Coarse-grained molecular dynamics simulation for uptake of nanoparticles into a charged lipid vesicle dominated by electrostatic interactions

Lateral Transport of Domains in Anionic Lipid Bilayer Membranes under DC Electric Fields: A Coarse-Grained Molecular Dynamics Study

Dynamic lateral transport of lipids, proteins, and self-assembled structures in biomembranes plays a crucial role in diverse cellular processes. In this study, we perform coarse-grained molecular dynamics simulations on a vesicle composed of a binary mixture of neutral and anionic lipids to investigate the lateral transport of individual lipid molecules and the self-assembled lipid domains upon an applied direct current (DC) electric field. Under the potential force of the electric field, a phase-separated domain rich in anionic lipids is trapped in the opposite direction of the electric field. The subsequent reversal of the electric field induces unidirectional domain motion. During the domain motion, the domain size remains constant, but a considerable amount of the anionic lipids is exchanged between the anionic-lipid-rich domain and the surrounding bulk. While the speed of the domain motion (collective lipid motion) shows a significant positive correlation with the electric field strength, the exchange of anionic lipids between the domain and bulk (individual lipid motion) exhibits no clear correlation with the field strength. The mean velocity field of the lipids surrounding the domain displays a two-dimensional (2D) source dipole. We revealed that the balance between the potential force of the applied electric field and the quasi-2D hydrodynamic frictional force well explains the dependence of the domain motions on the electric field strengths. The present results provide insight into the hierarchical dynamic responses of self-assembled lipid domains to the applied electric field and contribute to controlling the lateral transportation of lipids and membrane inclusions.

Polydots, soft nanoparticles, at membrane interfaces

Soft nanoparticles (NPs) are emerging candidates for nano medicine, particularly for intercellular imaging and targeted drug delivery. Their soft nature, manifested in their dynamics, allows translocation into organisms without damaging their membranes. A crucial step towards incorporating soft dynamic NPs in nano medicine, is to resolve their interrelation with membranes. Here using atomistic molecular dynamics (MD) simulations we probe the interaction of soft NPs formed by conjugated polymers with a model membrane. These NPs, often termed polydots, are confined to their nano dimensions without any chemical tethers, forming dynamic long lived nano structures. Specifically, polydots formed by dialkyl para poly phenylene ethylene (PPE), with a varying number of carboxylate groups tethered to the alkyl chains to tune the interfacial charge of the surface of the NP are investigated at the interface with a model membrane that consists of di-palmitoyl phosphatidylcholine (DPPC). We find that even though polydots are controlled only by physical forces, they retain their NP configuration as they transcend the membrane. Regardless of their size, neutral polydots spontaneously penetrate the membrane whereas carboxylated polydots must be driven in, with a force that depends on the charge at their interface, all without significant disruption to the membrane. These fundamental results provide a means to control the position of the nanoparticles with respect to the membrane interfaces, which is key to their therapeutic use.

Recent research advances on non-linear phenomena in various biosystems

All biological phenomena can be classified as open, dissipative and non-linear. Moreover, the most typical phenomena are associated with non-linearity, dissipation and openness in biological systems. In this review article, four research topics on non-linear biosystems are described to show the examples from various biological systems. First, membrane dynamics of a lipid bilayer for the cell membrane is described. Since the cell membrane separates the inside of the cell from the outside, self-organizing systems that form spatial patterns on membranes often depend on non-linear dynamics. Second, various data banks based on recent genomics analysis supply the data including vast functional proteins from many organisms and their variable species. Since the proteins existing in nature are only a very small part of the space represented by amino acid sequence, success of mutagenesis-based molecular evolution approach crucially depends on preparing a library with high enrichment of functional proteins. Third, photosynthetic organisms depend on ambient light, the regular and irregular changes of which have a significant impact on photosynthetic processes. The light-driven process proceeds through many redox couples in the cyanobacteria constituting chain of redox reactions. Forth topics focuses on a vertebrate model, the zebrafish, which can help to understand, predict and control the chaos of complex biological systems. In particular, during early developmental stages, developmental differentiation occurs dynamically from a fertilized egg to divided and mature cells. These exciting fields of complexity, chaos, and non-linear science have experienced impressive growth in recent decades. Finally, future directions for non-liner biosystems are presented.

Coarse-grained molecular dynamics simulation of cation distribution profiles on negatively charged lipid membranes during phase separation

Revealing the ion distributions on a charged lipid membrane in aqueous solution under the influence of long-range interactions is essential for understanding the origin of the stability of the bilayer structure and the interaction between biomembranes and various electrolytes. However, the ion distributions and their dynamics associated with the phase separation process of the lipid bilayer membrane are still unclear. We perform coarse-grained molecular dynamics simulations to reveal the Na⁺ and Cl^- distributions on charged phospholipid bilayer membranes during phase separation. During the phase separation, cations closely follow the position of negatively charged lipids on a microsecond timescale and are rapidly redistributed parallel to the lipid bilayer. In the homogenous mixture of zwitterionic and negatively charged lipids, cations weakly follow negatively charged lipids, indicating the strong interaction between cations and negatively charged lipids. We also compare cation concentrations as a function of surface charge density obtained by our simulation with those obtained by a modified Poisson-Boltzmann theory. Including the ion finite size makes the statistical results consistent, suggesting the importance of the ion-ion interactions in aqueous solution. Our simulation results advance our understanding of ion distribution during phase separation.

Shape control of deformable charge-patterned nanoparticles

Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50 nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.

Lipid nanoparticles with ionizable lipids: Statistical aspects

Lipid nanoparticles (LNPs) with size ∼100 nm are now used for fabrication of a new generation of drugs and antiviral vaccines. To optimize their function or, more specifically, interaction with cell membranes, their composition often includes ionizable lipids which are neutral or cationic (after association with H^{+}). Physically, such LNPs represent an interesting example of mesoscopic nanosystems with complex and far from understood properties. Experimentally, they can be studied at cell-membrane mimics. Herein, I analyze theoretically three related aspects. (i) I describe how the extent of protonation of ionizable lipids located at the surface of LNPs depends on the H^{+} concentration by using the phenomenological Langmuir-Stern and Poisson-Boltzmann models with continuum distribution of charges and the dipole model with discrete charges. In these frameworks, the H^{+} adsorption isotherms are predicted to be close to Langmuirian provided the fraction of ionizable lipids is smaller than 0.5. (ii) I scrutinize the interaction between charged LNPs and their interaction with a supported lipid bilayer (SLB) by using the phenomenological theory and lattice-gas model. The long-term association or attachment is predicted provided the charges are opposite. The models make it possible to estimate the size of the contact region (provided a LNP is not deformed) and the number of lipid-lipid bonds in this region. (iii) I briefly discuss denaturation of a LNP during interaction with the SLB and argue that it may occur via a few stepwise transitions.

Three-Phase Coexistence in Binary Charged Lipid Membranes in a Hypotonic Solution

We investigated the phase separation of dioleoylphosphatidylserine (DOPS) and dipalmitoylphosphatidylcholine (DPPC) in giant unilamellar vesicles in a hypotonic solution using fluorescence and confocal laser scanning microscopy. Although phase separation in charged lipid membranes is generally suppressed by the electrostatic repulsion between the charged headgroups, osmotic stress can promote the formation of charged lipid domains. Interestingly, we observed a three-phase coexistence even in the DOPS/DPPC binary lipid mixtures. The three phases were DPPC-rich, dissociated DOPS-rich, and nondissociated DOPS-rich phases. The two forms of DOPS were found to coexist owing to the ionization of the DOPS headgroup, such that the system could be regarded as quasi-ternary. The three formed phases with differently ionized DOPS domains were successfully identified experimentally by monitoring the adsorption of positively charged particles. In addition, coarse-grained molecular dynamics simulations confirmed the stability of the three-phase coexistence. Attraction mediated by hydrogen bonding between protonated DOPS molecules and reduction of the electrostatic interactions at the domain boundaries stabilized the three-phase coexistence.

Direct translocation of a negatively charged nanoparticle across a negatively charged model cell membrane

Nanoparticles have attracted much attention as a carrier for drug, gene, and macromolecule delivery in next-generation biomedical and therapeutic technologies. In delivery applications, nanoparticles tend to have negative charge due to the negative charge of biomolecules used as delivery cargo, while biological cell membranes are also negatively charged. This means that negatively charged nanoparticles (NC-NPs) are required to translocate across these negatively charged cell membranes (NC-CMs). However, this translocation is unlikely to occur because of electrostatic interactions. Here, we investigated the translocation of a NC-NP across a NC-CM under a transmembrane electric potential through coarse-grained molecular dynamics simulations. To model the transmembrane potential, two approaches were adopted: externally applied electric field and ionic charge imbalance. We showed that a NC-NP can directly translocate across a NC-CM via a non-disruptive pathway under a weak external electric field with an ionic charge imbalance. It was also found that the ionic charge imbalance contributes to the membrane crossing of a NC-NP as well as the self-resealing of the cell membrane after a NC-NP translocation. Our findings imply that NC-NPs can be delivered into a cell by combining applied electric field with membrane hyperpolarization/depolarization induced by an external stimulus.

Designing Surface Charge Patterns for Shape Control of Deformable Nanoparticles

Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable, patchy NPs tailored with surface charge patterns such as Janus patches, stripes, and polyhedrally distributed patches differently adapt their shape in response to changes in patterns and ionic strength, transforming into capsules, hemispheres, variably dimpled bowls, and polyhedra. The links between anisotropy in NP surface charge, shape, and the elastic energy density are discussed.