Adding a second AgGaS2 stage to Ti:sapphire/BBO/AgGaS2 setups increases mid-infrared power twofold.

We present a method for increasing the power of mid-infrared laser pulses generated by a conventional beta-barium borate (BBO) optical parametric amplifier (OPA) and AgGaS2 difference frequency generation (DFG) pumped by a Ti:sapphire amplifier. The method involves an additional stage of parametric amplification with a second AgGaS2 crystal pumped by selected outputs of the conventional DFG stage. This method does not require additional pump power from the Ti:sapphire laser source and improves the overall photon conversion efficiency for generating mid-infrared light. It merely requires an additional AgGaS2 crystal and dichroic mirrors. Following difference frequency generation, the method reuses near-infrared light (∼1.9 µm), typically discarded, to pump the additional AgGaS2 stage and amplifies the mid-infrared light twofold. We demonstrate and characterize the power, spectrum, duration, and noise of the mid-IR pulses before and after the second AgGaS2 stage. We observe small changes in center frequencies, bandwidth, and pulse duration for ∼150-fs pulses between 4 and 5 µm.

Evolution of Optimized Hydride Transfer Reaction and Overall Enzyme Turnover in Human Dihydrofolate Reductase.

Evolution of dihydrofolate reductase (DHFR) has been studied using the enzyme from Escherichia coli DHFR (ecDHFR) as a model, but less studies have used the enzyme from Homo sapiens DHFR (hsDHFR). Each enzyme maintains a short and narrow distribution of hydride donor-acceptor distances (DAD) at the tunneling ready state (TRS). Evolution of the enzyme was previously studied in ecDHFR where three key sites were identified as important to the catalyzed reaction. The corresponding sites in hsDHFR are F28, 62-PEKN, and 26-PPLR. Each of these sites was studied here through the creation of mutant variants of the enzyme and measurements of the temperature dependence of the intrinsic kinetic isotope effects (KIEs) on the reaction. F28 is mutated first to M (F28M) and then to the L of the bacterial enzyme (F28L). The KIEs of the F28M variant are larger and more temperature-dependent than wild-type (WT), suggesting a broader and longer average DAD at the TRS. To more fully mimic ecDHFR, we also study a triple mutant of the human enzyme (F32L-PP26N-PEKN62G). Remarkably, the intrinsic KIEs, while larger in magnitude, are temperature-independent like the WT enzymes. We also construct deletion mutations of hsDHFR removing both the 62-PEKN and 26-PPLR sequences. The results mirror those described previously for insertion mutants of ecDHFR. Taken together, these results suggest a balancing act during DHFR evolution between achieving an optimal TRS for hydride transfer and preventing product inhibition arising from the different intercellular pools of NADPH and NADP+ in prokaryotic and eukaryotic cells.

Low-Frequency Protein Motions Coupled to Catalytic Sites.

This review examines low-frequency vibrational modes of proteins and their coupling to enzyme catalytic sites. That protein motions are critical to enzyme function is clear, but the kinds of motions present in proteins and how they are involved in function remain unclear. Several models of enzyme-catalyzed reaction suggest that protein dynamics may be involved in the chemical step of the catalyzed reaction, but the evidence in support of such models is indirect. Spectroscopic studies of low-frequency protein vibrations consistently show that there are underdamped modes of the protein with frequencies in the tens of wavenumbers where overdamped behavior would be expected. Recent studies even show that such underdamped vibrations modulate enzyme active sites. These observations suggest that increasingly sophisticated spectroscopic methods will be able to unravel the link between low-frequency protein vibrations and enzyme function.

Edge-pixel referencing suppresses correlated baseline noise in heterodyned spectroscopies.

Referencing schemes are commonly used in heterodyned spectroscopies to mitigate correlated baseline noise arising from shot-to-shot fluctuations of the local oscillator. Although successful, these methods rely on careful pixel-to-pixel matching between the two spectrographs. A recent scheme introduced by Feng et al. [Opt. Express 27(15), 20323-20346 (2019)] employed a correlation matrix to allow free mapping between dissimilar spectrographs, leading to the first demonstration of floor noise limited detection on a multichannel array used in heterodyned spectroscopy. In addition to their primary results using a second reference spectrometer, Feng et al. briefly demonstrated the flexibility of their method by referencing to same-array pixels at the two spectral edges (i.e., edge-pixel referencing). We present a comprehensive study of this approach, which we term edge-pixel referencing, including optimization of the approach, assessment of the performance, and determination of the effects of background responses. We show that, within some limitations, the distortions due to background signals will not affect the 2D IR line shape or amplitude and can be mitigated by band narrowing of the pump beams. We also show that the performance of edge-pixel referencing is comparable to that of referencing to a second spectrometer in terms of noise suppression and that the line shapes and amplitudes of the spectral features are, within the measurement error, identical. Altogether, these results demonstrate that edge-pixel referencing is a powerful approach for noise suppression in heterodyned spectroscopies, which requires no new hardware and, so, can be implemented as a software solution for anyone performing heterodyned spectroscopy with multichannel array detectors already.

Evolution Conserves the Network of Coupled Residues in Dihydrofolate Reductase.

Understanding protein motions and their role in enzymatic reactions is an important and timely topic in enzymology. Protein motions that are involved in the chemical step of catalysis are particularly intriguing but difficult to identify. A global network of coupled residues in Escherichia coli dihydrofolate reductase (E. coli DHFR), which assists in catalyzing the chemical step, has previously been demonstrated through quantum mechanical/molecular mechanical and molecular dynamics simulations as well as bioinformatic analyses. A few specific residues (M42, G121, F125, and I14) were shown to function synergistically with measurements of single-turnover rates and the temperature dependence of intrinsic kinetic isotope effects (KIEsint) of site-directed mutants. This study hypothesizes that the global network of residues involved in the chemical step is evolutionarily conserved and probes homologous residues of the potential global network in human DHFR through measurements of the temperature dependence of KIEsint and computer simulations based on the empirical valence bond method. We study mutants M53W and S145V. Both of these remote residues are homologous to network residues in E. coli DHFR. Non-additive isotope effects on activation energy are observed between M53 and S145, indicating their synergistic effect on the chemical step in human DHFR, which suggests that both of these residues are part of a network affecting the chemical step in enzyme catalysis. This finding supports the hypothesis that human and E. coli DHFR share similar networks, consistent with evolutionary preservation of such networks.

Optimized reconstructions of compressively sampled two-dimensional infrared spectra.

Compressive sampling has the potential to dramatically accelerate the pace of data collection in two-dimensional infrared (2D IR) spectroscopy. We have previously introduced the Generic Iteratively Reweighted Annihilating Filter (GIRAF) reconstruction algorithm to solve the reconstruction in 2D IR compressive sampling. Here, we report a thorough assessment of this method and comparison to our earlier efforts using the Total Variation (TV) algorithm. We show that the GIRAF algorithm has some distinct advantages over TV. Although it is no better or worse in terms of ameliorating the impacts of compressive sampling on the measured 2D IR line shape, we find that the nature of those effects is different for GIRAF than they were for TV. In addition to assessing the impacts on the line shape of a single oscillator, we also test the ability of the algorithm to reconstruct spectra that have transitions from more than one oscillator, such as the coupled carbonyl oscillators in rhodium dicarbonyl. Finally, and perhaps most importantly, we show that the GIRAF algorithm has a distinct denoising effect on the signal-to-noise ratio (SNR) of the 2D IR spectra that can increase the SNR by as much as 4× without any additional signal averaging and collecting fewer data points, which should further enhance the acceleration of data collection that can be achieved using compressive sampling and enable even more challenging experimental measurements.

Evolutionary Effects on Bound Substrate p Ka in Dihydrofolate Reductase.

In the present study, we address the effect of active site structure and dynamics of different dihydrofolate reductase (DHFR) isoforms on the p Ka of the bound substrate 7,8-dihydrofolate, in an attempt to understand possible evolutionary trends. We apply a hybrid QM/MM free energy perturbation method to estimate the p Ka of the N5 position of the bound substrate. We observe a gradual increase in N5 basicity as we move from primitive to more evolved DHFR isoforms. Structural analysis of these isoforms reveals a gradual sequestering of water molecules from the active site in the more evolved enzymes, thereby modulating the local dielectric environment near the substrate. Furthermore, the present study reveals a clear correlation between active site hydration and the N5 p Ka of the substrate. We emphasize the role of the M20 loop in controlling the active site hydration level, via a preorganized active site with a more hydrophobic environment and reduced loop flexibility as evolution progresses from bacterial to the human enzyme.

Protein Mass Effects on Formate Dehydrogenase.

Isotopically labeled enzymes (denoted as "heavy" or "Born-Oppenheimer" enzymes) have been used to test the role of protein dynamics in catalysis. The original idea was that the protein's higher mass would reduce the frequency of its normal-modes without altering its electrostatics. Heavy enzymes have been used to test if the vibrations in the native enzyme are coupled to the chemistry it catalyzes, and different studies have resulted in ambiguous findings. Here the temperature-dependence of intrinsic kinetic isotope effects of the enzyme formate dehydrogenase is used to examine the distribution of H-donor to H-acceptor distance as a function of the protein's mass. The protein dynamics are altered in the heavy enzyme to diminish motions that determine the transition state sampling in the native enzyme, in accordance with a Born-Oppenheimer-like effect on bond activation. Findings of this work suggest components related to fast frequencies that can be explained by Born-Oppenheimer enzyme hypothesis (vibrational) and also slower time scale events that are non-Born-Oppenheimer in nature (electrostatic), based on evaluations of protein mass dependence of donor-acceptor distance and forward commitment to catalysis along with steady state and single turnover measurements. Together, the findings suggest that the mass modulation affected both local, fast, protein vibrations associated with the catalyzed chemistry and the protein's macromolecular electrostatics at slower time scales; that is, both Born-Oppenheimer and non-Born-Oppenheimer effects are observed. Comparison to previous studies leads to the conclusion that isotopic labeling of the protein may have different effects on different systems, however, making heavy enzyme studies a very exciting technique for exploring the dynamics link to catalysis in proteins.

Accelerating two-dimensional infrared spectroscopy while preserving lineshapes using GIRAF.

We introduce a computationally efficient structured low-rank algorithm for the reconstruction of two-dimensional infrared (2D IR) spectroscopic data from few measurements. The signal is modeled as a combination of exponential lineshapes that are annihilated by appropriately chosen filters. The annihilation relations result in a low-rank constraint on a Toeplitz matrix constructed from signal samples, which is exploited to recover the unknown signal samples. Quantitative and qualitative studies on simulated and experimental data demonstrate that the algorithm outperforms the discrete compressed sensing algorithm, both in uniform and non-uniform sampling settings.

Compressively Sampled Two-Dimensional Infrared Spectroscopy That Preserves Line Shape Information.

Two-dimensional infrared (2D IR) spectroscopy is a powerful tool to investigate molecular structures and dynamics on femtosecond to picosecond time scales and is applied to diverse systems. Current technologies allow for the acquisition of a single 2D IR spectrum in a few tens of milliseconds using a pulse shaper and an array detector, but demanding applications require spectra for many waiting times and involve considerable signal averaging, resulting in data acquisition times that can be many days or weeks of laboratory measurement time. Using compressive sampling, we show that we can reduce the time for collection of a 2D IR data set in a particularly demanding application from 8 to 2 days, a factor of 4×, without changing the apparatus and while accurately reproducing the line-shape information that is most relevant to this application. This result is a potent example of the potential of compressive sampling to enable challenging new applications of 2D IR.

Structural and Kinetic Studies of Formate Dehydrogenase from Candida boidinii.

The structure of formate dehydrogenase from Candida boidinii (CbFDH) is of both academic and practical interests. First, this enzyme represents a unique model system for studies on the role of protein dynamics in catalysis, but so far these studies have been limited by the availability of structural information. Second, CbFDH and its mutants can be used in various industrial applications (e.g., CO2 fixation or nicotinamide recycling systems), and the lack of structural information has been a limiting factor in commercial development. Here, we report the crystallization and structural determination of both holo- and apo-CbFDH. The free-energy barrier for the catalyzed reaction was 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 apoenzyme crystal was obtained under cocrystallization conditions with a saturating concentration of both the cofactor (NAD(+)) and inhibitor (azide), which has a nanomolar dissociation constant. It was found that the fraction of the apoenzyme present in the solution is less than 1.7 × 10(-7) (i.e., the solution is 99.9999% holoenzyme). This is an extreme case where the crystal structure represents an insignificant fraction of the enzyme in solution, and a mechanism rationalizing this phenomenon is presented.

Line shape analysis of two-dimensional infrared spectra.

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.

Relationship of femtosecond-picosecond dynamics to enzyme-catalyzed H-transfer.

At physiological temperatures, enzymes exhibit a broad spectrum of conformations, which interchange via thermally activated dynamics. These conformations are sampled differently in different complexes of the protein and its ligands, and the dynamics of exchange between these conformers depends on the mass of the group that is moving and the length scale of the motion, as well as restrictions imposed by the globular fold of the enzymatic complex. Many of these motions have been examined and their role in the enzyme function illuminated, yet most experimental tools applied so far have identified dynamics at time scales of seconds to nanoseconds, which are much slower than the time scale for H-transfer between two heavy atoms. This chemical conversion and other processes involving cleavage of covalent bonds occur on picosecond to femtosecond time scales, where slower processes mask both the kinetics and dynamics. Here we present a combination of kinetic and spectroscopic methods that may enable closer examination of the relationship between enzymatic C-H → C transfer and the dynamics of the active site environment at the chemically relevant time scale. These methods include kinetic isotope effects and their temperature dependence, which are used to study the kinetic nature of the H-transfer, and 2D IR spectroscopy, which is used to study the dynamics of transition-state- and ground-state-analog complexes. The combination of these tools is likely to provide a new approach to examine the protein dynamics that directly influence the chemical conversion catalyzed by enzymes.

2D IR spectroscopy using four-wave mixing, pulse shaping, and IR upconversion: a quantitative comparison.

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 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.

Characterizing the dynamics of functionally relevant complexes of formate dehydrogenase.

The potential for femtosecond to picosecond time-scale motions to influence the rate of the intrinsic chemical step in enzyme-catalyzed reactions is a source of significant controversy. Among the central challenges in resolving this controversy is the difficulty of experimentally characterizing thermally activated motions at this time scale in functionally relevant enzyme complexes. We report a series of measurements to address this problem using two-dimensional infrared spectroscopy to characterize the time scales of active-site motions in complexes of formate dehydrogenase with the transition-state-analog inhibitor azide (N(3)(-)). We observe that the frequency-frequency time correlation functions (FFCF) for the ternary complexes with NAD(+) and NADH decay completely with slow time constants of 3.2 ps and 4.6 ps, respectively. This result suggests that in the vicinity of the transition state, the active-site enzyme structure samples a narrow and relatively rigid conformational distribution indicating that the transition-state structure is well organized for the reaction. In contrast, for the binary complex, we observe a significant static contribution to the FFCF similar to what is seen in other enzymes, indicating the presence of the slow motions that occur on time scales longer than our measurement window.

Increasing Pump-Probe Signal toward Asymptotic Limits.

Optimization of pump-probe signal requires a complete understanding of how signal scales with experimental factors. In simple systems, signal scales quadratically with molar absorptivity, and linearly with fluence, concentration, and path length. In practice, scaling factors weaken beyond certain thresholds (e.g., OD > 0.1) due to asymptotic limits related to optical density, fluence and path length. While computational models can accurately account for subdued scaling, quantitative explanations often appear quite technical in the literature. This Perspective aims to present a simpler understanding of the subject with concise formulas for estimating absolute magnitudes of signal under both ordinary and asymptotic scaling conditions. This formulation may be more appealing for spectroscopists seeking rough estimates of signal or relative comparisons. We identify scaling dependencies of signal with respect to experimental parameters and discuss applications for improving signal under broad conditions. We also review other signal enhancement methods, such as local-oscillator attenuation and plasmonic enhancement, and discuss respective benefits and challenges regarding asymptotic limits that signal cannot exceed.

Hydrogen donor-acceptor fluctuations from kinetic isotope effects: a phenomenological model.

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 quantum mechanics/molecular mechanics (QM/MM) calculations to provide a quantitative molecular understanding. Currently available phenomenological models use a nonadiabatic 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. This 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 nonenzymatic 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. This analysis does not replace molecular QM/MM investigations, but it provides a fast and accessible way to quantitatively interpret KIEs in the context of a Marcus-like model.

2D IR spectroscopy of the C-D stretching vibration of the deuterated formic acid dimer.

We report transient grating and 2D IR spectra of the C-D stretching vibration of deuterated formic acid dimer. The C-D stretching transition is perturbed by an accidental Fermi resonance interaction that gives rise to a second transition. The transient grating results show that the population lifetime of these states, which are in rapid equilibrium, is 11 ps. 2D IR spectroscopy reveals the energies of the eigenstates in the regions of one quantum and two quanta of C-D stretching excitation. Using these eigenstate energies, we construct a simplified model for the zeroth-order states that we then use to simulate the 2D IR spectrum. The results of this simulation suggest that the model captures the essential features of the vibrational spectroscopy in the region of the C-D stretching transition and compares well with previous gas-phase spectroscopy of the C-D stretch of deuterated formic acid dimer.

Two-dimensional infrared spectroscopy of azido-nicotinamide adenine dinucleotide in water.

Mid-IR active analogs of enzyme cofactors have the potential to be important spectroscopic reporters of enzyme active site dynamics. Azido-nicotinamide adenine dinucleotide (NAD(+)), which has been recently synthesized in our laboratory, is a mid-IR active analog of NAD(+), a ubiquitous redox cofactor in biology. In this study, we measure the frequency-frequency time correlation function for the antisymmetric stretching vibration of the azido group of azido-NAD(+) in water. Our results are consistent with previous studies of pseudohalides in water. We conclude that azido-NAD(+) is sensitive to local environmental fluctuations, which, in water, are dominated by hydrogen-bond dynamics of the water molecules around the probe. Our results demonstrate the potential of azido-NAD(+) as a vibrational probe and illustrate the potential of substituted NAD(+)-analogs as reporters of local structural dynamics that could be used for studies of protein dynamics in NAD-dependent enzymes.

Least-Squares Fitting of Multidimensional Spectra to Kubo Line-Shape Models.

We report a comprehensive study of the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo line-shape models and introduce a novel least-squares fitting metric, termed the scale invariant gradient norm (SIGN), that enables a highly reliable and versatile algorithm. The precision of dephasing parameters is between 8× and 50× better for nonlinear model fitting compared to that for the centerline-slope (CLS) method, which effectively increases data acquisition efficiency by 1-2 orders of magnitude. Whereas the CLS method requires sequential fitting of both the nonlinear and linear spectra, our model fitting algorithm only requires nonlinear spectra but accurately predicts the linear spectrum. We show an experimental example in which the CLS time constants differ by 60% for independent measurements of the same system, while the Kubo time constants differ by only 10% for model fitting. This suggests that model fitting is a far more robust method of measuring spectral diffusion than the CLS method, which is more susceptible to structured residual signals that are not removable by pure solvent subtraction. Statistical analysis of the CLS method reveals a fundamental oversight in accounting for the propagation of uncertainty by Kubo time constants in the process of fitting to the linear absorption spectrum. A standalone desktop app and source code for the least-squares fitting algorithm are freely available, with example line-shape models and data. We have written the MATLAB source code in a generic framework where users may supply custom line-shape models. Using this application, a standard desktop fits a 12-parameter generalized Kubo model to a 106 data-point spectrum in a few minutes.