Modeling the Electrostatics and Size Effect within a Crowded Bioenvironment

Biological fluids typically contain a large number of macromolecules occupying up to 40% of the total volume. Current understanding of the effect of high concentration, or ‘macromolecular crowding’, on cellular processes is primarily based on the excluded-volume considerations in which all intermolecular interactions beyond the short-ranged repulsion are neglected. In this work, a density functional theory (DFT) accompanied by Monte Carlo simulations is employed to investigate the structural and thermodynamic properties of a crowded cellular environment within the primitive model where biomacromolecules are represented by neutral and charged hard spheres and the solvent by a continuous dielectric medium. The performance of the DFT has been tested with extensive results from Monte Carlo (MC) simulations for the pair correlation functions (PCFs), excess internal energies, and osmotic coefficients under a variety of solution conditions.     

Equation of state and structural properties of the Weeks-Chandler-Andersen fluid

Molecular dynamics simulations have been carried out for the equation of state and percolation properties of the Weeks-Chandler-Andersen (WCA) system in its fluid phase as functions of density and temperature. The compressibility factor Z collapses well for the various isotherms, using an effective particle diameter for the WCA particle which is (in the usual WCA reduced units) sigma(e)=2(16)(1+T)(16), where T is the temperature. A corresponding "effective" packing fraction is zeta(e)=pisigma(e) (3)N6V, for N particles in volume V, which therefore scales out the effects of temperature. Using zeta(e) the simulation derived Z can be fitted to a simple analytic form which is similar to the Carnahan-Starling hard sphere equation of state and which is valid at all temperatures and densities where the WCA fluid is thermodynamically stable. The data, however, are not scalable onto the hard sphere equation of state for the complete packing fraction range. We explored the continuum percolation behavior of the WCA fluids. The percolation distance sigma(p) for the various states collapses well onto a single curve when plotted as sigma(p)sigma(e) against zeta(e). The ratio sigma(p)sigma(e) exhibits a monotonic decrease with increasing zeta(e) between the percolation line for permeable spheres and the glass transition limit, where sigma(p)sigma(e) approximately 1. The percolation packing fraction was calculated as a function of effective packing fraction and fitted to an empirical expression. The local coordination number at the percolation threshold showed a transition between the soft core and hard core limits from ca. 2:74 to 1:5, as previously demonstrated in the literature for true hard spheres. A number of simple analytic expressions that represent quite well the percolation characteristics of the WCA system are proposed.     

Polydisperse hard spheres at a hard wall

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focused on the local density distribution rho(sigma,z), measuring the number density of particles of diameter sigma at a distance z from the wall. Estimates of rho(sigma,z) are obtained for bulk volume fractions eta(b)=0.2 and eta(b)=0.4, and for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity delta=11.5% and delta=40.4%, and a truncated Schulz form having delta=40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at eta(b)=0.2. A detailed analysis of rho(sigma,z) confirms the presence of oscillatory size segregation effects, as observed in a previous DFT study [I. Pagonabarraga, M. E. Cates, and G. J. Ackland, Phys. Rev. Lett. 84, 911 (2000)]. For large delta, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive sigma-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity delta(z) is suppressed in this region, while further from the wall it exhibits oscillations.     

The density profile of hard sphere liquid system under gravity

The density profile of hard sphere liquid under gravity is calculated by using density functional theory and Monte Carlo simulation method. The two methods give consistent results for a wide range of parameters. Meanwhile, the validity range of the density functional theory is also established. The results are quite different from the barometric height distribution rho(z)=rho(0) exp(-zL(G)) in almost all cases studied, which indicates that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the crystallizing phenomenon is also predicted at the bottom part of the system under strong gravitation.     

Relativistic effect on 77Se NMR chemical shifts of various selenium species in the framework of zeroth-order regular approximation

The relativistic effects on absolute magnetic shielding tensors (σ(Se)) are explicitly evaluated for various selenium species (40 species) with the DFT(BLYP)-GIAO method. Calculations are performed under relativistic and nonrelativistic conditions with the Slater-type basis sets in ADF 2010 in the framework of ZORA, employing the optimized structures under nonrelativistic conditions at B3LYP of Gaussian 03. Quadruple zeta all electron with four polarization functions (QZ4Pae) are mainly applied to evaluate σ(Se). Ranges of the effect on diamagnetic (σ(d)(Se)), paramagnetic shielding tensors (σ(p)(Se)), and σ(d+p)(Se) (= σ(d)(Se) + σ(p)(Se)) are -24 to -20 ppm, -115 to -3 ppm, and -136 to -26 ppm, respectively. The spin-orbit terms (σ(so)(Se)) are evaluated to be 92-225 ppm with QZ4Pae, which clarifies the effect on total shielding tensors (σ(t)(Se) = σ(d+p)(Se) + σ(so)(Se)) to be -8 to 152 ppm, at the spin-orbit ZORA level. The calculated σ(t)(Se) values reproduced well the observed values.     

Confinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments.     

Microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces: A hybrid density functional approach

We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.     

Evaluating the accuracy of a density functional theory of polymer solutions with additive hard sphere diameters

We assess the accuracy of a density functional theory for athermal polymer solutions, consisting of solvent particles with a smaller radius than that of the monomers. The monomer and solvent density profiles in a slit bound by hard, flat, and inert surfaces are compared with those obtained by a Metropolis Monte Carlo simulation. At the relatively high density at which the comparison is performed, there are considerable packing effects at the walls. The density functional theory introduces a simple weight function to describe nonlocal correlations in the fluid. A recent study of surface forces in polymer solutions used a different weighting scheme to that proposed in this article, leading to less accurate results. The implications of the conclusions of that study are discussed.     

Theory of repulsive charged colloids in slit-pores

Using classical density functional theory (DFT) we analyze the structure of the density profiles and solvation pressures of negatively charged colloids confined in slit pores. The considered model, which was already successfully employed to study a real colloidal (silica) suspension [S. H. L. Klapp et al., Phys. Rev. Lett. 100, 118303 (2008)], involves only the macroions which interact via the effective Derjaguin-Landau-Verwey-Overbeek (DLVO) potential supplemented by a hard core interaction. The solvent enters implicitly via the screening length of the DLVO interaction. The free energy functional describing the colloidal suspension consists of a hard sphere contribution obtained from fundamental measure theory and a long range contribution which is treated using two types of approximations. One of them is the mean field approximation (MFA) and the remaining is based on Rosenfeld's perturbative method for constructing the Helmholtz energy functional. These theoretical calculations are carried out at different bulk densities and wall separations to compare finally to grand canonical Monte Carlo simulations. We also consider the impact of charged walls. Our results show that the perturbative DFT method yields generally qualitatively consistent and, for some systems, also quantitatively reliable results. In MFA, on the other hand, the neglect of charge-induced correlations leads to a breakdown of this approach in a broad range of densities.     

Hopping time of a hard disk fluid in a narrow channel

We use Monte Carlo (MC) and molecular dynamics (MD) methods to study the self-diffusion of hard disk fluids, confined within a narrow channel. The channels have a pore radius of Rp, above the passing limit of hard disk diameter (sigma(hd)). We focus on the average time (tau(hop)) needed for a hard disk to hop past a nearest neighbor in the longitudinal direction. This parameter plays a key role in a recent theory of the crossover from single-file diffusion to the bulk limit. For narrow channels near the hopping threshold (Rp=1 in units of sigma(hd)), both MC and MD results for tau(hop) diverge as approximately (Rp-1)(-2). Our results indicate that the scaling law exponent does not appear to be dependent on the differences between the two dynamics. This exponent is consistent with the prediction of an approximate transition state theory.     

Preferential interaction between DNA and small ions in mixed-size counterion systems: Monte Carlo simulation and density functional study

Competitive binding between counterions around DNA molecule is characterized using the preferential interaction coefficient of individual ion in single and mixed electrolyte solutions. The canonical Monte Carlo (MC) simulation, nonlinear Poisson-Boltzmann (PB) equation, and density functional theory (DFT) proposed in our previous work [Wang, Yu, Gao, and Luo, J. Chem. Phys. 123, 234904 (2005)] are utilized to calculate the preferential interaction coefficients. The MC simulations and theoretical results show that for single electrolyte around DNA, the preferential interaction coefficient of electrolyte decreases as the cation size is increased, indicating that the larger cation has less accumulation ability in the vicinity of DNA. For the mixed electrolyte solution, it is found that cation diameter has a significant effect on the competitive ability while anion diameter has a negligible effect. It proves that the preferential interaction coefficients of all ions decrease as the total ionic concentration is increased. The DFT generally has better performance than the PB equation does when compared to the MC simulation data. The DFT behaves quite well for the real ionic solutions such as the KCl-NaCl-H2O, NaCl-CaCl2-H2O, and CaCl2-MgCl2-H2O systems.     

MONTE CARLO SIMULATION OF TRIBLOCK COPOLYMER/HOMOPOLYMER BLEND FILMS

The morphologies of triblock copolymer/homopolymer blend films, ABA/A and ABA/B,confined between two neutral hard walls were studied via Monte Carlo (MC) simulation on a simple cubic lattice. The effects of ψh (the volume fraction of homopolymer) and Mn/Mb (the molecular weight of homopolymer in relation to that of the corresponding blocks in the copolymer) on the morphologies were investigated in detail.     

MONTE CARLO SIMULATION OF TRIBLOCK COPOLYMER/HOMOPOLYMER BLEND FILMS

1. INTRODUCTION The extensive applications of block copolymer have been studied in detail due to their special molecular architecture and characteristic [1,2]. Recently, many studies including theoretical analysis and experimental techniques have addressed the polymer blend system of diblock copolymer/homopolymer [3~9]. An early investigation presented a quantitative analysis of homopolymer distributions in well-ordered copolymer microdomains through mixing polystyrene (PS) or poly methyl…     

Thermodynamics of symmetric dimers: lattice density functional theory predictions and simulations

A new lattice density functional theory (DFT) approach is proposed for symmetric dimers taking into account all possible configurations for molecules adjacent to a central dimer. Comparison with Monte Carlo simulations shows significant improvement of the proposed model compared to previously developed version of lattice DFT for dimers. It is shown that the new model gives accurate analytical solutions over a wide range of densities and temperatures. Phase transitions in dimers are analyzed and fundamental differences between dimers and monomers are discussed.     

温度和相结构对镧扩散动力学的影响

研究了等离了体渗氮过程中La在密排六方ε－Fe-3N(ε）和面心立方γ′－Fe4N(γ′)双相中的扩散动力学规律,与γ′相或ε＋γ′双相比较,发现ε相对La的扩散具有阻碍作用,一定温度下,随着渗氮时间的延长,ε相不断分解出γ′相,La在单相（如γ′相）和双相ε γ′中的扩散深度分别呈抛物线和近似指数规律增加,提高渗氮温度,La扩散的深度增加,但其扩散动力学规律并未因此而改变,温度从520度升高至560度使La扩散深度的增量较因相结构由ε转变为γ′相而引起的层深增加要小。     

Does confining the hard-sphere fluid between hard walls change its average properties?

We use grand canonical transition-matrix Monte Carlo and discontinuous molecular dynamics simulations to generate precise thermodynamic and kinetic data for the equilibrium hard-sphere fluid confined between smooth hard walls. These simulations show that the pronounced inhomogeneous structuring of the fluid normal to the confining walls, often the primary focus of density functional theory studies, has a negligible effect on many of its average properties over a surprisingly broad range of conditions. We present one consequence of this insensitivity to confinement: a simple analytical equation relating the average density of the confined fluid to that of the bulk fluid with equal activity. Nontrivial implications of confinement for average fluid properties do emerge in this system, but only when the fluid is both (i) dense and (ii) confined to a gap smaller than approximately three particle diameters. For this limited set of conditions, we find that "in-phase" oscillatory deviations in excess entropy and self-diffusivity (relative to the behavior of the bulk fluid at the same average density) occur as a function of gap size. These paired thermodynamic/kinetic deviations from bulk behavior appear to reflect the geometric packing frustration that arises when the confined space cannot naturally accommodate an integer number of particle layers.     

Radial distribution function of a hard-sphere fluid for the nearest neighbor surroundings

An expression for RDF as a function of two variables, the distance r and the packing factor η, was obtained by approximating the results of Monte Carlo simulation of a hard-sphere fluid. The mean square accuracy of the expressions presented is about ±0.0002 (1 ≤ r ≤ 1.5, 0 ≤ η ≤ 0.5). A continuous extension of RDF to the region of r < 1 is proposed, which provides the continuity of the first and second derivatives of RDF at the point r = 1. Analysis of the problem of determining the hard sphere diameter in WCA theory of simple liquids shows that the proposed expression makes it possible to directly calculate the hard sphere diameter without any simplifying approximations.     

Computational studies on the photophysical properties and NMR fluxionality of dinuclear platinum(II) A-frame alkynyl diphosphine complexes

The structural geometry, electronic structure, photophysical properties, and the fluxional behavior of a series of A-frame diplatinum alkynyl complexes, [Pt(2)(μ-dppm)(2)(μ-C≡CR)(C≡CR)(2)](+) [R = (t)Bu (1), C(6)H(5) (2), C(6)H(4)Ph-p (3), C(6)H(4)Et-p (4), C(6)H(4)OMe-p (5); dppm = bis(diphenylphosphino)methane], have been studied by density functional theory (DFT) and time-dependent TD-DFT associated with conductor-like polarizable continuum model (CPCM) calculations. The results show that the Pt···Pt distance strongly depends on the binding mode of the alkynyl ligands. A significantly shorter Pt···Pt distance is found in the symmetrical form, in which the bridging alkynyl ligand is σ-bound to the two metal centers, than in the unsymmetrical form where the alkynyl ligand is σ-bound to one metal and π-bound to another. For the two structural forms in 1-5, both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels show a dependence on the nature of the substituents attached to the alkynyl ligand. The energies of the HOMO and LUMO are found to increase and decrease, respectively, from R = (t)Bu to R = Ph and to R = C(6)H(4)Ph-p, because of the increase of the π- conjugation of the alkynyl ligand. On the basis of the TDDFT/CPCM calculations, the low-energy absorption band consists of two types of transitions, which are ligand-to-ligand charge-transfer (LLCT) [π(alkynyl) → σ*(dppm)]/metal-centered MC [dσ*(Pt(2)) → pσ(Pt(2))] transitions as well as interligand π → π* transition from the terminal alkynyl ligands to the bridging alkynyl ligand mixed with metal-metal-to-ligand charge transfer MMLCT [dσ*(Pt(2)) → π*(bridging alkynyl)] transition. The latter transition is lower in energy than the former. The calculation also indicates that the emission for the complexes originates from the triplet interligand π(terminal alkynyls) → π*(bridging alkynyl)/MMLCT [dσ*(Pt(2)) → π*(bridging alkynyl)] excited state. In terms of the fluxional behavior, calculations have been performed to study the details of the mechanisms for the three fluxional processes, which are the σ,π-alkynyl exchange, the ring-flipping, and the bridging-to-terminal alkynyl exchange processes.     

Perturbation theory for liquids with a hard sphere plus square well potential

Numerical data have been obtained for a series of perturbation theory in the form of Barker-Henderson discrete representation. A hard sphere liquid (864 particles) was modeled by the Monte Carlo method for 106 values of occupancy from the range η = 0.005–0.530 (step 0.005); the well width was varied from 0 to 1.5 hard sphere diameters. For each occupancy, averaging was done over 60·10⁶ ensembles. Approximating analytical expressions are given as functions of well density and width for the first three terms of the free energy decomposition. For reduced temperature T* = 1.0, the standard error in the free energy calculation (three orders of perturbation theory if the above expressions are used) is of the order of ±0.001. Analysis of four-particle correlations revealed peaks at distances of 1.35 Å and 1.65 Å (η = 0.53) in the high-density region of hard sphere liquids, which are absent in crystals and dense liquids. It is analyzed whether the results are useful for realization of WCA theory of simple liquids in second order perturbation theory.