We present an effective linear response approach to pump-probe femtosecond coherence spectroscopy in the well separated pulse limit. The treatment presented here is based on a displaced and squeezed state representation for the non-stationary states induced by an ultrashort pump laser pulse or a chemical reaction. The subsequent response of the system to a delayed probe pulse is modeled using closed form non-stationary linear response functions, valid for a multimode vibronically coupled system at arbitrary temperature. When pump-probe signals are simulated using the linear response functions, with the mean nuclear positions and momenta obtained from a rigorous moment analysis of the pump induced (doorway) state, the signals are found to be in excellent agreement with the conventional third order response approach. The key advantages offered by the moment analysis based linear response approach include a clear physical interpretation of the amplitude and phase of oscillatory pump-probe signals, a dramatic improvement in computation times, a direct connection between pump-probe signals and equilibrium absorption and dispersion lineshapes, and the ability to incorporate coherence such as those created by rapid non-radiative surface crossing. We demonstrate these aspects using numerical simulations, and also apply the present approach to the interpretation of experimental amplitude and phase measurements on reactive and non-reactive samples of the heme protein Myoglobin. The role played by inhomogeneous broadening in the observed amplitude and phase profiles is discussed in detail. We also investigate overtone signals in the context of reaction driven coherent motion.

The technique of femtosecond coherence spectroscopy (FCS) is applied to the heme protein myoglobin. Photostable samples of deoxy myoglobin (Mb) and photochemically active samples of the nitric oxide adduct (MbNO) are investigated. The pump-induced change in the probe transmittance for both samples displays coherent oscillations that, when transformed into the frequency domain, are in agreement with the resonance Raman spectrum of deoxy Mb. This indicates that the coherences associated with the photoreactive sample (MbNO) arise from the rapidly changing forces appearing in the crossing region(s) between the reactant and product state potential energy surfaces. The relative phase and amplitude of the Fe-His vibration, associated with the sole covalent linkage between the heme and the protein, are analyzed as a function of sample state and pump/probe carrier frequency. The dependence of the phase on carrier frequency is found to be significantly different for the "field driven" coherence in Mb and the "reaction driven" coherence in MbNO. In MbNO we observe a dip in amplitude and a phase flip near 439 nm for the Fe-His mode, whereas in deoxy Mb we observe a nearly constant phase and amplitude for this mode across the Soret absorption band. These observations are shown to be in good agreement with a simple theoretical model of the pump-probe experiment. Finally, we present recent observations of strong low-frequency oscillations, occurring near 40 cm -1 in both species and near 80 cm -1 for MbNO.

The spectral dynamics of photoexcited myoglobin (Mb) and its ligated species have been measured using both single wavelength and broadband continuum probes. Ultrafast spectral relaxation of the deoxy photoproduct involves an initially broadened and red-shifted absorption band, which is observed for all samples studied (deoxyMb, metMb, MbNO, MbCO). These results are consistent with an immediate (sub 100 fs) relaxation to the electronic ground state followed by vibrational equilibration. Relaxation of the "hot" photoproduct spectrum is well described using independent time scales for narrowing (400 fs) and blue shifting (0.4-4 ps) as the system returns to equilibrium. A previous multiple electronic intermediate state model, which is based on single wavelength measurements (Petrich, J. W.; Poyart, C.; Martin, J. L. Biochemistry 1988, 27, 4049), does not adequately explain the observed broadband spectral dynamics, particularly on the blue side of the Soret band (unless still more electronic states are postulated). The vibrational relaxation pathway in Mb is explored by using samples with a modified local heme environment (e.g., His93 f Gly mutation and protoporphyrin IX f porphine substitution). The His93 f Gly mutation experiment demonstrates that the covalent bond between the iron and the proximal histidine has little effect on the overall vibrational relaxation of the "hot" heme. In contrast, the protoporphyrin IX f porphine substitution experiment demonstrates the importance of the van der Waals contacts between the heme and the protein/solvent matrix in cooling the locally hot heme. Finally, we discuss the effects of the observed broadband spectral dynamics on timeresolved resonance Raman intensities and show how the time dependent line shape function plays an important role in the extraction of mode specific vibrational temperatures from the resonance Raman data.

We describe the application of a time domain diffuse fluorescence tomography system for whole body small animal imaging. The key features of the system are the use of point excitation in free space using ultrashort laser pulses and noncontact detection using a gated, intensified charge-coupled device (CCD) camera. Mouse shaped epoxy phantoms, with embedded fluorescent inclusions, were used to verify the performance of a recently developed asymptotic lifetime-based tomography algorithm. The asymptotic algorithm is based on a multiexponential analysis of the decay portion of the data. The multiexponential model is shown to enable the use of a global analysis approach for a robust recovery of the lifetime components present within the imaging medium. The surface boundaries of the imaging volume were acquired using a photogrammetric camera integrated with the imaging system, and implemented in a Monte-Carlo model of photon propagation in tissue. The tomography results show that the asymptotic approach is able to separate axially located fluorescent inclusions centered at depths of 4 and 10 mm from the surface of the mouse phantom. The fluorescent inclusions had distinct lifetimes of 0.5 and 0.95 ns. The inclusions were nearly overlapping along the measurement axis and shown to be not resolvable using continuous wave (CW) methods. These results suggest the practical feasibility and advantages of a time domain approach for whole body small animal fluorescence molecular imaging, particularly with the use of lifetime as a contrast mechanism.

The technique of femtosecond coherence spectroscopy is applied to a variety of photostable and photochemically active heme protein samples. With the exception of cobalt-substituted myoglobin, strong oscillations are detected near 40 cm -1 in all of the samples studied. Additional modes near 80, 120, and 160 cm -1 are observed in the photochemically active samples. The amplitude and phase behavior of the low-frequency modes are studied by tuning the pump/probe carrier wavelength across the Soret absorption spectrum. A simple harmonic model is not able to account for the observed relative intensities of these modes or the carrier wavelength dependence of their frequency and phase. As a result, we develop an anharmonic model where the oscillatory signal is damped as the result of heterogeneity in the potential surface. The underlying source of the heterogeneity in the anharmonic potential surface is found to be correlated with the inhomogeneous broadening of the Soret band. The presence of the higher harmonics in the photochemically active samples demonstrates that the anharmonic mode is strongly coupled to the ligand photodissociation reaction (i.e., upon photolysis it is displaced far from equilibrium). Moreover, the observation of the ∼40 cm -1 oscillations in all of the ironbased heme protein samples, including porphine and protoporphyrin IX model compounds, suggests that this mode is associated with nuclear motion of the core of the porphyrin macrocycle. Since normal mode calculations and prior kinetic models predict the frequency of the heme "doming mode" to be near 50 cm -1 , we suggest that the reaction coupled oscillations at ∼40 and ∼80 cm -1 are a direct reflection of anharmonic heme doming dynamics. Evidence for coupling between the heme doming dynamics and the Fe-His stretching mode is also presented.