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.

The Aer protein and the serine chemoreceptor Tsr independently sense intracellular energy levels and transduce oxygen, redox, and energy signals for Escherichia coli behavior

We identified a protein, Aer, as a signal transducer that senses intracellular energy levels rather than the external environment and that transduces signals for aerotaxis (taxis to oxygen) and other energy-dependent behavioral responses in Escherichia coli. Domains in Aer are similar to the signaling domain in chemotaxis receptors and the putative oxygen-sensing domain of some transcriptional activators. A putative FAD-binding site in the N-terminal domain of Aer shares a consensus sequence with the NifL, Bat, and Wc-1 signal-transducing proteins that regulate gene expression in response to redox changes, oxygen, and blue light, respectively. A double mutant deficient in aer and tsr, which codes for the serine chemoreceptor, was negative for aerotaxis, redox taxis, and glycerol taxis, each of which requires the proton motive force and/or electron transport system for signaling. We propose that Aer and Tsr sense the proton motive force or cellular redox state and thereby integrate diverse signals that guide E. coli to environments where maximal energy is available for growth.

The importance of reactant positioning in enzyme catalysis: A hybrid quantum mechanics/molecular mechanics study of a haloalkane dehalogenase

Hybrid quantum mechanics/molecular mechanics calculations using Austin Model 1 system-specific parameters were performed to study the SN2 displacement reaction of chloride from 1,2-dichloroethane (DCE) by nucleophilic attack of the carboxylate of acetate in the gas phase and by Asp-124 in the active site of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10. The activation barrier for nucleophilic attack of acetate on DCE depends greatly on the reactants having a geometry resembling that in the enzyme or an optimized gas-phase structure. It was found in the gas-phase calculations that the activation barrier is 9 kcal/mol lower when dihedral constraints are used to restrict the carboxylate nucleophile geometry to that in the enzyme relative to the geometries for the reactants without dihedral constraints. The calculated quantum mechanics/molecular mechanics activation barriers for the enzymatic reaction are 16.2 and 19.4 kcal/mol when the geometry of the reactants is in a near attack conformer from molecular dynamics and in a conformer similar to the crystal structure (DCE is gauche), respectively. This haloalkane dehalogenase lowers the activation barrier for dehalogenation of DCE by 2–4 kcal/mol relative to the single point energies of the enzyme's quantum mechanics atoms in the gas phase. SN2 displacements of this sort in water are infinitely slower than in the gas phase. The modest lowering of the activation barrier by the enzyme relative to the reaction in the gas phase is consistent with mutation experiments.

Introduction to quantum mechanics : a course at Los Alamos University /

Mode of access: Internet.

Linear operators and their spectra with applications to quantum mechanics.

From lectures given at the New York university Institute for mathematica and mechanics, by R. Cournat and others.

Selected tables from Atomic energy levels.

Volume I [compiled] by Charlotte E. Moore, reprinted from National Bureau of Standards Circular 467, issued 1949.

Stark energy levels of symmetric top molecules.

At head of title: NBS Project 8440-11-84141.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)

A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Supersymmetry and Ghosts in Quantum Mechanics

2000 Mathematics Subject Classification: 81Q60, 35Q40.

A disappearing act performed by magnesium: the nucleotide exchange mechanism of Ran GTPase by Quantum mechanics/Molecular mechanics studies

The Ran GTPase protein is a guanine nucleotide-binding protein (GNBP) with an acknowledged profile in cancer onset, progression and metastases. The complex mechanism adopted by GNBPs in exchanging GDP for GTP is an intriguing process and crucial for Ran viability. The successful completion of the process is a fundamental aspect of propagating downstream signalling events. QM/MM molecular dynamics simulations were employed in this study to provide a deeper mechanistic understanding of the initiation of nucleotide exchange in Ran. Results indicate significant disruption of the metal-binding site upon interaction with RCC1 (the Ran guanine nucleotide exchange factor), overall culminating in the prominent shift of the divalent magnesium ion. The observed ion drifting is reasoned to occur as a consequence of the complex formation between Ran and RCC1 and is postulated to be a critical factor in the exchange process adopted by Ran. This is the first report to observe and detail such intricate dynamics for a protein in Ras superfamily.

Energy levels and radiative rates for Cr-like Cu VI and Zn VII

Energy levels and radiative rates (. A-values) for transitions in Cr-like Cu VI and Zn VII are reported. These data are determined in the quasi-relativistic approach (QR), by employing a very large configuration interaction (CI) expansion which is highly important for these ions. No radiative rates are available in the literature to compare with our results, but our calculated energies are in close agreement with those compiled by NIST and other available theoretical data, for a majority of the levels. The A-values (and resultant lifetimes) are listed for all significantly contributing E1, E2 and M1 radiative transitions among the energetically lowest 322 levels of each ion.