Populations and coherence in femtosecond time resolved X-ray crystallography of the photoactive yellow protein

Abstract

Ultrafast X-ray crystallography of the Photoactive Yellow Protein with femtosecond delays using an X-ray Free Electron Laser has successfully probed the dynamics of an early FranckCondon species. The femtosecond pump-probe application of protein crystallography represents a new experimental regime that provides an X-ray structural probe for coherent processes that were previously accessible primarily using ultrafast spectroscopy. We address how the optical regime of the visible pump, that is necessary to successfully resolve ultrafast structural differences, affects the motions that are measured using the technique. The subpicosecond photochemical dynamics in PYP involves evolution of a mixture of electronic ground and excited state populations. Additionally, within the dephasing time structural motion include vibrational coherence arising from excited states, the ground state and a ground state intermediate under experimental conditions used for ultrafast crystallography. Intense optical pulses are required to convert population levels in PYP crystals that allow detection by X-ray crystallography, but the compromise currently needed for the optical bandwidth and power has consequences with regard to the contributions to the motions that are experimentally measured with femtosecond delays. We briefly review the ultrafast spectroscopy literature of the primary photoreactions of PYP and discuss relevant physical models taken from coherent control and femtosecond coherence spectroscopy literature that address both the population transfer as well 2 as the vibrational coherences. We apply linear response theory, with the additional use of a high power approximation, of on-resonance impulsive vibrational coherence in the ground state and the non-impulsive coherence in the excited state and discuss experimental approaches to manipulate the coherence contributions. The results are generalised and extended to discuss the future capabilities of high repetition rate XFEL instruments providing enhanced sensitivity to perform the crystallographic equivalent of an impulsive Raman measurement of vibrational coherence.

Photoinduced Structural Dynamics of Molecular Systems Mapped by Time-Resolved X-ray Methods

“…In addition to studies on hemoproteins, there is intense activity aimed at describing the early time dynamics of proteins such as the Photoactive Yellow Protein (PYP), 344,345 bacteriorhodopsin (bR) 346 and the Photosystem II (PSII) reaction centre, 347 using femtosecond resolved X-ray diffraction. However, sub-ps structural dynamics was only reported for PYP nanocrystals.…”

Optical control, selection and analysis of population dynamics in ultrafast protein X-ray crystallography

“…With off-resonance excitation, the resulting ground state coherence could be multiple times the minimized value. This demonstrates that position, impulse and phase can be controlled by the carrier frequency, laser pulse power and electronic lifetime and dephasing properties [34].…”

“…For pump-probe delays that are within the vibrational dephasing times of systems under study, a key consideration is that the origin of structural motion is completely different from those obtained on slower incoherent time scale. A previous discussion considered the theoretical analysis of nuclear coherence under such conditions [34]. In the static picture, a straight-forward hole-burning analysis provides the connection between optical parameters and the ground state coherence and excited state coherence that is created with a brief optical pulse.…”

“…Firstly, a pulse intensity, duration and laser spectrum is selected that is appropriate to generate low-frequency vibrational coherence within the dephasing time as well as a significant hole-burning amplitude. Using the high-intensity approximation equations [34], calculation of the spectral hole that is generated with pulses that are either below or above resonance conditions (figure 1) illustrate the result of using carrier frequency as a control parameter. The linear response theory predicts that while the resulting ground state total complex coherence amplitude |A1 g | = (Q 2 g + P 2 g ) would be unmodified, the sign of the instantaneous position Q g is inverted, and causing a phase φ = −tan −1 [P g0 /Q g0 ] difference in excess of π .…”

“…Calculation demonstrating the effect of detuning on spectral 'hole-burning' (a) when pumping a transition (peak cross section 1.68 × 10 −16 cm 2 ) with a 100 fs, 1.5 GW mm −2 optical pulse. The unperturbed absorption line (black), the on resonance (red) and two detuned cases (blue) are shown [34]. Also shown the absolute ground state displacement (b) and phase (c).…”