Toward a quantum-mechanical description of metal-assisted phosphoryl transfer in pyrophosphatase

The wealth of kinetic and structural information makes inorganic pyrophosphatases (PPases) a good model system to study the details of enzymatic phosphoryl transfer. The enzyme accelerates metal-complexed phosphoryl transfer 1010-fold: but how? Our structures of the yeast PPase product complex at 1.15 Å and fluoride-inhibited complex at 1.9 Å visualize the active site in three different states: substrate-bound, immediate product bound, and relaxed product bound. These span the steps around chemical catalysis and provide strong evidence that a water molecule (Onu) directly attacks PPi with a pKa vastly lowered by coordination to two metal ions and D117. They also suggest that a low-barrier hydrogen bond (LBHB) forms between D117 and Onu, in part because of steric crowding by W100 and N116. Direct visualization of the double bonds on the phosphates appears possible. The flexible side chains at the top of the active site absorb the motion involved in the reaction, which may help accelerate catalysis. Relaxation of the product allows a new nucleophile to be generated and creates symmetry in the elementary catalytic steps on the enzyme. We are thus moving closer to understanding phosphoryl transfer in PPases at the quantum mechanical level. Ultra-high resolution structures can thus tease out overlapping complexes and so are as relevant to discussion of enzyme mechanism as structures produced by time-resolved crystallography.

Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds for arbitrary atomic numbers and fine structure constant. We also announce bounds for the energy of many electrons and nuclei in a classical vector potential and for the eigenvalue sum of a one-electron Pauli Hamiltonian with magnetic field.

A statistical mechanical model for β-hairpin kinetics

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a β-hairpin, the minimal structural element of the antiparallel β-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, β-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 215 possible conformations and 15 × 215 possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the β-hairpin peptide.

From ab initio quantum mechanics to molecular neurobiology: A cation–π binding site in the nicotinic receptor

The nicotinic acetylcholine receptor is the prototype ligand-gated ion channel. A number of aromatic amino acids have been identified as contributing to the agonist binding site, suggesting that cation–π interactions may be involved in binding the quaternary ammonium group of the agonist, acetylcholine. Here we show a compelling correlation between: (i) ab initio quantum mechanical predictions of cation–π binding abilities and (ii) EC50 values for acetylcholine at the receptor for a series of tryptophan derivatives that were incorporated into the receptor by using the in vivo nonsense-suppression method for unnatural amino acid incorporation. Such a correlation is seen at one, and only one, of the aromatic residues—tryptophan-149 of the α subunit. This finding indicates that, on binding, the cationic, quaternary ammonium group of acetylcholine makes van der Waals contact with the indole side chain of α tryptophan-149, providing the most precise structural information to date on this receptor. Consistent with this model, a tethered quaternary ammonium group emanating from position α149 produces a constitutively active receptor.

Convex polytopes and quantization of symplectic manifolds

Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.

Long-time quantum simulation of the primary charge separation in bacterial photosynthesis.

Accurate quantum mechanical simulations of the primary charge transfer in photosynthetic reaction centers are reported. The process is modeled by three coupled electronic states corresponding to the photoexcited chlorophyll special pair (donor), the reduced bacteriopheophytin (acceptor), and the reduced accessory chlorophyll (bridge) that interact with a dissipative medium of protein and solvent degrees of freedom. The time evolution of the excited special pair is followed over 17 ps by using a fully quantum mechanical path integral scheme. We find that a free energy of the reduced accessory chlorophyll state approximately equal to 400 cm(-1) lower than that of the excited special pair state yields state populations in agreement with experimental results on wild-type and modified reaction centers. For this energetic configuration electron transfer is a two-step process.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

Peroxynitrite does not decompose to singlet oxygen (1ΔgO2) and nitroxyl (NO−)

According to Khan et al. [Khan, A. U., Kovacic, D., Kolbanovskiy, A., Desai, M., Frenkel, K. & Geacintov, N. E. (2000) Proc. Natl. Acad. Sci. USA 97, 2984–2989], peroxynitrite (ONOO−) decomposes after protonation to singlet oxygen (1ΔgO2) and singlet oxonitrate (nitroxyl, 1NO−) in high yield. They claimed to have observed nitrosyl hemoglobin from the reaction of NO− with methemoglobin; however, contamination with hydrogen peroxide gave rise to ferryl hemoglobin, the spectrum of which was mistakenly assigned to nitrosyl hemoglobin. We have carried out UV–visible and EPR experiments with methemoglobin and hydrogen peroxide-free peroxynitrite and find that no NO− is formed. With this peroxynitrite preparation, no light emission from singlet oxygen at 1270 nm is observed, nor is singlet oxygen chemically trapped; however, singlet oxygen was trapped when hydrogen peroxide was also present, as previously described [Di Mascio, P., Bechara, E. J. H., Medeiros, M. H. G., Briviba, K. & Sies, H. (1994) FEBS Lett. 355, 287–289]. Quantum mechanical and thermodynamic calculations show that formation of the postulated intermediate, a cyclic form of peroxynitrous acid (trioxazetidine), and the products 1NO− and 1ΔgO2 requires Gibbs energies of ca. +415 kJ⋅mol−1 and ca. +180 kJ⋅mol−1, respectively. Our results show that the results of Khan et al. are best explained by interference from contaminating hydrogen peroxide left from the synthesis of peroxynitrite.

Keeping Mars warm with new super greenhouse gases

Our selection of new super greenhouse gases to fill a putative “window” in a future Martian atmosphere relies on quantum-mechanical calculations. Our study indicates that if Mars could somehow acquire an Earth-like atmospheric composition and surface pressure, then an Earth-like temperature could be sustained by a mixture of five to seven fluorine compounds. Martian mining requirements for replenishing the fluorine could be comparable to current terrestrial extraction.

Mechanical behavior in living cells consistent with the tensegrity model

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.