Curvature coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study, we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than that from our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane such that forces along the trajectory are on average smaller than they would be for random particle positions.     

Influence of hydrodynamic coupling on the electric linear dichroism of DNA fragments

In the present work, we study the effect of translational-rotational hydrodynamic coupling on the stationary electric linear dichroism of DNA fragments. The theoretical resolution of the problem has, so far, been dealt with analytic methods valid only in the limit of low electric fields. In this work, we apply numerical methods that allow us to study the problem and also consider electric fields of arbitrary strength. We use the bent rod molecules model to describe DNA fragments with physical properties characterized by their electric charge, electric polarizability tensor, rotational diffusion tensor, and translation-rotation coupling diffusion tensor. The necessary orientational distribution function to calculate electric dichroism is obtained by solving the Fokker-Planck equation through the finite difference method. We analyze the different contributions due to electric polarizability and translational-rotational coupling to the electric dichroism.     

Influence of dry density on HTO diffusion in GMZ bentonite

With the low permeability and high swelling property, Gaomiaozi (GMZ) bentonite is regarded as the favorable candidate backfilling material for a potential repository. The diffusion behaviors of HTO in GMZ bentonite were studied to obtain effective diffusion coefficient (D _e) and accessible porosity (ε) by through- and out-diffusion experiments. A computer code named Fitting for diffusion coefficient (FDP) was used for the experimental data processing and theoretical modeling. The D _e and ε values were (5.2–11.2) × 10⁻¹¹ m²/s and 0.35–0.50 at dry density from 1,800 to 2,000 kg/m³, respectively. The D _e values at 1,800 kg/m³ was a little higher than that of at 2,000 kg/m³, whereas the D _e value at 1,600 kg/m³ was significantly higher (approximately twice) than that of at 1,800 and 2,000 kg/m³. It may be explained that the diffusion of HTO mainly occurred in the interlayer space for the highly compacted clay (dry density exceeding 1,300 kg/m³). 1,800 and 2,000 kg/m³ probably had similar interlayer space, whereas 1,600 kg/m³ had more. Both D _e and ε values decreased with increasing dry density. For compacted bentonite, the relationship of D _e and ε could be described by Archie’s law with exponent n = 4.5 ± 1.0.     

Strong effect of hydrodynamic coupling on the electric dichroism of bent rods

The effect of hydrodynamic coupling on the spatial orientation of rigid bent rods in electric fields has been analyzed by Brownian dynamics simulations. Bead models for smoothly bent rods were constructed with dimensions of DNA double helices, and established simulation procedures were used to calculate their diffusion tensor, including the translational-rotational coupling tensor. The electric and optical parameters were assigned on the basis of known properties of double helices. Brownian dynamics simulations of the orientation of these models in electric fields showed that both transients and amplitudes of the calculated dichroism are very strongly dependent on translational-rotational coupling over a wide range of electric field strengths. For example, the stationary dichroism of a smoothly bent 179 bp DNA fragment calculated at low field strengths is positive in the presence and negative in the absence of hydrodynamic coupling. The transients are converted from a biphasic to a monophasic shape, when hydrodynamic coupling is turned off. The large changes resulting from hydrodynamic coupling were controlled by calculations based on analytical expressions derived for electrooptical response curves in the limit of low electric field strengths; the results obtained by this independent approach are in very satisfactory agreement with our Brownian dynamics simulations. The effect is strongly dependent on the electric dipole and on its direction. In the absence of any dipole the coupling effect was not observed. The coupling effect increases with the size of the bent rods. Because most macromolecular structures are known to have induced and/or permanent dipole moments, large effects of hydrodynamic coupling on both the amplitudes and the transients of the electric dichroism/birefringence must be expected in general for structures with nonsymmetric shape.     

Quantum hydrodynamic model of density functional theory

In this paper, we extend the method in Cai et al. (J Math Phys 53:103503, 2012) to derive a class of quantum hydrodynamic models for the density-functional theory (DFT). The most popular implement of DFT is the Kohn–Sham equation, which transforms a many-particle interacting system into a fictitious non-interacting one-particle system. The Kohn–Sham equation is a non-linear Schrödinger equation, and the corresponding Wigner equation can be derived as an alternative implementation of DFT. We derive quantum hydrodynamic models of the Wigner equation by moment closure following Cai et al. (J Math Phys 53:103503, 2012). The derived quantum hydrodynamic models are globally hyperbolic thus locally wellposed. The contribution of the Kohn–Sham potential is turned into a nonlinear source term of the hyperbolic moment system. This work provides a new possible way to solve DFT problems.     

Effect of long-range hydrodynamic and direct intermacromolecular forces on translational diffusion

Within the framework of recently formulated microscopic theories of macromolecular diffusion it is shown that hydrodynamic forces act always to diminish the influence of direct forces, but never to reverse the sign of the correction term due to direct forces alone. Although the correction term D(k) to the intrinsic diffusion coefficient may vary with scattering vector |k|, it is shown that a reversal in sigh of the correction term with increasing |k|, if it occurs, must be associated with an amplitude of less than 10% of the correction term at |k| = 0. At |k| = 0 direct repulsive forces are predicted to always increase the apparent diffusion constant, even after accounting for hydrodynamic interactions. Although experiments on polylysine (1 mg/ml) at salt concentrations above 0.01 M are in qualitative accord with the theory, below 10^?3 M salt the apparent diffusion coefficient is reduced by a factor of about 20, concomitant with a much reduced intensity of scattered light. The strong contradiction of the theory implied by this observation is attributed to a dramatic rise in Stokes friction arising from long-range interionic forces in the low-salt solutions.     

Diffusion in polymers dependence on crosslink density

Kinetics of N-methyl pyrrolidone evaporation from swollen photo-crosslinked polyacrylate was monitored thermogravimetrically at temperatures ranging from 323 to 398 K. Crosslink density dependence of evaporation kinetics was investigated in photo-crosslinked polyacrylates with crosslinked density ranging from ≈1.2 × 10² to ≈1.7 × 10⁴ mol m⁻³ and number of main chain atoms between crosslinks ranging from ≈70 atoms to ≈6 atoms, respectively. As was shown, evaporation kinetics was controlled by the solvent diffusion in polymer. Activation energies of evaporation (diffusion) were deduced from the rate measurements at different temperatures. Apparent activation energy of evaporation decreased from 48.7 to 31.1 kJ mol⁻¹ with crosslink density increase. Activation energy of pure N-methyl pyrrolidone evaporation was 50.6 kJ mol⁻¹. Decrease of the rate of solvent diffusion and unexpected decrease of diffusion activation energy with increase of crosslink density of swollen polymer matrix was explained by decrease in polymer chain segments mobility, as indicated by Eyring’s approach to diffusion in polymers.     

Basis-set dependence of nuclear spin-spin coupling constants

The convergence of NMR indirect spin-spin coupling constants with the extension of the basis set is analyzed, based on calculations carried out at the multiconfigurational self-consistent-field level for the HF and H₂O systems. For the dominant and difficult Fermi-contact contribution, the standard correlation-consistent basis sets of electronic-structure theory are not suitable, lacking flexibility in the core region. Improved but not satisfactory convergence of the couplings is observed when decontracting the s functions of the correlation-consistent cc-pVXZ basis sets for 2≤X≤6. Next, by systematically extending these basis sets with tight s functions, new sets are obtained that are sufficiently flexible for accurate calculations of indirect nuclear spin-spin couplings, without sacrificing the smooth convergence behavior of the correlation-consistent basis sets. Received: 22 September 1997 / Accepted: 30 December 1997     

Analysis of the effect of translation-rotation coupling on diffusion along the molecular axes

The analysis of the microscopic diffusion processes of CO(2) and H(2)O in the coordinate system defined by the molecular orientation allows a new criterion to be introduced which provides information on the short and long time behavior of the rotation-translation coupling as well as to quantify the strength of this coupling. We discuss the general conditions under which this affects the translation diffusion "seen" by the molecule along its molecular axes. The results show that the translation-rotation coupling is correlated to the local environment in shaping the longitudinal and transversal translation dynamics of a molecule at a microscopic level.     

Anomalous dependence on the diffusion coefficients of the ionic relaxation time in electrolytes

We show, by using a numerical analysis, that the dynamic toward equilibrium for an electrolytic cell subject to a step-like external electric field is a multirelaxation process when the diffusion coefficients of positive and negative ions are different. By assuming that the diffusion coefficient of positive ions is constant, we observe that the number of involved relaxation processes increases when the diffusion coefficient of the negative ions diminishes. Furthermore, two of the relaxation times depend nonmonotonically on the ratio of the diffusion coefficients. This result is unexpected, because the ionic drift velocity, by means of which the ions move to reach the equilibrium distribution, increases with increasing ionic mobility.     

Coverage and nearest-neighbor dependence of adsorbate diffusion

We present data on the coverage and nearest-neighbor dependences of the diffusion of CO on Cu(111) by time-lapsed scanning tunneling microscope (STM) imaging. Most notable is a maximum in diffusivity of CO at a local coverage of one molecule per 20 substrate atoms and a repulsion between CO molecules upon approach closer than three adsites, which in combination with a less pronounced increase in potential energy at the diffusion transition state, leads to rapid diffusion of CO molecules around one another. We propose a new method of evaluating STM-based diffusion data that provides all parameters necessary for the modeling of the dynamics of an adsorbate population.     

Inverse temperature dependence of strain hardening in ultrahigh molecular weight polyethylene: role of lamellar coupling and entanglement density

Irradiation of ultrahigh molecular weight polyethylene (UHMWPE) with a dose of 150 kGy by an electron beam can effectively increase the entanglement density in the amorphous phase and has little influence on the properties of the crystalline phase, which provides examples to comparatively investigate the role of lamellar coupling and entanglement density in determining the strain-hardening effect in semicrystalline polymers. The strain-hardening modulus, deduced from the Haward plots of true stress-strain curves, is inversely temperature-dependent and has a sharp transition around 65 degrees C that corresponds to the mechanical alphaI-process of the crystalline phase for both nonirradiated and irradiated samples, irrespective of the entanglement density in the amorphous phase. Lamellar coupling takes more effect in determining the strain-hardening behavior before the mechanical alphaI-process is activated. With further increasing temperature, lamellar coupling becomes weaker and the role of the entangled amorphous phase is gradually presented. However, the same temperature dependence of the strain-hardening modulus in both nonirradiated and irradiated samples indicates that the strain-hardening behavior in semicrystalline polymer is mostly determined by lamellar coupling rather than by entanglement density.     

Measurement of the hydrodynamic radii of PEE-G dendrons by diffusion spectroscopy on a benchtop NMR spectrometer

Benchtop nuclear magnetic resonance (NMR) spectroscopy is a useful tool for the rapid determination of the self-diffusion coefficient and the hydrodynamic radius of dendrons. The self-diffusion coefficients of the first four generations of poly ethoxy ethyl glycinamide (PEE-G) dendrons are measured by diffusion-ordered spectroscopy (DOSY) on a benchtop NMR equipped with diffusion gradient coils. The hydrodynamic radii of the dendrons are calculated via the Stokes–Einstein equation. The effects of solvent and pH are determined with the hydrodynamic radius increasing with generation and decreasing upon neutralization of an acidic solution. These measurements provide valuable information for biological and pharmaceutical applications of dendrons.     

Capillary zone electrophoresis for the determination of average hydrodynamic velocity and diffusion coefficient

The determination of the average hydrodynamic velocity and diffusion coefficient by capillary zone electrophoresis is described. The present simple method only requires basic experimental data, such as peak area, peak height and migration time to complete the task of determining the diffusion coefficient and the average hydrodynamic velocity.     

Ligand-length dependence of the intramolecular electron transfer through-bond coupling parameter

For a donor-bridging-ligand-acceptor molecule excited in a non-ionized state, a Bloch transformation is used to decompose the time-dependent Schrödinger equation and to construct an effective evolution with the Bloch effective hamiltonian. The effective through-bond coupling is calculated in a tight-binding approximation as a function of the number of ligand active units. The precision of the effective coupling is tested by a comparison between exact and effective transfer rate. A class of hamiltonians is given where this coupling does not decrease with an increase of the ligand length.     

Capillary zone electrophoresis for the determination of average hydrodynamic velocity and diffusion coefficient

The determination of the average hydrodynamic velocity and diffusion coefficient by capillary zone electrophoresis is described. The present simple method only requires basic experimental data, such as peak area, peak height and migration time to complete the task of determining the diffusion coefficient and the average hydrodynamic velocity. Received: 29 September 1998 / Revised: 14 May 1999 / Accepted: 19 May 1999