Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions

We study the driven translocation of polymers under time-dependent driving forces using N-particle Langevin dynamics simulations. We consider the force to be either sinusoidally oscillating in time or dichotomic noise with exponential correlation time, to mimic both plausible experimental setups and naturally occurring biological conditions. In addition, we consider both the case of purely repulsive polymer-pore interactions and the case with additional attractive polymer-pore interactions, typically occurring inside biological pores. We find that the nature of the interaction fundamentally affects the translocation dynamics. For the non-attractive pore, the translocation time crosses over to a fast translocation regime as the frequency of the driving force decreases. In the attractive pore case, because of a free energy well induced inside the pore, the translocation time can be a minimum at the optimal frequency of the force, the so-called resonant activation. In the latter case, we examine the effect of various physical parameters on the resonant activation, and explain our observations using simple theoretical arguments.     

Atomic force microscopy study of cellulose surface interaction controlled by cellulose binding domains

Colloidal probe microscopy has been used to study the interaction between model cellulose surfaces and the role of cellulose binding domain (CBD), peptides specifically binding to cellulose, in interfacial interaction of cellulose surfaces modified with CBDs. The interaction between pure cellulose surfaces in aqueous electrolyte solution is dominated by double layer repulsive forces with the range and magnitude of the net force dependent on electrolyte concentration. AFM imaging reveals agglomeration of CBD adsorbed on cellulose surface. Despite an increase in surface charge owing to CBD binding to cellulose surface, force profiles are less repulsive for interactions involving, at least, one modified surface. Such changes are attributed to irregularity of the topography of protein surface and non-uniform distribution of surface charges on the surface of modified cellulose. Binding double CBD hybrid protein to cellulose surfaces causes adhesive forces at retraction, whereas separation curves obtained with cellulose modified with single CBD show small adhesion only at high ionic strength. This is possibly caused by the formation of the cross-links between cellulose surfaces in the case of double CBD.     

Surfactant-induced forces between carbon nanotubes

Dissipative particle dynamics simulations are employed to study surfactant-mediated forces between a pair of perpendicular carbon nanotubes (CNTs) coated by surfactants which form spherical micelles in bulk solution and on the tubes. Two force regimes are observed: at small tube/tube distances the force is attractive, whereas it is repulsive at larger distances. The attractive regime is dominated by a central micelle binding the tubes, while in the repulsive regime the contact region is depleted. The two regimes are separated by a discontinuous transition. The repulsive regime is critical for stabilizing CNT suspensions. Viewing rebundling as a thermally activated process, a connection between the repulsive force and the rebundling rate is established. We find that a larger hydrophilic surfactant headgroup creates a stronger and longer ranged tube/tube force, which reduces the rebundling rate significantly. The longer range originates directly from the further reaching head corona of the adsorbed surfactant layer. The larger magnitude of the force appears to be related to the axial compression force the adsorbed phase can sustain. This compression force appears to be the most critical factor for suspension design.     

Relationship between interfacial forces measured by colloid-probe atomic force microscopy and protein resistance of poly(ethylene glycol)-grafted poly(L-lysine) adlayers on niobia surfaces

Adsorbed layers of "comb-type" copolymers consisting of PEG chains grafted onto a poly(l-lysine) (PLL) backbone on niobium oxide substrates were studied by colloid-probe AFM in order to characterize the interfacial forces associated with coatings of varying architectures (PEG/PLL ratios and PEG chain lengths) and their relevance to protein resistance. The steric and electrostatic forces measured varied substantially with the architecture of the PLL-g-PEG copolymers. Varying the ionic strength of the buffer solutions enabled discrimination between electrostatic and steric-entropic contributions to the net interfacial force. For high PEG grafting densities the steric component was most prominent, but at low ionic strengths and high grafting densities, a repulsive electrostatic surface force was also observed; its origin was assigned to the niobia charges beneath the copolymer, as insufficient protonated amine groups in the PLL backbone were available for compensation of the oxide surface charges. For lower grafting densities and lower ionic strengths there was a substantial attractive electrostatic contribution arising from interaction of the electrical double layer arising from the protonated amine groups, with that of the silica probe surface (as under low ionic strength conditions, the electrical double layer was thicker than the PEG layer). For these PLL-g-PEG coatings the net interfacial force can thus be a markedly varying superposition of electrostatic and steric-entropic contributions, depending on various factors. The force curves correlate with protein adsorption data, demonstrating the utility of AFM colloid-probe force measurements for quantitative analysis of surface forces and how they determine interfacial interactions with proteins. Such characterization of the net interfacial forces is essential to elucidate the multiple types of interfacial forces relevant to the interactions between PLL-g-PEG coatings and proteins and to advance interpretation of protein adsorption or repellence beyond the oversimplified steric barrier model; in particular, our data demonstrate the importance of an ionic-strength-dependent minimum PEG layer thickness to screen the electrostatic interactions of charged interfaces.     

Role of attractive methane-water interactions in the potential of mean force between methane molecules in water

On the basis of a Gaussian quasichemical model of hydration, a model of non-van der Waals character, we explore the role of attractive methane-water interactions in the hydration of methane and in the potential of mean force between two methane molecules in water. We find that the hydration of methane is dominated by packing and a mean-field energetic contribution. Contributions beyond the mean-field term are unimportant in the hydration phenomena for a hydrophobic solute such as methane. Attractive solute-water interactions make a net repulsive contribution to these pair potentials of mean force. With no conditioning, the observed distributions of binding energies are super-Gaussian and can be effectively modeled by a Gumbel (extreme value) distribution. This further supports the view that the characteristic form of the unconditioned distribution in the high-epsilon tail is due to energetic interactions with a small number of molecules. Generalized extreme value distributions also effectively model the results with minimal conditioning, but in those cases the distributions are sufficiently narrow that the details of their shape are not significant.     

Theoretical effects of macromolecule concentration and charge on membrane rejection coefficients

A hydrodynamic model for the convection of rigid, spherical solutes through cylindrical pores, which includes both steric and electrostatic interactions between pairs of solute particles and between solutes and the pore wall, has been developed to examine the effects of solute concentration and charge on solute rejection by membrane pores during ultrafiltration. Calculations have been performed for a wide range of charge conditions and the results are presented in terms of the membrane rejection coefficient at infinite dilution and a correction factor which accounts for the first-order effects of concentration. For pores and solutes of like charge, the rejection coefficient is predicted to decrease with increasing feed concentration or ionic strength.     

Electrolytes in a nanometer slab-confinement: ion-specific structure and solvation forces

We study the liquid structure and solvation forces of dense monovalent electrolytes (LiCl, NaCl, CsCl, and NaI) in a nanometer slab-confinement by explicit-water molecular dynamics (MD) simulations, implicit-water Monte Carlo (MC) simulations, and modified Poisson-Boltzmann (PB) theories. In order to consistently coarse-grain and to account for specific hydration effects in the implicit methods, realistic ion-ion and ion-surface pair potentials have been derived from infinite-dilution MD simulations. The electrolyte structure calculated from MC simulations is in good agreement with the corresponding MD simulations, thereby validating the coarse-graining approach. The agreement improves if a realistic, MD-derived dielectric constant is employed, which partially corrects for (water-mediated) many-body effects. Further analysis of the ionic structure and solvation pressure demonstrates that nonlocal extensions to PB (NPB) perform well for a wide parameter range when compared to MC simulations, whereas all local extensions mostly fail. A Barker-Henderson mapping of the ions onto a charged, asymmetric, and nonadditive binary hard-sphere mixture shows that the strength of structural correlations is strongly related to the magnitude and sign of the salt-specific nonadditivity. Furthermore, a grand canonical NPB analysis shows that the Donnan effect is dominated by steric correlations, whereas solvation forces and overcharging effects are mainly governed by ion-surface interactions. However, steric corrections to solvation forces are strongly repulsive for high concentrations and low surface charges, while overcharging can also be triggered by steric interactions in strongly correlated systems. Generally, we find that ion-surface and ion-ion correlations are strongly coupled and that coarse-grained methods should include both, the latter nonlocally and nonadditive (as given by our specific ionic diameters), when studying electrolytes in highly inhomogeneous situations.     

Mixing of partially fluorinated carboxylic acids with their hydrocarbon analogs at the air-water interface

Rheological behavior of surfactant-stabilized colloidal dispersions of silica particles under extreme conditions (low pH, high ionic strength) has been investigated in relation to interparticle forces and stability of the dispersion. The surfactant used as the dispersing agent was C(12)TAB, a cationic surfactant. Stability analysis through turbidity measurements indicated that there is a sharp increase in the stability of the dispersion when the surfactant concentration is in the range of 8 to 10 mM in the system. The state of the dispersion changes from an unstable regime to a stable regime above a critical concentration of C(12)TAB in the system. In the case of interaction forces measured between the silica substrate and AFM tip, no repulsive force was observed up to a surfactant concentration of 8 mM and a transition from no repulsive forces to steric repulsive forces occurred between 8 and 10 mM. Rheological measurements as a function of C(12)TAB concentration indicated a significant decrease in the viscosity and linear viscoelastic functions of the dispersion over the same range of surfactant concentration (8 to 10 mM C(12)TAB), showing a strong correlation between the viscosity behavior, interparticle forces, and structure development in the dispersion.     

Interaction forces and molecular adhesion between pre-adsorbed poly(ethylene imine) layers

Interaction forces between pre-adsorbed layers of branched poly(ethylene imine) (PEI) of different molecular mass were studied with the colloidal probe technique, which is based on atomic force microscopy (AFM). During approach, the long-ranged forces between the surfaces are repulsive due to overlap of diffuse layers down to distances of a few nanometers, whereby regulation of the surface charge is observed. The ionic strength dependence of the observed diffuse layer potentials can be rationalized with a surface charge of 2.3 mC/m2. The forces remain repulsive down to contact, likely due to electro-steric interactions between the PEI layers. These electro-steric forces have a range of a few nanometers and appear to be superposed to the force originating from the overlap of diffuse layers. During retraction of the surfaces, erratic attractive forces are observed due to molecular adhesion events (i.e., bridging adhesion). The frequency of the molecular adhesion events increases with increasing the ionic strength. The force response of the PEI segments is dominated by rubber-like extension profiles. Strong adhesion forces are observed for low molecular mass PEI at short distances directly after separation, while for high molecular mass weaker adhesion forces at larger distances are more common. The work of adhesion was estimated by integrating the retraction force profiles, and it was found to increase with the ionic strength.     

Investigation of the interaction force between Cryptosporidium parvum oocysts and solid surfaces

Interaction force profiles between single Cryptosporidium parvum oocysts and positively charged, silane-coated silica particles were measured in aqueous solutions using an atomic force microscope. The oocysts were immobilized for the measurements by entrapment in Millipore polycarbonate membranes with 3 microm pore size. Experiments were performed in both NaCl and CaCl2 solutions at ionic strengths ranging from 1 to 100 mM. For both electrolytes, the decay length of the repulsive force profile was found to be nearly independent of the ionic strength and always much larger than the theoretical Debye length of the system. In addition, the magnitude of the force was found to be essentially the same for both electrolytes, suggesting that the long-range repulsive forces are primarily steric in nature. These results support the theory that the interaction force between oocysts and surfaces is controlled by an outer, weakly charged or uncharged carbohydrate layer. Measurements were also performed with oocysts that had been deactivated using either chemical (formalin) or heat treatment. The force profiles obtained with formalin-treated oocysts appear to be essentially the same as for the untreated oocysts, whereas the profiles measured with the heat-treated oocysts show a much stronger dependence on solution ionic strength. With either the heat-treated or formalin-treated oocysts, adhesion was observed much more frequently than with untreated oocysts, which is consistent with the increased deposition rate observed with treated oocysts by Kuznar and Elimelech (Kuznar, Z. A.; Elimelech, M. Langmuir 2005, 21, 710-716). These results also suggest that treated oocysts, especially ones that have been inactivated by heating, may not be good surrogates for viable oocysts in laboratory studies.     

Dielectric exclusion of ions from membranes

Dielectric exclusion is caused by the interactions of ions with the bound electric charges induced by ions at interfaces between media of different dielectric constants. It is considered as one of mechanisms of nanofiltration. The transport properties of capillary model are expressed through ion distribution and diffusion coefficients. Due to local equilibrium the distribution coefficient is directly related to the excess solvation energy of ion. First, this energy is considered for single ions in single neutral pores in terms of pore size, ion charge, dielectric constants of solvent and membrane matrix and pore geometry. The dielectric exclusion from pores with closed geometry like circular cylinders is shown to be essentially stronger than that from pores with relatively open geometry like slits. Furthermore, the role of finite membrane porosity is analysed for the model of infinite slabs with alternating dielectric constants. The presence of other ions is accounted for within the scope of a mean-field approach, and the screening of dielectric exclusion is thus introduced and considered in some detail. A fixed electric charge is shown to cause additional screening. At the same time the dielectric exclusion makes the Donnan exclusion of ions stronger. Therefore the interaction between those two rejection mechanisms turns out to be non-trivial. Finally, the effect of solvent molecular structure is considered within the scope of non-local electrostatics. It is shown that the solvent non-locality typically results in somewhat stronger dielectric exclusion, however, its most important effect is slowing down the decline of dielectric exclusion with increasing bulk electrolyte concentration.     

Combined depletion and electrostatic forces in polymer-induced membrane adhesion: a theoretical model

We develop a semi-quantitative analytical theory to describe adhesion between two identical planar charged surfaces embedded in a polymer-containing electrolyte solution. Polymer chains are uncharged and differ from the solvent by their lower dielectric permittivity. The solution mimics physiological fluids: It contains 0.1 M of monovalent ions and a small number of divalent cations that form tight bonds with the headgroups of charged lipids. The components have heterogeneous spatial distributions. The model was derived self-consistently by combining: (a) a Poisson-Boltzmann like equation for the charge densities, (b) a continuum mean-field theory for the polymer profile, (c) a solvation energy forcing the ions toward the polymer-poor regions, and (d) surface interactions of polymers and electrolytes. We validated the theory via extensive coarse-grained Molecular Dynamics (MD) simulations. The results confirm our analytical model and reveal interesting details not detected by the theory. At high surface charges, polymer chains are mainly excluded from the gap region, while the concentration of ions increases. The model shows a strong coupling between osmotic forces, surface potential and salting-out effects of the slightly polar polymer chains. It highlights some of the key differences in the behaviour of monomeric and polymeric mixed solvents and their responses to Coulomb interactions. Our main findings are: (a) the onset of long-ranged ion-induced polymer depletion force that increases with surface charge density and (b) a polymer-modified repulsive Coulomb force that increases with surface charge density. Overall, the system exhibits homeostatic behaviour, resulting in robustness against variations in the amount of charges. Applications and extensions of the model are briefly discussed.     

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary "evaporation," from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (～0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.     

Anomalous transport in molecularly confined spaces

We develop a novel theory to predict the density dependence of the diffusivity of simple fluids in a molecularly sized nanopore with diffusely reflecting walls, incorporating nearest neighbor intermolecular interactions within the framework of the recent oscillator model of low density transport arising from this laboratory. It is shown that when the pore width is about two molecular diameters, at sufficiently high densities these interactions lead to a repulsive inner core, as a result of which the diffusing molecules undergo more frequent reflections at the wall. This leads to a reduction in diffusivity with increase in density, which is consistent with molecular dynamics simulation results, and contrasts with the behavior in larger pores where the transport coefficient has previously been shown to increase with increase in density due to viscouslike intermolecular interactions. At low densities the behavior is opposite, with the inner core becoming more attractive with increase in density, which can lead to an increase in diffusivity. The theory consistently explains molecular dynamics simulation results when the inhomogeneous pair distribution function of moving particles in the pore is axially periodic, suggesting concerted motion of neighboring molecules. It is also shown that a potential of mean force concept is inadequate for describing the influence of intermolecular interactions on transport.     

Long-Range Interaction Forces between Polymer-Supported Lipid Bilayer Membranes

Much of the short-range forces and structures of softly supported DMPC bilayers has been described previously. However, one interesting feature of the measured force-distance profile that remained unexplained is the presence of a long-range exponentially decaying repulsive force that is not observed between rigidly supported bilayers on solid mica substrate surfaces. This observation is discussed in detail here based on recent static and dynamic surface force experiments. The repulsive forces in the intermediate distance regime (mica-mica separations from 15 to 40 nm) are shown to be due not to an electrostatic force between the bilayers but to compression (deswelling) of the underlying soft polyelectrolyte layer, which may be thought of as a model cytoskeleton. The experimental data can be fit by simple theoretical models of polymer interactions from which the elastic properties of the polymer layer can be deduced.     

Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions.The counterions consist of two rigidly bonded point charges,each of valency Z.The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges.The system is analyzed by employing a self-consistent field theory,which treats the short and long range interactions of the counterions within different approximations.We find that in the weak coupling limit,the interactions are only repulsive.In the intermediate coupling regime,the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods,bridging contributes to the attractive interaction.In the strong coupling limit,the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces.Two minima can then appear in the force curve between surfaces.     

Direct surface force measurements of polyelectrolyte multilayer films containing nanocrystalline cellulose

Polyelectrolyte multilayer films containing nanocrystalline cellulose (NCC) and poly(allylamine hydrochloride) (PAH) make up a new class of nanostructured composite with applications ranging from coatings to biomedical devices. Moreover, these materials are amenable to surface force studies using colloid-probe atomic force microscopy (CP-AFM). For electrostatically assembled films with either NCC or PAH as the outermost layer, surface morphology was investigated by AFM and wettability was examined by contact angle measurements. By varying the surrounding ionic strength and pH, the relative contributions from electrostatic, van der Waals, steric, and polymer bridging interactions were evaluated. The ionic cross-linking in these films rendered them stable under all solution conditions studied although swelling at low pH and high ionic strength was inferred. The underlying polymer layer in the multilayered film was found to dictate the dominant surface forces when polymer migration and chain extension were facilitated. The precontact normal forces between a silica probe and an NCC-capped multilayer film were monotonically repulsive at pH values where the material surfaces were similarly and fully charged. In contrast, at pH 3.5, the anionic surfaces were weakly charged but the underlying layer of cationic PAH was fully charged and attractive forces dominated due to polymer bridging from extended PAH chains. The interaction with an anionic carboxylic acid probe showed similar behavior to the silica probe; however, for a cationic amine probe with an anionic NCC-capped film, electrostatic double-layer attraction at low pH, and electrostatic double-layer repulsion at high pH, were observed. Finally, the effect of the capping layer was studied with an anionic probe, which indicated that NCC-capped films exhibited purely repulsive forces which were larger in magnitude than the combination of electrostatic double-layer attraction and steric repulsion, measured for PAH-capped films. Wherever possible, DLVO theory was used to fit the measured surface forces and apparent surface potentials and surface charge densities were calculated.     

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

Direct measurement of interactions between stimulation-responsive drug delivery vehicles and artificial mucin layers by colloid probe atomic force microscopy

A novel thermo- and pH-sensitive nanogel particle, which is a core-shell structured particle with a poly(N-isopropylacrylamide) (p(NIPAAm)) hydrogel core and a poly(ethylene glycol) monomethacrylate grafted poly(methacrylic acid) (p(MMA-g-EG)) shell, is of interest as a vehicle for the controlled release of peptide drugs. The interactions between such nanogel particles and artificial mucin layers during both approach and separation were successfully measured by using colloid probe atomic force microscopy (AFM) under various compression forces, scan velocities, and pH values. While the magnitudes of the compression forces and scan velocities did not affect the interactions during the approach process, the adhesive force during the separation process increased with these parameters. The pH values significantly influenced the interactions between the nanogel particles and a mucin layer. A large steric repulsive force and a long-range adhesive force were measured at neutral pH due to the swollen p(MMA-g-EG) shell. On the other hand, at low pH values, the steric repulsive force disappeared and a short-range adhesive force was detected, which resulted from the collapse of the shell layer. The nanogel particles possessed a pH response that was sufficient to protect the incorporated peptide drug under the harsh acidic conditions in the stomach and to effectively adhere to the mucin layer of the small intestine, where the pH is neutral. The relationships among the nanogel particle-mucin layer interactions, pH conditions, scan velocities, and compression forces were systemically investigated and discussed.     

Toward the description of electrostatic interactions between globular proteins: potential of mean force in the primitive model

Monte Carlo simulations are used to calculate the exact potential of mean force between charged globular proteins in aqueous solution. The aim of the present paper is to study the influence of the ions of the added salt on the effective interaction between these nanoparticles. The charges of the model proteins, either identical or opposite, are either central or distributed on a discrete pattern. Contrarily to Poisson-Boltzmann predictions, attractive, and repulsive direct forces between proteins are not screened similarly. Moreover, it has been shown that the relative orientations of the charge patterns strongly influence salt-mediated interactions. More precisely, for short distances between the proteins, ions enhance the difference of the effective forces between (i) like-charged and oppositely charged proteins, (ii) attractive and repulsive relative orientations of the proteins, which may affect the selectivity of protein/protein recognition. Finally, such results observed with the simplest models are applied to a more elaborate one to demonstrate their generality.