Monte Carlo Study of Polyelectrolyte Adsorption on Mixed Lipid Membrane

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

Structures of cationic and anionic polyelectrolytes in aqueous solutions: the sign effect

In this study, we use molecular dynamics simulation to explore the structures of anionic and cationic polyelectrolytes in aqueous solutions. We first confirm the significantly stronger solvation effects of single anions compared to cations in water at the fixed ion radii, due to the reversal orientations of asymmetric dipolar H₂O molecules around the ions. Based on this, we demonstrate that the solvation discrepancy of cations/anions and electrostatic correlations of ionic species can synergistically cause the nontrivial structural difference between single anionic and cationic polyelectrolytes. The cationic polyelectrolyte shows an extended structure whereas the anionic polyelectrolyte exhibits a collapsed structure, and their structural differences decline with increasing the counterion size. Furthermore, we corroborate that multiple cationic polyelectrolytes or multiple anionic polyelectrolytes can exhibit largely differential molecular architectures in aqueous solutions. In the solvation dominant regime, the polyelectrolyte solutions exhibit uniform structures; whereas, in the electrostatic correlation dominant regime, the polyelectrolyte solutions exhibit heterogeneous structures, in which the likely charged chains microscopically aggregate through counterion condensations. Increasing the intrinsic chain rigidity causes polyelectrolyte extension and hence moderately weakens the inter-chain clustering. Our work highlights the various, unique structures and molecular architectures of polyelectrolytes in solutions caused by the multi-body correlations between polyelectrolytes, counterions and asymmetric dipolar solvent molecules, which provides insights into the fundamental understanding of ion-containing polymers.

Heterogeneity in Lateral Distribution of Polycations at the Surface of Lipid Membrane: From the Experimental Data to the Theoretical Model

Natural and synthetic polycations of different kinds attract substantial attention due to an increasing number of their applications in the biomedical industry and in pharmacology. The key characteristic determining the effectiveness of the majority of these applications is the number of macromolecules adsorbed on the surface of biological cells or their lipid models. Their study is complicated by a possible heterogeneity of polymer layer adsorbed on the membrane. Experimental methods reflecting the structure of the layer include the electrokinetic measurements in liposome suspension and the boundary potential of planar bilayer lipid membranes (BLM) and lipid monolayers with a mixed composition of lipids and the ionic media. In the review, we systematically analyze the methods of experimental registration and theoretical description of the laterally heterogeneous structures in the polymer layer published in the literature and in our previous studies. In particular, we consider a model based on classical theory of the electrical double layer, used to analyze the available data of the electrokinetic measurements in liposome suspension with polylysines of varying molecular mass. This model suggests a few parameters related to the heterogeneity of the polymer layer and allows determining the conditions for its appearance at the membrane surface. A further development of this theoretical approach is discussed.

Structure and dynamics of ions in dipolar solvents: a coarse-grained simulation study

We employ the coarse-grained molecular dynamics simulation to investigate the fundamental structural and dynamic properties of the ionic solution with and without the application of an external electric field. Our simulations, in which the solvent molecules are treated as Stockmayer fluids and the ions are modeled as spheres, can effectively account for the multi-body correlations between ion-ion, ion-dipole, and dipole-dipole interactions, which are often ignored by the mean-field theories or coarse-grained simulations based on a dielectric continuum. By focusing on the coupling between effects of ion solvation, electrostatic correlations and applied electric field, we highlight some nontrivial microscopic molecular features of the systems, such as the reorganization of the dipolar solvent, clustering of the ions, and diffusions of ions and dipolar solvent molecules. Particularly, our simulation indicates the nonmonotonic dependence of the ionic clustering and ion diffusion rates on the dipolar nature of the solvent molecules, as well as the amplification of these tendencies caused by the electric field application. This work provides insights into the fundamental understanding of physicochemical properties for ion-containing liquids and contributes to the design and development of ion-containing materials.

Inhomogeneity of polylysine adsorption layers on lipid membranes revealed by theoretical analysis of electrokinetic data and molecular dynamics simulations

The adsorption of large polycations on a charged lipid membrane is qualitatively different from the small inorganic cations, which almost uniformly populate the membrane surface. We assume that the polycationic adsorption layer might be laterally inhomogeneous starting from a certain polymer length, and this effect can be more visible for membranes with low anionic lipid content. To study systems with inhomogeneous adsorption layers, we carried out electrokinetic measurements of mobility of liposomes containing anionic and neutral phospholipids in the presence of polylysine molecules. Some of these systems were simulated by all-atom molecular dynamics. Here we proposed a theoretical approach accounting for the formation of separated regions at the membrane surface, which differ in charge density and surface potential. Our model allowed us to determine the adsorption layer's geometric parameters such as surface coverage and surface-bound monomer fraction of polymer, which correlate with the molecular dynamics (MD) simulations. We demonstrated that the configuration polylysine adopts on the membrane surface (tall or planar) depends on the polymer/membrane charge ratio. Both theory and MD indicate a decrease in the anionic lipid content, alongside with a decrease in the bound monomer fraction and corresponding increase in the extension length of the adsorbed polymers.

Coarse-grained simulation studies on the adsorption of polyelectrolyte complexes upon lipid membranes

Conformations of a polyelectrolyte complex irreversibly bound to a zwitterionic lipid bilayer.

Application of Monte Carlo simulation in addressing key issues of complex coacervation formed by polyelectrolytes and oppositely charged colloids

This paper reviews the recent advance of Monte Carlo (MC) simulation in addressing key issues of complex coacervation between polyelectrolytes and oppositely charged colloids. Readers were first supplied with a brief overview of current knowledge and experimental strategies in the study of complex coacervation. In the next section, the general MC simulation procedures as well as representative strategies applied in complex coacervation were summarized. The unique contributions of MC simulation in either capturing delicate features, easing the experimental trials or proving the concept were then elucidated through the following aspects: i) identify phase boundary and decouple interaction contributions; ii) clarify composition distribution and internal structure; iii) predict the influences of physicochemical conditions on complex coacervation; iv) delineate the mechanisms for "binding on the wrong side of the isoelectric point". Finally, current challenges as well as prospects of MC simulation in complex coacervation are also discussed. The ultimate goal of this review is to provide readers with basic guideline for synergistic design of experiments in combination with MC simulation, and deliver convincing interpretation and reliable prediction for the structure and behavior in polyelectrolyte-macroion complex coacervation.

Adsorption of Synthetic Cationic Polymers on Model Phospholipid Membranes: Insight from Atomic-Scale Molecular Dynamics Simulations

Although synthetic cationic polymers represent a promising class of effective antibacterial agents, the molecular mechanisms behind their antimicrobial activity remain poorly understood. To this end, we employ atomic-scale molecular dynamics simulations to explore adsorption of several linear cationic polymers of different chemical structure and protonation (polyallylamine (PAA), polyethylenimine (PEI), polyvinylamine (PVA), and poly-l-lysine (PLL)) on model bacterial membranes (4:1 mixture of zwitterionic phosphatidylethanolamine (PE) and anionic phosphatidylglycerol (PG) lipids). Overall, our findings show that binding of polycations to the anionic membrane surface effectively neutralizes its charge, leading to the reorientation of water molecules close to the lipid/water interface and to the partial release of counterions to the water phase. In certain cases, one has even an overcharging of the membrane, which was shown to be a cooperative effect of polymer charges and lipid counterions. Protonated amine groups of polycations are found to interact preferably with head groups of anionic lipids, giving rise to formation of hydrogen bonds and to a noticeable lateral immobilization of the lipids. While all the above findings are mostly defined by the overall charge of a polymer, we found that the polymer architecture also matters. In particular, PVA and PEI are able to accumulate anionic PG lipids on the membrane surface, leading to lipid segregation. In turn, PLL whose charge twice exceeds charges of PVA/PEI does not induce such lipid segregation due to its considerably less compact architecture and relatively long side chains. We also show that partitioning of a polycation into the lipid/water interface is an interplay between its protonation level (the overall charge) and hydrophobicity of the backbone. Therefore, a possible strategy in creating highly efficient antimicrobial polymeric agents could be in tuning these polycation's properties through proper combination of protonated and hydrophobic blocks.

Spatial Rearrangement and Mobility Heterogeneity of an Anionic Lipid Monolayer Induced by the Anchoring of Cationic Semiflexible Polymer Chains

We use Monte Carlo simulations to investigate the interactions between cationic semiflexible polymer chains and a model fluid lipid monolayer composed of charge-neutral phosphatidyl-choline (PC), tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP₂), and univalent anionic phosphatidylserine (PS) lipids. In particular, we explore how chain rigidity and polymer concentration influence the spatial rearrangement and mobility heterogeneity of the monolayer under the conditions where the cationic polymers anchor on the monolayer. We find that the anchored cationic polymers only sequester the tetravalent PIP₂ lipids at low polymer concentrations, where the interaction strength between the polymers and the monolayer exhibits a non-monotonic dependence on the degree of chain rigidity. Specifically, maximal anchoring occurs at low polymer concentrations, when the polymer chains have an intermediate degree of rigidity, for which the PIP₂ clustering becomes most enhanced and the mobility of the polymer/PIP₂ complexes becomes most reduced. On the other hand, at sufficiently high polymer concentrations, the anchoring strength decreases monotonically as the chains stiffen-a result that arises from the pronounced competitions among polymer chains. In this case, the flexible polymers can confine all PIP₂ lipids and further sequester the univalent PS lipids, whereas the stiffer polymers tend to partially dissociate from the monolayer and only sequester smaller PIP₂ clusters with greater mobilities. We further illustrate that the mobility gradient of the single PIP₂ lipids in the sequestered clusters is sensitively modulated by the cooperative effects between anchored segments of the polymers with different rigidities. Our work thus demonstrates that the rigidity and concentration of anchored polymers are both important parameters for tuning the regulation of anionic lipids.

Tuning the mobility coupling of quaternized polyvinylpyridine and anionic phospholipids in supported lipid bilayers

Binding of biomacromolecules to anionic lipids in the plasma membrane is a common motif in many cell signaling pathways. Previous work has shown that macromolecules with cationic sequences can form nanodomains with sequestered anionic lipids, which alters the lateral distribution and mobility of the membrane lipids. Such sequestration is believed to result from the formation of a lipid-macromolecule complex. To date, however, the molecular structure and dynamics of the lipid-polymer interface are poorly understood. We have investigated the behavior of polycationic quaternized polyvinylpyridine (QPVP) on supported lipid bilayers doped with phosphatidylserine (PS) or phosphatidylinositol phosphate (PIP) lipids using time-resolved fluorescence microscopy, including pulsed interleaved excitation fluorescence cross-correlation spectroscopy (PIE-FCCS). PIE-FCCS is a dual-color fluorescence spectroscopy that translates fluctuations in fluorescence signal into a measurement of diffusion and colocalization. By labeling the polymer and lipids, we investigated the adsorption-induced translational mobility of lipids and systematically studied the influence of lipid charge density and solution ionic strength. Our results show that alteration of anionic lipid lateral mobility is dependent on the net charge of the lipid headgroup and is modulated by the ionic strength of the solution, indicating that electrostatic interactions drive the decrease in lateral mobility of anionic lipids by adsorbed QPVP. At physiological salt concentration we observe that the lipid lateral mobility is weakly influenced by QPVP and that there is no evidence of stable lipid-polymer complexes.

Compositional redistribution and dynamic heterogeneity in mixed lipid membrane induced by polyelectrolyte adsorption: effects of chain rigidity

Monte Carlo simulation is employed to investigate the interaction between a polyelectrolyte and a fluid mixed membrane containing neutral (phosphatidyl-choline, PC), monovalent anionic (phosphatidylserine, PS), and multivalent anionic (phosphatidylinositol, PIP2) lipids. The effects of the intrinsic polyelectrolyte rigidity and solution ionic strength on the lateral rearrangement and dynamics of different anionic lipid species are systematically studied. Our results show that, the increase of polyelectrolyte chain rigidity reduces the loss of polyelectrolyte conformational entropy and the energy gains in electrostatic interaction, but raises the demixing entropy loss of the segregated anionic lipids. Therefore, the polyelectrolyte/membrane adsorption strength exhibits a non-monotonic dependence on the polyelectrolyte rigid parameter k ang, and there exists a certain optimal k ang for which the adsorption strength is maximal. Because the less loss of chain conformational entropy dominates the increase of the demixing entropy loss of the segregated anionic lipids and the decreases of the electrostatic energy gains, the semiflexible polyelectrolyte adsorbs onto the membrane more firmly than the flexible one. Whereas, for the adsorption of rigid polyelectrolyte, larger anionic lipid demixing entropy loss and less energy gain in the electrostatic interaction dominate over the decrease of the polyelectrolyte conformation entropy loss, leading to the desorption of the chain from the membrane. By decreasing the ionic concentration of the salt solution, the certain optimal k ang shifts to larger values. The cooperative effects of the adsorbing polyelectrolyte beads determine the concentration gradients and hierarchical mobility of the bound anionic lipids, as well as the polyelectrolyte dynamics.