Ultrafast two-dimensional infrared (2D IR) spectroscopy probes femtosecond to picosecond time scale dynamics ranging from solvation to protein motions. The frequency-frequency correlation function (FFCF) is the quantitative measure of the spectral diffusion that reports those dynamics and, within certain approximations, can be extracted directly from 2D IR line shapes. A variety of methods have been developed to extract the FFCF from 2D IR spectra, which, in principle, should give the same FFCF parameters, but the complexity of real experimental systems will affect the results of these analyses differently. Here, we compare five common analysis methods using both simulated and experimental 2D IR spectra to understand the effects of apodization, anharmonicity, phasing errors, and finite signal-to-noise ratios on the results of each of these analyses. Our results show that although all of the methods can, in principle, yield the FFCF under idealized circumstances, under more realistic experimental conditions they behave quite differently, and we find that the centerline slope analysis yields the best compromise between the effects we test and is most robust to the distortions that they cause.

Recent technological advances have led to major changes in the apparatuses used to collect 2D IR spectra. Pulse shaping offers several advantages including rapid data collection, inherent phase stability, and phase cycling capabilities. Visible array detection via upconversion allows the use of visible detectors that are cheaper, faster, more sensitive, and less noisy than IR detectors. However, despite these advantages, many researchers are reluctant to implement these technologies. Here we present a quantitative study of the S/N of 2D IR spectra collected with a traditional four-wave mixing (FWM) apparatus, with a pulse shaping apparatus, and with visible detection via upconversion to address the question of whether or not weak chromophores at low concentrations are still accessible with such an apparatus. We find that the enhanced averaging capability of the pulse shaping apparatus enables the detection of small signals that would be challenging to measure even with the traditional FWM apparatus, and we demonstrate this ability on a sample of cyanylated dihydrofolate reductase (DHFR).

Enzymes move on a variety of length and timescales. While much is known about large structural fluctuations which impact binding of the substrates and release of products, little is known about faster motions of enzymes and how these motions may influence enzyme catalyzed reactions. This letter reports frequency fluctuations of azide anion bound to the active site of formate dehydrogenase measured via 2D IR spectroscopy. These measurements reveal an underdamped oscillatory component to the frequency-frequency correlation function when the azide is bound to the NAD+ ternary complex. This oscillation disappears when the reduced cofactor is added, indicating that the oscillating contributions most likely come from the charged nicotinamide ring. These oscillatory motions may be relevant to donor-acceptor distance sampling of the catalyzed hydride transfer, and therefore may give future insights into the dynamic behavior involved in enzyme catalysis.

Thermal motions of enzymes have been invoked to explain the temperature dependence of kinetic isotope effects (KIEs) in enzyme-catalyzed hydride transfers. Formate dehydrogenase (FDH) from Candida boidinii exhibits a temperature-independent KIE that becomes temperature-dependent upon mutation of hydrophobic residues in the active site. Ternary complexes of FDH that mimic the transition state structure allow investigation of how these mutations influence active-site dynamics. A combination of X-ray crystallography, two-dimensional infrared (2D IR) spectroscopy, and molecular dynamic simulations characterize the structure and dynamics of the active site. FDH exhibits oscillatory frequency fluctuations on the picosecond timescale, and the amplitude of these fluctuations correlates with the temperature dependence of the KIE. Both the kinetic and dynamic phenomena can be reproduced computationally. These results provide experimental evidence for a connection between the temperature dependence of KIEs and motions of the active site in an enzyme-catalyzed reaction consistent with activated tunneling models of the hydride transfer reaction.

Isotope substitution of enzymes has become a means of addressing the participation of protein motions in enzyme-catalyzed reactions. The idea is that only the enzyme mass will be altered and not the electrostatics, so that the protein dynamics are essentially the same but at lower frequencies because of the mass change. In this study, we variably label all carbon atoms in formate dehydrogenase (FDH) with 13C, all nitrogen atoms with 15N, and all nonexchangeable hydrogen atoms with deuterium and investigate the impact that isotopic substitution has on the dynamics at the active site by two-dimensional infrared spectroscopy and compare with the measurements of the temperature dependence of the intrinsic kinetic isotope effects (KIEs). We show that 15N labeling of FDH has the largest effect and makes the active site more heterogeneous, whereas the addition of nonexchangeable deuterium appears to have the opposite effect of 15N on active-site dynamics, resulting in a behavior similar to that of native FDH. Nevertheless, the temperature dependence of the KIEs shows a monotonic trend with protein mass that does not correspond with the changes in dynamics. These results suggest that isotope labeling has more than just a mass effect on enzyme dynamics and may influence electrostatics in ways that complicate the interpretation of the protein isotope effect.