Transport of biomolecules in asymmetric nanofilter arrays

We propose a theoretical model for describing the electric-field-driven migration of rod-like biomolecules in nanofilters comprising a periodic array of shallow passages connecting deep wells. The electrophoretic migration of the biomolecules is modeled as transport of point-sized Brownian particles, with the orientational degree of freedom captured by an entropy term. Using appropriate projections, the formulation dimensionality is reduced to one physical dimension, requiring minimal computation and making it ideal for device design and optimization. Our formulation is used to assess the effect of slanted well walls on the energy landscape and resulting molecule mobility. Using this approach, we show that asymmetry in the well shape, such as a well with one slanted and one vertical wall, may be used for separation using low-frequency alternating-current fields because the mobility of a biomolecule is different in the two directions of travel. Our results show that, compared to methods using direct-current fields, the proposed method remains effective at higher field strengths and can achieve comparable separation using a significantly shorter device.     

Diffusion in Confined Geometries

Diffusive transport of particles or, more generally, small objects, is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions, transport is controlled both by the fluctuation statistics of the jittering objects and the phase space available to their dynamics. Consequently, the study of transport at the macro‐ and nanoscales must address both Brownian motion and entropic effects. Herein we report on recent advances in the theoretical and numerical investigation of stochastic transport occurring either in microsized geometries of varying cross sections or in narrow channels wherein the diffusing particles are hindered from passing each other (single‐file diffusion). For particles undergoing biased diffusion in static suspension media enclosed by confining geometries, transport exhibits intriguing features such as 1) a decrease in nonlinear mobility with increasing temperature or also 2) a broad excess peak of the effective diffusion above the free diffusion limit. These paradoxical aspects can be understood in terms of entropic contributions resulting from the restricted dynamics in phase space. If, in addition, the suspension medium is subjected to external, time‐dependent forcing, rectification or segregation of the diffusing Brownian particles becomes possible. Likewise, the diffusion in very narrow, spatially modulated channels is modified via contact particle–particle interactions, which induce anomalous sub‐diffusion. The effective sub‐diffusion constant for a driven single file also develops a resonance‐like structure as a function of the confining coupling constant.     

Effective thickness of the diffusion layer during hydrogen ion reduction in aqueous hydrochloric acid solutions

The process of mass transport during hydrogen ion reduction in aqueous hydrochloric acid solutions is examined both with and without excess supporting electrolyte. The study of this process is based on a numerical solution to a system of equations of material balance and the movement of particles in solution under the influence of forces for diffusion, migration, and convection. The homogeneous chemical reaction of water dissociation is also taken into account. The results of calculations show that a diffusion layer forms near the electrode during the passage of current in these solutions and that the effective thickness of this layer is the same at any instant for all particles participating in mass transport in solution in spite of differences in their diffusion coefficients. The value of the diffusion coefficient measured in these multicomponent solutions by the methods of chronopotentiometry and rotating disk electrode should differ little from that of hydrogen ions in spite of the fact that other particles with different diffusion coefficients participate in the mass transport.     

Effect of equilibrium potential on anodic peaks of a reversible electrode process in conditions of stripping voltammetry at a linear alteration of potential on a thin-film mercury electrode

The full contour of a stripping-voltammetry peak for a reversible electrode process in conditions of boundedly semi-infinite and symmetrical diffusion on a thin-film mercury electrode at a linearly altering potential is calculated with an exact explicit equation allowing for the equilibrium-potential effect in a broad range of values of parameter H (which are defined by the film thickness, potential scan rate, and diffusion coefficient). The height, position of maximum, and full width at half-maximum of anodic peaks are evaluated as a function of parameter H and equilibrium potential. The latter is shown to exert substantial influence on the parameters and shape of anodic peaks.To the Centennial of B.N. KabanovDeceasedTranslated from Elektrokhimiya, Vol. 41, No. 1, 2005, pp. 69–75.Original Russian Text Copyright © 2005 by Nazarov, Stromberg, Larionova.     

Modeling the electrostatic potential of asymmetric lipopolysaccharide membranes: The MEMPOT algorithm implemented in DelPhi

Four chemotypes of the rough lipopolysaccharides (LPS) membrane from Pseudomonas aeruginosa were investigated by a combined approach of explicit water molecular dynamics (MD) simulations and Poisson–Boltzmann continuum electrostatics with the goal to deliver the distribution of the electrostatic potential across the membrane. For the purpose of this investigation, a new tool for modeling the electrostatic potential profile along the axis normal to the membrane, MEMbrane POTential (MEMPOT), was developed and implemented in DelPhi. Applying MEMPOT on the snapshots obtained by MD simulations, two observations were made: (a) the average electrostatic potential has a complex profile but is mostly positive inside the membrane due to the presence of Ca²⁺ ions, which overcompensate for the negative potential created by lipid phosphate groups; and (b) correct modeling of the electrostatic potential profile across the membrane requires taking into account the water phase, while neglecting it (vacuum calculations) results in dramatic changes including a reversal of the sign of the potential inside the membrane. Furthermore, using DelPhi to assign different dielectric constants for different regions of the LPS membranes, it was investigated whether a single frame structure before MD simulations with appropriate dielectric constants for the lipid tails, inner, and the external leaflet regions, can deliver the same average electrostatic potential distribution as obtained from the MD‐generated ensemble of structures. Indeed, this can be attained by using smaller dielectric constant for the tail and inner leaflet regions (mostly hydrophobic) than for the external leaflet region (hydrophilic) and the optimal dielectric constant values are chemotype‐specific. © 2014 Wiley Periodicals, Inc.     

Exploring the similarities between potential smoothing and simulated annealing

Simulated annealing and potential function smoothing are two widely used approaches for global energy optimization of molecular systems. Potential smoothing as implemented in the diffusion equation method has been applied to study partitioning of the potential energy surface (PES) for N‐Acetyl‐Ala‐Ala‐N‐Methylamide (CDAP) and the clustering of conformations on deformed surfaces. A deformable version of the united‐atom OPLS force field is described, and used to locate all local minima and conformational transition states on the CDAP surface. It is shown that the smoothing process clusters conformations in a manner consistent with the inherent structure of the undeformed PES. Smoothing deforms the original surface in three ways: structural shifting of individual minima, merging of adjacent minima, and energy crossings between unrelated minima. A master equation approach and explicit molecular dynamics trajectories are used to uncover similar features in the equilibrium probability distribution of CDAP minima as a function of temperature. Qualitative and quantitative correlations between the simulated annealing and potential smoothing approaches to enhanced conformational sampling are established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 531–552, 2000     

Proof of finiteness of Kohn–Sham theory electron interaction potential at the nucleus of atoms

We employ Kato's theorem to prove that the electron interaction potential of Kohn–Sham density functional theory is finite at the nucleus of spherically symmetric and sphericalized atoms and ions. Therefore, this finiteness is a direct consequence of the electron–nucleus cusp condition for the density. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 205–208, 2000     

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

The exact expression for the Fermi potential yielding the Hartree–Fock electron density within an orbital‐free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles’ nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital‐free density functional formalism is shown to be the Slater potential.     

Use of the Rotation Vector in Brownian Dynamics Simulation of Transient Electro‐Optical Properties

We have recently developed a new singularity‐free algorithm for Brownian dynamics simulation of free rotational diffusion. The algorithm is rigorously derived from kinetic theory and makes use of the Cartesian components of the rotation vector as the generalized coordinates describing angular orientation. Here, we report on the application of this new algorithm in Brownian dynamics simulations of transient electro‐optical properties. This work serves two main purposes. Firstly, it demonstrates the integrity of the new algorithm for BD‐simulations of the most common transient electro‐optic experiments. Secondly, it provides new insight into the performance of the new algorithm compared to algorithms that make use of the Euler angles. We study the transient electrically induced birefringence in dilute solutions of rigid particles with anisotropic polarization tensor in response to external electric field pulses. The use of both one single electric pulse and two electric pulses with opposite polarity are being analyzed. We document that the new singularity‐free algorithm performs flawlessly. We find that, for these types of systems, the new singularity‐free algorithm, in general, outperforms similar algorithms based on the Euler angles. In a wider perspective, the most important aspect of this work is that it serves as an important reference for future development of efficient BD‐algorithms for studies of more complex systems. These systems include polymers consisting of rigid segments with single‐segment translational–rotational coupling, segment–segment fluid‐dynamic interactions and holonomic constraints.

     

Higher order hydrodynamic interactions in the calculation of polymer transport properties

Higher order hydrodynamics interactions are short-range modifications to the Oseen tensor T _ij and its self-interaction counterpart T _ii. They differ from the Oseen tensor in having terms of higher order than the first in a/R, a being a bead radius and R being a bead-bead distance. Effects of higher order hydrodynamic interactions on whole chain–whole chain hydrodynamic interactions are here computed. Higher order hydrodynamic interactions are shown to lead to a concentration dependence of the diffusion and friction coefficients of a free monomer. However, while higher order interactions make contributions of the same nature to the drag coefficients of a monomer and of a whole chain, the contributions are not simply multiplicative, removing a justification for the common practice of correcting polymer solution transport data for “monomer friction effects” via a normalization with data on friction coefficients of free monomers. © 1993 John Wiley & Sons, Inc.     

On the theory of radiative transitions in centrosymmetric complexes

The theory of radiative transitions, in centrosymmetric complexes, is examined in great detail, within the framework of the crystal field method.In connection with radiative transitions, the current method of calculations, with and without invoking closure approximation, are considered from a purely theoretical point of view, by taking advantage of the irreducible tensor method put forward by Griffith.Explicit equations are derived throughout the course of this work to account for the vibronic electric dipole moments, associated with d-d and f-f type of excitations.At high Academy of Pedagogic Sciences, Santiago, Chile.     

密度泛函理论和从头算方法对富勒烯分子静电势的比较研究

分别在Hartree-Fock和密度泛函B3LYP理论下,用6-31G*基组研究了C60和C70分子的静电势,比较了这方法计算得到上述分子静电势值的大小,静电势图形和静电势差值曲线,分析了富勒烯的电子相关效应.     

BROMOC suite: Monte Carlo/Brownian dynamics suite for studies of ion permeation and DNA transport in biological and artificial pores with effective potentials

The transport of ions and solutes by biological pores is central for cellular processes and has a variety of applications in modern biotechnology. The time scale involved in the polymer transport across a nanopore is beyond the accessibility of conventional MD simulations. Moreover, experimental studies lack sufficient resolution to provide details on the molecular underpinning of the transport mechanisms. BROMOC, the code presented herein, performs Brownian dynamics simulations, both serial and parallel, up to several milliseconds long. BROMOC can be used to model large biological systems. IMC‐MACRO software allows for the development of effective potentials for solute–ion interactions based on radial distribution function from all‐atom MD. BROMOC Suite also provides a versatile set of tools to do a wide variety of preprocessing and postsimulation analysis. We illustrate a potential application with ion and ssDNA transport in MspA nanopore. © 2014 Wiley Periodicals, Inc.     

Energy transport in the inductively coupled plasma

Time- and space-resolved electron density measurements, made both above the load coil and in the load coil region of a pulsed inductively coupled plasma, are presented. These data, coupled with argon and calcium emission data, give values for the rates of both radial and vertical transport in the plasma. The data indicate that analyte emission behavior is governed primarily by the rate at which the central channel can be heated through radial transport processes. The electron densities measured in the load coil region agree well with electron densities calculated by models assuming local thermodynamic equilibrium, but agree poorly with non-equilibrium models. Some of the timedependent emission behavior observed in previous work with modulated plasmas is explained by non-uniform heating of argon in the load coil region.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, Austria     

Solution of equation for a current-voltage curve describing reversible metal electrodissolution with linear boundedly semi-infinite diffusion and a linear alteration of potential in the stripping voltammetry method

An exact, sufficiently simple, explicit expression is obtained and a full contour of the stripping-voltammetry peak is calculated for a reversible process on a thin-film mercury electrode of finite thickness (linear boundedly semi-infinite diffusion is taken into account) in conditions of stripping voltammetry at a linearly altering potential. That these results were obtained at all, is due to use made of two extra boundary conditions (Nemovs and Nazarovs). The addends in the four forms of equations derived are the limiting expressions and corrections in the form of Nemovs or Nazarovs boundary conditions. It is shown that it is advisable to employ different forms of equations at large and small values of parameter H. The peaks height, full width at half-maximum, and potential are found to depend on H.Translated from Elektrokhimiya, Vol. 41, No. 1, 2005, pp. 54–68.Original Russian Text Copyright © 2005 by Nazarov, Stromberg.To the Centennial of B.N. Kabanov.Deceased.     

Exploiting threefold symmetry in asymmetric catalysis: the case of tris(oxazolinyl)ethanes ("trisox")

Rotational molecular symmetry, modularity and other aspects of ligand design have played a role in the development of a new class of stereodirecting ligands. The use of highly symmetrical, stereodirecting ligands may reduce the number of transition states and diastereomeric reaction intermediates and, in favourable cases, this degeneration of alternative reaction pathways may lead to high stereoselectivity in catalytic reactions and greatly simplifies the analysis of such transformations. In this concept article, we describe the way in which these considerations have played a role in the development of a new class of stereodirecting ligands. Tris(oxazolinyl)ethanes ("trisox") have proved to be versatile ligand systems for the development of enantioselective catalysts of the d- and f-block metals employed in a wide range of catalytic conversions. These include Lewis acid catalysed transesterifications, C-C and C-N coupling reactions, the catalytic polymerisation of alpha-olefins as well as Pd-catalysed allylic alkylations. An overview of the current state of this field is given and the potential for further development will be highlighted.