Critical polyelectrolyte adsorption under confinement: planar slit, cylindrical pore, and spherical cavity

We explore the properties of adsorption of flexible polyelectrolyte chains in confined spaces between the oppositely charged surfaces in three basic geometries. A method of approximate uniformly valid solutions for the Green function equation for the eigenfunctions of polymer density distributions is developed to rationalize the critical adsorption conditions. The same approach was implemented in our recent study for the "inverse" problem of polyelectrolyte adsorption onto a planar surface, and on the outer surface of rod-like and spherical obstacles. For the three adsorption geometries investigated, the theory yields simple scaling relations for the minimal surface charge density that triggers the chain adsorption, as a function of the Debye screening length and surface curvature. The encapsulation of polyelectrolytes is governed by interplay of the electrostatic attraction energy toward the adsorbing surface and entropic repulsion of the chain squeezed into a thin slit or small cavities. Under the conditions of surface-mediated confinement, substantially larger polymer linear charge densities are required to adsorb a polyelectrolyte inside a charged spherical cavity, relative to a cylindrical pore and to a planar slit (at the same interfacial surface charge density). Possible biological implications are discussed briefly in the end.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

Solute partitioning into lipid bilayer membranes

We have measured the membrane/water partition coefficients of benzene into lipid bilayers as a function of the surface density of the phospholipid chains. A simple 2H NMR method was used for the measurement of surface densities; it is shown to give results similar to those obtained from more demanding X-ray diffraction measurements. We observe that benzene partitioning into the bilayer is dependent not only on the partitioning chemistry, characterized by the oil/water partition coefficient, but also on the surface density of the bilayer chains. Increasing surface density leads to solute exclusion: benzene partitioning decreases by an order of magnitude as the surface density increases from 50% to 90% of its maximum value, a range readily accessible in bilayers and biomembranes under physiological conditions. This effect is independent of the nature of the agent used to alter surface density: temperature, cholesterol, and phospholipid chain length were tested here. These observations support the recent statistical thermodynamic theory of solute partitioning into chain molecule interphases, which predicts that the expulsion of solute is due to entropic effects of the orientational ordering among the phospholipid chains. We conclude that the partitioning of solutes into bilayer membranes, which are interfacial phases, is of a fundamentally different nature than partitioning into bulk oil and octanol phases.     

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.     

Effects of inter-organism interactions in biofouling on microtopographic surfaces

An extended model of the surface energetic attachment (SEA) model is introduced to study the fouling of marine organisms on microtopographic surfaces, taking into account the excluded volume interaction and the attraction between the organisms. It is shown that the excluded volume interaction leads to changes in the site-typed attachment probabilities which increase with the average spore density on the surface. As a result of these changes, the spore density map is flattened under very high density fouling. The attractive interaction on the other hand leads to aggregation of spores and the average aggregate size increased with the strength of attraction. The model can be mapped to a specific experiment to determine the attachment energy parameters. In contrast to various prior empirical approaches, the extended SEA model is rigorous from the statistical mechanics viewpoint, thus it provides a reliable tool for studying complex attachment behaviors of microorganisms on topographic surfaces.     

Molecular dynamics simulation of the folding of single alkane chains with different lengths on single-walled carbon nanotubes and graphene

Chain folding is an important step during polymer crystallization. In order to study the effects of the surface on chain folding, molecular dynamics simulations of the folding of different alkane chains on three kinds of single-walled carbon nanotubes (SWCNTs) and graphene were performed. The folding behaviors of the single alkane chains on these surfaces were found to be different from their folding behaviors in vacuum. The end-to-end distances of the chains were calculated to explore the chain folding. An increasing tendency to fold into two or more stems with increasing alkane chain length was observed. This result indicates that the occurrence and the stability of chain folding are related to the surface curvature, the diameter of the SWCNT, and surface texture. In addition, the angle between the direction of the alkane chain segment and the direction of the surface texture was measured on different surfaces.     

Wang–Landau sampling of the interplay between surface adsorption and folding of HP lattice proteins

Generic features associated with the adsorption of proteins on solid surfaces are reviewed within the framework of the hydrophobic-polar (HP) lattice protein model. The thermodynamic behaviour and structural properties of various HP protein sequences interacting with attractive surfaces have been studied using extensive Wang–Landau sampling with different types of surfaces, each of which attracts either: all monomers, only hydrophobic (H) monomers or only polar (P) monomers, respectively. Consequently, different types of folding behaviour occur for varied surface strengths. Analysis of the combined patterns of various structural observables, e.g. the derivatives of the number of interaction contacts, together with the specific heat, leads to the identification of fundamental categories of folding and transition hierarchies. We also inferred a connection between the transition categories and the relative surface strengths, i.e. the ratios of the surface attractive strengths to the intra-chain attraction among H monomers. Thus, we believe that the folding hierarchies and identification scheme are generic for different HP sequences interacting with attractive surfaces, regardless of the chain length, sequence or surface attraction.     

Experimental and Monte Carlo simulation studies of the thermodynamics of polyethyleneglycol chains grafted to lipid bilayers.

Experimental measurements of the affinity of binding of fluorescent acylated polyethyleneglycol (PEG) conjugates to bilayers containing varying levels of phosphatidylethanolamine-PEGs (PE-PEGs) have been combined with Monte Carlo simulations to investigate the properties of the polymer chains at a PEG-grafted lipid interface. The affinity of binding of such conjugates to large unilamellar phosphatidylcholine/phosphatidylethanolamine (9:1) vesicles decreases 27-fold as the size of the coupled PEG chain increases from 1 to 114 monomer units. Incorporation of increasing amounts of PE-PEG2000 or PE-PEG5000 into the vesicles progressively reduces the affinity of binding of acylpeptide-PEG2000 or -PEG5000 conjugates. Monte Carlo simulations of surfaces with grafted PEG chains revealed no significant dependence of several characteristic properties of the polymer chains, including the average internal energy per polymer and the radii of gyration, on the grafting density in the range examined experimentally. The average conformation of a surface-grafted PEG2000 or PEG5000 chain was calculated to be fairly extended even at low grafting densities, and the projected cross-sectional areas of the grafted PEG chains are considerably smaller than those predicted on the basis of the estimated Flory radius. The experimental variation of the binding affinity of acylated conjugates for bilayers containing varying mole fractions of PE-PEG2000 or -PEG5000 is well explained by expressions treating the surface-grafted PEG polymers either as a van der Waals gas or as a system of rigid discs described by scaled particle theory. From the combined results of our experimental and simulation studies we conclude that the grafted PEG chains exist in a "mushroom" regime throughout the range of polymer densities examined experimentally and that the diminished affinity of binding of acylated-PEG conjugates to bilayers containing PE-PEGs results from occlusion of the surface area accessible for conjugate binding by the mobile PE-PEG polymer chains.     

Hypocrea jecorina (Trichoderma reesei) Cel7A as a molecular machine: A docking study

Hypocrea jecorina (formerly Trichoderma reesei) Cel7A has a catalytic domain (CD) and a cellulose-binding domain (CBD) separated by a highly glycosylated linker. Very little is known of how the 2 domains interact to degrade crystalline cellulose. Based on the interaction energies and forces on cello-oligosaccharides computationally docked to the CD and CBD, we propose a molecular machine model, where the CBD wedges itself under a free chain end on the crystalline cellulose surface and feeds it to the CD active site tunnel. Enzyme-substrate interactions produce the forces required to pull cellulose chains from the surface and also to help the enzyme move on the cellulose chain for processive hydrolysis. The energy to generate these forces is ultimately derived from the chemical energy of glycosidic bond breakage.     

Characterisation of the hydrophobic collapse of polystyrene in water using free energy techniques

We characterise the hydrophobic collapse of single polystyrene chains in water using molecular dynamics simulations. Specifically, we calculate the potential of mean force for the collapse of a single polystyrene chain in water using metadynamics, comparing the results between all atomistic with coarse-grained (CG) molecular simulation. We next explore the scaling behaviour of the collapsed globular shape at the minimum energy configuration, characterised by the radius of gyration, as a function of chain length. The exponent is close to one third, consistent with that predicted for a polymer chain in bad solvent. We also explore the scaling behaviour of the solvent accessible surface area (SASA) as a function of chain length, finding a similar exponent for both all atomistic and CG simulations. Furthermore, calculation of the local water density as a function of chain length near the minimum energy configuration suggests that intermediate chain lengths are more likely to form dewetted states, as compared to shorter or longer chain lengths.     

Entropic interaction chromatography: separating proteins on the basis of size using end-grafted polymer brushes

Partitioning of a macromolecule into the interfacial volume occupied by a grafted polymer brush decreases the configurational entropy (DeltaSbrush(c)) of the terminally attached linear polymer chains due to a loss of free volume. Self-consistent field theory (SCF) calculations are used to show that DeltaSbrush(c) is a strong function of both the size (MWp) of the partitioning macromolecule and the depth of penetration into the brush volume. We further demonstrate that the strong dependence of DeltaSbrush(c) on MWp provides a novel and powerful platform, which we call entropic interaction chromatography (EIC), for efficiently separating mixtures of proteins on the basis of size. Two EIC columns, differing primarily in polymer grafting density, were prepared by growing a brush of poly(methoxyethyl acrylamide) chains on the surface of a wide-pore (1,000-A pores, 64-microm diameter rigid beads) resin (Toyopearl AF-650M) bearing surface aldehyde groups. Semipreparative 0.1-L columns packed with either EIC resin provide reduced-plate heights of 2 or less for efficient separation of globular protein mixtures over at least three molecular-weight decades. Protein partitioning within these wide-pore EIC columns is shown to be effectively modeled as a thermodynamically controlled process, allowing partition coefficients (K(P)) and elution chromatograms to be accurately predicted using a column model that combines SCF calculation of K(P) values with an equilibrium-dispersion type model of solute transport through the column. This model is used to explore the dependence of column separation efficiency on brush properties, predicting that optimal separation of proteins over a broad MWp range is achieved at low to moderate grafting densities and intermediate chain lengths.     

Adhesive cell cultivation on polymer particle having grafted epoxy polymer chain

In this study, we synthesized a new cell immobilization support having poly(glycidyl methacrylate) as a graft polymer chain and used this support for cell cultivation. Base polymer particle was synthesized by suspension polymerization and epoxy polymer chain was extended from particle surface on graft polymerization. Produced polymer particles had broad particle size distribution ranging from 20 to 1000 μm and the degree of polymerization of grafted polymer chain was ranged from 500 to 1000. The effects of various factors, such as grafted polymer chain length and its surface density, composition of base polymer network and graft polymer chain, on the cell growth of murine fibroblast cell line (MS-5 cell) on polymer particle were studied. This polymer particle could cultivate not only fibroblast cell line but also epidermal cell line (HeLa cell), osteoblast cell line (MC3T3E1 cell), and chondrocyte cell line (ch-8 cell) on its surface. Growth rate is almost the same as that of cells using poly(styrene) tissue culture dish. To apply this cell cultivation system for examination of cell co-culture, HeLa cell immobilized on 100 μm of polymer particle was successfully co-cultured with MS-5 cell immobilized on 300 μm of polymer particle for four weeks.     

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads—only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.     

How to develop globular proteins into adhesives

To make globular proteins suitable for application in adhesives, the specific bonds and interactions which shape their structure have to broken. Only then, a layer of relatively large, flexible and interwoven polymer chains, which are firmly attached to the solid surface by adsorption, can be created. Such a network layer is essential to save the adhesive bond under an applied force, because it can distribute the concentration of stresses generated at the interface into the bulk. Unfolding and swelling of a protein can be achieved by changing the solvent quality. For the globular whey protein beta-lactoglobulin, the optimal conditions for unfolding and swelling is found with 98% formic acid as a solvent. In formic acid, beta-lactoglobulin looses its amphoteric character (it is protonated, probably for approximately 20%). In addition, formic acid is less polar than water and thus a better solvent for the apolar parts of the protein. The swelling and unfolding behaviour of beta-lactoglobulin is studied by viscosity and CD-spectroscopy measurements. For the interpretation of the results we apply the Kuhn formalism that the conformation of a protein can be described in terms of a statistical chain which consists of segments of an average persistence length P. The statistical segment length P, which varies with the experimental conditions, is directly related to the adsorption energy required for a strong adhesion between coil and surface. It determines the depletion energy kT P(-2) m(-2) which must be overcome by specific attraction between side groups of the protein chain and the surface. For beta-lactoglobulin in 98% formic acid, we find a P value of approximately 2.2 nm, pointing at a relatively flexible chain. The minimum net adsorption energy kT P(-2) is then approximately 1 mJ m(-2), a relatively small value to be exceeded. Preliminary results of destructive adhesion tests on beech wood lap-shear joints reveal promising tensile strengths of approximately 2.9+/-1.1 N mm(-2), indeed.     

A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch.

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness dP, embedded in a lipid bilayer of unperturbed thickness doL. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when dP > doL) in order to bridge over the lipid-protein hydrophobic mismatch (dP-doL). The bilayer's hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isometric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy delta F is calculated as a function of dP-doL. Most calculations are for C14 amphiphiles which, in the absence of a protein, pack at an average area per head-group ao approximately equal to 32 A2 (doL approximately 24.5 A), corresponding to the fluid state of the membrane. When dP = doL, delta F > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When dP > doL, the interaction free energy is further increased due to the enhanced stretching of the tails. When dP < doL, chain flexibility (entropy) increases, but this contribution to delta F is overcounted by the increase in the interfacial free energy. Thus, delta F obtains a minimum at dP-doL approximately 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the discussion.     

Impurity and end effects on finite polymer chains--Ising model approach

By the use of a new trick, the open one-dimensional Ising model with nearest neighbor interactions is solved exactly to examine impurity and end effects on finite polymer chains. Melting curves are plotted for various distributions of AT and GC bonds as a function of interaction strength and chain length. Results are compared with previous calculations on infinite length chains by Montroll &; Goel. Correlation effects between impurity bonds on a finite, pure-basis chain are also studied and their implications to further studies of polymer chains indicated.     

Influence of chain length on exciton migration to low-energy sites in single fluorene copolymers.

Fluorescence spectroscopy was performed on single molecules of two 9,9-dialkylfluorene-benzothiadazole (FxBT) copolymers with a 10-fold difference in average molecular weight. Molecules of both polymers exhibit red-shifted emission indicative of energy migration to low-energy sites (LES) on the polymer chains; however, "red" spectra are much more common for the longer polymer. Since singlet-exciton migration is found to occur on the molecular length scale in both cases, the increased number of red-shifted spectra observed for the longer polymer is evidence that the likelihood of LES formation increases with chain length. This relationship is discussed in terms of three possible causes of low-energy sites: local polymer conformations, chromophores with extended conjugation lengths, and random chemical defects.     

Nanoparticle-induced assembly of hydrophobically modified chitosan

Hydrophobically modified chitosan (HMC) self-assembles in solution to form gels, making it suitable for applications in oil dispersion, hydrogel design and wound dressing. The self-assembly of HMC is driven by the association of hydrophobic moieties that are attached to chitosan monomers along the polymer chain. We present the results of discontinuous molecular dynamics simulations aimed at understanding how the length and density of the hydrophobic modification chains attached to HMC affect self-assembly and the structure of the resulting network. Long modification chains are required to promote the formation of a stable network in solution at a modification density of 5%; the networks form more readily at a modification density of 10%. The pore size distribution of the resulting HMC network is relatively independent of the modification chain length and density. Insertion of different sized hydrophobic nanoparticles into HMC has a significant impact on network formation, with the particles acting as junction points that promote the association of several HMC chains. The networks form faster in the presence of many small nanoparticles than in the presence of few large nanoparticles. We conclude that HMC could be a viable candidate to form hydrogels in solution.     

The lipopeptide antibiotic A21978C has a specific interaction with DMPC only in the presence of calcium ions

The A21978C group are lipopeptide antibiotics which kill Gram-positive bacteria only in the presence of calcium ions. The calcium requirement of the antibacterial activity of A21978C correlates well with an in vitro calcium-dependent insertion into phospholipid vesicles. In this paper the interaction of A21978C with phosphatidylcholine is investigated in mixed monomolecular films. The spontaneity of the antibiotic-lipid mixing was determined by calculating the free energy change. On a Ca2+ containing subphase there is a specific interaction between the components at all antibiotic-lipid ratios. This is not true on K+ subphases, where specific interactions never occur. On Mg2+ subphases specific interactions occur only in monolayers containing very little lipid. By analysing the fluorescence of the kynurenine residue we have followed the effects of two factors on the penetration of the antibiotic into lipid bilayer vesicles. Firstly, the phospholipid gel to liquid crystalline phase transition which in the absence of calcium leads to an exclusion of the antibiotic from the bilayer. This trend is completely reversed in the presence of Ca2+. Secondly, the role of this lipopeptide's lipid tail was clarified by use of a series of versions of increasing fatty acyl chain length. The results indicate that the interaction promoted by calcium is not simply a hydrophobic attraction between fatty acyl chains but is more likely to be a specific interaction between polar headgroups.