Multidimensional tunneling, recrossing, and the transmission coefficient for enzymatic reactions

Development of an Elementary Reaction-Based Kinetic Model to Predict the Aqueous-Phase Fate of Organic Compounds Induced by Reactive Free Radicals

ConspectusAqueous-phase free radicals such as reactive oxygen, halogen, and nitrogen species play important roles in the fate of organic compounds in the aqueous-phase advanced water treatment processes and natural aquatic environments under sunlight irradiation. Predicting the fate of organic compounds in aqueous-phase advanced water treatment processes and natural aquatic environments necessitates understanding the kinetics and reaction mechanisms of initial reactions of free radicals with structurally diverse organic compounds and other reactions. Researchers developed conventional predictive models based on experimentally measured transformation products and determined reaction rate constants by fitting with the time-dependent concentration profiles of species due to difficulties in their measurements of unstable intermediates. However, the empirical treatment of lumped reaction mechanisms had a model prediction limitation with respect to the specific parent compound's fate. We use ab initio and density functional theory quantum chemical computations, numerical solutions of ordinary differential equations, and validation of the outcomes of the model with experiments. Sensitivity analysis of reaction rate constants and concentration profiles enables us to identify an important elementary reaction in formating the transformation product. Such predictive elementary reaction-based kinetics models can be used to screen organic compounds in water and predict their potentially toxic transformation products for a specific experimental investigation.Over the past decade, we determined linear free energy relationships (LFERs) that bridge the kinetic and thermochemical properties of reactive oxygen species such as hydroxyl radicals (HO•), peroxyl radicals (ROO•), and singlet oxygen (1O2); reactive halogen species such as chlorine radicals (Cl•) and bromine radicals (Br•); reactive nitrogen species (NO2•); and carbonate radicals (CO3•-). We used literature-reported experimental rate constants as kinetic information. We considered the theoretically calculated aqueous-phase free energy of activation or reaction to be a kinetic or a thermochemical property, and obtained via validated ab initio or density functional theory-based quantum chemical computations using explicit and implicit solvation models. We determined rate-determining reaction mechanisms involved in reactions by observing robust LFERs. The general accuracy of LFERs to predict aqueous-phase rate constants was within a difference of a factor of 2-5 from experimental values.We developed elementary reaction-based kinetic models and predicted the fate of acetone induced by HO• in an advanced water treatment process and methionine by photochemically produced reactive intermediates in sunlit fresh waters. We provided mechanistic insight into peroxyl radical reaction mechanisms and critical roles in the degradation of acetone and the formation of transformation products. We highlighted different roles of triplet excited states of two surrogate CDOMs, 1O2, and HO•, in methionine degradation. Predicted transformation products were compared to those obtained via benchtop experiments to validate our elementary reaction-based kinetic models. Predicting the reactivities of reactive halogen and nitrogen species implicates our understanding of the formation of potentially toxic halogen- and nitrogen-containing transformation products during water treatment processes and in natural aquatic environments.

Quantum Tunneling Instability in Pericyclic Reactions

Several cycloreversion reactions of the retro-Diels-Alder type were computationally assessed to understand their quantum tunneling (QT) reactivity. N2, CO, and other leaving groups were considered based on their strong exothermicity, as it reduces their thermodynamic and kinetic stabilities. Our results indicate that for many of these reactions, it is essential to take into account their QT decomposition rate, which can massively weaken their molecular stability and shorten their half-lives even at deep cryogenic temperatures. In practical terms, this indicates that many supposedly stable molecules will actually be unsynthesizable or unisolable, and therefore trying to prepare or detect them would be a futile attempt. In addition, we discuss the importance of tunneling to correctly understand the enthalpy of activation and the collective atomic effect on the tunneling kinetic isotope effects to test if third-row atoms can tunnel in a chemical reaction. This project raises the question of the importance of in silico chemistry to guide in vitro chemistry, especially in cases where the latter cannot solve its own uncertainties.

Computational Investigation of the Covalent Inhibition Mechanism of Bruton's Tyrosine Kinase by Ibrutinib

Covalent inhibitors represent a promising class of therapeutic compounds. Nonetheless, rationally designing covalent inhibitors to achieve a right balance between selectivity and reactivity remains extremely challenging. To better understand the covalent binding mechanism, a computational study is carried out using the irreversible covalent inhibitor of Bruton tyrosine kinase (BTK) ibrutinib as an example. A multi-μs classical molecular dynamics trajectory of the unlinked inhibitor is generated to explore the fluctuations of the compound associated with the kinase binding pocket. Then, the reaction pathway leading to the formation of the covalent bond with the cysteine residue at position 481 via a Michael addition is determined using the string method in collective variables on the basis of hybrid quantum mechanical-molecular mechanical (QM/MM) simulations. The reaction pathway shows a strong correlation between the covalent bond formation and the protonation/deprotonation events taking place sequentially in the covalent inhibition reaction, consistent with a 3-step reaction with transient thiolate and enolates intermediate states. Two possible atomistic mechanisms affecting deprotonation/protonation events from the thiolate to the enolate intermediate were observed: a highly correlated direct pathway involving proton transfer to the Cα of the acrylamide warhead from the cysteine involving one or a few water molecules and a more indirect pathway involving a long-lived enolate intermediate state following the escape of the proton to the bulk solution. The results are compared with experiments by simulating the long-time kinetics of the reaction using kinetic modeling.

Activation volume and quantum tunneling in the hydrogen transfer reaction between methyl radical and methane: A first computational study

We present a theory of the effect of quantum tunneling on the basic parameter that characterizes the effect of pressure on the rate constant of chemical reactions in a dense phase, the activation volume. This theory results in combining, on the one hand, the extreme pressure polarizable continuum model, a quantum chemical method to describe the effect of pressure on the reaction energy profile in a dense medium, and, on the other hand, the semiclassical version of the transition state theory, which includes the effect of quantum tunneling through a transmission coefficient. The theory has been applied to the study of the activation volume of the model reaction of hydrogen transfer between methyl radical and methane, including the primary isotope substitution of hydrogen with deuterium (H/D). The analysis of the numerical results offers, for the first time, a clear insight into the effect of quantum tunneling on the activation volume for this hydrogen transfer reaction: this effect results from the different influences that pressure has on the competing thermal and tunneling reaction mechanisms. Furthermore, the computed kinetic isotope effect (H/D) on the activation volume for this model hydrogen transfer correlates well with the experimental data for more complex hydrogen transfer reactions.

The Intrinsic Barrier Width and Its Role in Chemical Reactivity

Chemical reactions are in virtually all cases understood and explained on the basis of depicting the molecular potential energy landscape, i.e., the change in atomic positions vs the free-energy change. With such landscapes, the features of the reaction barriers solely determine chemical reactivities. The Marcus dissection of the barrier height (activation energy) on such a potential into the thermodynamically independent (intrinsic) and the thermodynamically dependent (Bell-Evans-Polanyi) contributions successfully models the interplay of reaction rate and driving force. This has led to the well-known and ubiquitously used reactivity paradigm of "kinetic versus thermodynamic control". However, an analogous dissection concept regarding the barrier width is absent. Here we define and outline the concept of intrinsic barrier width and the driving force effect on the barrier width and report experimental as well as theoretical studies to demonstrate their distinct roles. We present the idea of changing the barrier widths of conformational isomerizations of some simple aromatic carboxylic acids as models and use quantum mechanical tunneling (QMT) half-lives as a read-out for these changes because QMT is particularly sensitive to barrier widths. We demonstrate the distinct roles of the intrinsic and the thermodynamic contributions of the barrier width on QMT half-lives. This sheds light on resolving conflicting trends in chemical reactivities where barrier widths are relevant and allows us to draw some important conclusions about the general relevance of barrier widths, their qualitative definition, and the consequences for more complete descriptions of chemical reactions.

Concerted versus stepwise proton transfer reactions in the [2, 2'-bipyridyl]-3-3'-diol molecule: A static and dynamic ab-initio investigation

The double proton transfer (PT) reaction has been investigated in the [2,2'-bipyridyl]-3-3'-diol, a complex molecule where the proton movements is coupled to significant rearrangement of the electronic structure. Moreover, the reaction could be concerted, that is the two protons are exchanged simultaneously, or stepwise, where the two protons are transferred sequentially. To this end, a static exploration of the potential energy surface (PES) was carried together with the analysis of the free-energy surface (FES), both surfaces being evaluated at density functional theory level and different exchange-correlation functionals. While the concerted mechanism has been clearly discharged, the characteristics of the stepwise PT significantly depends on the chosen functionals, some suggesting a clear stepwise mechanism characterized by a stable reaction intermediates and two transitions states, whereas other approaches propend for a asynchronous PT, with a single TS. These features appear on both PES and FES, albeit some differences appears due to their different nature.

Entropic barrier of water permeation through single-file channels

Facilitated water permeation through narrow biological channels is fundamental for all forms of life. Despite its significance in health and disease as well as for biotechnological applications, the energetics of water permeation are still elusive. Gibbs free energy of activation is composed of an enthalpic and an entropic component. Whereas the enthalpic contribution is readily accessible via temperature dependent water permeability measurements, estimation of the entropic contribution requires information on the temperature dependence of the rate of water permeation. Here, we estimate, by means of accurate activation energy measurements of water permeation through Aquaporin-1 and by determining the accurate single channel permeability, the entropic barrier of water permeation through a narrow biological channel. Thereby the calculated value for [Formula: see text] = 2.01 ± 0.82 J/(mol·K) links the activation energy of 3.75 ± 0.16 kcal/mol with its efficient water conduction rate of ~10¹⁰ water molecules/second. This is a first step in understanding the energetic contributions in various biological and artificial channels exhibiting vastly different pore geometries.

Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations

We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of 16/18O and 32/34S primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.

Experimental and Computational Study of Aryl-thiosemicarbazones Inhibiting Cruzain Reveals Reversible Inhibition and a Stepwise Mechanism

Trypanosoma cruzi is a parasite that infects about 6-7 million people worldwide, mostly in Latin America, causing Chagas disease. Cruzain, the main cysteine protease of T. cruzi, is a validated target for developing drug candidates for Chagas disease. Thiosemicarbazones are one of the most relevant warheads used in covalent inhibitors targeting cruzain. Despite its relevance, the mechanism of inhibition of cruzain by thiosemicarbazones is unknown. Here, we combined experiments and simulations to unveil the covalent inhibition mechanism of cruzain by a thiosemicarbazone-based inhibitor (compound 1). Additionally, we studied a semicarbazone (compound 2), which is structurally similar to compound 1 but does not inhibit cruzain. Assays confirmed the reversibility of inhibition by compound 1 and suggested a two-step mechanism of inhibition. The K_i was estimated to be 36.3 μM and K_i* to be 11.5 μM, suggesting the pre-covalent complex to be relevant for inhibition. Molecular dynamics simulations of compounds 1 and 2 with cruzain were used to propose putative binding modes for the ligands. One-dimensional (1D) quantum mechanics/molecular mechanics (QM/MM) potential of mean force (PMF) and gas-phase energies showed that the attack of Cys25-S^- on the C═S or C═O bond yields a more stable intermediate than the attack on the C═N bond of the thiosemicarbazone/semicarbazone. Two-dimensional (2D) QM/MM PMF revealed a putative reaction mechanism for compound 1, involving the proton transfer to the ligand, followed by the Cys25-S^- attack at C═S. The ΔG and energy barrier were estimated to be -1.4 and 11.7 kcal/mol, respectively. Overall, our results shed light on the inhibition mechanism of cruzain by thiosemicarbazones.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Quantum Tunneling in Reactions Modulated by External Electric Fields: Reactivity and Selectivity

Quantum tunneling and external electric fields (EEFs) can promote some reactions. However, the synergetic effect of an EEF on a tunneling-involving reaction and its temperature-dependence is not very clear. In this study, we extensively investigated how EEFs affect three reactions that involve hydrogen- or (ground- and excited-state) carbon-tunneling using reliable DFT, DLPNO-CCSD(T1), and variational transition-state theory methods. Our study revealed that oriented EEFs can significantly reduce the barrier and corresponding barrier width (and vice versa) through more electrostatic stabilization in transition states. These EEF effects enhance the nontunneling and tunneling-involving rates. Such EEF effects also decrease the crossover temperatures and quantum tunneling contribution, albeit with lower and thinner barriers. Moreover, EEFs can modulate and switch on/off the tunneling-driven 1,2-H migration of hydroxycarbenes under cryogenic conditions. Furthermore, our study predicts for the first time that EEF/tunneling synergy can control the chemo- or site-selectivity of one molecule bearing two similar/same reactive sites.

Origin of Catalysis by Nitroalkane Oxidase

The rate of proton abstraction of the carbon acid nitroethane by Asp402 is accelerated by a factor of 10⁸ in the enzyme nitroalkane oxidase (NAO) relative to that by the organic base acetate ion in water. The Cα proton of nitroalkanes is known to exhibit an abnormal correlation between its acidity strength and the rate of deprotonation, with an unusually slow rate of deprotonation in water. This work examines the origin of NAO catalysis, revealing that the rate enhancement by the enzyme is due to transition-state stabilization, restoring the normal behavior of the linear free energy relationship of Bronsted acids. Interestingly, NAO employs the ubiquitous cofactor flavin adenosine diphosphate (FAD) to perform the subsequent oxidation. Does the FAD cofactor also affect the catalytic rate of the initial proton transfer process of the overall nitroalkane oxidation? Classical molecular dynamics and path-integral simulations using a reaction-specific combined quantum mechanics/molecular mechanics (QM/MM) approach were carried out to obtain the free energy reaction profiles, or the potentials of mean force, for the enzymatic reaction and for a model reaction in aqueous solution, as well as for the 2'-deoxy-FAD co-factor-modified NAO. Free energy perturbation calculations suggest that transition-state stabilization of the reactive fragment is the primary cause of the catalytic effect. It is found that the FAD cofactor plays a crucial role in increasing the Cα proton acidity, via specific hydrogen bonding and π-stacking interactions, although these factors have a smaller effect on the enhancement of the rate of deprotonation. Model QM calculations of the π-stacking complexes between the FAD isoalloxazine ring and the neutral and anionic nitroethane, respectively, reveal that the anionic π-stacking complex is more stable than the neutral one by 15.7 kcal/mol, and a net π-stacking energy of 17.3 kcal/mol is obtained. Hence, the isoalloxazine ring, in addition to serving as a very potent oxidizing agent via the formation of covalent intermediate structures, is able to exert a considerable amount of catalytic effect through noncovalent π-stacking interactions.

C-H Insertion in Dirhodium Tetracarboxylate-Catalyzed Reactions despite Dynamical Tendencies toward Fragmentation: Implications for Reaction Efficiency and Catalyst Design

Rh-catalyzed C-H insertion reactions to form β-lactones suffer from post-transition state bifurcations, with the same transition states leading to ketones and ketenes via fragmentation in addition to β-lactones. In such a circumstance, traditional transition state theory cannot predict product selectivity, so we employed ab initio molecular dynamics simulations to do so and provide a framework for rationalizing the origins of said selectivity. Weak interactions between the catalyst and substrate were studied using energy decomposition and noncovalent interaction analyses, which unmasked an important role of the 2-bromophenyl substituent that has been used in multiple β-lactone-forming C-H insertion reactions. Small and large catalysts were shown to behave differently, with the latter providing a means of overcoming dynamically preferred fragmentation by lowering the barrier for the recombination of the product fragments in the grip of the large catalyst active site cavity.

Exploring the Photophysics of a Zn2+ Fluorescence Sensor and Its Sensing Mechanism

Sensor X is a turn-on sensor, which is applied in the fluorescence detection of Zn²⁺ ions. Its photophysical process is comprehensively investigated to clarify its weak fluorescence. With the aid of density functional theory (DFT) and time-dependent density functional theory (TDDFT), the potential energy surfaces (PES) of X on both ground and first excited states are studied. Excited-state intramolecular proton transfer (EPT) processes as well as molecule twisting motion are observed, which induces several minima on the excited-state PES. Transition states as well as rate constants for these dynamic processes are obtained to evaluate their occurrences. The twisting motion of the sensor is an ultrafast process, which is initiated by a specific EPT process and leads to a nonemissive twisted intramolecular charge transfer (TICT) state. The fluorescence of the sensor is barely observable because of the easily attainable TICT state on the excited PES. This mechanism is trustworthy and intrinsically different from the previously proposed mechanism. After clarifying the photophysical process of the sensor, the Zn²⁺ sensing mechanism is uncovered. Also, the selectivity against Cd²⁺ and Hg²⁺ is fully discussed.

Modulation of proton-coupled electron transfer reactions in lysine-containing alpha-helixes: alpha-helixes promoting long-range electron transfer

The proton-coupled electron transfer (PCET) reaction plays an important role in promoting many biological and chemical reactions. Usually, the rate of the PCET reaction increases with an increase in the electron transfer distance because long-range electron transfer requires more free energy barriers. Our density functional theory calculations here reveal that the mechanism of PCET occurring in lysine-containing alpha(α)-helixes changes with an increasing number of residues in the α-helical structure and the different conformations because of the modulation of the excess electron distribution by the α-helical structures. The rate constants of the corresponding PCET reactions are independent of or substantially shallower dependent on the electron transfer distances along α-helixes. This counter-intuitive behavior can be attributed to the fact that the formation of larger macro-cylindrical dipole moments in longer helixes can promote electron transfer along the α-helix with a low energy barrier. These findings may be useful to gain insights into long-range electron transfer in proteins and design α-helix-based electronics via the regulation of short-range proton transfer.

Modeling the Ligand Effect on the Structure of CYP 450 Within the Density Functional Theory

An improved understanding of the P450 structure is relevant to the development of biomimetic catalysts and inhibitors for controlled CH-bond activation, an outstanding challenge of synthetic chemistry. Motivated by the experimental findings of an unusually short Fe-S bond of 2.18 Å for the wild-type (WT) OleT P450 decarboxylase relative to a cysteine pocket mutant form (A369P), a computational model that captures the effect of the thiolate axial ligand on the iron-sulfur distance is presented. With the computational efficiency and streamlined analysis in mind, this model combines a cluster representation of the enzyme─40-110 atoms, depending on the heme and ligand truncation level─with a density functional theory (DFT) description of the electronic structure (ES) and is calibrated against the experimental data. The optimized Fe-S distances show a difference of 0.25 Å between the low and high spin states, in agreement with the crystallographic structures of the OleT WT and mutant forms. We speculate that this difference is attributable to the packing of the ligand; the mutant is bulkier due to an alanine-to-proline replacement, meaning that it is excluded from the energetically favored low-spin minimum because of steric constraints. The presence of pure spin-state pairs and the intersection of the low/high spin states for the enzyme model is indicative of the limitations of single-reference ES methods in such systems and emphasizes the significance of using the proper state when modeling the hydrogen atom transfer (HAT) reaction catalyzed by OleT. At the same time, the correct characterization of both the short and long Fe-S bonds within a small DFT-based model of 42 atoms paves the way for quantum dynamics modeling of the HAT step, which initiates the OleT decarboxylation reaction.

Experimental and Theoretical Examination of the Kinetic Isotope Effect in Cytochrome P450 Decarboxylase OleT

Using a combination of experimental studies, theory, simulation, and modeling, we investigate the hydrogen atom transfer (HAT) reaction by the high-valent ferryl cytochrome P450 (CYP) intermediate known as Compound I, a species that is central to innumerable and important detoxification and biosynthetic reactions. The P450 decarboxylase known as OleT converts fatty acids, a sustainable biological feedstock, into terminal alkenes and thus is of high interest as a potential means to produce fungible biofuels. Previous experimental work has established the intermediacy of Compound I in the C─C scission reaction catalyzed by OleT and an unprecedented ability to monitor the HAT process in the presence of bound fatty acid substrates. Here, we leverage the kinetic simplicity of the OleT system to measure the activation barriers for CYP HAT and the temperature dependence of the substrate ²H kinetic isotope effect. Notably, neither measurement has been previously accessible for a CYP to date. Theoretical analysis alludes to the significance of substrate fatty acid coordination for generating the hydrogen donor/acceptor configurations that are most conducive for HAT to occur. The analysis of the two-dimensional potential energy surface, based on multireference electronic wave functions, illustrates the uncoupled character of the hydrogen motion. Quantum dynamics calculations along the hydrogen reaction path demonstrate that hydrogen tunneling is essential to qualitatively capture the experimental isotope effect, its temperature dependence, and appropriate activation energies. Overall, a more fundamental understanding of the OleT reaction coordinate contributes to the development of biomimetic catalysts for controlled C─H bond activation, an outstanding current challenge for (bio)synthetic chemistry.

New Insights and Predictions into Complex Homogeneous Reactions Enabled by Computational Chemistry in Synergy with Experiments: Isotopes and Mechanisms

Homogeneous catalysis and biocatalysis have been widely applied in synthetic, medicinal, and energy chemistry as well as synthetic biology. Driven by developments of new computational chemistry methods and better computer hardware, computational chemistry has become an essentially indispensable mechanistic "instrument" to help understand structures and decipher reaction mechanisms in catalysis. In addition, synergy between computational and experimental chemistry deepens our mechanistic understanding, which further promotes the rational design of new catalysts. In this Account, we summarize new or deeper mechanistic insights (including isotope, dispersion, and dynamical effects) into several complex homogeneous reactions from our systematic computational studies along with subsequent experimental studies by different groups. Apart from uncovering new mechanisms in some reactions, a few computational predictions (such as excited-state heavy-atom tunneling, steric-controlled enantioswitching, and a new geminal addition mechanism) based on our mechanistic insights were further verified by ensuing experiments.The Zimmerman group developed a photoinduced triplet di-π-methane rearrangement to form cyclopropane derivatives. Recently, our computational study predicted the first excited-state heavy-atom (carbon) quantum tunneling in one triplet di-π-methane rearrangement, in which the reaction rates and ¹²C/¹³C kinetic isotope effects (KIEs) can be enhanced by quantum tunneling at low temperatures. This unprecedented excited-state heavy-atom tunneling in a photoinduced reaction has recently been verified by an experimental ¹²C/¹³C KIE study by the Singleton group. Such combined computational and experimental studies should open up opportunities to discover more rare excited-state heavy-atom tunneling in other photoinduced reactions. In addition, we found unexpectedly large secondary KIE values in the five-coordinate Fe(III)-catalyzed hetero-Diels-Alder pathway, even with substantial C-C bond formation, due to the non-negligible equilibrium isotope effect (EIE) derived from altered metal coordination. Therefore, these KIE values cannot reliably reflect transition-state structures for the five-coordinate metal pathway. Furthermore, our density functional theory (DFT) quasi-classical molecular dynamics (MD) simulations demonstrated that the coordination mode and/or spin state of the iron metal as well as an electric field can affect the dynamics of this reaction (e.g., the dynamically stepwise process, the entrance/exit reaction channels).Moreover, we unveiled a new reaction mechanism to account for the uncommon Ru(II)-catalyzed geminal-addition semihydrogenation and hydroboration of silyl alkynes. Our proposed key gem-Ru(II)-carbene intermediates derived from double migrations on the same alkyne carbon were verified by crossover experiments. Additionally, our DFT MD simulations suggested that the first hydrogen migration transition-state structures may directly and quickly form the key gem-Ru-carbene structures, thereby "bypassing" the second migration step. Furthermore, our extensive study revealed the origin of the enantioselectivity of the Cu(I)-catalyzed 1,3-dipolar cycloaddition of azomethine ylides with β-substituted alkenyl bicyclic heteroarenes enabled by dual coordination of both substrates. Such mechanistic insights promoted our computational predictions of the enantioselectivity reversal for the corresponding monocyclic heteroarene substrates and the regiospecific addition to the less reactive internal C═C bond of one diene substrate. These predictions were proven by our experimental collaborators. Finally, our mechanistic insights into a few other reactions are also presented. Overall, we hope that these interactive computational and experimental studies enrich our mechanistic understanding and aid in reaction development.

Quantum Tunnelling Driven H2 Formation on Graphene

It is commonly believed that it is unfavorable for adsorbed H atoms on carbonaceous surfaces to form H₂ without the help of incident H atoms. Using ring-polymer instanton theory to describe multidimensional tunnelling effects, combined with ab initio electronic structure calculations, we find that these quantum-mechanical simulations reveal a qualitatively different picture. Recombination of adsorbed H atoms, which was believed to be irrelevant at low temperature due to high barriers, is enabled by deep tunnelling, with reaction rates enhanced by tens of orders of magnitude. Furthermore, we identify a new path for H recombination that proceeds via multidimensional tunnelling but would have been predicted to be unfeasible by a simple one-dimensional description of the reaction. The results suggest that hydrogen molecule formation at low temperatures are rather fast processes that should not be ignored in experimental settings and natural environments with graphene, graphite, and other planar carbon segments.

Ruthenium hydrides encapsulated in sol–gel glasses exhibit new ultrafast vibrational dynamics

Vibrational dynamics were measured by IR pump–probe spectroscopy and two-dimensional IR spectroscopy for triruthenium dodecacarbonyl and the undecacarbonyl hydride that forms when it is encapsulated in an alumina sol–gel glass. For comparison, a triruthenium undecacarbonyl hydride salt was also synthesized and studied in neat solution to identify the potential influence of the confined solvent environment on the dynamics experienced by carbon monoxide ligands. The vibrational lifetime was found to be significantly decreased for both hydride species relative to the dodecacarbonyl compound. Conversely, spectral diffusion of the CO vibrations was measured to be faster for the parent compound. The most significant dynamic changes occurred upon transformation from the starting compound to the hydride, while only minor differences were observed between the dynamics of the freely dissolved and sol–gel encapsulated hydrides. The results suggest that the structural change to the hydride has the largest impact on the dynamics and that its improved catalytic properties likely do not originate from confined solvent effects.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Structural basis of the membrane intramolecular transacylase reaction responsible for lyso-form lipoprotein synthesis

Lipoproteins serve diverse functions in the bacterial cell and some are essential for survival. Some lipoproteins are adjuvants eliciting responses from the innate immune system of the host. The growing list of membrane enzymes responsible for lipoprotein synthesis includes the recently discovered lipoprotein intramolecular transacylase, Lit. Lit creates a lipoprotein that is less immunogenic, possibly enabling the bacteria to gain a foothold in the host by stealth. Here, we report the crystal structure of the Lit enzyme from Bacillus cereus and describe its mechanism of action. Lit consists of four transmembrane helices with an extracellular cap. Conserved residues map to the cap-membrane interface. They include two catalytic histidines that function to effect unimolecular transacylation. The reaction involves acyl transfer from the sn-2 position of the glyceryl moiety to the amino group on the N-terminal cysteine of the substrate via an 8-membered ring intermediate. Transacylation takes place in a confined aromatic residue-rich environment that likely evolved to bring distant moieties on the substrate into proximity and proper orientation for catalysis.

Mechanistic Insight into the Reactivities of Aqueous-Phase Singlet Oxygen with Organic Compounds

Singlet oxygen (¹O₂) is a selective reactive oxygen species that plays a key role for the fate of various organic compounds in the aquatic environment under sunlight irradiation, engineered water oxidation systems, atmospheric water droplets, and biomedical systems. While the initial rate-determining charge-transfer reaction mechanisms and kinetics of ¹O₂ have been studied extensively, no comprehensive studies have been performed to elucidate the reaction mechanisms with organic compounds that have various functional groups. In this study, we use density functional theory calculations to determine elementary reaction mechanisms with a wide variety of organic compounds. The theoretically calculated aqueous-phase free energies of activation of single electron transfer and ¹O₂ addition reactions are compared to the experimentally determined rate constants in the literature to determine linear free-energy relationships. The theoretically calculated free energies of activation for the groups of phenolates and phenols show excellent correlations with the Hammett constants that accept electron densities by through-resonance. The dominant elementary reaction mechanism is discussed for each group of compounds. As a practical implication, we demonstrate the fate of environmentally relevant organic compounds induced by photochemically produced intermediate species at different pH and evaluate the impact of predicting rate constants to the half-life.

Large Anharmonic Effects on Tunneling and Kinetics: Reaction of Propane with Muonium

Calculations of kinetic isotope effects (KIEs) provide challenging tests of quantal mass effects on reaction rates, and muonium KIEs are the most challenging. Here, we show that it can be very important to include reaction-coordinate-dependent vibrational anharmonicity along the whole reaction path to calculate tunneling probabilities and KIEs. For the reaction of propane with Mu, this decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants. Our results agree well with the experimental observations.

Chemical reactivity from the vibrational ground-state level. The role of the tunneling path in the tautomerization of urea and derivatives

Recent developments of low-temperature techniques are providing valuable knowledge about chemical processes that manifest in the quantum regimen. The tunneling effect from the vibrational ground-state is the main mechanism of these reactions, which usually involves the motion or transfer of hydrogen atoms. Theoretical methods can enrich the information supplied by these experimental methods through an insightful analysis of the tunneling process. In this context, canonical variational transition state theory with multidimensional tunneling corrections (CVT/MT) can handle this type of reaction, and it has been applied to several systems within the small-curvature approximation for tunneling (SCT). This method is of proven reliability for polyatomic reactions occurring at room temperature and above, but no tests have been performed to check its performance when only the lowest energy level is populated. In this work, we compare SCT against the least-action tunneling (LAT) method to study the tautomerization and cis-trans interconversion reactions in the enol forms of urea, thiourea, and selenourea. To the best of our knowledge, this is the first time that the LAT method is applied to a polyatomic reaction occurring in the deep-tunneling region. The theoretical results indicate that the reaction mechanisms are controlled by tunneling. The SCT and LAT tautomerization reaction times are in good agreement with the experimental values; however, LAT seems superior to SCT for reactions (tautomerizations) that involve moderate reaction path curvature, whereas the opposite is true for reactions with small curvature (interconversions). These results led us to introduce and recommend the microcanonically optimized tunneling path that selects the tunneling probability as the maximum between the SCT and LAT tunneling probabilities.

Multi-level free energy simulation with a staged transformation approach

Combining multiple levels of theory in free energy simulations to balance computational accuracy and efficiency is a promising approach for studying processes in the condensed phase. While the basic idea has been proposed and explored for quite some time, it remains challenging to achieve convergence for such multi-level free energy simulations as it requires a favorable distribution overlap between different levels of theory. Previous efforts focused on improving the distribution overlap by either altering the low-level of theory for the specific system of interest or ignoring certain degrees of freedom. Here, we propose an alternative strategy that first identifies the degrees of freedom that lead to gaps in the distributions of different levels of theory and then treats them separately with either constraints or restraints or by introducing an intermediate model that better connects the low and high levels of theory. As a result, the conversion from the low level to the high level model is done in a staged fashion that ensures a favorable distribution overlap along the way. Free energy components associated with different steps are mostly evaluated explicitly, and thus, the final result can be meaningfully compared to the rigorous free energy difference between the two levels of theory with limited and well-defined approximations. The additional free energy component calculations involve simulations at the low level of theory and therefore do not incur high computational costs. The approach is illustrated with two simple but non-trivial solution examples, and factors that dictate the reliability of the result are discussed.

Electric Field Measurements Reveal the Pivotal Role of Cofactor-Substrate Interaction in Dihydrofolate Reductase Catalysis

The contribution of ligand–ligand electrostatic interaction to transition state formation during enzyme catalysis has remained unexplored, even though electrostatic forces are known to play a major role in protein functions and have been investigated by the vibrational Stark effect (VSE). To monitor electrostatic changes along important steps during catalysis, we used a nitrile probe (T46C-CN) inserted proximal to the reaction center of three dihydrofolate reductases (DHFRs) with different biophysical properties, Escherichia coli DHFR (EcDHFR), its conformationally impaired variant (EcDHFR-S148P), and Geobacillus stearothermophilus DHFR (BsDHFR). Our combined experimental and computational approach revealed that the electric field projected by the substrate toward the probe negates those exerted by the cofactor when both are bound within the enzymes. This indicates that compared to previous models that focus exclusively on subdomain reorganization and protein–ligand contacts, ligand–ligand interactions are the key driving force to generate electrostatic environments conducive for catalysis.

Kinetic Isotope Effects and Hydrogen Tunnelling in PCET Oxidations of Ascorbate: New Insights into Aqueous Chemistry?

Recent experimental studies of kinetic isotope effects (KIE-s) and hydrogen tunnelling comprising three proton-coupled electron transfer (PCET) oxidations of ascorbate monoanion, (a) in aqueous reaction solutions, (b) in the mixed water-organic cosolvent systems, (c) in aqueous solutions of various salts and (d) in fairly diluted aqueous solutions of the various partial hydrophobes are reviewed. A number of new insights into the wealth of the kinetic isotope phenomena in the PCET reactions have been obtained. The modulation of KIE-s and hydrogen tunnelling observed when partially hydrophobic solutes are added into water reaction solution, in the case of fairly diluted solutions is revealed as the strong linear correlation of the isotopic ratios of the Arrhenius prefactors Ah/Ad and the isotopic differences in activation energies ΔE_a (D,H). The observation has been proposed to be a signature of the involvement of the collective intermolecular excitonic vibrational dynamics of water in activation processes and aqueous chemistry.

Role of Microsolvation and Quantum Effects in the Accurate Prediction of Kinetic Isotope Effects: The Case of Hydrogen Atom Abstraction in Ethanol by Atomic Hydrogen in Aqueous Solution

Hydrogen abstraction from ethanol by atomic hydrogen in aqueous solution is studied using two theoretical approaches: the multipath variational transition state theory (MP-VTST) and a path-integral formalism in combination with free-energy perturbation and umbrella sampling (PI-FEP/UM). The performance of the models is compared to experimental values of H kinetic isotope effects (KIE). Solvation models used in this study ranged from purely implicit, via mixed–microsolvation treated quantum mechanically via the density functional theory (DFT) to fully explicit representation of the solvent, which was incorporated using a combined quantum mechanical-molecular mechanical (QM/MM) potential. The effects of the transition state conformation and the position of microsolvating water molecules interacting with the solute on the KIE are discussed. The KIEs are in good agreement with experiment when MP-VTST is used together with a model that includes microsolvation of the polar part of ethanol by five or six water molecules, emphasizing the importance of explicit solvation in KIE calculations. Both, MP-VTST and PI-FEP/UM enable detailed characterization of nuclear quantum effects accompanying the hydrogen atom transfer reaction in aqueous solution.

A Proton Wire Mediates Proton Coupled Electron Transfer from Hydroxyurea and Other Hydroxamic Acids to Tyrosyl Radical in Class Ia Ribonucleotide Reductase

Proton-coupled electron transfer (PCET) is fundamental to many important biological reactions, including solar energy conversion and DNA synthesis. For example, class Ia ribonucleotide reductases (RNRs) contain a tyrosyl radical-diiron cofactor with one aspartate ligand, D84. The tyrosyl radical, Y122^•, in the β2 subunit acts as a radical initiator and oxidizes an active site cysteine in the α2 subunit. A transient quaternary α2/β2 complex is induced by substrate and effector binding. The hydroxamic acid, hydroxyurea (HU), reduces Y122^• in a PCET reaction involving an electron and proton. This reaction is associated with the loss of activity, a conformational change at Y122, and a change in hydrogen bonding to the Fe1 ligand, D84. Here, we use isotopic labeling, solvent isotope exchange, proton inventories, and reaction-induced Fourier transform infrared (RIFT-IR) spectroscopy to show that the PCET reactions of hydroxamic acids are associated with a characteristic spectrum, which is assignable to electrostatic changes at nonligating aspartate residues. Notably, RIFT-IR spectroscopy reveals this characteristic spectrum when the effects of HU, hydroxylamine, and N-methylhydroxylamine are compared. A large solvent isotope effect is observed for each of the hydroxamic acid reactions, and proton inventories predict that the reactions are associated with the transfer of multiple protons in the transition state. The reduction of Y122^• with 4-methoxyphenol does not lead to these characteristic carboxylate shifts and is associated with only a small solvent isotope effect. In addition to studies of the effects of hydroxamic acids on β2 alone, the reactions involving the quaternary α2β2 complex were also investigated. HU treatment of the quaternary complex, α2/β2/ATP/CDP, leads to a similar carboxylate shift spectrum, as observed with β2 alone. The use of globally labeled ¹³C chimeras (¹³C α2, ¹³C β2) confirms the assignment. Because the spectrum is sensitive to ¹³C β2 labeling, but not ¹³C α2 labeling, the quaternary complex spectrum is assigned to electrostatic changes in β2 carboxylate groups. Examination of the β2 X-ray structure reveals a hydrogen-bonded network leading from the protein surface to Y122. This predicted network includes nonligating aspartates, glutamate ligands to the iron cluster, and predicted crystallographically resolved water molecules. The network is similar when class Ia RNR structures from Escherichia coli, human, and mouse are compared. We propose that the PCET reactions of hydroxamic acids are mediated by a hydrogen-bonded proton wire in the β2 subunit.

A protocol to obtain multidimensional quantum tunneling corrections derived from QM(DFT)/MM calculations for an enzyme reaction

The multidimensional small-curvature tunneling (SCT) method with Electrostatic Embedding calculations is a compromise between an accessible computational cost and the attainment of an accurate enough estimation of tunneling for an enzyme reaction.

Enhanced Rates of C-H Bond Cleavage by a Hydrogen-Bonded Synthetic Heme High-Valent Iron(IV) Oxo Complex

Secondary coordination sphere interactions are critical in facilitating the formation, stabilization, and enhanced reactivity of high-valent oxidants required for essential biochemical processes. Herein, we compare the C-H bond oxidizing capabilities of spectroscopically characterized synthetic heme iron(IV) oxo complexes, F8Cmpd-II (F8 = tetrakis(2,6-difluorophenyl)porphyrinate), and a 2,6-lutidinium triflate (LutH+) Lewis acid adduct involving ferryl O-atom hydrogen-bonding, F8Cmpd-II(LutH+). Second-order rate constants utilizing C-H and C-D substrates were obtained by UV-vis spectroscopic monitoring, while products were characterized and quantified by EPR spectroscopy and gas chromatography (GC). With xanthene, F8Cmpd-II(LutH+) reacts 40 times faster (k2 = 14.2 M-1 s-1; -90 °C) than does F8Cmpd-II, giving bixanthene plus xanthone and the heme product [F8FeIIIOH2]+. For substrates with greater C-H bond dissociation energies (BDEs) F8Cmpd-II(LutH+) reacts with the second order rate constants k2(9,10-dihydroanthracene; DHA) = 0.485 M-1 s-1 and k2(fluorene) = 0.102 M-1 s-1 (-90 °C); by contrast, F8Cmpd-II is unreactive toward these substrates. For xanthene vs xanthene-(d2), large, nonclassical deuterium kinetic isotope effects are roughly estimated for both F8Cmpd-II and F8Cmpd-II(LutH+). The deuterated H-bonded analog, F8Cmpd-II(LutD+), was also prepared; for the reaction with DHA, an inverse KIE (compared to F8Cmpd-II(LutH+)) was observed. This work originates/inaugurates experimental investigation of the reactivity of authentic H-bonded heme-based FeIV═O compounds, critically establishing the importance of oxo H-bonding (or protonation) in heme complexes and enzyme active sites.

Why are some Enzymes Dimers? Flexibility and Catalysis in Thermotoga Maritima Dihydrofolate Reductase

Dihydrofolate reductase from Thermotoga maritima (TmDFHFR) is a dimeric thermophilic enzyme that catalyzes the hydride transfer from the cofactor NADPH to dihydrofolate less efficiently than other DHFR enzymes, such as the mesophilic analogue Escherichia coli DHFR (EcDHFR). Using QM/MM potentials, we show that the reduced catalytic efficiency of TmDHFR is most likely due to differences in the amino acid sequence that stabilize the M20 loop in an open conformation, which prevents the formation of some interactions in the transition state and increases the number of water molecules in the active site. However, dimerization provides two advantages to the thermophilic enzyme: it protects its structure against denaturation by reducing thermal fluctuations and it provides a less negative activation entropy, toning down the increase of the activation free energy with temperature. Our molecular picture is confirmed by the analysis of the temperature dependence of enzyme kinetic isotope effects in different DHFR enzymes.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

Convergence of theory and experiment on the role of preorganization, quantum tunneling and enzyme motions into flavoenzyme-catalyzed hydride transfer

Hydride transfer is one of the most common reactions catalyzed by enzymatic systems and it has become an object of study due to possible significant quantum tunneling effects. In the present work, we provide a combination of theoretical QM/MM simulations and experimental measurements of the rate constants and kinetic isotopic effects (KIEs) for the hydride transfer reaction catalyzed by morphinone reductase, MR. Quantum mechanical tunneling coefficients, computed in the framework of variational transition-state theory, play a significant role in this reaction, reaching values of 23.8 ± 5.5 for the lightest isotopologue; one of the largest values reported for enzymatic systems. This prediction is supported by the agreement between the theoretically predicted rate constants and the corresponding experimental values. Simulations indicate that the role of protein motions can be satisfactorily described as equilibrium fluctuations along the reaction coordinate, in line with a high degree of preorganization displayed by this enzyme.

Quantum Suppression of Intramolecular Deuterium Kinetic Isotope Effects in a Pericyclic Hydrogen Transfer Reaction

It is generally accepted that hydrogen tunneling enhances both primary and secondary H/D kinetic isotope effects (KIEs) over what would be expected under the assumptions of classical barrier transition. Previous studies have exclusively shown that the effects of tunneling upon primary H/D KIEs have been much larger than those observed for secondary H/D KIEs. Here we present a series of experimental H/D KIE results associated with the Chugaev elimination of methyl xanthate derived from β-phenylethanol over the temperature range of 180 to 290 °C. Intramolecular H/D KIEs computed according to classical transition state theory (TST) are markedly overestimated relative to experimentally measured values. Experimental intermolecular H/D KIEs and direct dynamic calculations based on canonical variational transition state theory (CVT) with small-curvature tunneling correction (SCT) reveal that this result is largely the consequence of extraordinary tunneling enhancement of the secondary H/D KIE. This unexpected behavior is examined in the context of other similar hydrogen transfer reactions.

Linking inhibitor motions to proteolytic stability of sunflower trypsin inhibitor-1

The remarkable capability of an enzyme isn't only determined by its active site but also controlled by the environment. To unravel the environment role in catalysis, the dynamic motions as well as the static mechanism need to be studied. In this work, QM/MM MD simulations were employed to study the proteolysis process of SFTI-1 and BiKF, which revealed that a combination of static non-bonded interactions and dynamic motions along the reaction coordinate can account for the different hydrolysis rates between them. A comparison among SFTI-1 and three analogs with similar non-bonded interactions further revealed a positive correlation between the mobility of inhibitors and the hydrolysis rates. Apart from the cyclic backbone and disulfide bond, intramolecular hydrogen bonds also increase the rigidity of the backbone of inhibitors, and therefore hinder inhibitor motions to resist proteolysis. These new detailed mechanistic insights suggest the need to consider inhibitor motions in the rational design of peptide inhibitors.

Besides the non-bonded interactions, inhibitor motions especially rotation of the scissile bond also influence proteolytic stability.

Pushing the limits of concertedness. A waltz of wandering carbocations

Among the array of complex terpene-forming carbocation cyclization/rearrangement reactions, the so-called "triple shift" reactions are among the most unexpected. Such reactions involve the asynchronous combination of three 1,n-shifts into a concerted process, e.g., a 1,2-alkyl shift followed by a 1,3-hydride shift followed by a second 1,2-alkyl shift. This type of reaction so far has been proposed to occur during the biosynthesis of diterpenes and the sidechains of sterols. Here we describe efforts to push the limits of concertedness in this type of carbocation reaction by designing, and characterizing with quantum chemical computations, systems that could couple additional 1,n-shift events to a triple shift leading, in principle to quadruple, pentuple, etc. shifts. While our designs did not lead to clear-cut examples of quadruple, etc. shifts, they did lead to reactions with surprisingly flat energy surfaces where more than five chemical events connect reactants and plausible products. Ab initio molecular dynamics simulations demonstrate that the formal minima on these surfaces interchange on short timescales, both with each other and with additional unexpected structures, allowing us a glimpse into a very complex manifold that allows ready access to great structural diversity.

Computational Understanding of the Selectivities in Metalloenzymes

Metalloenzymes catalyze many different types of biological reactions with high efficiency and remarkable selectivity. The quantum chemical cluster approach and the combined quantum mechanics/molecular mechanics methods have proven very successful in the elucidation of the reaction mechanism and rationalization of selectivities in enzymes. In this review, recent progress in the computational understanding of various selectivities including chemoselectivity, regioselectivity, and stereoselectivity, in metalloenzymes, is discussed.

Temperature dependence of dynamic, tunnelling and kinetic isotope effects in formate dehydrogenase

The origin of the catalytic power of enzymes has been a question of debate for a long time. In this regard, the possible contribution of protein dynamics in enzymatic catalysis has become one of the most controversial topics. In the present work, the hydride transfer step in the formate dehydrogenase (FDH EC 1.2.1.2) enzyme is studied by means of molecular dynamic (MD) simulations with quantum mechanics/molecular mechanics (QM/MM) potentials in order to explore any correlation between dynamics, tunnelling effects and the rate constant. The temperature dependence of the kinetic isotope effects (KIEs), which is one of the few tests that can be studied by experiments and simulations to shed light on this debate, has been computed and the results have been compared with previous experimental data. The classical mechanical free energy barrier and the number of recrossing trajectories seem to be temperature-independent while the quantum vibrational corrections and the tunnelling effects are slightly temperature-dependent over the interval of 5-45 °C. The computed primary KIEs are in very good agreement with previous experimental data, being almost temperature-independent within the standard deviations. The modest dependence on the temperature is due to just the quantum vibrational correction contribution. These results, together with the analysis of the evolution of the collective variables such as the electrostatic potential or the electric field created by the protein on the key atoms involved in the reaction, confirm that while the protein is well preorganised, some changes take place along the reaction that favour the hydride transfer and the product release. Coordinates defining these movements are, in fact, part of the real reaction coordinate.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.