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

Inducing pH control over the critical micelle concentration of zwitterionic surfactants via polyacids adsorption: Effect of chain length and structure

HYPOTHESIS

The critical concentration above which micelles form from zwitterionic surfactant solutions and their thermodynamic stability is affected by the interaction with weak Brønsted polyacid chains (A_n) via the formation of charged hydrogen bonds between the latter and anionic moieties.

EXPERIMENTS

The interaction between zwitterionic micelles and polyacids capable of forming hydrogen bonds, and its dependence on the environmental pH and polymer structure, has been studied with constant-pH simulations and a restricted primitive model for all electrolytes.

FINDINGS

At low pH, the formation of polyacid/micelle complexes is witnessed independently of the polymer size or structure, so that the concentration above which micelles form is substantially decreased compared to polyacid-free cases. Upon rising pH, polymer desorption takes place within a narrow range of pH values, its location markedly depending on the size and structure of polyacids, and on the relative disposition between headgroup charged moieties. Thus, the desorption onset for long linear polyacids (A₆₀) interacting with sulphobetainic headgroups is roughly two pH units higher than for six decameric chains (6A₁₀) adsorbed onto micelles bearing phosphorylcholinic headgroups. This effect, together with the preferential desorption of chain ends at intermediate pH, may be exploited for drug delivery purposes or building advanced metamaterials.

Adsorption of lysozyme into a charged confining pore

Several applications arise from the confinement of proteins on surfaces because their stability and biological activity are enhanced. It is also known that the way in which a protein adsorbs on the surface is important for its biological function since its active sites should not be obstructed. In this study, the adsorption properties of hen egg-white lysozyme, HEWL, into a negatively charged silica pore is examined by employing a coarse-grained model and constant-pH Monte Carlo simulations. The role of electrostatic interactions is taken into account via including the Debye-Hückel potentials into the Cα structure-based model. We evaluate the effects of pH, salt concentration, and pore radius on the protein preferential orientation and spatial distribution of its residues regarding the pore surface. By mapping the residues that stay closer to the pore surface, we find that the increase of pH leads to orientational changes of the adsorbed protein when the solution pH gets closer to the HEWL isoelectric point. Under these conditions, the pK_a shift of these important residues caused by the adsorption into the charged confining surface results in a HEWL charge distribution that stabilizes the adsorption in the observed protein orientation. We compare our observations to the results of the pK_a shift for HEWL available in the literature and to some experimental data.

On the distribution of hydrophilic polyelectrolytes and their counterions around zwitterionic micelles: the possible impact on the charge density in solution

Despite their charge neutrality, micelles composed of surfactants with zwitterionic headgroups selectively accumulate anions at their hydrophobic core/solution interphase due to electrostatic interactions if headgroup positive moieties are the innermost. This tendency may be markedly enhanced if polyions substitute simple ions. To investigate this possibility, solutions composed of zwitterionic micelles and hydrophilic polyanions have been investigated with Monte Carlo simulations representing the studied systems via primitive electrolyte models. Structural and energetic properties are obtained to highlight the impact of connecting simple ions into polyions on the interactions between electrolytes and micelles. Despite the latter, polyanions conserve their conformational properties. A marked increase in the concentration of charged species inside the micellar corona is, instead, found when polyions are present independently of their charge sign or the headgroup structure. Thus, polyelectrolytes act as "shuttle" for all charged species, with the potential of increasing reactions rates involving the latter due to mass effects. Besides, results for the polyions/micelles mixing free energy and Helmholtz energy profiles indicate that the critical micelle concentration is impacted minimally by hydrophilic polyelectrolytes, an outcome agreeing with experiments. This finding is entirely due to weak enthalpic effects while mixing hydrophilic polyions and micelles. A strong reduction in the screening of the micelle negative charge, acquired following the adsorption of anions in the corona and due to counterions layering just outside it (the so called "chameleon effect"), is forecasted when polyanions substitute monovalent anions.

Critical adsorption of multiple polyelectrolytes onto a nanosphere: splitting the adsorption-desorption transition boundary

Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption-the phase-separation curve between the adsorbed and desorbed states of the PEs-as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE-SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption-desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.

Monte Carlo study of the effects of macroion charge distribution on the ionization and adsorption of weak polyelectrolytes and concurrent counterion release

HYPOTHESIS

Adsorption of weak polyelectrolytes onto charged nanoparticles, and concurrent effects such as spatial partitioning of ions may be influenced by details of the polyelectrolyte structure (linear or star-like) and size, by the mobility of the nanoparticle surface charge, or the valence of the nanoparticle counterions.

EXPERIMENTS

Ionization and complexation of weak polyelectrolytes on spherical macroions with monovalent and divalent countrions has been studied with constant-pH Monte Carlo titrations and primitive electrolyte models for linear and star-like polymers capable, also, of forming charged hydrogen bonds. Nanoparticles surface charge has been represented either as a single colloid-centered total charge (CCTC) or as surface-tethered mobile monovalent spherical charges (SMMSC).

FINDINGS

Differences in the average number of adsorbed polyelectrolyte arms and their average charge, and in the relative amount of macroion counterions (m-CI's) released upon polymer adsorption are found between CCTC and SMMSC nanoparticles. The amount of the counterions released also depends on the polymer structure. As CCTC adsorbs a lower number of star-like species arms, the degree of condensation of polymer counterions (p-CI's) onto the polyelectrolyte is also substantially higher for the CCTC colloid, with a concurrent decrease of the osmotic coefficient values.

Standalone interferometry-based calibration of convex lens-induced confinement microscopy with nanoscale accuracy

Strongly confined environments (confined dimensions between 1-100 nm) represent unique challenges and opportunities for understanding and manipulating molecular behavior due to the significant effects of electric double layers, high surface-area to volume ratios, and other phenomena at the nanoscale. Convex Lens-induced Confinement (CLiC) can be used to analyze the dynamics of individual molecules or particles confined in a planar slit geometry with continuously varying gap thickness. We describe an interferometry-based method for precise measurement of the slit pore geometry. Specifically, this approach permitted accurate characterization of separation distances as small as 5 nm, with 1 nm precision, without a priori knowledge or assumptions about the contact geometry, as well as a greatly simplified experimental setup that required only a lens, coverslip, and inverted microscope. The interferometry-based measurement of gap height offered a distinct advantage over conventional fluorescent dye-based methods; e.g., accurate interferometric height measurements were made at low gap heights regardless of solution conditions, while the concentration of fluorescent dye was significantly impacted by solution conditions such as ionic strength or pH. The accuracy of the interferometric measurements was demonstrated by comparing the experimentally measured concentration of a charged fluorescent dye as a function of gap thickness with dye concentration profiles calculated using Debye-Hückel theory. Accurate characterization of nanoscale gap thickness will enable researchers to study a variety of practical and biologically relevant systems within the CLiC geometry.

Adsorption and encapsulation of flexible polyelectrolytes in charged spherical vesicles

We present a theory of adsorption of flexible polyelectrolytes on the interior and exterior surfaces of a charged vesicle in an electrolyte solution. The criteria for adsorption and the density profiles of the adsorbed polymer chain are derived in terms of various characteristics of the polymer, vesicle, and medium, such as the charge density and length of the polymer, charge density and size of the vesicle, electrolyte concentration and dielectric constant of the medium. For adsorption inside the vesicle, the competition between the loss of conformational entropy and gain in adsorption energy results in two kinds of encapsulated states, depending on the strength of the polymer-vesicle interaction. By considering also the adsorption from outside the vesicle, we derive the entropic and energy contributions to the free energy change to transfer an adsorbed chain in the interior to an adsorbed chain on the exterior. In this paper, we have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. The present WKB results are compared with the previous results based on variational methods. The WKB and variational results are in good agreement for both the interior and exterior states of adsorption, except in the zero-salt limit for adsorption in the exterior region. The adsorption criteria and density profiles for both the interior and exterior states are presented in terms of various experimentally controllable variables. Calculation of the dependencies of free energy change to transfer an adsorbed chain from the interior to the exterior surface on salt concentration and vesicle radius shows that the free energy penalty to expel a chain from a vesicle is only of the order of thermal energy.

Critical adsorption of periodic and random polyampholytes onto charged surfaces

How different are the properties of critical adsorption of polyampholytes and polyelectrolytes onto charged surfaces? How important are the details of polyampholyte charge distribution on the onset of critical adsorption transition? What are the scaling relations governing the dependence of critical surface charge density on salt concentration in the surrounding solution? Here, we employ Metropolis Monte Carlo simulations and uncover the scaling relations for critical adsorption for quenched periodic and random charge distributions along the polyampholyte chains. We also evaluate and discuss the dependence of the adsorbed layer width on solution salinity and details of the charge distribution. We contrast our findings to the known results for polyelectrolyte adsorption onto oppositely charged surfaces, in particular, their dependence on electrolyte concentration.

Inverted critical adsorption of polyelectrolytes in confinement

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.

Polymer Looping Is Controlled by Macromolecular Crowding, Spatial Confinement, and Chain Stiffness

We study by extensive computer simulations the looping characteristics of linear polymers with varying persistence length inside a spherical cavity in the presence of macromolecular crowding. For stiff chains, the looping probability and looping time reveal wildly oscillating patterns as functions of the chain length. The effects of crowding differ dramatically for flexible versus stiff polymers. While for flexible chains the looping kinetics is slowed down by the crowders, for stiffer chains the kinetics turns out to be either decreased or facilitated, depending on the polymer length. For severe confinement, the looping kinetics may become strongly facilitated by crowding. Our findings are of broad impact for DNA looping in the crowded and compartmentalized interior of living biological cells.

Molecular dynamics simulation of heterogeneous nucleation on nanotubes

Condensation rate inside and outside the tube depends on the pore diameter and length.

Critical adsorption of polyelectrolytes onto charged Janus nanospheres

The conditions of critical polyelectrolyte adsorption onto spherical charged Janus nano-particles are exploited by Monte-Carlo computer simulations and theoretically.

Nonrandom adsorption of polyelectrolyte chains on finite regularly charged surfaces

Adsorption phenomena are relevant in a wide variety of subjects, from biophysics to technological applications. Different aspects, such as molecular recognition, multilayer deposition, and dynamics of polymer adsorption have been addressed. The methodologies used range from analytical and numerical methods to molecular dynamics or Monte Carlo simulations. In this work, a coarse-grained model is used to explore the adsorption of charged backbones to oppositely charged regions of a surface. These regions encompass those small enough to prevent complete adsorption, but extend to surfaces sufficiently large to promote adsorption with minimal effect on the three-dimensional conformation in bulk. Apart from the different surface areas explored, variations on the surface charge density, polyelectrolyte chain length, and chain stiffness were also considered. The degree of compaction of the polyelectrolyte, on adsorption, is different from that found in the bulk. Also, results indicate an nonuniform adsorption pattern on regularly charged surfaces.

Polyelectrolyte adsorption onto oppositely charged interfaces: image-charge repulsion and surface curvature

We analyze theoretically the influence of low-dielectric boundaries on the adsorption of flexible polyelectrolytes onto planar and spherical oppositely charged surfaces in electrolyte solutions. We rationalize to what extent polymer chains are depleted from adsorbing interfaces by repulsive image forces. We employ the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function of the Edwards equation to determine the adsorption equilibrium. Scaling relations are determined for the critical adsorption strength required to initiate polymer adsorption onto these low-dielectric supports. Image-force repulsion shifts the equilibrium toward the desorbed state, demanding larger surface charge densities and polyelectrolyte linear charge densities for the adsorption to take place. The effect is particularly pronounced for a planar interface in a low-salt regime, where a dramatic change in the scaling behavior for the adsorption-desorption transition is predicted. For the adsorbed state, polymers with higher charge densities are displaced further from the interface by image-charge repulsions. We discuss relevant experimental evidence and argue about possible biological applications of the results.