Salt Effect on Osmotic Pressure of Polyelectrolyte Solutions: Simulation Study

All-atom molecular dynamics simulations of polymer and polyelectrolyte brushes

Densely grafted polymer and polyelectrolyte (PE) brushes, owing to their significant abilities to functionalize surfaces for a plethora of applications in sensing, diagnostics, current rectification, surface wettability modification, drug delivery, and oil recovery, have attracted significant attention over the past several decades. Unfortunately, most of the attention has primarily focused on understanding the properties of the grafted polymer and the PE chains with little attention devoted to studying the behavior of the brush-supported ions (counterions needed to screen the PE chains) and water molecules. Over the past few years, our group has been at the forefront of addressing this gap: we have employed all-atom molecular dynamics (MD) simulations for studying a wide variety of polymer and PE brush systems with specific attention to unraveling the properties and behavior of the brush-supported water molecules and ions. Our findings have revealed some of the most fascinating properties of such brush-supported ions and water molecules, including the most remarkable control of nanofluidic transport afforded by the specific ion and water responses induced by the PE brushes grafted on the inner walls of the nanochannel. This feature article aims to summarize some of our key contributions associated with such atomistic simulations of polymer and PE brushes and brush-supported water molecules and counterions.

STMP and PVPA as Templating Analogs of Noncollagenous Proteins Induce Intrafibrillar Mineralization of Type I Collagen via PCCP Process

The phosphorylated noncollagenous proteins (NCPs) play a vital role in manipulating biomineralization, while the mechanism of phosphorylation of NCPs in intrafibrillar mineralization of collagen fibril has not been completely deciphered. Poly(vinylphosphonic acid) (PVPA) and sodium trimetaphosphate (STMP) as templating analogs of NCPs induce hierarchical mineralization in cooperation with indispensable sequestration analogs such as polyacrylic acid (PAA) via polymer-induced liquid-like precursor (PILP) process. Herein, STMP-Ca and PVPA-Ca complexes are proposed to achieve rapid intrafibrillar mineralization through polyelectrolyte-Ca complexes pre-precursor (PCCP) process. This strategy is further verified effectively for remineralization of demineralized dentin matrix both in vitro and in vivo. Although STMP micromolecule fails to stabilize amorphous calcium phosphate (ACP) precursor, STMP-Ca complexes facilely permeate into intrafibrillar interstices and trigger phase transition of ACP to hydroxyapatite within collagen. In contrast, PVPA-stabilized ACP precursors lack liquid-like characteristic and crystallize outside collagen due to rigid conformation of PVPA macromolecule, while PVPA-Ca complexes infiltrate into partial intrafibrillar intervals under electrostatic attraction and osmotic pressure as evidenced by intuitionistic 3D stochastic optical reconstruction microscopy (3D-STORM). The study not only extends the variety and size range of polyelectrolyte for PCCP process but also sheds light on the role of phosphorylation for NCPs in biomineralization.

Virtual cell model for osmotic pressure calculation of charged biomolecules

The osmotic pressure of dilute electrolyte solutions containing charged macro-ions as well as counterions can be computed directly from the particle distribution via the well-known cell model. Originally derived within the Poisson-Boltzmann mean-field approximation, the cell model considers a single macro-ion centered into a cell, together with counterions needed to neutralize the total cell charge, while it neglects the phenomena due to macro-ion correlations. While extensively applied in coarse-grained Monte Carlo (MC) simulations of continuum solvent systems, the cell model, in its original formulation, neglects the macro-ion shape anisotropy and details of the surface charge distribution. In this paper, by comparing one-body and two-body coarse-grained MC simulations, we first establish an upper limit for the assumption of neglecting correlations between macro-ions, and second, we validate the approximation of using a non-spherical macro-ion. Next, we extend the cell model to all-atom molecular dynamics simulations and show that protein concentration-dependent osmotic pressures can be obtained by confining counterions in a virtual, spherical subspace defining the protein number density. Finally, we show the possibility of using specific interaction parameters for the protein-ion and ion-ion interactions, enabling studies of protein concentration-dependent ion-specific effects using merely a single protein molecule.

Molecular dynamics insight into viscosity reduction of hydrolysed polyacrylamide by using carbon quantum dots

Hydrolysed polyacrylamide (HPAM) is widely used in many industrial fields where its rheological properties play a leading role. Recent discovery of the reduction of HPAM's viscosity by adding carbon quantum dots (CQDs), however, is controversial to the established theories. By using all atom molecular dynamics simulation with an OPLS-AA force field, this study aims to provide detailed molecular insight into such an uncommon phenomenon. The dynamic structures of the HPAM chain in the presence or absence of CQDs were clearly captured from the molecular aspect. The results reveal that the adsorption of CQD reduces the gyration radius of the HPAM chain, and it is the corresponding hydration effect that leads to the reduction of the viscosity. The amide rather than the carboxylate group along the HPAM chain is dominant in terms of the interaction with the CQDs, and the driven atoms depend on the surface where the polymer is adsorbed.

Polyelectrolyte-calcium complexes as a pre-precursor induce biomimetic mineralization of collagen

Polyelectrolytes such as polyaspartic acid (PAsp) are critical in biomimetic mineralization as stabilizers of amorphous calcium phosphate (ACP) precursors and as nucleation inhibitors similar to non-collagenous proteins (NCPs). Nevertheless, the application of polyelectrolyte-calcium complexes as a pre-precursor, such as PAsp-Ca complexes, in the mineralization of collagen is unexplored. Herein, we propose a polyelectrolyte-Ca complex pre-precursor (PCCP) process for collagen mineralization. By combining three-dimensional (3D) STORM, potential measurements, and cryogenic transmission electron microscopy with molecular dynamics simulations, we show that liquid-like electropositive PAsp-Ca complexes along with free calcium ions infiltrate electronegative collagen fibrils. The PAsp-Ca complexes are immobilized within the fibrils via chelation and hydrogen bonds, and outward movement of free calcium ions is prevented while phosphate and hydroxide are recruited through electrostatic attractions. Afterwards, ACP instantly forms and gradually crystallizes. The PCCP process not only unites two distinct crystallization pathways (classical (free Ca/P ions) and non-classical (polyelectrolyte-Ca complexes)), but also provides a novel strategy for rapid biomimetic mineralization of collagen.

Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions

We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.

Magnesium, Calcium, Potassium, Sodium, Phosphorus, Selenium, Zinc, and Chromium Levels in Alcohol Use Disorder: A Review

Macronutrients and trace elements are important components of living tissues that have different metabolic properties and functions. Trace elements participate in the regulation of immunity through humoral and cellular mechanisms, nerve conduction, muscle spasms, membrane potential regulation as well as mitochondrial activity and enzymatic reactions. Excessive alcohol consumption disrupts the concentrations of crucial trace elements, also increasing the risk of enhanced oxidative stress and alcohol-related liver diseases. In this review, we present the status of selected macroelements and trace elements in the serum and plasma of people chronically consuming alcohol. Such knowledge helps to understand the mechanisms of chronic alcohol-use disorder and to progress and prevent withdrawal effects, also improving treatment strategies.

Food Polyelectrolytes Compress the Colonic Mucus Hydrogel by a Donnan Mechanism

Systems consisting of a polyelectrolyte solution in contact with a cross-linked polyelectrolyte network are ubiquitous (e.g., biofilms, drug-delivering hydrogels, and mammalian extracellular matrices), yet the underlying physics governing these interactions is not well understood. Here, we find that carboxymethyl cellulose, a polyelectrolyte commonly found in processed foods and associated with inflammation and obesity, compresses the colonic mucus hydrogel (a key regulator of host-microbe interactions and a protective barrier) in mice. The extent of this polyelectrolyte-induced compression is enhanced by the degree of polymer negative charge. Through animal experiments and numerical calculations, we find that this phenomenon can be described by a Donnan mechanism. Further, the observed behavior can be quantitatively described by a simple, one-parameter model. This work suggests that polymer charge should be considered when developing food products because of its potential role in modulating the protective properties of colonic mucus.

Osmotic pressure in polyelectrolyte solutions: cell-model and bulk simulations

The osmotic pressure of polyelectrolyte solutions as a function of concentration has been calculated by Monte Carlo simulations of a spherical cell model and by molecular dynamics simulations with periodic boundary conditions. The results for the coarse-grained polyelectrolyte model are in good agreement with experimental results for sodium polyacrylate and the cell model is validated by the bulk simulations. The cell model offers an alternative perspective on osmotic pressure and also forms a direct link to even simpler models in the form of the Poisson-Boltzmann approximation applied to cylindrical and spherical geometries. As a result, the non-monotonic behaviour of the osmotic coefficient seen in simulated salt-free solutions is shown not to rely on a transition between a dilute and semi-dilute regime, as is often suggested when the polyion is modelled as a linear flexible chain. The non-monotonic behaviour is better described as the combination of a finite-size effect and a double-layer effect. Parameters that represent the linear nature of the polyion, including an alternative to monomer concentration, make it possible to display a generalised behaviour of equivalent chains, at least at low concentrations. At high concentrations, local interactions become significant and the exact details of the model become important. The effects of added salt are also discussed and one conclusion is that the empirical additivity rule, treating the contributions from the polyelectrolyte and any salt separately, is a reasonable approximation, which justifies the study of salt-free solutions.

Effect of Dendrigraft Generation on the Interaction between Anionic Polyelectrolytes and Dendrigraft Poly(l-Lysine)

In this present work, three generations of dendrigraft poly(l-Lysine) (DGL) were studied regarding their ability to interact with linear poly (acrylamide-co-2-acrylamido-2-methyl-1-propanesulfonate) (PAMAMPS) of different chemical charge densities (30% and 100%). Frontal analysis continuous capillary electrophoresis (FACCE) was successfully applied to determine binding constants and binding stoichiometries. The effect of DGL generation on the interaction was evaluated for the first three generations (G2, G3, and G4) at different ionic strengths, and the effect of ligand topology (linear PLL vs. dendrigraft DGL) on binding parameters was evaluated. An increase of the biding site constants accompanied with a decrease of the DGL-PAMAMPS (n:1) stoichiometry was observed for increasing DGL generation. The logarithm of the global binding constants decreased linearly with the logarithm of the ionic strength. This double logarithmic representation allowed determining the extent of counter-ions released from the association of DGL molecules onto one PAMAMPS chain that was compared to the total entropic reservoir constituted by the total number of condensed counter-ions before the association.

Collagen intrafibrillar mineralization as a result of the balance between osmotic equilibrium and electroneutrality

Mineralization of fibrillar collagen with biomimetic process-directing agents has enabled scientists to gain insight into the potential mechanisms involved in intrafibrillar mineralization. Here, by using polycation- and polyanion-directed intrafibrillar mineralization, we challenge the popular paradigm that electrostatic attraction is solely responsible for polyelectrolyte-directed intrafibrillar mineralization. As there is no difference when a polycationic or a polyanionic electrolyte is used to direct collagen mineralization, we argue that additional types of long-range non-electrostatic interaction are responsible for intrafibrillar mineralization. Molecular dynamics simulations of collagen structures in the presence of extrafibrillar polyelectrolytes show that the outward movement of ions and intrafibrillar water through the collagen surface occurs irrespective of the charges of polyelectrolytes, resulting in the experimentally verifiable contraction of the collagen structures. The need to balance electroneutrality and osmotic equilibrium simultaneously to establish Gibbs-Donnan equilibrium in a polyelectrolyte-directed mineralization system establishes a new model for collagen intrafibrillar mineralization that supplements existing collagen mineralization mechanisms.

The Effect of Molar Mass and Charge Density on the Formation of Complexes between Oppositely Charged Polyelectrolytes

The interactions between model polyanions and polycations have been studied using frontal continuous capillary electrophoresis (FACCE) which allows the determination of binding stoichiometry and binding constant of the formed polyelectrolyte complex (PEC). In this work, the effect of the poly(l-lysine) (PLL) molar mass on the interaction with statistical copolymers of acrylamide and 2-acrylamido-2-methyl-1-propanesulfonate (PAMAMPS) has been systematically investigated for different PAMAMPS chemical charge densities (15% and 100%) and different ionic strengths. The study of the ionic strength dependence of the binding constant allowed the determination of the total number of released counter-ions during the formation of the PEC, which can be compared to the total number of counter-ions initially condensed on the individual polyelectrolyte partners before the association. Interestingly, this fraction of released counter-ions, which was strongly dependent on the PLL molar mass, was almost independent of the PAMAMPS charge density. These findings are useful to predict the binding constant according to the molar mass and charge density of the polyelectrolyte partners.

Polyelectrolyte Threading through a Nanopore

Threading charged polymers through a nanopore, driven by electric fields E, is investigated by means of Langevin dynamics simulations. The mean translocation time 〈 τ 〉 is shown to follow a scaling law Nα, and the exponent α increases monotonically from 1.16 (4) to 1.40 (3) with E. The result is double-checked by the calculation of mean square displacement of translocation coordinate, which asserts a scaling behavior tβ (for t near τ) with β complying with the relation αβ = 2. At a fixed chain length N, 〈τ〉 displayed a reciprocal scaling behavior E-1 in the weak and also in the strong fields, connected by a transition E-1.64(5) in the intermediate fields. The variations of the radius of gyration of chain and the positions of chain end are monitored during a translocation process; far-from-equilibrium behaviors are observed when the driving field is strong. A strong field can strip off the condensed ions on the chain when it passes the pore. The total charges of condensed ions are hence decreased. The studies for the probability and density distributions reveal that the monomers in the trans-region are gathered near the wall and form a pancake-like density profile with a hump cloud over it in the strong fields, due to fast translocation.