Density functional theory for the selective adsorption of small molecules on a surface modified with polymer brushes

A density functional method based on weighted density approximation is extended to study the selective adsorption of small molecules on a surface modified with end-grafted square-well chains. The excess part of the Helmholtz free energy functional is divided into two components: the hard sphere repulsion and the square-well attraction. The equation of state for hard sphere chain fluids developed by Liu et al. is used to calculate the repulsive part of the excess Helmholtz free energy functional, and the equation of state for square-well chain fluid with variable range developed by Li et al. is employed to calculate the attractive part. With this theoretical model, we examine the physical properties of the grafted polymer and the selective adsorption of small molecules on the modified surface.     

Liquid–vapour interface varying the softness and range of the interaction potential

Molecular dynamics simulations in a canonical ensemble were carried out for simple fluids. The inter-particles interaction law is described by the Morse function plus a repulsive term. This kind of combination allows to tune the repulsive term of the interaction function by fitting the range of the attractive well and vice versa. As a relevant result, we show that for an inhomogeneous system the particle softness affects the vapour pressure, the surface tension and also the equilibrium densities of a simple fluid. Lower numerical values for these same properties were obtained by using a more repulsive interaction potential. The differences among these same interfacial properties are bigger when the range of the attractive interaction is longer. The surface tension written in terms of the corresponding critical parameters, such as scaled surface tension, was plotted for different softness degrees. And from this comparison, a unique master curve was not found.     

Temperature dependence of the solubility of non-polar gases in water

An explanation is provided for the experimentally observed temperature dependence of the solubility and the solubility minimum of non-polar gases in water. The influence of solute size and solute-water attractive interactions on the solubility minimum temperature is investigated. The transfer of a non-polar solute from the ideal gas into water is divided into two steps: formation of a cavity in water with the size and shape of the solute and insertion of the solute in this cavity which is equivalent to 'turning on' solute-water attractive interactions. This two step process divides the excess chemical potential of the non-polar solute in water into repulsive and attractive contributions, respectively. The reversible work for cavity formation is modeled using an information theory model of hydrophobic hydration. Attractive contributions are calculated by modeling the water structure in the vicinity of non-polar solutes. These models make a direct connection between microscopic quantities and macroscopic observables. Moreover, they provide an understanding of the peculiar temperature dependences of the hydration thermodynamics from properties of pure water; specifically, bulk water density and the water oxygen-oxygen radial distribution function.     

Stability of molecular adhesion mediated by confined polymer repellers and ligand-receptor bonds

Experiments have shown that stable adhesion of a variety of animal cells on substrates prepared with precisely controlled ligand distribution can be formed only if the ligand spacing is below 58 nm. To explain this phenomenon, here we propose a confined polymer model to study the stability of molecular adhesion mediated by polymer repellers and ligand-receptor bonds. In this model, both repellers and binders are treated as wormlike chains confined in a nanoslit, and the stability of adhesion is considered as a competition between attractive interactions of ligand-receptor binding and repulsive forces due to the size mismatch between repellers and binders. The force on each ligand-receptor bond is calculated from the confined polymer model, and the classic model of Bell is used to describe the association/dissociation reactions of ligand-receptor bonds. The calculated equilibrium bond distribution shows that there exists a critical ligand density for stable adhesion, corresponding to a critical ligand spacing which agrees not only qualitatively but also quantitatively with the experimental observation. In the case of stable adhesion, the model predicts an equilibrium separation between adhesion surfaces below 60% of the contour length of the ligand-receptor bonds.     

A grand canonical Monte Carlo simulation study of argon and krypton confined inside weakly attractive slit pores

Grand canonical Monte Carlo simulations are performed to investigate the adsorption of argon and krypton inside weakly attractive slit pores. We examine the effects of confinement on these monoatomic fluids (modelled using the triangle-well potential) in a hard wall slit pore as also when the pore-fluid interactions are uniformly and weakly attractive. The effects of temperature and pressure on the adsorption isotherms of these confined fluids are found to be the same as those reported in literature. The equilibrium density profiles for argon and krypton exhibit both uniform distribution and layering under different conditions. In addition, for krypton, under specific conditions inside the narrow pores, we note the development of frustrated layering.     

On the relationship between the sequence conservation and the packing density profiles of the protein complexes

We have recently showed that the weighted contact number profiles (or the packing density profiles) of proteins are well correlated with those of the corresponding sequence conservation profiles. The results suggest that a protein structure may contain sufficient information about sequence conservation comparable to that derived from multiple homologous sequences. However, there are ambiguities concerning how to compute the packing density of the subunit of a protein complex. For the subunits of a complex, there are different ways to compute its packing density – one including the packing contributions of the other subunits and the other one excluding their contributions. Here we selected two sets of enzyme complexes. Set A contains complexes with the active sites comprising residues from multiple subunits, while set B contains those with the active sites residing on single subunits. In Set A, if the packing density profile of a subunit is computed considering the contributions of the other subunits of the complex, it will agree better with the sequence conservation profile. But in Set B the situations are reversed. The results may be due to the stronger functional and structural constraints on the evolution processes on the complexes of Set A than those of Set B to maintain the enzymatic functions of the complexes. The comparison of the packing density and the sequence conservation profiles may provide a simple yet potentially useful way to understanding the structural and evolutionary couplings between the subunits of protein complexes. Proteins 2013; 81:1192–1199. © 2013 Wiley Periodicals, Inc.     

Subject-specific modeling of the scapula bone tissue adaptation

Adaptation of the scapula bone tissue to mechanical loading is simulated in the current study using a subject-specific three-dimensional finite element model of an intact cadaveric scapula. The loads experienced by the scapula during different types of movements are determined using a subject-specific large-scale musculoskeletal model of the shoulder joint. The obtained density distributions are compared with the CT-measured density distribution of the same scapula. Furthermore, it is assumed that the CT-measured density distribution can be estimated as a weighted linear combination of the density distributions calculated for different loads experienced during daily life. An optimization algorithm is used to determine the weighting factors of fourteen different loads such that the difference between the weighted linear combination of the calculated density distributions and the CT-measured density is minimal. It is shown that the weighted linear combination of the calculated densities matches the CT-measured density distribution better than every one of the density distributions calculated for individual movements. The weighting factors of nine out of fourteen loads were estimated to be zero or very close to zero. The five loads that had larger weighting factors were associated with either one of the following categories: (1) small-load small-angle abduction or flexion movements that occur frequently during our daily lives or (2) large-load large-angle abduction or flexion movements that occur infrequently during our daily lives.     

Statistical mechanics approach to inhomogeneous van der Waals fluids

A general methodology is proposed to formulate density functional approximation (DFA) for inhomogeneous van der Waals fluids. The present methodology needs as input only a hard sphere DFA, second order direct correlation function (DCF) and pressure of coexistence bulk fluid, and therefore can be applicable to both supercitical and subcritical temperature regions. As illustrating example, the present report combines a recently proposed hard sphere “Formally exact truncated non-uniform excess Helmholtz free energy density functional approximation” with the present methodology, and applies the resultant DFA to calculate density profile of the inhomogeneous Lennard-Jones (LJ) fluid in coexistence with a bulk LJ fluid being situated at “dangerous” regions, i.e. the coexistence bulk state is near the critical temperature or the gas-liquid coexistence line. The theoretical predictions are in very good agreement with the recent simulation results, it is concluded that the present DFA is a globally excellent one. A discussion is given why the present methodology can lead to so excellent DFA.     

Effect of cut-off distance used in molecular dynamics simulations on fluid properties

The effect of cut-off distance used in molecular dynamics (MD) simulations on fluid properties was studied systematically in both canonical (NVT) and isothermal–isobaric (NPT) ensembles. Results show that the cut-off distance in the NVT ensemble plays little role in determining the equilibrium structure of fluid if the ensemble has a high density. However, pressures calculated in the same NVT ensembles strongly depend on the cut-off distance used. In the NPT ensemble, cut-off distance plays a key role in determining fluid equilibrium structure, density and self-diffusion coefficient. The characteristic of the radial distribution function of fluid in NPT ensembles depending on the cut-off distance used in MD simulations means that the WCA theory (a perturbation theory developed by Weeks, Chandler and Andersen) is not suitable for NPT ensembles because the assumption (the effect of the attractive force in determining the liquid structure is negligible) used in the WCA theory is not valid. The dependence of fluid properties on the cut-off distance also indicates that using the WCA potential (the repulsive part of the intermolecular potential proposed in the WCA theory) to calculate fluid transport in heterogeneous systems could lead to significant errors or incorrect results.     

Properties of Confined Square-well Fluids using the Gibbs Ensemble Simulation Technique

In this work we have used the extension of the Gibbs ensemble simulation technique to inhomogeneous fluids [Panagiotopoulos, A.Z. (1987) "Adsorption and capillary condensation of fluid in cylindrical pores by Monte Carlo simulation in the Gibbs ensemble", Mol. Phys. , 62 (3), 701-719], which has been applied to adsorption phenomena of confined fluids. Fluid molecules are described by spherical particles interacting via a square-well potential. The fluid is confined in two types of walls: symmetrical (two hard walls) and non-symmetrical (one square-well wall and one hard wall). In order to analyze the behavior of the confined fluid by varying the potential parameters, we evaluated the bulk and confined densities, the internal energies and the density profiles for different supercritical temperatures. A variety of adsorption profiles can be obtained by using this model. The simulation data reported here complements the available simulation data for this system and can be useful in the development of inhomogeneous fluid theories. Since the square-well parameters can be related to real molecules this system can also be used to understand real adsorption systems.     

Formation of ordered domains in membrane-bound DNA.

The interactions between DNA molecules adsorbed on fluid membranes are calculated. The adsorbing DNA perturbs the equilibrium packing of the lipids, thereby giving rise to membrane-induced, attractive interactions. These balance the direct repulsive interactions between DNA molecules. As a result, DNA adsorbed on membranes is predicted to form ordered domains characterized by a finite spacing, which varies with the membrane characteristics and the solution Debye screening length. Comparing the model predictions to recent experiments (Yang et al. 1996) yields excellent agreement with only one free (i.e., experimentally unknown) parameter.     

Automatic classification of chromosomes as part of a routine system for clinical analysis

A procedure for automatic classification of G-banded human chromosomes has been implemented on a semiautomated system for routine clinical analysis. Chromosomes represented by their density profiles are described by so-called weighted density distributions (WDDs) by application of a number of weighting functions and classified by a parametric discriminant analysis. During 16 mo of routine use of the system, 2,794 metaphases (127,925 chromosomes) from amniotic fluid have been karyotyped by the system with an error rate of 8-9%. This corresponds to 4-5 errors per metaphase. These errors can immediately be corrected by the operator on a displayed karyogram with a light pen.     

Force Balances in Systems of Cylindrical Polyelectrolytes

A detailed analysis is made of the model system of two parallel cylindrical polyelectrolytes which contain ionizable groups on their surfaces and are immersed in an ionic bathing medium. The interaction between the cylinders is examined by considering the interplay between repulsive electrostatic forces and attractive forces of electrodynamic origin. The repulsive force arises from the screened coulomb interaction between the surface charge distributions on the cylinders and has been treated by developing a solution to the linearized Poisson-Boltzmann equation. The boundary condition at the cylinder surfaces is determined as a self-consistent functional of the potential, with the input consisting of the density of ionizable groups and their dissociation constants. It is suggested that a reasonably accurate representation for the form of the attractive force can be obtained by performing a pairwise summation of the individual interatomic forces. A quantitative estimate is obtained using a Hamaker constant chosen on the basis of rigorous calculations on simpler systems. It is found that a balance exists between these repulsive and attractive forces at separations in good agreement with those observed in arrays of tobacco mosaic virus and in the A band myosin lattice in striated muscle. The behavior of the balance point as a function of the pH and ionic strength of the bathing medium closely parallels that seen experimentally.     

Butterfly species identification by branch length similarity entropy

We previously developed a shape recognition methodology that uses “branch length similarity” (BLS) entropy, which is defined as a simple branching network consisting of a single node and branches. The simple network is referred to as a “unit branching network” (UBN). Our approach involves obtaining BLS entropy profiles from UBNs created by joining each pixel in the outline of a shape with every other pixel in the shape's border. The profiles successfully characterize the shapes by comparing their BLS entropy profiles. Presently, we modified this approach to facilitate its application to butterfly species identification by partitioning and weighting the entropy profile. As a test, we identified the butterfly species Colias erate, Parnassius bremeri, Eurema hecabe, Gonepteryx rhamni, and Papilio maackii. Each species group consisted of 10 specimens. We used wing shape to identify a species. We extracted evenly spaced x–y coordinates of boundary pixels for the wing shapes in a counter counterclockwise direction. The number of the pixels was 749. We then sequentially partitioned 749 x–y pairs into 15 groups, calculated entropy profiles for the groups, and weighted the profiles. The profiles were combined in order, resulting in a single weighted BLS entropy profile for a wing's shape. Subsequently, we statistically compared the correlation coefficient among the weighted BLS profiles. Our experimental results showed that this method was statistically successful for butterfly species identification. The advantage of the partitioning and weighting process in shape recognition is also discussed.     

Vapour–liquid phase equilibria of simple fluids confined in patterned slit pores

We present the influence of surface heterogeneity on the vapour–liquid phase behaviour of square-well fluids in slit pores using grand-canonical transition-matrix Monte Carlo simulations along with the histogram-reweighting method. Properties such as phase coexistence envelopes, critical properties and local density profiles of the confined SW fluid are reported for chemically and physically patterned slit surfaces. It is observed that in the chemically patterned pores, fluid–fluid and surface attraction parameters along with the width of attractive and inert stripes play fundamentally different roles in the phase coexistence and critical properties. On the other hand, pillar gap and height significantly affect the vapour–liquid equilibria in the physically patterned slit pores. We also present the effect of chemically and physically patterned slit surfaces on the spreading pressure.     

Structure and interactive properties of highly fluorinated phospholipid bilayers.

Because liposomes containing fluoroalkylated phospholipids are being developed for in vivo drug delivery, the structure and interactive properties of several fluoroalkylated glycerophosphocholines (PCs) were investigated by x-ray diffraction/osmotic stress, dipole potential, and hydrophobic ion binding measurements. The lipids included PCs with highly fluorinated tails on both alkyl chains and PCs with one hydrocarbon chain and one fluoroalkylated chain. Electron density profiles showed high electron density peaks in the center of the bilayer corresponding to the fluorine atoms. The height and width of these high density peaks varied systematically, depending on the number of fluorines and their position on the alkyl chains, and on whether the bilayer was in the gel or liquid crystalline phase. Wide-angle diffraction showed that in both gel and liquid crystalline bilayers the distance between adjacent alkyl chains was greater in fluoroalkylated PCs than in analogous hydrocarbon PCs. For interbilayer separations of less than about 8 A, pressure-distance relations for fluoroalkylated PCs were similar to those previously obtained from PC bilayers with hydrocarbon chains. However, for bilayer separations greater than 8A, the total repulsive pressure depended on whether the fluoroalkylated PC was in a gel or liquid-crystalline phase. We argue that these pressure-distance relations contain contributions from both hydration and entropic repulsive pressures. Dipole potentials ranged from -680 mV for PCs with both chains fluoroalkylated to -180 mV for PCs with one chain fluoroalkylated, compared to +415 mV for egg PC. The change in dipole potential as a function of subphase concentration of tetraphenyl-boron was much larger for egg PC than for fluorinated PC monolayers, indicating that the fluorine atoms modified the binding of this hydrophobic anion. Thus, compared to conventional liposomes, liposomes made from fluoroalkylated PCs have different binding properties, which may be relevant to their use as drug carriers.     

Pair distribution functions of bacteriorhodopsin and rhodopsin in model bilayers.

The pair distribution functions have been measured from freeze-fracture pictures of bacteriorhodopsin and rhodopsin recombinants with diacyl phosphatidylcholines (PC) of various hydrocarbon chain lengths. Pictures were used of samples that had been frozen from above the phase transition temperature of the lipid. Measured functions were compared with those calculated from two model interparticle potential energy functions, (a) a hard-disk repulsion only, and (b) a hard-disk repulsion plus electrostatic repulsion for a point charge buried in the membrane. The measured functions for bacteriorhodopsin di 12:0 PC, di 14:0 PC, and di 16:0 PC recombinants can be simulated using an interparticle hard-disk repulsion only. Bleached rhodopsin di 12:0 PC and di 18:1 trans-PC recombinants, and dark-adapted rhodopsin di 10:0 PC recombinants yield functions that are better simulated by assuming an additional repulsive interaction. The measured functions resemble those calculated using the hard-disk plus electrostatic repulsion model. The picture of dark-adapted rhodopsin in di 18:1 trans-PC frozen from 20 degrees C shows partial aggregation that is apparent in the measured pair distribution function. This attractive interaction persists even at 37 degrees C, where the measured function shows deviations from the hard-disk repulsive model, indicative of an attractive interparticle interaction. Implications of these results are discussed in terms of protein-lipid interactions.     

Computer assisted size measurement on a digitising tablet of nucleic acid and protein molecules from gels

A method is presented for the rapid and convenient determination of molecular weight or chain length of macromolecules from their electrophoretic mobility on gels, using a computer-controlled digitising tablet. A novel feature is accurate compensation for 'smile' or 'frown' profiles as well as for the possible splay or curvature of lanes. A family of monotonic, asymptotic, generalised quadratics is calculated to fit locally the known values in a marker track, and a weighting function is then applied to these enveloping curves so that the prediction algorithm simulates the interpolation of unknown values from a smooth graph drawn through the known bands. Results for double stranded DNA, single and double stranded RNA, and protein molecules are given. The average error of the predicted values against the known molecular sizes was 0.2% for dsDNA, 1.7% for dsRNA, 0.7% for ssRNA and 3.6% for protein molecules.     

Aggregation pattern transitions by slightly varying the attractive/repulsive function

Among collective behaviors of biological swarms and flocks, the attractive/repulsive (A/R) functional links between particles play an important role. By slightly changing the cutoff distance of the A/R function, a drastic transition between two distinct aggregation patterns is observed. More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster. Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant. Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations. This work bridges the aggregation phenomena of physical particles and swarming of organisms in nature upon revealing some common mechanism behind them by slightly varying their inter-individual attractive/repulsive functions, and may find its potential engineering applications, for example, in the formation design of multi-robot systems and unmanned aerial vehicles (UAVs).