Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics.

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events.

On the Possibility That Bond Strain Is the Mechanism of RING E3 Activation in the E2-Catalyzed Ubiquitination Reaction.

Ubiquitination is a type of post-translational modification wherein the small protein ubiquitin (Ub) is covalently bound to a lysine on a target protein. Ubiquitination can signal for several regulatory pathways including protein degradation. Ubiquitination occurs by a series of reactions catalyzed by three types of enzymes: ubiquitin activating enzymes, E1; ubiquitin conjugating enzymes, E2; and ubiquitin ligases, E3. E2 enzymes directly catalyze the transfer of Ub to the target protein─the RING E3 improves the efficiency. Prior to its transfer, Ub is covalently linked to the E2 via a thioester bond and the Ub∼E2 conjugate forms a quaternary complex with the RING E3. It is hypothesized that the RING E3 improves the catalytic efficiency of ubiquitination by placing the E2∼Ub conjugate in a "closed" position, which tensions and weakens the thioester bond. We interrogate this hypothesis by analyzing the strain on the thioester during molecular dynamics simulations of both open and closed E2∼Ub/E3 complexes. Our data indicate that the thioester is strained when the E2∼Ub conjugate is in the closed position. We also show that the amount of strain is consistent with the experimental rate enhancement caused by the RING E3. Finally, our simulations show that the closed configuration increases the populations of key hydrogen bonds in the E2∼Ub active site. This is consistent with another hypothesis stating that the RING E3 enhances reaction rates by preorganizing the substrates.

A conserved asparagine in a ubiquitin-conjugating enzyme positions the substrate for nucleophilic attack.

The mechanism used by the ubiquitin-conjugating enzyme, Ubc13, to catalyze ubiquitination is probed with three computational techniques: Born-Oppenheimer molecular dynamics, single point quantum mechanics/molecular mechanics energies, and classical molecular dynamics. These simulations support a long-held hypothesis and show that Ubc13-catalyzed ubiquitination uses a stepwise, nucleophilic attack mechanism. Furthermore, they show that the first step-the formation of a tetrahedral, zwitterionic intermediate-is rate limiting. However, these simulations contradict another popular hypothesis that supposes that the negative charge on the intermediate is stabilized by a highly conserved asparagine (Asn79 in Ubc13). Instead, calculated reaction profiles of the N79A mutant illustrate how charge stabilization actually increases the barrier to product formation. Finally, an alternate role for Asn79 is suggested by simulations of wild-type, N79A, N79D, and H77A Ubc13: it stabilizes the motion of the electrophile prior to the reaction, positioning it for nucleophilic attack. © 2019 Wiley Periodicals, Inc.

Far-Infrared Synchrotron Spectroscopy and Quantum Chemical Calculations of the Potentially Important Interstellar Molecule, 2-Chloroethanol.

The high brightness of the Australian synchrotron allowed for detailed spectra to be collected at high resolution (0.00096 cm-1) in the vicinity of the a/ b/ c-type ν19 band of 2-chloroethanol, which involves O-H torsional motion about the C-O bond. A rovibrational analysis was performed for both chlorine isotopologues in the ν19 fundamental (centered at ∼344 cm-1) which involved the assignment of 7153 lines ( J ≤ 90, K a ≤ 41). A global fit to these lines in addition to 119 microwave lines ( J ≤ 29, K a ≤ 11) led to the determination of spectroscopic constants up to the sextic level in both the ground and excited states using Watson's A-reduction Hamiltonian. The constants agree well with those calculated at the anharmonic MP2/cc-pVTZ level and allow for spectroscopically accurate predictions of rotational transitions in the ground vibrational state to be made over a broad range of rotational energies ( TR < 1000 K). We explored the role that 2-chloroethanol might play in interstellar molecular clouds by performing calculations on the substitution reaction between HCl and ethylene glycol, and the addition reaction between HCl and oxirane, all of which have been observed in Sagittarius B2(N) and are expected to play important roles in the chemistry that occurs on the icy mantles of interstellar dust grains. While both reactions have relatively high activation barriers, the HCl + oxirane reaction was found be much more exothermic; further calculations on it indicate that a water-like environment significantly reduces the barrier while slightly increasing its exothermicity. These results suggest that 2-chloroethanol could be efficiently produced from the cosmic ray bombardment of common interstellar ices.

The Disulfide Bonds within BST-2 Enhance Tensile Strength during Viral Tethering.

Human BST-2/tetherin is a host factor that inhibits the release of enveloped viruses, including HIV-1, HIV-2, and SIV, from the cell surface by tethering viruses to the host cell membrane. BST-2 has an α-helical ectodomain that forms disulfide-linked dimers between two monomers forming a coiled coil. The ectodomain contains three cysteine residues that can participate in disulfide bond formation and are critical for viral tethering. The role of the disulfides in viral tethering is unknown but proposed to be for maintaining the dimer. We explored the role of the disulfides in the structure of BST-2 using experimental, biophysical methods. To understand the role of the disulfides in viral tethering, we used a new approach in viral tethering, steered molecular dynamics. We find that the disulfides coordinate the unfolding of the BST-2 monomers, which adds tensile strength to the coiled coil. Structural differences between oxidized and reduced BST-2 are apparent during unfolding, showing the monomers slide past each other in the absence of the disulfides. We found no evidence to support dissociation of the dimer upon reduction of the disulfide bonds. Moreover, the structure of BST-2 in the absence of the disulfides is similar to that of the oxidized form of BST-2, supporting previous X-ray crystallography and cellular work that showed the disulfides are not required for expression of BST-2. These data provide new insights into viral tethering by using novel techniques in the analysis of BST-2 to give amino acid level insight into functions of BST-2.

Hydrogen tunneling in an enzyme active site: a quantum wavepacket dynamical perspective.

We study the hydrogen tunneling problem in a model system that represents the active site of the biological enzyme, soybean lipoxygenase-1. Toward this, we utilize quantum wavepacket dynamics performed on potential surfaces obtained by using hybrid density functional theory under the influence of a dynamical active site. The kinetic isotope effect is computed by using the transmission amplitude of the wavepacket, and the experimental value is reproduced. By computing the hydrogen nuclear orbitals (eigenstates) along the reaction coordinate, we note that tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical s-type proton wave functions and p-type polarized proton wave functions for transfer along the donor-acceptor axis. In addition, there is also a significant population transfer through distorted p-type proton wave functions directed perpendicular to the donor-acceptor axis (via intervening pi-type proton eigenstate interactions) which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor-acceptor axis and along directions perpendicular to the donor-acceptor axis. Furthermore, the tunneling process is facilitated by the occurrence of curve crossings and avoided crossings along the proton eigenstate adiabats.

Combining quantum wavepacket ab initio molecular dynamics with QM/MM and QM/QM techniques: Implementation blending ONIOM and empirical valence bond theory.

We discuss hybrid quantum-mechanics/molecular-mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) generalizations to our recently developed quantum wavepacket ab initio molecular dynamics methodology for simultaneous dynamics of electrons and nuclei. The approach is a synergy between a quantum wavepacket dynamics, ab initio molecular dynamics, and the ONIOM scheme. We utilize this method to include nuclear quantum effects arising from a portion of the system along with a simultaneous description of the electronic structure. The generalizations provided here make the approach a potentially viable alternative for large systems. The quantum wavepacket dynamics is performed on a grid using a banded, sparse, and Toeplitz representation of the discrete free propagator, known as the "distributed approximating functional." Grid-based potential surfaces for wavepacket dynamics are constructed using an empirical valence bond generalization of ONIOM and further computational gains are achieved through the use of our recently introduced time-dependent deterministic sampling technique. The ab initio molecular dynamics is achieved using Born-Oppenheimer dynamics. All components of the methodology, namely, quantum dynamics and ONIOM molecular dynamics, are harnessed together using a time-dependent Hartree-like procedure. We benchmark the approach through the study of structural and vibrational properties of molecular, hydrogen bonded clusters inclusive of electronic, dynamical, temperature, and critical quantum nuclear effects. The vibrational properties are constructed through a velocity/flux correlation function formalism introduced by us in an earlier publication.

Molecular dynamics simulations reveal a new role for a conserved active site asparagine in a ubiquitin-conjugating enzyme.

The role of a highly conserved active site asparagine (N79) in the ubiquitin conjugating enzyme, Ubc13, is probed using molecular dynamics simulations. Both wild type and mutant enzymes (N79A and N79D) are studied. Contrary to a popular hypothesis, we show that it is unlikely that N79 stabilizes a reaction intermediate, but instead preferentially hydrogen bonds to a loop near the active site. This keeps the sidechain carboxylate of an aspartate in the loop (D119) near the sidechain amine of the substrate lysine. Our simulations show that this distance increases in the mutants. D119 has been hypothesized to play a variety of roles in the enzyme, including deprotonating the substrate lysine, so changing this distance can have an effect on the enzyme's efficiency. Finally, we show that it is possible for the aspartate to deprotonate the substrate even across long distances if short water wires form that connect the proton donor and acceptor. Short water wires form with greater probability in the wild type than in mutant enzymes.

Mechanical dissociation of the M-band titin/obscurin complex is directionally dependent.

Titin and obscurin, two giant muscle proteins, bind to each other in an antiparallel Ig-Ig fashion at the M-band. This interaction must be able to withstand the mechanical strain that the M-band typically experiences and remain intact. The mechanical force on these domains is likely exerted along one of two axes: a longitudinal axis, resulting in a 'shearing' force, or a lateral axis, resulting in a 'peeling' force. Here we present molecular dynamics data suggesting that these forces result in distinct unraveling pathways of the titin/obscurin complex and that peeling the domains apart requires less work and force.

Proton transport pathways in [NiFe]-hydrogenase.

Hydrogenases reversibly catalyze the production of molecular hydrogen. Current interest in these enzymes is focused on understanding the catalysis, since this may prove useful for hydrogen-based fuel cell and photosynthetic hydrogen production cell technologies. A key step in the hydrogenase catalytic cycle and the focus of this work is proton transport (PT) to and from the active site. The PT mechanism of the enzyme is studied using reactive molecular dynamics simulations of the full protein and the excess proton transfers via the multistate empirical valence bond (MS-EVB) method. Pathways connecting the bulk and the active site are located that suggest possible participation by several protonatable residues. PT free energy surfaces are calculated to differentiate the pathways.

Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events.

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

Analysis of Hydrogen Tunneling in an Enzyme Active Site using von Neumann Measurements.

We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme, soybean lipoxygenase-1, by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the "transition state" towards the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further "tailor" the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.

Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects.

We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

Computational Improvements to Quantum Wave Packet ab Initio Molecular Dynamics Using a Potential-Adapted, Time-Dependent Deterministic Sampling Technique.

In a recent publication, we introduced a computational approach to treat the simultaneous dynamics of electrons and nuclei. The method is based on a synergy between quantum wave packet dynamics and ab initio molecular dynamics. Atom-centered density-matrix propagation or Born-Oppenheimer dynamics can be used to perform ab initio dynamics. In this paper, wave packet dynamics is conducted using a three-dimensional direct product implementation of the distributed approximating functional free-propagator. A fundamental computational difficulty in this approach is that the interaction potential between the two components of the methodology needs to be calculated frequently. Here, we overcome this problem through the use of a time-dependent deterministic sampling measure that predicts, at every step of the dynamics, regions of the potential which are important. The algorithm, when combined with an on-the-fly interpolation scheme, allows us to determine the quantum dynamical interaction potential and gradients at every dynamics step in an extremely efficient manner. Numerical demonstrations of our sampling algorithm are provided through several examples arranged in a cascading level of complexity. Starting from a simple one-dimensional quantum dynamical treatment of the shared proton in [Cl-H-Cl](-) and [CH3-H-Cl](-) along with simultaneous dynamical treatment of the electrons and classical nuclei, through a complete three-dimensional treatment of the shared proton in [Cl-H-Cl](-) as well as treatment of a hydrogen atom undergoing donor-acceptor transitions in the biological enzyme, soybean lipoxygenase-1 (SLO-1), we benchmark the algorithm thoroughly. Apart from computing various error estimates, we also compare vibrational density of states, inclusive of full quantum effects from the shared proton, using a novel unified velocity-velocity, flux-flux autocorrelation function. In all cases, the potential-adapted, time-dependent sampling procedure is seen to improve the computational scheme tremendously (by orders of magnitude) with minimal loss of accuracy.