Steven D. Schwartz

Quantum mechanical rate constants for bimolecular reactions

Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state‐to‐state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one‐dimensional test problem (the Eckart barrier).

Enzymatic transition states and dynamic motion in barrier crossing

What are the atomic motions at enzymatic catalytic sites on the timescale of chemical change? Combined experimental and computational chemistry approaches take advantage of transition-state analogs to reveal dynamic motions linked to transition-state formation. QM/MM transition path sampling from reactive complexes provides both temporal and dynamic information for barrier crossing. Fast (femtosecond to picosecond) dynamic motions provide essential links to enzymatic barrier crossing by local or promoting-mode dynamic searches through bond-vibrational space. Transition-state lifetimes are within the femtosecond timescales of bond vibrations and show no manifestations of stabilized, equilibrated complexes. The slow binding and protein conformational changes (microsecond to millisecond) also required for catalysis are temporally decoupled from the fast dynamic motions forming the transition state. According to this view of enzymatic catalysis, transition states are formed by fast, coincident dynamic excursions of catalytic site elements, while the binding of transition-state analogs is the conversion of the dynamic excursions to equilibrated states.

Reaction coordinate of an enzymatic reaction revealed by transition path sampling

The transition path sampling method previously applied in our group to the reaction catalyzed by lactate dehydrogenase was used to generate a transition path ensemble for this reaction. Based on analysis of the reactive trajectories generated, important residues behind the active site were implicated in a compressional motion that brought the donor–acceptor atoms of the hydride closer together. In addition, residues behind the active site were implicated in a relaxational motion, locking the substrate in product formation. Although this suggested that the compression-relaxation motions of these residues were important to catalysis, it remained unproven. In this work, we used committor distribution analysis to show that these motions are integral components of the reaction coordinate.

Atomic detail of chemical transformation at the transition state of an enzymatic reaction

Transition path sampling (TPS) has been applied to the chemical step of human purine nucleoside phosphorylase (PNP). The transition path ensemble provides insight into the detailed mechanistic dynamics and atomic motion involved in transition state passage. The reaction mechanism involves early loss of the ribosidic bond to form a transition state with substantial ribooxacarbenium ion character, followed by dynamic motion from the enzyme and a conformational change in the ribosyl group leading to migration of the anomeric carbon toward phosphate, to form the product ribose 1-phosphate. Calculations of the commitment probability along reactive paths demonstrated the presence of a broad energy barrier at the transition state. TPS identified (i) compression of the O4′···O5′ vibrational motion, (ii) optimized leaving group interactions, and (iii) activation of the phosphate nucleophile as the reaction proceeds through the transition state region. Dynamic motions on the femtosecond timescale provide the simultaneous optimization of these effects and coincide with transition state formation.

20-, 23-, and 25-gauge vitreous cutters: performance and characteristics evaluation.

Purpose: The flow rate of nine vitreous cutters was tested in two different viscosity environments. Physical features of each probe, such as flexibility and internal lumen diameter, were measured. Methods: For each probe, a total of 26 aspiration tests were performed in two different liquids. The stiffness of the shaft of each probe was calculated by measuring the displacement of the tip of the probe under a known constant force. All the probes were dissected and the internal lumen diameter was measured. Results: Significant differences in flow rates were observed among the three separate conditions, among the three different gauge groups (25-, 23-, and 20-gauge vitreous cutter), and also within each gauge group. Internal lumen diameters and probe stiffness characteristics are presented. Conclusion: Vacuum, internal lumen diameter, and duty cycle seem to be the critical features governing actual flow rate. Knowledge of flow rate and stiffness of the various probes may aid surgeons in making an educated choice and may improve patient care.

Feasibility study of intraocular robotic surgery with the da Vinci surgical system.

Purpose: To assess the feasibility of performing intraocular robotic surgery with the da Vinci Surgical System (Intuitive Surgical, Sunnyvale, CA). Methods: Using modified robotic instruments, 25-gauge pars plana vitrectomy, intraocular foreign body removal, and anterior capsulorhexis were performed with the da Vinci system on porcine eyes. We assessed the surgical system’s ability to provide the control, dexterity, maneuverability, and visualization necessary for intraocular surgery. Results: Control of the robotic wristlike instruments allowed for full range of movement. The dexterity of the robotic arms was excellent, with steady instrument motion. Controlling the robotic arms was not as intuitive as moving the wrist. A high stable point of rotation induced motion-related stress at the site of instrument insertion. Visualization of the external operative field during intraocular procedures required camera realignment, and absent retroillumination made anterior segment surgery hard to perform. Conclusions: The da Vinci Surgical System provided adequate dexterity for performing delicate intraocular manipulations. In the current design, the kinematics of the robotic arms was found to be insufficient for standard intraocular surgery. The system’s endoscope did not did not yield the same detail acquired by an ophthalmic microscope.

A model of calcium-activation of the cardiac thin filament

The cardiac thin filament regulates actomyosin interactions through calcium-dependent alterations in the dynamics of cardiac troponin and tropomyosin. Over the past several decades, many details of the structure and function of the cardiac thin filament and its components have been elucidated. We propose a dynamic, complete model of the thin filament that encompasses known structures of cardiac troponin, tropomyosin, and actin and show that it is able to capture key experimental findings. By performing molecular dynamics simulations under two conditions, one with calcium bound and the other without calcium bound to site II of cardiac troponin C (cTnC), we found that subtle changes in structure and protein contacts within cardiac troponin resulted in sweeping changes throughout the complex that alter tropomyosin (Tm) dynamics and cardiac troponin--actin interactions. Significant calcium-dependent changes in dynamics occur throughout the cardiac troponin complex, resulting from the combination of the following: structural changes in the N-lobe of cTnC at and adjacent to sites I and II and the link between them; secondary structural changes of the cardiac troponin I (cTnI) switch peptide, of the mobile domain, and in the vicinity of residue 25 of the N-terminus; secondary structural changes in the cardiac troponin T (cTnT) linker and Tm-binding regions; and small changes in cTnC-cTnI and cTnT-Tm contacts. As a result of these changes, we observe large changes in the dynamics of the following regions: the N-lobe of cTnC, the mobile domain of cTnI, the I-T arm, the cTnT linker, and overlapping Tm. Our model demonstrates a comprehensive mechanism for calcium activation of the cardiac thin filament consistent with previous, independent experimental findings. This model provides a valuable tool for research into the normal physiology of cardiac myofilaments and a template for studying cardiac thin filament mutations that cause human cardiomyopathies.

Barrier crossing in dihydrofolate reductase does not involve a rate-promoting vibration

We have studied atomic motions during the chemical reaction catalysed by the enzyme dihydrofolate reductase of Escherichia coli (EcDHFR), an important enzyme for nucleic acid synthesis. In our earlier work on the enzymes human lactate dehydrogenase and purine nucleoside phosphorylase, we had identified fast sub-ps motions that are part of the reaction coordinate. We employed Transition Path Sampling (TPS) and our recently developed reaction coordinate identification methodology to investigate if such fast motions couple to the reaction in DHFR on the barrier-crossing timescale. While we identified some protein motions near the barrier crossing event, these motions do not constitute a compressive promoting vibration, and do not appear as a clearly identifiable protein component in reaction.

Activated chemistry in the presence of a strongly symmetrically coupled vibration

In the gas phase, tunneling reaction rates can be significantly enhanced if the reaction coordinate is symmetrically coupled to a harmonic oscillation, as has been emphasized by Benderskii and co-workers [Adv. Chem. Phys. 88, 1 (1994)]. This is due to the fact that the symmetric coupling leads to modulation of the barrier height. Similar effects have been observed in reactions in model condensed phase studies, as in the Hamiltonians that have been studied by Borgis and Hynes [J. Chem. Phys. 94, 3619 (1991)] and Suarez and Silbey [J. Chem. Phys. 94, 4809 (1991)]. All of these works assume that tunneling proceeds from the ground state. In this paper, we use the exponential resummation technique that we used in our recent work on the quantum Kramers problem, to study the case when there can be excitations to higher states and activated transmission over a barrier. We present a general methodology to exactly include direct coupling between the reaction coordinate and the symmetrically coupled promoting vibrat...

Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: a model for enzymatic catalysis.

A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.