Comparison of Three Molecular Simulation Approaches for Cyclodextrin-Ibuprofen Complexation

Cyclodextrins are widely used for the solubilisation of poorly soluble drugs in the formulations. However, current cyclodextrin formulation development strongly depends on trial-and-error in the laboratory, which is time-consuming and high cost. The aim of this research was to compare three modeling approaches (Docking, molecular dynamics (MD), and quantum mechanics (QM)) for cyclodextrin/drug complexation. Ibuprofen was used as a model drug. Binding free energy from three simulation methods was calculated as an important parameter to compare with the experimental results. Docking results from AutoDock Vina program showed that the scoring of complexation capability between ibuprofen and cyclodextrins is alpha (α), gamma (γ), beta (β), and HP-beta-cyclodextrins, which indicated similar ranking with the results from phase, solubility diagram experiments. MD simulation indicated that ibuprofen could form the stable complexes with β-, γ-, and HP-β-cyclodextrins, but not for alpha cyclodextrin. Binding free energies from the MD simulation for β-, γ-, and HP-β-cyclodextrins were −3.67, −0.67, and −3.87 kcal/mol, individually. The enthalpies of QM simulation for β-, γ-, and HP-β-cyclodextrins were −17.22, −14.75, and −20.28 kcal/mol, respectively. Results from all three modeling approaches showed similar ranking between ibuprofen and four cyclodextrin molecules as the experimental data. However, MD simulation with entropy calculation had the closest value to experimental data for β and HP-beta-cyclodextrins. Thus, MD simulation with MM-PBSA method may be fit to in silico screen for cyclodextrin formulations

Direct Imaging of Graphene Edges: Atomic Structure and Electronic Scattering

We report an atomically-resolved scanning tunneling microscopy (STM) investigation of the edges of graphene grains synthesized on Cu foils by chemical vapor deposition (CVD). Most of the edges are macroscopically parallel to the zigzag directions of graphene lattice. These edges have microscopic roughness that is found to also follow zigzag directions at atomic scale, displaying many ~120 degree turns. A prominent standing wave pattern with periodicity ~3a/4 (a being the graphene lattice constant) is observed near a rare-occurring armchair-oriented edge. Observed features of this wave pattern are consistent with the electronic intervalley backscattering predicted to occur at armchair edges but not at zigzag edges

Instantons and the spectral function of electrons in the half-filled Landau level

We calculate the instanton-anti-instanton action $S_{M {\bar M}} (\tau)$ in the gauge theory of the half-filled Landau level. It is found that $S_{M {\bar M}} (\tau) = (3 - \eta) \left [ \Omega_0 (\eta) \ \tau \right ]^{1 / (3 - \eta)}$ for a class of interactions $v ({\bf q}) = V_0 / q^{\eta} \ ( 0 \leq \eta < 2 )$ between electrons. This means that the instanton-anti-instanton pairs are confining so that a well defined `charged' composite fermion can exist. It is also shown that $S_{M {\bar M}} (\tau)$ can be used to calculate the spectral function of electrons from the microscopic theory within a semiclassical approximation. The resulting spectral function varies as $e^{ - \left [ \Omega_0 (\eta) / \omega \right ]^{1 / ( 2 - \eta ) } }$ at low energies.Comment: 13 pages, Plain Tex, MIT-CMT-APR-9

Theory of Fermion Liquids

We develop a general theory of fermion liquids in spatial dimensions greater than one. The principal method, bosonization, is applied to the cases of short and long range longitudinal interactions, and to transverse gauge interactions. All the correlation functions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau Fermi fixed point. Novel fixed points are found, however, in the cases of a super-long range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the 2+1-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction $V({\bf q}) \propto |{\bf q}|^{y-1}$ which controls the density, and hence gauge, fluctuations. For $y < 0$ we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for $y > 0$ the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case $y = 0$ (Coulomb interaction) which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator which is of a marginal Fermi liquid form. Using Ward Identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion, nor vertex corrections, alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also investigate the gauge-invariant density response function. Near momentum $Q = 2 k_F$, in addition to the Kohn anomaly we find singular behavior. In Appendices we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter $f_0 \neq 0$. We also show how Kohn's theorem isComment: Minor corrections and clarifications, and additional references. 30 pages, RevTex 3.0, 3 figures in uuencoded postscript files

Influence of gauge-field fluctuations on composite fermions near the half-filled state

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial \mu} \propto e^{- \Delta \omega_c / 2 T} \left ( 1 + {A (\eta) \over \eta - 1} {(\Delta \omega_c)^{2 \over 1 + \eta} \over T} \right )$ for $T \ll \Delta \omega_c$, where $\Delta \omega_c = {e \Delta B \over mc}$. Here we assume that the interaction between the fermions is given by $v ({\bf q}) = V_0 / q^{2 - \eta} \ (1 \le \eta \le 2)$, where $A (\eta)$ is a $\eta$ dependent constant. This result can be interpreted as a divergent correction to the activation energy gap and is consistent with the divergent renormalization of the effective mass of the composite fermions.Comment: Plain Tex, 24 pages, 5 figures available upon reques

Specific heat and validity of quasiparticle approximation in the half-filled Landau level

We calculate the specific heat of composite fermion system in the half-filled Landau level. Two different methods are used to examine validity of the quasiparticle approximation when the two-body interaction is given by $V(q) = V_0 / q^{2-\eta}$ ($1 \le \eta \le 2$). The singular part of the specific heat is calculated from the free energy of the gauge field, which is compared with the specific heat calculated from the quasiparticle approximation via the singular self-energy correction due to the gauge field fluctuations. It turns out that two results are in general different and they coincide only for the case of the Coulomb interaction ($\eta = 1$). This result supports the fact that the quasiparticle approximation is valid only for the case of the Coulomb interaction. It is emphasized that this result is obtained by looking at a gauge-invariant quantity -- the specific heat.Comment: 8 pages, Revte

Gauge-invariant response functions of fermions coupled to a gauge field

We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be cancelled by those from the vertex correction for small $q$ and $\Omega$. As a result, the remaining contributions are not singular enough to change the leading order results of the random phase approximation. It is also shown that the gauge field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small $q$ and $\Omega$, but for all ratios of $\Omega / v_F q$ and we conclude that they can be described by Fermi liquid forms without a diverging effective mass.Comment: Plain Tex, 35 pages, 5 figures available upon request, Revised Version (Expanded discussion), To be published in Physical Review B 50, (1994) (December 15 issue

Quantum Boltzmann equation of composite fermions interacting with a gauge field

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $\nu = 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge field fluctuations suggests that there is no well defined Landau-quasi-particle. Therefore, we cannot assume the existence of the Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi surface displacement which corresponds to the local variation of the chemical potential in momentum space. {}From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at $\nu = 1/2$ (in the long wave length and the low frequency limits) and the singular behavior of the energy gap obtained from the finite temperature activation behavior of the compressibility near $\nu = 1/2$. Implications of these results to the recent experiments are also discussed.Comment: 44 pages, Plain Tex, 5 figures (ps files) available upon reques

Genetically Determined Plasma Lipid Levels and Risk of Diabetic Retinopathy: A Mendelian Randomization Study.

Results from observational studies examining dyslipidemia as a risk factor for diabetic retinopathy (DR) have been inconsistent. We evaluated the causal relationship between plasma lipids and DR using a Mendelian randomization approach. We pooled genome-wide association studies summary statistics from 18 studies for two DR phenotypes: any DR (N = 2,969 case and 4,096 control subjects) and severe DR (N = 1,277 case and 3,980 control subjects). Previously identified lipid-associated single nucleotide polymorphisms served as instrumental variables. Meta-analysis to combine the Mendelian randomization estimates from different cohorts was conducted. There was no statistically significant change in odds ratios of having any DR or severe DR for any of the lipid fractions in the primary analysis that used single nucleotide polymorphisms that did not have a pleiotropic effect on another lipid fraction. Similarly, there was no significant association in the Caucasian and Chinese subgroup analyses. This study did not show evidence of a causal role of the four lipid fractions on DR. However, the study had limited power to detect odds ratios less than 1.23 per SD in genetically induced increase in plasma lipid levels, thus we cannot exclude that causal relationships with more modest effect sizes exist