High-resolution electrospray ionization fourier transform mass spectrometry with infrared multiphoton dissociation of glucokinase from Bacillus stearothermophilus

Glucokinase (GK, EC 2.7.1.2), a member of the enzyme family of hexokinases, has been shown to be linked to maturity-onset diabetes of the young type II (MODY-2). Although nucleotide and amino acid sequence information are available for the human varieties, they are not known for the variety from Bacillus stearothermophilus, which is often used in protein binding studies. Here, a combination of electrospray Fourier transform mass spectrometry (FTMS) and infrared multiphoton dissociation (IRMPD) is used to obtain accurate molecular weight and preliminary amino acid sequence information for the protein. Electrospray FTMS provides evidence of a solution phase dimer. In addition, dithiothreitol reduction shows no shift in high-resolution isotopic distributions, indicating a probable absence of disulfide bonds in the protein. The partial sequence information obtained from IRMPD could be the basis for creating a DNA probe for the protein.     

Nonlocal van der Waals density functional: the simpler the better

We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.     

Uniqueness of Positive Ground State Solutions of the Logarithmic Schrödinger Equation

We prove the uniqueness of positive ground state solutions of the problem \({ {\frac {d^{2}u}{dr^{2}}} + {\frac {n-1}{r}}{\frac {du}{dr}} + u \ln(|u|) = 0}\), \({u(r) > 0~\forall r \ge 0}\), and \({(u(r),u'(r)) \to (0, 0)}\) as \({r \to \infty}\). This equation is derived from the logarithmic Schrödinger equation \({{\rm i}\psi_{t} = {\Delta} \psi + u \ln \left(|u|^{2}\right)}\), and also from the classical equation \({{\frac {\partial u}{\partial t}} = {\Delta} u +u \left(|u|^{p-1}\right) -u}\). For each \({n \ge 1}\), a positive ground state solution is \({ u_{0}(r) = \exp \left(-{\frac{r^2}{4}} + {\frac{n}{2}}\right),~0 \le r < \infty}\). We combine \({u_{0}(r)}\) with energy estimates and associated Ricatti equation estimates to prove that, for each \({n \in \left[1, 9 \right]}\), \({u_{0}(r)}\) is the only positive ground state. We also investigate the stability of \({u_{0}(r)}\). Several open problems are stated.     

Symmetry properties in systems of semilinear elliptic equations

We investigate symmetry properties of solutions of systems of semilinear elliptic equations. The two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane. An application to the Belousov-Zhabotinskii chemical reaction is given.     

Large amplitude periodic solutions of a system of equations derived from the Hodgkin-Huxley equations

The Hodgkin-Huxley equations form the most widely accepted model of nerve conduction in the squid axon.We make several appropriate assumptions on the functions and parameters occurring in the current clamped version of these equations. These assumptions reduce the original system of four partial differential equations to a system of three ordinary differential equations. We show that there is a range of parameters over which the reduced system has a large amplitude periodic solution.     

Self-consistent implementation of a nonlocal van der Waals density functional with a Gaussian basis set

Nearly all common density functional approximations fail to properly describe dispersion interactions responsible for binding in van der Waals complexes. Empirical corrections can fix some of the failures but cannot fully grasp the complex physics and may not be reliable for systems dissimilar to the fitting set. In contrast, the recently proposed nonlocal van der Waals density functional (vdW-DF) was derived from first principles, describes dispersion interactions in a seamless fashion, and yields the correct asymptotics. Implementation of this functional is somewhat cumbersome: Nonlocal dependence on the electron density requires numerical double integration over the space variables and functional derivatives are nontrivial. This paper shows how vdW-DF can be implemented self-consistently with Gaussian basis functions. The gradients of the energy with respect to nuclear displacements have also been derived and coded, enabling efficient geometry optimizations. We test the vdW-DF correlation functional in combination with several exchange approximations. We also study the sensitivity of the method to the basis set size and to the quality of the numerical quadrature grid. For weakly interacting systems, acceptable accuracy in semilocal exchange is achieved only with fine grids, whereas for nonlocal vdW-DF correlation even rather coarse grids are sufficient. The current version of vdW-DF is not well suited for pairing with Hartree-Fock exchange, leading to considerable overbinding.     

Gas phase spectra of all-benzenoid polycyclic aromatic hydrocarbons: triphenylene

The jet-cooled laser-induced fluorescence and dispersed fluorescence spectra of the S1(A1')<--S0(A1') transition of triphenylene are reported. The spectra exhibit false origins of e' symmetry which are modeled by performing calculations of Herzberg-Teller coupling using time-dependent density functional theory. It is found that this level of theory reproduces the main features of the observed spectra. The oscillator strength of the strongest band is calculated to be f=7x10(-4). From a combination of theory and the observed upper state lifetime of 41 ns, an estimate of the fluorescence yield is made of PhiF=0.084, in agreement with previous studies in the condensed phase.