Weak coupling perturbative calculations of the Wilson loop for the standard action

Wilson loops of size m × n with m, n≤6 are evaluated to second order in weak coupling perturbation theory. The results are compared with earlier estimates by Hattori and Kawai.     

Improved continuum limit lattice action for QCD with wilson fermions

Two possible ways of extending Symanzik's improvement programme to lattice fermions namely improvement to first and second order in the lattice sppacing a are discussed. The corresponding lattice actions for fermions are constructed and tree-level improvement conditions are derived by considering “classical” improvement. The concept of “on-shell” improvement is generalized to the lattice fermions studied here and the free parameters are determined for O(a) and O(a²) on-shell improved actions to all orders of perturbation theory. No evidence is found that the complicated structure of the O(a²) on-shell improved action, especially thearising fermion contact terms can be removed beyond tree level. The effect of terms in the action that explicitly break chiral symmetry and therefore remove the phenomenon of species doubling are investigated by considering the energy-momentum relations of the arising tree-level improved actions. Our main result is that the O(a) improved action is a slightly modified Wilson fermion action can still be written with only nearest-neighbour fermion interactions.     

Free energy surfaces for the interaction of D-glucose with planar aromatic groups in aqueous solution

Multidimensional potentials of mean force for the interactions in aqueous solution of both anomers of D-glucopyranose with two planar aromatic molecules, indole and para-methyl-phenol, have been calculated using molecular dynamics simulations with umbrella sampling and were subsequently used to estimate binding free energies. Indole and para-methyl-phenol serve as models for the side chains of the amino acids tryptophan and tyrosine, respectively. In all cases, a weak affinity between the glucose molecules and the flat aromatic surfaces was found. The global minimum for these interactions was found to be for the case when the pseudoplanar face of β-D-glucopyranose is stacked against the planar surfaces of the aromatic residues. The calculated binding free energies are in good agreement with both experiment and previous simulations. The multidimensional free energy maps suggest a mechanism that could lend kinetic stability to the complexes formed by sugars bound to sugar-binding proteins.     

Effects of frequency modulated tones and vowel formants on perioral muscle activity during isometric lip rounding

Two studies were conducted to assess the sensitivity of perioral muscles to vowel-like auditory stimuli. In one study, normal young adults produced an isometric lip rounding gesture while listening to a frequency modulated tone (FMT). The fundamental of the FMT was modulated over time in a sinusoidal fashion near the frequency ranges of the first and second formants of the vowels /u/ and /i/ (rate of modulation = 4.5 or 7 Hz). In another study, normal young adults produced an isometric lip rounding gesture while listening to synthesized vowels whose formant frequencies were modulated over time in a sinusoidal fashion to simulate repetitive changes from the vowel /u/ to /i/ (rate of modulation = 2 or 4 Hz). The FMTs and synthesized vowels were presented binaurally via headphones at 75 and 60 dB SL, respectively. Muscle activity from the orbicularis oris superior and inferior and from lip retractors was recorded with surface electromyography (EMG). Signal averaging and spectral analysis of the rectified and smoothed EMG failed to show perioral muscle responses to the auditory stimuli. Implications for auditory feedback theories of speech control are discussed.     

Dynamics of cellulose-water interfaces: NMR spin-lattice relaxation times calculated from atomistic computer simulations

Solid-state nuclear magnetic resonance (CP/MAS 13C NMR) spectroscopy has often been used to study cellulose structure, but some features of the cellulose NMR spectrum are not yet fully understood. One such feature is a doublet around 84 ppm, a signal that has been proposed to originate from C4 atoms at cellulose fibril surfaces. The two peaks yield different T1, differing by approximately a factor of 2 at 75 MHz. In this study, we calculate T1 from C4-H4 vector dynamics obtained from molecular dynamics computer simulations of cellulose I beta-water interfacial systems. Calculated and experimentally obtained T1 values for C4 atoms in surface chains fell within the same order of magnitude, 3-20 s. This means that the applied force field reproduces relevant surface dynamics for the cellulose-water interface sufficiently well. Furthermore, a difference in T1 of about a factor of 2 in the range of Larmor frequencies 25-150 MHz was found for C4 atoms in chains located on top of two different crystallographic planes, namely, (110) and (10). A previously proposed explanation that the C4 peak doublet could derive from surfaces parallel to different crystallographic planes is herewith strengthened by computationally obtained evidence. Another suggested basis for this difference is that the doublet originates from C4 atoms located in surface anhydro-glucose units with hydroxymethyl groups pointing either inward or outward. This was also tested within this study but was found to yield no difference in calculated T1.     

Role of hydrogen bonding in cellulose deformation: the leverage effect analyzed by molecular modeling

The axial modulus of the cellulose Iβ crystal is as high as 120–160 GPa. The importance of hydrogen bonds is often emphasized in this context, although intrinsic stiffness of the hydrogen bonds is relatively low. Here, hydrogen bond–covalent bond synergies are investigated quantitatively using molecular mechanics and molecular dynamics simulations for the so-called leverage effect, a model introduced recently in which strains for intra-molecular hydrogen bonds are higher than for the cellulose chain as a whole, thereby amplifying their contribution to the total stiffness. The present work also includes simulation of the hydrogen bonding band shifts in vibrational spectra during cellulose deformation, which are compared with FT-IR data. The leverage effect hypothesis was supported by the results, although the total contribution to cellulose stiffness is only 12 %. Hydrogen bonding is still critically important and would lower the modulus much more than 12 %, if “artificially” removed in the model. The reason is that intra-molecular hydrogen bonding preserves the crystal structure and directs axial deformation mechanisms towards higher energy deformation and high stiffness.     

Quantifying the influence of dispersion interactions on the elastic properties of crystalline cellulose

Dispersion and electrostatic interactions both contribute significantly to the tight assembly of macromolecular chains within crystalline polysaccharides. Using dispersion-corrected density functional theory (DFT) calculation, we estimated the elastic tensor of the four crystalline cellulose allomorphs whose crystal structures that are hitherto available, namely, cellulose Iα, Iβ, II, III_I. Comparison between calculations with and without dispersion correction allows quantification of the exact contribution of dispersion to stiffness at molecular level.

     

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.