Wavelength selective modulation in femtosecond pump–probe spectroscopy and its application to heme proteins

Theoretical model of femtosecond coherence spectroscopy of vibronic excitons in molecular aggregates

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment-protein complexes.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

Signatures of Vibrational and Electronic Quantum Beats in Femtosecond Coherence Spectra

Femtosecond laser pulses can produce oscillatory signals in transient-absorption spectroscopy measurements. The quantum beats are often studied using femtosecond coherence spectra (FCS), the Fourier domain amplitude, and phase profiles at individual oscillation frequencies. In principle, one can identify the mechanism that gives rise to each quantum-beat signal by comparing its measured FCS to those arising from microscopic models. To date, however, most measured FCS deviate from the ubiquitous harmonic oscillator model. Here, we expand the inventory of models to which the measured spectra can be compared. We develop quantum-mechanical models of the fundamental, overtone, and combination-band FCS arising from harmonic potentials, the FCS of anharmonic potentials, and the FCS of a purely electronic dimer. This work solidifies the use of FCS for identifying electronic coherences that can arise in measurements of molecular aggregates including photosynthetic proteins. Furthermore, future studies can use the derived expressions to fit the measured FCS and thereby extract microscopic parameters of molecular potential-energy surfaces.

Ultrafast Dynamics and Vibrational Relaxation in Six-Coordinate Heme Proteins Revealed by Femtosecond Stimulated Raman Spectroscopy

Identifying the structural rearrangements during photoinduced reactions is a fundamental challenge for understanding from a microscopic perspective the dynamics underlying the functional mechanisms of heme proteins. Here, femtosecond stimulated Raman spectroscopy is applied to follow the ultrafast evolution of two different proteins, each bearing a six-coordinate heme with two amino acid axial ligands. By exploiting the sensitivity of Raman spectra to the structural configuration, we investigate the effects of photolysis and the binding of amino acid residues in cytochrome c and neuroglobin. By comparing the system response for different time delays and Raman pump resonances, we show how detailed properties of atomic motions and energy redistribution can be unveiled. In particular, we demonstrate substantially faster energy flow from the dissociated heme to the protein moiety in cytochrome c, which we assign to the presence of covalent heme–protein bonds.

NO binding kinetics in myoglobin investigated by picosecond Fe K-edge absorption spectroscopy

Diatomic ligands in hemoproteins and the way they bind to the active center are central to the protein's function. Using picosecond Fe K-edge X-ray absorption spectroscopy, we probe the NO-heme recombination kinetics with direct sensitivity to the Fe-NO binding after 532-nm photoexcitation of nitrosylmyoglobin (MbNO) in physiological solutions. The transients at 70 and 300 ps are identical, but they deviate from the difference between the static spectra of deoxymyoglobin and MbNO, showing the formation of an intermediate species. We propose the latter to be a six-coordinated domed species that is populated on a timescale of ∼ 200 ps by recombination with NO ligands. This work shows the feasibility of ultrafast pump-probe X-ray spectroscopic studies of proteins in physiological media, delivering insight into the electronic and geometric structure of the active center.

Nuclear resonance vibrational spectra of five-coordinate imidazole-ligated iron(II) porphyrinates

Nuclear resonance vibrational spectra have been obtained for six five-coordinate imidazole-ligated iron(II) porphyrinates, [Fe(Por)(L)] (Por = tetraphenylporphyrinate, octaethylporphyrinate, tetratolylporphyrinate, or protoporphyrinate IX and L = 2-methylimidazole or 1,2-dimethylimidazole). Measurements have been made on both powder and oriented crystal samples. The spectra are dominated by strong signals around 200-300 cm(-1). Although the in-plane and out-of-plane vibrations are seriously overlapped, oriented crystal spectra allow their deconvolution. Thus, oriented crystal experimental data, along with density functional theory (DFT) calculations, enable the assignment of key vibrations in the spectra. Molecular dynamics are also discussed. The nature of the Fe-N(Im) vibrations has been elaborated further than was possible from resonance Raman studies. Our study suggests that the Fe motions are coupled with the porphyrin core and peripheral groups motions. Both peripheral groups and their conformations have significant influence on the vibrational spectra (position and shape).

Femtosecond Coherence Spectroscopic Study of the Onset of Chemical Denaturation of Myoglobin upon Addition of Minor Amounts of Urea

The interaction of urea with myoglobin, as a benchmark system for heme-containing proteins, is studiedviafemtosecond coherence spectroscopy. The work focuses on the effect of urea on the appearance of low-wavenumber oscillations, which are a measure of the geometrical structure of the heme group and its interaction with the polypeptide chain. Pursuing this approach, structural alterations (i.e.changes in the vibrational dynamics of the heme group) are detected at denaturant concentrations below the full denaturation limit of 6 M urea for myoglobin. In particular, the low-wavenumber oscillation associated with the heme-doming (i.e.the out-off-plane vibration of the propyrin macrocycle) is found to appear spectrally shifted with a concentration of only 3 M urea. These results suggest that the local environment around the heme is already altered despite the fact that macroscopic unfolding as manifested in the thermodynamic properties of the polypeptide chain is not complete at these urea concentrations.

Observation of terahertz vibrations in the nitrogenase FeMo cofactor by femtosecond pump-probe spectroscopy

We have used Impulsive Coherent Vibrational Spectroscopy (ICVS) to study the FeMo-cofactor of nitrogenase from Azotobacter vinelandii as the extracted small molecule ‘FeMoco’. In the ICVS experiment, a 15 fs visible laser pulse pumps the sample to an excited electronic state, and a second <10 fs pulse probes the change in transmission as a function of the time delay. FeMoco was observed to relax to the ground state by a single exponential decay with a time constant of ~200 fs. Superimposed on this relaxation are oscillations caused by the coherent excitation of vibrational modes in both excited and ground electronic states. Fourier transformation reveals the FeMoco vibrational frequencies that are coherently excited by the short laser pulse.

The frequencies obtained by the ICVS technique were compared with values from normal mode calculations. The strongest ICVS bands are at 215 and 420 cm−1. The 420 cm−1 band is attributed to Fe-S stretching motion, whereas the 215 cm−1 band, which is the strongest feature in the spectrum, is attributed to a breathing mode of FeMoco. Over the years, nitrogenase and FeMoco have resisted characterization by resonance Raman spectroscopy. The current results demonstrate the promise of ICVS as an alternative probe of FeMoco dynamics.

Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. III. The nu(4) and nu(7) modes of nonplanar nickel porphyrin models

The time scales and pathways of vibrational energy relaxation (VER) of the nu(4) and nu(7) modes of three nickel porphyrin models, nickel porphine (NiP), nickel protoporphyrin IX (Ni-heme), and nickel octaethylporphyrin (NiOEP), were studied using a non-Markovian time-dependent perturbation theory at the B3LYP/6-31G(d) level. When NiP is calculated with D(4h) symmetry, it has the planar structure and the same VER properties as ferrous iron porphine (FeP). The porphine cores of both Ni-heme and NiOEP were distorted from a planar geometry, assuming a nonplanar structure, similar to that of the heme structure in cytochrome c. The VER time scales of Ni-heme are found to be similar to those predicted for a planar iron heme, but the derived pathways have distinctly different features. In particular, the strong coupling between the nu(7) mode and the overtone of the approximately 350 cm(-1) gamma(7) mode, observed for planar porphyrins, is absent in both nonplanar nickel porphyrins. Direct energy exchange between the nu(4) and nu(7) modes is not observed in NiOEP, but is found to play an essential role in the VER of the nu(4) mode in Ni-heme. The Ni-heme isopropionate groups are involved in the dominant VER pathways of both the nu(4) and nu(7) modes of Ni-heme. However, in contrast with VER pathways derived in planar iron heme, the isopropionate groups are not observed to play an essential role relative to other side chains in spatially directing the vibrational energy flow.

Excited-state molecular vibration observed for a probe pulse preceding the pump pulse by real-time optical spectroscopy

It is shown experimentally that the absorbance change observed in the "negative" time range, where probe pulse precedes pump pulse in real-time vibrational spectroscopy is induced only by the excited-state wave-packet motion as theoretically expected. Coherent molecular vibration of a polymer in the excited state was observed in the real-time trace without the effect of wave-packet motion in the ground state, which usually makes it difficult to ascribe the signal either to the ground state or to the excited state.

Observation of terahertz vibrations in Pyrococcus furiosus rubredoxin via impulsive coherent vibrational spectroscopy and nuclear resonance vibrational spectroscopy – interpretation by molecular mechanics

We have used impulsive coherent vibrational spectroscopy (ICVS) to study the Fe(S-Cys)(4) site in oxidized rubredoxin (Rd) from Pyrococcus furiosus (Pf). In this experiment, a 15 fs visible laser pulse is used to coherently pump the sample to an excited electronic state, and a second <10 fs pulse is used to probe the change in transmission as a function of the time delay. PfRd was observed to relax to the ground state by a single exponential decay with time constants of approximately 255-275 fs. Superimposed on this relaxation are oscillations caused by coherent excitation of vibrational modes in both excited and ground electronic states. Fourier transformation reveals the frequencies of these modes. The strongest ICV mode with 570 nm excitation is the symmetric Fe-S stretching mode near 310 cm(-1), compared to 313 cm(-1) in the low temperature resonance Raman. If the rubredoxin is pumped at 520 nm, a set of strong bands occurs between 20 and 110 cm(-1). Finally, there is a mode at approximately 500 cm(-1) which is similar to features near 508 cm(-1) in blue Cu proteins that have been attributed to excited state vibrations. Normal mode analysis using 488 protein atoms and 558 waters gave calculated spectra that are in good agreement with previous nuclear resonance vibrational spectra (NRVS) results. The lowest frequency normal modes are identified as collective motions of the entire protein or large segments of polypeptide. Motion in these modes may affect the polar environment of the redox site and thus tune the electron transfer functions in rubredoxins.

Temperature-dependent studies of NO recombination to heme and heme proteins

The rebinding kinetics of NO to the heme iron of myoglobin (Mb) is investigated as a function of temperature. Below 200 K, the transition-state enthalpy barrier associated with the fastest (approximately 10 ps) recombination phase is found to be zero and a slower geminate phase (approximately 200 ps) reveals a small enthalpic barrier (approximately 3 +/- 1 kJ/mol). Both of the kinetic rates slow slightly in the myoglobin (Mb) samples above 200 K, suggesting that a small amount of protein relaxation takes place above the solvent glass transition. When the temperature dependence of the NO recombination in Mb is studied under conditions where the distal pocket is mutated (e.g., V68W), the rebinding kinetics lack the slow phase. This is consistent with a mechanism where the slower (approximately 200 ps) kinetic phase involves transitions of the NO ligand into the distal heme pocket from a more distant site (e.g., in or near the Xe4 cavity). Comparison of the temperature-dependent NO rebinding kinetics of native Mb with that of the bare heme (PPIX) in glycerol reveals that the fast (enthalpically barrierless) NO rebinding process observed below 200 K is independent of the presence or absence of the proximal histidine ligand. In contrast, the slowing of the kinetic rates above 200 K in MbNO disappears in the absence of the protein. Generally, the data indicate that, in contrast to CO, the NO ligand binds to the heme iron through a "harpoon" mechanism where the heme iron out-of-plane conformation presents a negligible enthalpic barrier to NO rebinding. These observations strongly support a previous analysis (Srajer et al. J. Am. Chem. Soc. 1988, 110, 6656-6670) that primarily attributes the low-temperature stretched exponential rebinding of MbCO to a quenched distribution of heme geometries. A simple model, consistent with this prior analysis, is presented that explains a variety of MbNO rebinding experiments, including the dependence of the kinetic amplitudes on the pump photon energy.

Determination of the Fe−CO Bond Energy in Myoglobin Using Heterodyne-Detected Transient Thermal Phase Grating Spectroscopy

The bond energies at active sites of proteins are intimately coupled to the structure-function relationship in biological systems. Due to the unknown nature of the protein relaxation along a reaction coordinate, it has not been possible to directly determine bond energies relevant to protein function. By embedding proteins in trehalose glasses, it is possible to freeze out protein relaxation on short time scales and determine the bond energies of photolabile ligands using photothermal spectroscopies. As a prototypical example, the photodissociation dynamics and energetics of carboxy-myoglobin (MbCO) in a trehalose glass matrix at room temperature were studied by transient absorption (or pump-probe) and transient thermal phase grating spectroscopy to determine the CO recombination dynamics and associated energetics, respectively. Both the initial energetics of the bond breaking and the energy released upon bond reformation could be used, on a time scale faster than significant protein relaxation, to determine the Fe-CO bond energy as 34 +/- 4 kcal/mol. This bond energy is significantly larger than that typically cited (25 kcal/mol) on the basis of indirect measurements but is in good agreement with recent theoretical predictions (35 kcal/mol) (Rovira, C.; Parrinello, M. Int. J. Quantum Chem. 2000, 80, 1172). This result in combination with the theoretical study suggests that protein structure plays a significant role in the bond energies at active sites which in turn provides a tuning element of the effective barrier heights independent to the transition state region.

Nonlinear optical studies of heme protein dynamics: Implications for proteins as hybrid states of matter

Protein structure is fundamentally related to function. However, static structures alone are insufficient to understand how a protein works. Dynamics play an equally important role. Given that proteins are highly associated aperiodic systems, it may be expected that protein dynamics would follow glass-like dynamics. However, protein functions occur on time scales orders of magnitude faster than the time scales typically associated with glassy systems. It is becoming clear that the reaction forces driving functions do not sample entirely the large number of configurations available to a protein but are highly directed along an optimized pathway. Could there be any correlation between specific topological features in protein structures and dynamics that leads to strongly correlated atomic displacements in the dynamical response to a perturbation? This review will try to provide an answer by focusing upon recent nonlinear optical studies with the aim of directly observing functionally important protein motions over the entire dynamic range of the protein response function. The specific system chosen is photoinduced dynamics of ligand dissociation at the active site in heme proteins, with myoglobin serving as the simplest model system. The energetics and nuclear motions from the very earliest events involved in bond breaking on the femtosecond time scale all the way out to ligand escape and bimolecular rebinding on the microsecond and millisecond time scale have been mapped out. The picture that is emerging is that the system consists of strongly coupled motions from the very instant the bond breaks at the active site that cascade into low frequency collective modes specific to the protein structure. It is this coupling that imparts the ability of a protein to function on time scales more commensurate with liquids while simultaneously conserving structural integrity akin to solids.

Quantitative vibrational dynamics of iron in nitrosyl porphyrins

We use quantitative experimental and theoretical approaches to characterize the vibrational dynamics of the Fe atom in porphyrins designed to model heme protein active sites. Nuclear resonance vibrational spectroscopy (NRVS) yields frequencies, amplitudes, and directions for 57Fe vibrations in a series of ferrous nitrosyl porphyrins, which provide a benchmark for evaluation of quantum chemical vibrational calculations. Detailed normal mode predictions result from DFT calculations on ferrous nitrosyl tetraphenylporphyrin Fe(TPP)(NO), its cation [Fe(TPP)(NO)]+, and ferrous nitrosyl porphine Fe(P)(NO). Differing functionals lead to significant variability in the predicted Fe-NO bond length and frequency for Fe(TPP)(NO). Otherwise, quantitative comparison of calculated and measured Fe dynamics on an absolute scale reveals good overall agreement, suggesting that DFT calculations provide a reliable guide to the character of observed Fe vibrational modes. These include a series of modes involving Fe motion in the plane of the porphyrin, which are rarely identified using infrared and Raman spectroscopies. The NO binding geometry breaks the four-fold symmetry of the Fe environment, and the resulting frequency splittings of the in-plane modes predicted for Fe(TPP)(NO) agree with observations. In contrast to expectations of a simple three-body model, mode energy remains localized on the FeNO fragment for only two modes, an N-O stretch and a mode with mixed Fe-NO stretch and FeNO bend character. Bending of the FeNO unit also contributes to several of the in-plane modes, but no primary FeNO bending mode is identified for Fe(TPP)(NO). Vibrations associated with hindered rotation of the NO and heme doming are predicted at low frequencies, where Fe motion perpendicular to the heme is identified experimentally at 73 and 128 cm-1. Identification of the latter two modes is a crucial first step toward quantifying the reactive energetics of Fe porphyrins and heme proteins.

Observation of the cascaded atomic-to-global length scales driving protein motion

Model studies of the ligand photodissociation process of carboxymyoglobin have been conducted by using amplified few-cycle laser pulses short enough in duration (<10 fs) to capture the phase of the induced nuclear motions. The reaction-driven modes are observed directly in real time and depict the pathway by which energy liberated in the localized reaction site is efficiently channeled to functionally relevant mesoscale motions of the protein.