Transition State Region Research Articles

Quantum Mechanical Description of Electrostatics Provides a Unified Picture of Catalytic Action Across Methyltransferases.

Methyl transferases (MTases) are a well-studied class of enzymes for which competing enzymatic enhancement mechanisms have been suggested, ranging from structural methyl group CH···X hydrogen bonds (HBs) to electrostatic- and charge-transfer-driven stabilization of the transition state (TS). We identified all Class I MTases for which reasonable resolution (<2.0 Å) crystal structures could be used to form catalytically competent ternary complexes for multiscale (i.e., quantum-mechanical/molecular-mechanical or QM/MM) simulation of the SN2 methyl transfer reaction coordinate. The four Class I MTases studied have both distinct functions (e.g., protein repair or biosynthesis) and substrate nucleophiles (i.e., C, N, or O). While CH···X HBs stabilize all reactant complexes, no universal TS stabilization role is found for these interactions in MTases. A consistent picture is instead obtained through analysis of charge transfer and electrostatics, wherein much of cofactor-substrate charge separation is maintained in the TS region, and electrostatic potential is correlated with substrate nucleophilicity (i.e., intrinsic reactivity).

Sampling the Folding Transition State Ensemble in a Tube-like Model of Protein

We used the tube model with Go-like potential for native contacts to study the folding transition of a designed three-helix bundle and a designed protein G-like structure. It is shown that both proteins in this model are two-state folders with a cooperative folding transition coincided with the collapse transition. We defined the transition states as protein conformations in a small region around the saddle point on a free energy surface with the energy and the conformationalroot mean square deviation (rmsd) from the native state as the coordinates. The transition state region on the free energy surface then was sampled by using umbrella sampling technique. We show that the transition state ensemble is broad consisting of different conformations that have different folded and unfolded elements.

Counter-propagating wave packets in the quantum transition state approach to reactive scattering.

The quantum transition state concept provides an intuitive and numerically efficient framework for the description of quantum state-resolved reactive scattering and thermal reaction processes. Combining multiconfigurational time-dependent Hartree wave packet dynamics calculations with a flux correlation function based analysis, rigorous full-dimensional calculations of initial state-selected and state-to-state reaction probabilities for six atom reactions are feasible. In these calculations, a set of wave packets is generated in the transition state region, propagated into the asymptotic area, and analyzed. In the present work, an alternative approach which employs counter-propagating sets of wave packets is introduced. Outgoing wave packets started in the transition state region are matched with incoming wave packets generated in the reactant (or product) asymptotic area. Studying the H + CH4 → H2 + CH3 reaction as a prototypical example, one finds that the incoming wave packets can be propagated closely up to the transition state region with minor numerical effort. Employing cross correlation functions of incoming and outgoing wavefunctions, the propagation times required for the outgoing wave packet and thus the numerical costs of the entire calculation can be reduced significantly. Detailed full-dimensional calculations studying initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction are presented to illustrate the new approach. It is found that converged results can be obtained using shorter propagation times of the outgoing wave packets and less single-particle functions.

Enhanced Sampling of Transition States.

The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes, enhanced sampling methods are used. While many such methods are able to obtain sufficient sampling in order to draw the free energy, the transition states are often sparsely sampled. We propose an approach based on the Variationally Enhanced Sampling Method to enhance sampling in the transition region. To this effect, we introduce a dynamic target distribution which uses the derivative of the instantaneous free energy surface to locate the transition regions on the fly and modulate the probability of sampling different regions. Finally, we exemplify the effectiveness of this approach in enriching the number of configurations in the transition state region in the cases of a chemical reaction and of a nucleation process.

Vibronically and spin-orbit coupled diabatic potentials for X(P) + CH4 → HX + CH3 reactions: General theory and application for X(P) = F(2P).

An approach to systematically construct vibronically and spin-orbit coupled diabatic potential energy surfaces (PESs) for X(P) + CH4 → HX + CH3 reactions is proposed. Permutational symmetry and permutational invariants of the S4 group and its S3 and S2 × S2 subgroups are used to construct a diabatic model which properly describes the reaction starting from reactants to products. As a first example, the approach is applied to the construction of diabatic potentials for the F(2P) + CH4 → HF + CH3 reaction. The description of the entrance channel relies on a set of vibronically and spin-orbit coupled diabatic PESs previously developed by Westermann et al. [Angew. Chem., Int. Ed. 53, 1122 (2014)]. The same set of diabatic electronic states is also used in the transition state region and all four exit channels. There the lowest adiabatic PES derived from the diabatic model reproduces the CSBB-PES of Czakó et al. [J. Chem. Phys. 130, 084301 (2009)]. Interesting aspects of the newly developed diabatic potential matrix and the corresponding adiabatic PESs are discussed.

Unbiased Atomistic Insight into the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation.

Association and dissociation of proteins are fundamental processes in nature. Although simple to understand conceptually, the details of the underlying mechanisms and role of the solvent are poorly understood. Here, we investigate the dissociation of the hydrophilic β-lactoglobulin dimer by employing transition path sampling. Analysis of the sampled path ensembles reveals a variety of mechanisms: (1) a direct aligned dissociation (2) a hopping and rebinding transition followed by unbinding, and (3) a sliding transition before unbinding. Reaction coordinate and transition-state analysis predicts that, besides native contact and neighboring salt-bridge interactions, solvent degrees of freedom play an important role in the dissociation process. Bridging waters, hydrogen-bonded to both proteins, support contacts in the native state and nearby lying transition-state regions, whereas they exhibit faster dynamics in further lying transition-state regions, rendering the proteins more mobile and assisting in rebinding. Analysis of the structure and dynamics of the solvent molecules reveals that the dry native interface induces enhanced populations of both disordered hydration water near hydrophilic residues and tetrahedrally ordered hydration water nearby hydrophobic residues. Although not exhaustive, our sampling of rare unbiased reactive molecular dynamics trajectories enhances the understanding of protein dissociation via complex pathways including (multiple) rebinding events.

Can reactions follow non-traditional second-order saddle pathways avoiding transition states?

We report here an ab initio (CASSCF/6-31+G*) trajectory simulation study on the mechanisms of the denitrogenation of 1-pyrazoline and its subsituted analogue that reveals reaction pathways via a high energy second-order saddle (SOS) region. This mechanism involves the molecule adopting a five-membered planar structure contrary to the traditional boat-like transition state. The SOS offers a trifurcation point where a pathway branches into three, different from the single pathway associated with a transitions state. We observe that the molecules following the SOS path exhibit distinctive dynamical features and form products with high translational energies and low rotational energies compared to those following the traditional pathways. In addition, the SOS pathway provides an alternative mechanism for the formation of stereo-selective products. Interestingly, although the reaction proceeds via a trimethylene diradical intermediate, the simulations show that the product cyclopropane is formed with a major single inversion of the configuration consistent with experimental observations. They also reveal mechanisms that do not follow the minimum energy paths and exhibit non-statistical dissociation dynamics.

Ultrafast X-ray Transient Absorption Spectroscopy of Gas-Phase Photochemical Reactions: A New Universal Probe of Photoinduced Molecular Dynamics.

Time-resolved spectroscopic investigations of light-induced chemical reactions with universal detection capitalize recently on single-photon molecular probing using laser pulses in the extreme ultraviolet or X-ray regimes. Direct and simultaneous mappings of the time-evolving populations of ground-state reactants, Franck-Condon (FC) and transition state regions, excited-state intermediates and conical intersections (CI), and photoproducts in photochemical reactions utilize probe pulses that are broadband and energy-tunable. The limits on temporal resolution are set by the transit- or dwell-time of the photoexcited molecules at specific locations on the potential energy surface, typically ranging from a few femtoseconds to several hundred picoseconds. Femtosecond high-harmonic generation (HHG) meets the stringent demands for a universal spectroscopic probe of large regions of the intramolecular phase-space in unimolecular photochemical reactions. Extreme-ultraviolet and soft X-ray pulses generated in this manner with few-femtosecond or sub-femtosecond durations have enormous bandwidths, allowing the probing of many elements simultaneously through excitation or ionization of core-electrons, creating molecular movies that shed light on entire photochemical pathways. At free electron lasers (FELs), powerful investigations are also possible, recognizing their higher flux and tunability but more limited bandwidths. Femtosecond time-resolved X-ray transient absorption spectroscopy, in particular, is a valuable universal probe of reaction pathways that maps changes via the fingerprint core-to-valence resonances. The particular power of this method over valence-ionization probes lies in its unmatched element and chemical-site specificities. The elements carbon, nitrogen, and oxygen constitute the fundamental building blocks of life; photochemical reactions involving these elements are ubiquitous, diverse, and manifold. However, table-top HHG sources in the "water-window" region (280-550 eV), which encompasses the 1s-absorption edges of carbon (284 eV), nitrogen (410 eV), and oxygen (543 eV), are far from abundant or trivial. Recent breakthroughs in the laboratory have embraced this region by using long driving-wavelength optical parametric amplifiers coupled with differentially pumped high-pressure gas source cells. This has opened avenues to study a host of photochemical reactions in organic molecules using femtosecond time-resolved transient absorption at the carbon K-edge. In this Account, we summarize recent efforts to deploy a table-top carbon K-edge source to obtain crucial chemical insights into ultrafast, ultraviolet-induced chemical reactions involving ring-opening, nonadiabatic excited-state relaxation, bond dissociation and radical formation. The X-ray probe provides a direct spectroscopic viewport into the electronic characters and configurations of the valence electronic states through spectroscopic core-level transitions into the frontier molecular orbitals of the photoexcited molecules, laying fertile ground for the real-time mapping of the evolving valence electronic structure. The profound detail and mechanistic insights emerging from the pioneering experiments at the carbon K-edge are outlined here. Comparisons of the experimental methodology with other techniques employed to study similar reactions are drawn, where applicable and relevant. We show that femtosecond time-resolved X-ray transient absorption spectroscopy blazes a new trail in the study of nonadiabatic molecular dynamics. Despite table-top implementations being largely in their infancy, future chemical applications of the technique will set the stage for widely applicable, universal probes of photoinduced molecular dynamics with unprecedented temporal resolution.

A bonding evolution theory study on the catalytic Noyori hydrogenation reaction

ABSTRACTThe electronic rearrangements involved in Noyori hydrogenation reactions with double bonds (ethene and formaldehyde) are analysed using the bonding evolution theory. The study and analysis of the changes on the electron localisation function topology along a given reaction path reveals fluxes of electron density, allowing to unambiguously identify the main chemical events happening along the chemical reactions. This analysis shows that the first hydrogen transfer (with hydride character) occurs before the transition state (TS), while the second hydrogen transfer (with proton character) takes places after having reached the TS. The lower energy barrier found for formaldehyde over ethene is explained by two reasons. First, the hydride transfer is favoured for the C = O bond over C = C due to the electrophilic character of the carbon atom. Second, a negatively charged CH3–X (X = CH2, O) hidden intermediate is formed in the proximities of the TS region. The oxygen atom is able to stabilise this negatively charged species more effectively than the CH2 group due to its higher electronegativity and the presence of V(O) lone pairs. The obtained analysis explains and rationalises catalyst chemoselectivity (C = O vs. C = C). Finally, a curly arrow representation diagram accounting for the electronic rearrangements is proposed on the basis of BET results.

Adiabatic Ligand Binding in Heme Proteins: Ultrafast Kinetics of Methionine Rebinding in Ferrous Cytochrome c.

The dynamics of methionine geminate recombination following photodissociation in ferrous cytochrome c is investigated over a broad temperature range. The kinetic response, above the solvent glass transition ( Tg), is nearly monoexponential and displays a weak temperature dependence. Below Tg, the rebinding kinetics are nonexponential and can be explained using a quenched distribution of enthalpic rebinding barriers, arising from a relatively narrow distribution of heme out-of-plane displacements. The Arrhenius prefactor of this (Δ S = 2) reaction is ∼1011 s-1, which is similar to what has been found for the (Δ S = 1) NO binding reaction in heme proteins. This observation, along with other examples of ultrafast CO binding, provides strong evidence that ligand binding to heme is an adiabatic reaction with a spin-independent prefactor. In order to simultaneously account for the adiabatic nature of the reaction as well as the temperature dependence of both ultrafast CO and methionine geminate rebinding, it is proposed that a spin triplet state intersects and strongly couples to the reactant ( S = 2) and product ( S = 0) state surfaces in the transition state region along the reaction coordinate. It is also suggested that the nature of the intersecting triplet state and the reaction path may depend upon the proximity of the photolyzed ligand relative to the iron atom. At temperatures below ∼60 K, the kinetic data suggest that there is either an unexpected retardation of the heme photoproduct relaxation or that heavy atom quantum mechanical tunneling becomes significant.

The analysis of HF molecule by means of infrared transitions in H + F2 collinear scattering on two different potential energy surfaces

In this study, infrared vibrational modes and intensities are calculated for F2 + H → HF + F reaction according to distance between F and H atoms by using DFT-B3LYP/6-311++G (d, p) level of theory. Also for the relevant reaction, the vibrational energy eigenvalues of the nascent H-F molecule at specific locations of the separated fluorine atom are obtained using the Schrödinger wave equation on the most realistic potential energy surface for this reaction. Since the main aim of the work is to analysis nascent molecular structure by the help of IR transitions, in the light of these two studies indicated above, the most appropriate vibration quantum states supporting the relevant IR transitions are determined and are verified by comparison with experimental results for some transitions that are available in the literature. Moreover, the transition state regions relating to both the reaction and the nascent HF molecule are detected by means of these.

Tests of Kramers' Theory at the Single-Molecule Level: Evidence for Folding of an Isolated RNA Tertiary Interaction at the Viscous Speed Limit.

Dissipation and friction influence the conformational dynamics of biological polymers as they traverse barriers on rugged free energy surfaces. It is well established that the "speed limit" for macromolecular folding is dictated by a combination of (i) solvent friction, which depends on solvent viscosity, η, and (ii) internal friction, which is independent of solvent and depends solely on the molecular folding pathway. In this work, single-molecule Förster resonance energy transfer (FRET) confocal spectroscopy is used to study viscosity-dependent folding kinetics of an isolated RNA tertiary motif, that of the GAAA tetraloop receptor, allowing both solvent and internal frictional contributions to be investigated and extracted independently for both flexible PEG- and RNA-based (rU7, rA7) linkers in the unimolecular construct. Specifically, our single-molecule data reveal that (i) folding rate constants scale linearly with the inverse solvent viscosity (η), which supports Kramers'/Grote-Hynes' rate theory for η-dependent RNA folding and that (ii) they provide quantitative upper limits for the intrinsic viscosity, [ηint ≈ 0.1(2) cP], arising from internal friction associated with folding/unfolding of an isolated RNA tertiary interaction. Furthermore, in contrast to strong viscosity-induced shifts in the folding/unfolding rate constants, temperature-dependent studies demonstrate that the enthalpic, entropic, and free energy contributions to the transition state barrier are largely insensitive to the solvent viscosity. This supports a very simple picture for the conformational kinetics of isolated RNA tertiary interactions wherein rate constants for folding/unfolding are both inversely dependent on viscosity and limited by diffusional access to the transition state region on a multidimensional free energy surface. Particularly under cellular conditions, where ηsolv > 1 cp, this suggests that RNAs fold/unfold at a "speed limit" dictated by solvent viscosity and transition-state barrier thermodynamics rather than internal molecular friction.

Mechanistic Insights on Human Phosphoglucomutase Revealed by Transition Path Sampling and Molecular Dynamics Calculations.

Human α-phosphoglucomutase 1 (α-PGM) catalyzes the isomerization of glucose-1-phosphate into glucose-6-phosphate (G6P) through two sequential phosphoryl transfer steps with a glucose-1,6-bisphosphate (G16P) intermediate. Given that the release of G6P in the gluconeogenesis raises the glucose output levels, α-PGM represents a tempting pharmacological target for type 2 diabetes. Here, we provide the first theoretical study of the catalytic mechanism of human α-PGM. We performed transition-path sampling simulations to unveil the atomic details of the two catalytic chemical steps, which could be key for developing transition state (TS) analogue molecules with inhibitory properties. Our calculations revealed that both steps proceed through a concerted SN 2-like mechanism, with a loose metaphosphate-like TS. Even though experimental data suggests that the two steps are identical, we observed noticeable differences: 1) the transition state ensemble has a well-defined TS region and a late TS for the second step, and 2) larger coordinated protein motions are required to reach the TS of the second step. We have identified key residues (Arg23, Ser117, His118, Lys389), and the Mg2+ ion that contribute in different ways to the reaction coordinate. Accelerated molecular dynamics simulations suggest that the G16P intermediate may reorient without leaving the enzymatic binding pocket, through significant conformational rearrangements of the G16P and of specific loop regions of the human α-PGM.

ETS-NOCV decomposition of the reaction force for double-proton transfer in formamide-derived systems

The analysis of the electronic-structure changes along IRC paths for double-proton-transfer reactions in the formamide dimer (R1), formamide–thioformamide system (R2), and the thioformamide dimer (R3) was performed based on the extended-transition-state natural orbitals for chemical valence (ETS-NOCV) partitioning of the reaction force, considering the intra-fragments strain and the inter-fragments interaction terms, and further—the electrostatic, Pauli-repulsion and orbital interaction components, with the latter being decomposed into the NOCV components. Two methods of the system partitioning into the fragments were considered (‘reactant perspective’/bond-formation, ‘product perspective’ / bond-breaking). In agreement with previous studies, the results indicate that the major changes in the electronic structure occur in the transition state region; the bond-breaking processes are, however, initiated already in the reactant region, prior to entering the TS region. The electrostatic contributions were identified as the main factor responsible for the increase in the activation barrier in the order R1 < R2 < R3.

Experimental and Theoretical Studies of the F• + H-F Transition-State Region by Photodetachment of [F-H-F

The transition-state (TS) region of the simplest heavy-light-heavy type of reaction, F• + H-F → F-H + F•, is investigated in this work by a joint experimental and theoretical approach. Photodetaching the bifluoride anion, [F···H···F]-, generates a negative ion photoelectron (NIPE) spectrum with three partially resolved bands in the electron binding energy (eBE) range of 5.4-7.0 eV. These bands correspond to the transition from the ground state of the anion to the electronic ground state of [F-H-F]• neutral, with associated vibrational excitations. The significant increase of eBE of the bifluoride anion, relative to that of F-, reflects a hydrogen bond energy between F- and HF of ∼46 kcal/mol. Theoretical modeling reveals that the antisymmetric motion of H between the two F atoms, near the TS on the neutral [F-H-F]• surface, dominates the observed three bands, while the F-H-F bending, F-F symmetric stretching modes, and the couplings between them are calculated to account for the breadth of the observed spectrum. From the NIPE spectrum, a lower limit on the activation enthalpy for F• + H-F → F-H + F• can be estimated to be ΔH‡ = 12 ± 2 kcal/mol, a value below that of ΔH‡ = 14.9 kcal/mol, given by our G4 calculations.

Theoretical analyses of the time-resolved nuclear dynamics of the transition state for the 1,3,5,7-cyclooctatetraene unimolecular reaction

When a stable negative ion is similar in structure to the transition state for the neutral reaction, photodetachment of the anion can be used to directly access the transition state region of the neutral potential energy surface. In this work, from the theoretical side, we address the femtosecond time-resolved experiment for the cyclooctatetraene (COT) unimolecular reaction which has been previously performed by Zewail et al. (2004), where the time-evolution of the nuclear wave packet, which is initially localized around the transition state region via instantaneous photodetachment, is monitored by an ionization laser. The oscillatory behavior of the ionization efficiency observed in their experiment is analyzed in detail using both the reduced-dimensionality quantum dynamics calculations and full-dimensional direct dynamics calculations on the CASSCF-level potential energy surfaces. We found that the behavior observed in an early stage can be attributable to the ring-inversion dynamics of COT.

Influence of the Transition-Metal Fragment on the Reactivity of Metallaanthracenes.

The influence of the nature of the transition-metal fragment on the Diels-Alder reactivity of metallaanthracenes has been explored computationally within the Density Functional Theory framework. It is found that the cycloaddition reactions with maleic anhydride become kinetically less favored for those processes involving metallaanthracenes compared with the analogous reaction involving the parent anthracene. The origins of this reduction in the Diels-Alder reactivity have been quantitatively analyzed in detail by using the activation strain model of reactivity in combination with the energy decomposition analysis method. In general, the transition-metal fragment makes the interaction energy between the reactants significantly lower, particularly at the transition state region, which is translated into a higher activation barrier. In addition, the influence of the aromaticity strength of the metallabenzene present in the considered metallaanthracenes on the barriers of the cycloaddition reactions has also been assessed.

Variation of potential energy surface height and bound state depth induced by laser phase along the reaction path in atom-molecule reactions: Application to Li + CH4 → LiH + CH3

Laser atom-molecule reaction interaction through polarizability and dipole moment contribution leads to potential energy surface barrier reshaping and bound states along the reaction path. The polarizability is maximum in the transition state. We will show here by using gauge representation (electric field gauge) for wave length λ = 20.6 μm, intensity I = 1 × 1012 W/cm2, I = 5 × 1012 W/cm2, I = 1 × 1013 W/cm2, I = 3 × 1013 W/cm2, that we can create laser induced potential energy surface barrier reshaping in the transition state region (–1–0.5 a. u.). We illustrate such effects for the LiH + CH3 ↔ Li + CH4 reaction with a barrier using ab-initio methods for calculating the reaction path, polarizability and dipole moment contribution of the atom-molecule reaction.

Computational Modeling of the Catalytic Cycle of Glutathione Peroxidase Nanomimic.

To elucidate the role of a derivative of ebselen as a mimic of the antioxidant selenoenzyme glutathione peroxidase, density functional theory and solvent-assisted proton exchange (SAPE) were applied to model the reaction mechanism in a catalytic cycle. This mimic plays the role of glutathione peroxidase through a four-step catalytic cycle. The first step is described as the oxidation of 1 in the presence of hydrogen peroxide, while selenoxide is reduced by methanthiol at the second step. In the third step of the reaction, the reduction of selenenylsulfide occurs by methanthiol, and the selenenic acid is dehydrated at the final step. Based on the kinetic parameters, step 4 is the rate-determining step (RDS) of the reaction. The bond strength of the atoms involved in the RDS is discussed with the quantum theory of atoms in molecules (QTAIM). Low value of electron density, ρ(r), and positive Laplacian values are the evidence for the covalent nature of the hydrogen bonds rupture (O30-H31, O33-H34). A change in the sign of the Laplacian, L(r), from the positive value in the reactant to a negative character at the transition state indicates the depletion of the charge density, confirming the N5-H10 and O11-Se1 bond breaking. The analysis of electron location function (ELF) and localized orbital locator (LOL) of the Se1-N5 and Se1-O11 bonds have been done by multi-WFN program. High values of ELF and LOL at the transition state regions between the Se, N, and O atoms display the bond formation. Finally, the main donor-acceptor interaction energies were analyzed using the natural bond orbital analysis for investigation of their stabilization effects on the critical bonds at the RDS.

Hydrodynamic description of protein folding: the decrease of the probability fluxes as an indicator of transition states in two-state folders

Using hydrodynamic description of protein folding, the process of the first-passage folding of ubiquitin has been studied. Since a large number of folding trajectories were required to obtain converged folding flows, a coarse-grained representation of the protein in the form of a C-bead Gō-model was employed, and discrete molecular dynamics was used to perform simulations. It has been found that the free energy surface has a maximum width in the transition state region, so that the densities of folding flows (probability fluxes) decrease to minimum when the system passes through the transition state. There are indications that the increasing number of different protein conformations in the transition state region compared with those in the neighboring regions of semi-compact and native-like states is responsible for the present phenomena. It has also been shown that if the free energy is projected onto a single reaction coordinate, the low populations of the transition states can be compensated by the increasing number of states, which can lead to a considerable decrease or even disappearance of the free energy barrier in the transition state.