represents the photoexcitation process and the black line is the proposed trajectory through the relevant ES.

Experiment

Solutions of horse heart cyt c were purchased from Sigma–Aldrich and prepared at 3–4 mM in 100 mM, pH 7.2 phosphate buffer. Cyt c was purified by FPLC on a cation exchange column using NaCl as elutant. Purified protein was dialyzed for ~24 h and then concentrated to 3–4 mM, as determined by UV-Vis spectroscopy. Solutions were reduced using sodium dithionite immediately before the experiment. Complete reduction was confirmed by changes in the UV-Vis spectrum (appearance of 520 nm and 550 nm bands, disappearance of 695 nm band). The Kβ XES and XSS data were collected during two different experimental runs at the X-ray Pump Probe (XPP) instrument⁴⁴ at the Linac Coherent Light Source (LCLS). Experimental details for the Kβ XES measurements were previously described in Mara et al.⁸. The sample was flowed through a 100 µm inner diameter capillary to form a ~100 µm diameter cylindrical liquid jet, using an HPLC pump. The sample was optically pumped and probed by 8 keV self-amplified stimulated emission (SASE) X-ray pulses (~10¹² photons/pulse, 120 Hz, 50 fs) shortly after exiting the capillary in the region of laminar flow. The jet was held under helium atmosphere, preventing oxidation to ferric cyt c. Optical excitation was performed nearly collinearly to the X-rays with 50 fs FWHM, 520 nm laser pulses (~20 mJ/cm²) generated by optical parametric amplification of the 800 nm output of a Ti:sapphire regenerative amplifier laser system (Coherent, Legend). The pump laser fluence was determined by a power titration measurement at the beginning of the experiment and chosen to maximize the excited-state fraction while minimizing multiphoton absorption effects. The time delay between the laser and X-ray pulse was determined via the timing tool installed at XPP⁴⁴. The X-ray pulses were focused using Be compound refractive lenses to a 50 µm diameter spot size on the sample jet. A high-energy resolution X-ray emission spectrometer, based on the von Hamos geometry, was used to capture the Fe Kβ XES signal⁴⁵. The spectrometer was equipped with 4 cylindrically bent (0.5 m radius) Ge(620) crystal analyzers and set to cover the Bragg angle range from 78.1° to 80.5° corresponding to an energy range of 7.027 to 7.083 keV. A 140k Cornell-SLAC Pixel Array Detector⁴⁶ (CSPAD, 388 × 370 pixels) collected the Bragg diffracted X-rays. During the second experiment, both the Kβ XES and XSS data were measured simultaneously and the two resulting Kβ XES datasets were temporally aligned (Supplementary Note 6). A similar setup as during the first experiment was used for sample delivery with 3–4 mM solutions of cyt c flowing in a slightly smaller 75 µm diameter cylindrical liquid jet. Optical excitation was performed using the same wavelength and fluence. The Kβ XES data were collected using an ePix100 detector⁴⁶. To detect the XSS data, a 2.3 M CSPAD⁴⁶ was used in forward scattering geometry. Full 2D images of the XES and XSS detectors were read out shot-to-shot and subsequently processed and binned according to their pump-probe delay. XES spectra were extracted by integrating the intensity in a rectangular area of interest containing a few pixels along the non-dispersive axis. The emission energy was calibrated by matching the laser off spectrum to a singlet reference spectrum²⁰.

Theory

Models for singlet, triplet, and quintet species were generated by DFT calculations. Ground state geometry optimizations were performed using Gaussian 09⁴⁷, with the unrestricted functional BP86, modified to include Hartree-Fock (HF) mixing of 20% with a triple-zeta (6–311 G*) basis set on Fe, N, and S, and a double-zeta (6–31 G*) basis set on all other atoms, as used in our previous studies^8,48. This model includes the cross-linked cysteine side chains on the heme, which were kept fixed during geometry optimizations. This model was derived from cyt c crystal structure 1HRC⁴⁹. Population analysis of the optimized structures was performed using Gaussview, and molecular orbital images were generated using VMD⁵⁰.