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

Highlights

• Polylysine binding to anionic membrane leads to a very heterogeneous adsorption layer.

• The adsorption layer's heterogeneity is registered in the electrokinetic experiments.

• Bound polylysine's conformation depends on both anionic lipid content and PL loading.

• PL attaches the surface with a tip and extends to the bulk being in excess.

• PL-covered and PL-free areas have different surface potential.

Abstract

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.

Introduction

Several natural and synthetic polymers demonstrating biological activity are polycations. Being adsorbed at negatively charged biological membranes, polycations demonstrate complex behavior. For instance, polyethyleneimines, polydiallylamines, and arginine-containing polypeptides can initiate local defects in the plasmatic membrane, ensuring their bactericidal effect. Various research and review articles has been interested in the accurate physicochemical characterization of polycation membrane-disrupting activity [1], [2], [3]. Apart from the membrane-disrupting activity of polycations, high effective adsorption of cationic polymers have been actively exploited in the design of drug-delivery systems [4], including the improvement of oral drug availability [5]. Thus, the detailed understanding of polycations’ adsorption on membranes and the accurate determination of the related physicochemical characteristics is of direct importance in pharmacology and biomedicine. The physicochemical research of polycations–membrane interaction is challenging for different reasons. Firstly, many forces govern polyelectrolyte adsorption such as electrostatic attraction to the surface, electrostatic repulsion between polymers in the adsorbate layer, volume exclusion, non-electrostatic attraction to the surface, and entropy of polymer conformation [6]. Secondly, the lipid membrane is fluid and its structure is susceptible to polycation binding [7]. Finally, the molecular diversity of both polycations and phospholipids makes it difficult to formulate general principles of their interaction.

Synthetic polymers and polypeptides are convenient objects in experimental studies and theoretical analysis of peptide–lipid interactions. Their adsorption on lipid membranes is a model for the interaction between water-soluble proteins and high-molecular drugs with the cell surface [8]. Previous experimental research suggested the use of well-characterized liposome suspensions and electrokinetic measurements to control the charge of these colloid particles [9], [10]. The relatively simple Gouy-Chapman-Stern (GCS) model describes the electric potential distribution at the membrane-water interface considering monovalent ion adsorption [11], and was verified by several methods [12]. This model assumes that the electric potential is distributed uniformly in a lateral direction. This assumption works well in small cationic substance adsorption [13], [14]. However, this approach is oversimplified for macromolecule adsorption when the uniformity condition is not applicable. For instance, adsorption experiments on mica indicated incomplete polymer coverage of the surface [15]. On the other side, sophisticated models such as presented in works of [16], [17], provide other parameters extracted from electrokinetic data. Thus, we consider the GCS model to be the most appropriate and straightforward approach in our study. However, we have modified this model in order to consider the possible inhomogeneity in the polymer adsorption layer.

One source of discontinuities in the polymer layer is related to charge inhomogeneity at the surface caused by lipid segregation in the membranes of mixed composition and accumulation of negatively charged lipids under a polycationic molecule [7], [18]. This process has been extensively studied in some theoretical works [19] and computational studies [20]. Polycationic molecules by themselves constitute another source of inhomogeneity. For instance, polylysine (PL) adsorption does not form a homogeneous layer as PL molecules bind to the bilayer almost irreversibly, starting from some polymer length [21], [22]. It is not surprising that macromolecules may form different structures at the surface. In fact, this has been reported via molecular modeling, especially when the anionic lipid density is low [20], [23]. So, a local charge inhomogeneity appears to be especially significant in polymer layer formation. Another kind of heterogeneity is the discreetness of surface charges. Numeric Poisson-Boltzmann calculations applied to small oligopeptides Lys-8 showed ζ-potential increment to be much larger than from calculations by simple GCS relations [24]. Naturally, the effect of surface inhomogeneity should be manifested more strongly when the number of binding sites at the surface is low and the adsorbed polymer length is high. Accordingly, the best way to test these effects is to study the adsorption of polycations differing in size and adsorbed at negatively charged lipid membranes of varied compositions [25], [26], [27]. This setting is also well suitable for direct experimental control in electrophoretic measurements.

In the present research, we choose poly-L-lysines of different lengths adsorbed on a membrane composed of zwitterionic phosphatidylcholine (PC) and anionic cardiolipin (CL), as a model system. PC was selected as a “background” lipid as it is the most abundant zwitterionic lipid in animals, and it was shown not to interact with PL polymers. This was particularly proved for pentalysine by NMR in a previous study [28]. Anionic CL, a group of glycerophospholipids, is the most abundant anionic lipids in the mitochondrial inner membrane [29] and provides a negative charge in the bacterial plasmatic membrane. PL is a biocompatible polycation broadly used in various biomedical applications including drug and gene delivery [30], [31]. Additionally, it is also used as an intermembrane linker for modelling membrane stacks [32]. Interactions of polycations to anionic lipids are widely studied. However, little information is accessible for different anionic lipid contents. Our research fills this gap, describing PL adsorption to systems with a wide range of CL content. Although systems with anionic content significantly > 20% can hardly be found in nature, such constructions are applicable in delivery systems development [33]. It should be noted that PL is almost totally protonated under physiological pH and, thus, the role of electrostatic interactions in its adsorption is crucial. Based on electrokinetic measurements of a liposome suspension in the presence of PLs, we compared the model that considers the uniform charge distribution to the alternative (heterogeneous) model that accounts for the existence of local areas with varying charge and potential. In the framework of the heterogeneous model, we compared parameters characterizing the adsorption layer’s geometry with the atomistic details found in corresponding in silico experiments.

All-atom molecular dynamics (MD) simulations were performed for several systems to visualize polymer behavior in the adsorption layer. It is evident that, with the increase in the degree of polymerization, the effect of lateral inhomogeneity was more pronounced. However, very long polymeric chains were too big for the simulation at an atomic resolution, and most simulations of polymer–with–membrane systems were restricted to 20-meres or shorter species [20], [23], [24]. Coarse-grained models could overcome this limitation, but there are only a few examples of such MD models [34]. Monte-Carlo coarse-grain simulations were published for 100-meres [35], [36] but without polymer-to-polymer interactions. Generally no lucid correspondence between molecular structures (obtained from simulations) and theoretical adsorption models has often been described. Our study filled this gap, demonstrating how some simple geometrical parameters reflect in molecular simulations of analogous systems.

Our paper is structured as follows: firstly, we characterized adsorption via electrokinetic measurements with liposome suspension with different lipid composition and in the presence of PL of several average molecular weights. Next, we described these results with homogenous and inhomogeneous theoretical approaches. Finally, we used MD simulations of the same systems to prove a second approach.