Isotopic Labeling of Formate Dehydrogenase Perturbs the Protein Dynamics

Study of the Effects of Remote Heavy Group Vibrations on the Temperature Dependence of Hydride Kinetic Isotope Effects of the NADH/NAD+ Model Reactions

It has recently been observed that the temperature(T)-dependence of KIEs in H-tunneling reactions, characterized by isotopic activation energy difference (ΔEa = EaD - EaH), is correlated to the rigidity of the tunneling ready states (TRSs) in enzymes. A more rigid system with narrowly distributed H-donor-acceptor distances (DADs) at the TRSs gives rise to a weaker T-dependence of KIEs (i.e., a smaller ΔEa). Theoreticians have attempted to develop new H-tunneling models to explain this, but none has been universally accepted. In order to further understand the observations in enzymes and provide useful data to build new theoretical models, we have studied the electronic and solvent effects on ΔEa's for the hydride-tunneling reactions of NADH/NAD+ analogues. We found that a tighter charge-transfer (CT) complex system gives rises to a smaller ΔEa, consistent with the enzyme observations. In this paper, we use the remote heavy group (R) vibrational effects to mediate the system rigidity to study the rigidity-ΔEa relationship. The specific hypothesis is that slower vibrations of a heavier remote group would broaden the DAD distributions and increase the ΔEa value. Four NADH/NAD+ systems were studied in acetonitrile but most of such heavy group vibrations do not appear to significantly increase the ΔEa. The remote heavy group vibrations in these systems may have not affected the CT complexation rigidity to a degree that can significantly increase the DADs, and further, the ΔEa values.

Structural Effects on the Temperature Dependence of Hydride Kinetic Isotope Effects of the NADH/NAD+ Model Reactions in Acetonitrile: Charge-Transfer Complex Tightness Is a Key

It has recently frequently been found that the kinetic isotope effect (KIE) is independent of temperature (T) in H-tunneling reactions in enzymes but becomes dependent on T in their mutants. Many enzymologists found that the trend is related to different donor-acceptor distances (DADs) at tunneling-ready states (TRSs), which could be sampled by protein dynamics. That is, a more rigid system of densely populated short DADs gives rise to a weaker T dependence of KIEs. Theoreticians have attempted to develop H-tunneling theories to explain the observations, but none have been universally accepted. It is reasonable to assume that the DAD sampling concept, if it exists, applies to the H-transfer reactions in solution, as well. In this work, we designed NADH/NAD+ model reactions to investigate their structural effects on the T dependence of hydride KIEs in acetonitrile. Hammett correlations together with N-CH3/CD3 secondary KIEs were used to provide the electronic structure of the TRSs and thus the rigidity of their charge-transfer complexation vibrations. In all three pairs of reactions, a weaker T dependence of KIEs always corresponds to a steeper Hammett slope on the substituted hydride acceptors. It was found that a tighter/rigid charge-transfer complexation system corresponds with a weaker T dependence of KIEs, consistent with the observations in enzymes.

Correlation of temperature dependence of hydride kinetic isotope effects with donor-acceptor distances in two solvents of different polarities

Recently observed nearly temperature (T)-independent kinetic isotope effects (KIEs) in wild-type enzymes and T-dependent KIEs in variants were used to suggest that H-tunneling in enzymes is assisted by the fast protein vibrations that help sample short donor-acceptor distances (DADs). This supports the recently proposed role of protein vibrations in DAD sampling catalysis. However, use of T-dependence of KIEs to suggest DAD sampling associated with protein vibrations is debated. We have formulated a hypothesis regarding the correlation and designed experiments in solution to investigate it. The hypothesis is, a more rigid system with shorter DADTRS's at the tunneling ready states (TRSs) gives rise to a weaker T-dependence of KIEs, i.e., a smaller ΔEa (= EaD - EaH). In a former work, the solvent effects of acetonitrile versus chloroform on the ΔEa of NADH/NAD+ model reactions were determined, and the DADPRC's of the productive reactant complexes (PRCs) were computed to substitute the DADTRS for the DADTRS-ΔEa correlation study. A smaller ΔEa was found in the more polar acetonitrile where the positively charged PRC is better solvated and has a shorter DADPRC, indirectly supporting the hypothesis. In this work, the TRS structures of different DADTRS's for the hydride tunneling reaction from 1,3-dimethyl-2-phenylimidazoline to 10-methylacridinium were computed. The N-CH3/CD3 secondary KIEs on both reactants were calculated and fitted to the observed values to find the DADTRS order in both solutions. It was found that the equilibrium DADTRS is shorter in acetonitrile than in chloroform. Results directly support the DADTRS-ΔEa correlation hypothesis as well as the explanation that links T-dependence of KIEs to DAD sampling catalysis in enzymes.

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.

Solvent Effects on the Temperature Dependence of Hydride Kinetic Isotope Effects: Correlation to the Donor-Acceptor Distances

Protein structural effects on the temperature (T) dependence of kinetic isotope effects (KIEs) in H-tunneling reactions have recently been used to discuss about the role of enzyme thermal motions in catalysis. Frequently observed nearly T-independent KIEs in the wild-type enzymes and T-dependent KIEs in variants suggest that H-tunneling in the former is assisted by the naturally evolved protein constructive vibrations that help sample short donor-acceptor distances (DADs) needed. This explanation that correlates the T-dependence of KIEs with DAD sampling has been highly debated as simulations following other H-tunneling models sometimes gave alternative explanations. In this paper, solvent effects on the T-dependence of KIEs of two hydride tunneling reactions of NADH/NAD⁺ analogues (represented by ΔE_a = E_aD - E_aH) were determined in attempts to replicate the observations in enzymes and test the protein vibration-assisted DAD sampling concept. Effects of selected aprotic solvents on the DAD_PRC's of the productive reactant complexes (PRCs) and the DAD_TRS's of the activated tunneling ready states (TRSs) were obtained through computations and analyses of the kinetic data, including 2° KIEs, respectively. A weaker T-dependence of KIEs (i.e., smaller ΔE_a) was found in a more polar aprotic solvent in which the system has a shorter average DAD_PRC and DAD_TRS. Further results show that a charge-transfer (CT) complexation made of a stronger donor/acceptor gives rise to a smaller ΔE_a. Overall, the shorter and less broadly distributed DADs resulting from the stronger CT complexation vibrations give rise to a smaller ΔE_a. Our results appear to support the explanation that links the T-dependence of KIEs to the donor-acceptor rigidity in enzymes.

Method for Identifying Common Features in Reactive Trajectories of a Transition Path Sampling Ensemble

Simulation methods like transition path sampling (TPS) generate an abundance of information buried in the collection of reactive trajectories that they generate. However, only limited use has been made of this information, mainly for the identification of the reaction coordinate. The standard TPS tools have been designed for monitoring the progress of the system from reactants to products. However, the reaction coordinate does not contain all the information regarding the mechanism. In our earlier work, we have used TPS on enzymatic systems and have identified important motions in the reactant well that prepares the system for the reaction. Since these events take place in the reactant well, they are beyond the reach of standard TPS postprocessing methods. We present a simple scheme for identifying the common trends in enzymatic trajectories. This scheme was designed for a specific class of enzymatic reactions: it can be used for identifying motions that guide the system to reaction-ready conformations. We have applied it to two enzymatic systems that we have studied in the past, formate dehydrogenase and purine nucleoside phosphorylase, and we were able to identify interactions, far from the transition state, that are important for preparing the system for the reaction but that had been overlooked in earlier work.

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.

Temperature-Dependent Low-Frequency Modes in the Active Site of Bovine Carbonic Anhydrase II Probed by 2D-IR Spectroscopy

Enzyme catalysis achieves tremendous rate accelerations. Enzyme reaction centers provide a constraint geometry that preferentially binds an activated form of the substrate and thus lowers the energy barrier. However, this transition state picture neglects the flexibility of proteins and its role in enzymatic catalysis. Especially for proton transfer reactions, it has been suggested that motions of the protein modulate the donor-acceptor distance and prepare a tunneling-ready state. We report the detection of frequency fluctuations of an azide anion (N₃^-) bound in the active site of the protein carbonic anhydrase II, where a low-frequency mode of the protein has been proposed to facilitate proton transfer over two water molecules during the catalyzed reaction. 2D-IR spectroscopy resolves an underdamped low-frequency mode at about 1 THz (30 cm^-1). We find its frequency to be viscosity- and temperature-dependent and to decrease by 6 cm^-1 between 230 and 320 K, reporting the softening of the mode's potential.

Transparent window 2D IR spectroscopy of proteins

Proteins are complex, heterogeneous macromolecules that exist as ensembles of interconverting states on a complex energy landscape. A complete, molecular-level understanding of their function requires experimental tools to characterize them with high spatial and temporal precision. Infrared (IR) spectroscopy has an inherently fast time scale that can capture all states and their dynamics with, in principle, bond-specific spatial resolution. Two-dimensional (2D) IR methods that provide richer information are becoming more routine but remain challenging to apply to proteins. Spectral congestion typically prevents selective investigation of native vibrations; however, the problem can be overcome by site-specific introduction of amino acid side chains that have vibrational groups with frequencies in the "transparent window" of protein spectra. This Perspective provides an overview of the history and recent progress in the development of transparent window 2D IR of proteins.

Cryo-kinetics Reveal Dynamic Effects on the Chemistry of Human Dihydrofolate Reductase

Effects of isotopic substitution on the rate constants of human dihydrofolate reductase (HsDHFR), an important target for anti‐cancer drugs, have not previously been characterized due to its complex fast kinetics. Here, we report the results of cryo‐measurements of the kinetics of the HsDHFR catalyzed reaction and the effects of protein motion on catalysis. Isotopic enzyme labeling revealed an enzyme KIE (k_H^LE/k_H^HE) close to unity above 0 °C; however, the enzyme KIE was increased to 1.72±0.15 at −20 °C, indicating that the coupling of protein motions to the chemical step is minimized under optimal conditions but enhanced at non‐physiological temperatures. The presented cryogenic approach provides an opportunity to probe the kinetics of mammalian DHFRs, thereby laying the foundation for characterizing their transition state structure.

Role of Protein Motions in Catalysis by Formate Dehydrogenase

We have analyzed the reaction catalyzed by formate dehydrogenase using transition path sampling. This system has recently received experimental attention using infrared spectroscopy and heavy-enzyme studies. Some of the experimental results point to the possible importance of protein motions that are coupled to the chemical step. We found that the residue Val123 that lies behind the nicotinamide ring occasionally comes into van der Waals contact with the acceptor and that in all reactive trajectories, the barrier-crossing event is preceded by this contact, meaning that the motion of Val123 is part of the reaction coordinate. Experimental results have been interpreted with a two-dimensional formula for the chemical rate, which cannot capture effects such as the one we describe.

The Energetic Origin of Different Catalytic Activities in Temperature-Adapted Trypsins

Psychrophilic enzymes were always observed to have higher catalytic activity (k cat) than their mesophilic homologs at room temperature, while the origin of this phenomenon remains obscure. Here, we used two different temperature-adapted trypsins, the psychrophilic Atlantic cod trypsin (ACT) and the mesophilic bovine trypsin (BT), as a model system to explore the energetic origin of their different catalytic activities using computational methods. The results reproduce the characteristic changing trends in the activation free energy, activation enthalpy, and activation entropy between the psychrophilic and mesophilic enzymes, where, in particular, the slightly decreased activation free energy of ACT is determined by its considerably reduced activation enthalpy rather than by its more negative activation entropy compared to BT. The calculated electrostatic contributions to the solvation free energies in the reactant state/ground sate (RS/GS) and transition state (TS) show that, going from BT to ACT, the TS stabilization has a predominant effect over the RS stabilization on lowering the activation enthalpy of ACT. Comparison between the solvation energy components reveals a more optimized electrostatic preorganization to the TS in ACT, which provides a larger stabilization to the TS through reducing the reorganization energy, thus resulting in the lower activation enthalpy and hence lower activation free energy of ACT. Thus, it can be concluded that it is the difference in the protein electrostatic environment, and hence its different stabilizing effects on the TS, that brings about the different catalytic activities of different temperature-adapted trypsins.

Ultrafast Vibrational Energy Transfer between Protein and Cofactor in a Flavoenzyme

Protein motions and enzyme catalysis are often linked. It is hypothesized that ultrafast vibrations (femtosecond-picosecond) enhance the rate of hydride transfer catalyzed by members of the old yellow enzyme (OYE) family of ene-reductases. Here, we use time-resolved infrared (TRIR) spectroscopy in combination with stable "heavy" isotopic labeling (2H, 13C, 15N) of protein and/or cofactor to probe the vibrational energy transfer (VET) between pentaerythritol tetranitrate reductase (a member of the OYE family) and its noncovalently bound flavin mononucleotide (FMN) cofactor. We show that when the FMN cofactor is photoexcited with visible light, vibrational energy is transferred from the flavin to the surrounding protein environment on the picosecond timescale. This finding expands the scope of VET investigation in proteins, which are limited by suitable intrinsic probes, and may have implications in the understanding of the mechanism of recently discovered photoactive flavoenzymes.