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.

Estimating the probability for a protein to have a new fold: A statistical computational model

Structural genomics aims to solve a large number of protein structures that represent the protein space. Currently an exhaustive solution for all structures seems prohibitively expensive, so the challenge is to define a relatively small set of proteins with new, currently unknown folds. This paper presents a method that assigns each protein with a probability of having an unsolved fold. The method makes extensive use of protomap, a sequence-based classification, and scop, a structure-based classification. According to protomap, the protein space encodes the relationship among proteins as a graph whose vertices correspond to 13,354 clusters of proteins. A representative fold for a cluster with at least one solved protein is determined after superposition of all scop (release 1.37) folds onto protomap clusters. Distances within the protomap graph are computed from each representative fold to the neighboring folds. The distribution of these distances is used to create a statistical model for distances among those folds that are already known and those that have yet to be discovered. The distribution of distances for solved/unsolved proteins is significantly different. This difference makes it possible to use Bayes' rule to derive a statistical estimate that any protein has a yet undetermined fold. Proteins that score the highest probability to represent a new fold constitute the target list for structural determination. Our predicted probabilities for unsolved proteins correlate very well with the proportion of new folds among recently solved structures (new scop 1.39 records) that are disjoint from our original training set.

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.

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.

Tuning DNA “strings”: Modulating the rate of DNA replication with mechanical tension

Recent experiments have measured the rate of replication of DNA catalyzed by a single enzyme moving along a stretched template strand. The dependence on tension was interpreted as evidence that T7 and related DNA polymerases convert two (n = 2) or more single-stranded template bases to double helix geometry in the polymerization site during each catalytic cycle. However, we find structural data on the T7 enzyme–template complex indicate n = 1. We also present a model for the “tuning” of replication rate by mechanical tension. This model considers only local interactions in the neighborhood of the enzyme, unlike previous models that use stretching curves for the entire polymer chain. Our results, with n = 1, reconcile force-dependent replication rate studies with structural data on DNA polymerase complexes.

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.

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.

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.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

How can statistical mechanics contribute to social science?

A model of interdependent decision making has been developed to understand group differences in socioeconomic behavior such as nonmarital fertility, school attendance, and drug use. The statistical mechanical structure of the model illustrates how the physical sciences contain useful tools for the study of socioeconomic phenomena.

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.