We investigate the sensitivity of femtosecond Fourier transform two-dimensional infrared spectroscopy to protein secondary structure with a study of antiparallel beta-sheets. The results show that 2D IR spectroscopy is more sensitive to structural differences between proteins than traditional infrared spectroscopy, providing an observable that allows comparison to quantitative models of protein vibrational spectroscopy. 2D IR correlation spectra of the amide I region of poly-l-lysine, concanavalin A, ribonuclease A, and lysozyme show cross-peaks between the IR-active transitions that are characteristic of amide I couplings for polypeptides in antiparallel hydrogen-bonding registry. For poly-l-lysine, the 2D IR spectrum contains the eight-peak structure expected for two dominant vibrations of an extended, ordered antiparallel beta-sheet. In the proteins with antiparallel beta-sheets, interference effects between the diagonal and cross-peaks arising from the sheets, combined with diagonally elongated resonances from additional amide transitions, lead to a characteristic "Z"-shaped pattern for the amide I region in the 2D IR spectrum. We discuss in detail how the number of strands in the sheet, the local configurational disorder in the sheet, the delocalization of the vibrational excitation, and the angle between transition dipole moments affect the position, splitting, amplitude, and line shape of the cross-peaks and diagonal peaks.

Using idealized models for parallel and antiparallel ␤ sheets, we calculate the linear and two-dimensional infrared spectra of the amide I vibration as a function of size and secondary structure. The model assumes transition-dipole coupling between the amide I oscillators in the sheet and accounts for the anharmonic nature of these oscillators. Using analytical and numerical methods, we show that the nature of the one-quantum vibrational eigenstates, which govern the linear spectrum, is, to a large extent, determined by the symmetry of the system and the relative magnitude of interstrand interactions. We also find that the eigenstates, in particular their trends with system size, depend sensitively on the secondary structure of the sheet. While in practice these differences may be difficult to distinguish in congested linear spectra, we demonstrate that they give rise to promising markers for secondary structure in the two-dimensional spectra. In particular, distinct differences occur between the spectra of parallel and antiparallel ␤ sheets and between ␤ hairpins and extended ␤ sheets.

Kinetic isotope effects (KIEs) and their temperature dependence can probe the structural and dynamic nature of enzyme-catalyzed proton or hydride transfers. The molecular interpretation of their temperature dependence requires expensive and specialized QM/MM calculations to provide a quantitative molecular understanding. Currently available phenomenological models use a non-adiabatic assumption that is not appropriate for most hydride and proton-transfer reactions, while others require more parameters than the experimental data justify. Here we propose a phenomenological interpretation of KIEs based on a simple method to quantitatively link the size and temperature dependence of KIEs to a conformational distribution of the catalyzed reaction. The present model assumes adiabatic hydrogen tunneling, and by fitting experimental KIE data, the model yields a population distribution for fluctuations of the distance between donor and acceptor atoms. Fits to data from a variety of proton and hydride transfers catalyzed by enzymes and their mutants, as well as non-enzymatic reactions, reveal that steeply temperature-dependent KIEs indicate the presence of at least two distinct conformational populations, each with different kinetic behaviors. We present the results of these calculations for several published cases and discuss how the predictions of the calculations might be experimentally tested. The current analysis does not replace molecular quantum mechanics/molecular mechanics (QM/MM) investigations, but it provides a fast and accessible way to quantitatively interpret KIEs in the context of a Marcus-like model.

The structure of formate dehydrogenase from Candida boidinii (CbFDH) is of both academic and practical interests. First, this enzyme represents a unique model system in studies of the role of protein dynamics in catalysis, but so far these studies were limited by the availability of structural information. Second, CbFDH and its mutants are of use in various industrial applications (e.g., CO2 fixation or nicotinamide recycling systems), and the lack of structural information has been a limiting factor in its commercial development. Here, we report the crystallization and structural determination of both holo-CbFDH and apo-CbFDH. The free energy barrier for the catalyzed reaction is computed, and indicates that this structure indeed represents a catalytically competent form of the enzyme. Complementing kinetic examinations demonstrate that the recombinant CbFDH has a well-organized reactive state. Finally, a fortuitous observation has been made: The apo-enzyme crystal was obtained under co-crystallization conditions with a saturating concentration of both the cofactor (NAD+) and inhibitor (azide), which has a nM dissociation constant. It was found that the fraction of the apo-enzyme present in the solution is less than 1.7x10−7 (i.e. the solution is 99.9999% holo-enzyme). This is an extreme case where the crystal structure represents an insignificant fraction of enzyme in solution, and a mechanism rationalizing this phenomenon is presented.