One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes

Physical Principles of Nanoparticle Cellular Endocytosis

This review article focuses on the physiochemical mechanisms underlying nanoparticle uptake into cells. When nanoparticles are in close vicinity to a cell, the interactions between the nanoparticles and the cell membrane generate forces from different origins. This leads to the membrane wrapping of the nanoparticles followed by cellular uptake. This article discusses how the kinetics, energetics, and forces are related to these interactions and dependent on the size, shape, and stiffness of nanoparticles, the biomechanical properties of the cell membrane, as well as the local environment of the cells. The discussed fundamental principles of the physiochemical causes for nanoparticle-cell interaction may guide new studies of nanoparticle endocytosis and lead to better strategies to design nanoparticle-based approaches for biomedical applications.

Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network

The membrane of the red blood cell (RBC) consists of spectrin tetramers connected at actin junctional complexes, forming a two-dimensional (2D) sixfold triangular network anchored to the lipid bilayer. Better understanding of the erythrocyte mechanics in hereditary blood disorders such as spherocytosis, elliptocytosis, and especially, sickle cell disease requires the development of a detailed membrane model. In this study, we introduce a mesoscale implicit-solvent coarse-grained molecular dynamics (CGMD) model of the erythrocyte membrane that explicitly describes the phospholipid bilayer and the cytoskeleton, by extending a previously developed two-component RBC membrane model. We show that the proposed model represents RBC membrane with the appropriate bending stiffness and shear modulus. The timescale and self-consistency of the model are established by comparing our results with experimentally measured viscosity and thermal fluctuations of the RBC membrane. Furthermore, we measure the pressure exerted by the cytoskeleton on the lipid bilayer. We find that defects at the anchoring points of the cytoskeleton to the lipid bilayer (as in spherocytes) cause a reduction in the pressure compared with an intact membrane, whereas defects in the dimer-dimer association of a spectrin filament (as in elliptocytes) cause an even larger decrease in the pressure. We conjecture that this finding may explain why the experimentally measured diffusion coefficients of band-3 proteins are higher in elliptocytes than in spherocytes, and higher than in normal RBCs. Finally, we study the effects that possible attractive forces between the spectrin filaments and the lipid bilayer have on the pressure applied on the lipid bilayer by the filaments. We discover that the attractive forces cause an increase in the pressure as they diminish the effect of membrane protein defects. As this finding contradicts with experimental results, we conclude that the attractive forces are moderate and do not impose a complete attachment of the filaments to the lipid bilayer.

Vesiculation of healthy and defective red blood cells

Vesiculation of mature red blood cells (RBCs) contributes to removal of defective patches of the erythrocyte membrane. In blood disorders, which are related to defects in proteins of the RBC membrane, vesiculation of the plasma membrane is intensified. Several hypotheses have been proposed to explain RBC vesiculation but the exact underlying mechanisms and what determines the sizes of the vesicles are still not completely understood. In this work, we apply a two-component coarse-grained molecular dynamics RBC membrane model to study how RBC vesiculation is controlled by the membrane spontaneous curvature and by lateral compression of the membrane. Our simulation results show that the formation of small homogeneous vesicles with a diameter less than 40 nm can be attributed to a large spontaneous curvature of membrane domains. On the other hand, compression on the membrane can cause the formation of vesicles with heterogeneous composition and with sizes comparable with the size of the cytoskeleton corral. When spontaneous curvature and lateral compression are simultaneously considered, the compression on the membrane tends to facilitate formation of vesicles originating from curved membrane domains. We also simulate vesiculation of RBCs with membrane defects connected to hereditary elliptocytosis (HE) and to hereditary spherocytosis (HS). When the vertical connectivity between the lipid bilayer and the membrane skeleton is elevated, as in normal RBCs, multiple vesicles are shed from the compressed membrane with diameters similar to the cytoskeleton corral size. In HS RBCs, where the connectivity between the lipid bilayer and the cytoskeleton is reduced, larger-size vesicles are released under the same compression ratio as in normal RBCs. Lastly, we find that vesicles released from HE RBCs can contain cytoskeletal filaments due to fragmentation of the membrane skeleton while vesicles released from the HS RBCs are depleted of cytoskeletal filaments.

Multiple stiffening effects of nanoscale knobs on human red blood cells infected with Plasmodium falciparum malaria parasite

Our coarse-grained molecular dynamics (CGMD) simulations show that the deposition of nanoscale knobs, rather than spectrin network remodeling, is the primary cause of the dramatically increased stiffness of the Plasmodium falciparum (Pf)-infected red blood cell (RBC) membranes. Our analyses further reveal that the knobs stiffen the RBC membrane in a unique manner by simultaneously harnessing composite strengthening, strain hardening, and knob density-dependent vertical coupling effects. In addition to providing a fundamental understanding of the stiffening mechanism of Pf-infected RBCs, our simulation results suggest potential targets for antimalarial therapies.

During its asexual development within the red blood cell (RBC), Plasmodium falciparum (Pf), the most virulent human malaria parasite, exports proteins that modify the host RBC membrane. The attendant increase in cell stiffness and cytoadherence leads to sequestration of infected RBCs in microvasculature, which enables the parasite to evade the spleen, and leads to organ dysfunction in severe cases of malaria. Despite progress in understanding malaria pathogenesis, the molecular mechanisms responsible for the dramatic loss of deformability of Pf-infected RBCs have remained elusive. By recourse to a coarse-grained (CG) model that captures the molecular structures of Pf-infected RBC membrane, here we show that nanoscale surface protrusions, known as “knobs,” introduce multiple stiffening mechanisms through composite strengthening, strain hardening, and knob density-dependent vertical coupling. On one hand, the knobs act as structural strengtheners for the spectrin network; on the other, the presence of knobs results in strain inhomogeneity in the spectrin network with elevated shear strain in the knob-free regions, which, given its strain-hardening property, effectively stiffens the network. From the trophozoite to the schizont stage that ensues within 24–48 h of parasite invasion into the RBC, the rise in the knob density results in the increased number of vertical constraints between the spectrin network and the lipid bilayer, which further stiffens the membrane. The shear moduli of Pf-infected RBCs predicted by the CG model at different stages of parasite maturation are in agreement with experimental results. In addition to providing a fundamental understanding of the stiffening mechanisms of Pf-infected RBCs, our simulation results suggest potential targets for antimalarial therapies.

Effects of lipid composition and solution conditions on the mechanical properties of membrane vesicles

The mechanical properties of cell-sized giant unilamellar liposomes were studied by manipulating polystyrene beads encapsulated within the liposomes using double-beam laser tweezers. Mechanical forces were applied to the liposomes from within by moving the beads away from each other, which caused the liposomes to elongate. Subsequently, a tubular membrane projection was generated in the tip at either end of the liposome, or the bead moved out from the laser trap. The force required for liposome transformation reached maximum strength just before formation of the projection or the moving out of the bead. By employing this manipulation system, we investigated the effects of membrane lipid compositions and environment solutions on the mechanical properties. With increasing content of acidic phospholipids, such as phosphatidylglycerol or phosphatidic acid, a larger strength of force was required for the liposome transformation. Liposomes prepared with a synthetic dimyristoylphosphatidylcholine, which has uniform hydrocarbon chains, were transformed easily compared with liposomes prepared using natural phosphatidylcholine. Surprisingly, bovine serum albumin or fetuin (soluble proteins that do not bind to membranes) decreased liposomal membrane rigidity, whereas the same concentration of sucrose showed no particular effect. These results show that the mechanical properties of liposomes depend on their lipid composition and environment.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

Destruction of cancer cells by laser-induced shock waves: recent developments in experimental treatments and multiscale computer simulations

In this emerging area article we review recent progress in the mechanical destruction of cancer cells using laser-induced shock waves. The pure mechanical damaging and destruction of cancer cells associated with this technique possibly opens up a new route to tumor treatments and the corresponding therapies. At the same time progress in multiscale simulation techniques makes it possible to simulate mechanical properties of soft biological matter such as membranes, cytoskeletal networks and even whole cells and tissue. In this way an interdisciplinary approach to understanding key mechanisms in shock wave interactions with biological matter has become accessible. Mechanical properties of biological materials are also critical for many physiological processes and cover length scales ranging from the atomistic to the macroscopic scale. We argue that the latest developments and progress in experimentation enable the investigation of the shock wave interaction with cancer cells on multiple time- and length-scales. In this way the integrated use of experiment and simulation can address key challenges in this field. The exploration of the biological effects of laser-generated shock waves on a fundamental level constitutes an emerging multidisciplinary research area combining scientific methods from the areas of physics, biology, medicine and computer science.

Role of nanoparticle geometry in endocytosis: laying down to stand up

Nanoparticles (NPs) hold great promises for targeted disease diagnosis and therapy. Despite considerable progress in biomimetic design of NP-bioconjugates, the roles of NP size and shape in endocytosis are still not fully understood. Using an efficient coarse-grained molecular dynamics (CGMD) model, we simulate receptor-mediated endocytosis of NPs of various sizes and shapes. Our simulations demonstrate that both NP size and shape modulate the kinetics of endocytosis. For spherical NPs, there exists an optimal size at which endocytosis takes the shortest time. For a spherocylindrical NP with the initial upright docking position on the membrane plane, endocytosis proceeds through a laying-down-then-standing-up sequence. A free energy analysis reveals that NP size primarily determines whether endocytosis can complete, while NP shape breaks the symmetry of curvature energy landscape and hence dictates the endocytic pathway and the angle of entry. The findings shed light on the rational design of NP-based diagnostic and therapeutic agents with improved cellular targeting.

Graphene microsheets enter cells through spontaneous membrane penetration at edge asperities and corner sites

Understanding and controlling the interaction of graphene-based materials with cell membranes is key to the development of graphene-enabled biomedical technologies and to the management of graphene health and safety issues. Very little is known about the fundamental behavior of cell membranes exposed to ultrathin 2D synthetic materials. Here we investigate the interactions of graphene and few-layer graphene (FLG) microsheets with three cell types and with model lipid bilayers by combining coarse-grained molecular dynamics (MD), all-atom MD, analytical modeling, confocal fluorescence imaging, and electron microscopic imaging. The imaging experiments show edge-first uptake and complete internalization for a range of FLG samples of 0.5- to 10-μm lateral dimension. In contrast, the simulations show large energy barriers relative to kBT for membrane penetration by model graphene or FLG microsheets of similar size. More detailed simulations resolve this paradox by showing that entry is initiated at corners or asperities that are abundant along the irregular edges of fabricated graphene materials. Local piercing by these sharp protrusions initiates membrane propagation along the extended graphene edge and thus avoids the high energy barrier calculated in simple idealized MD simulations. We propose that this mechanism allows cellular uptake of even large multilayer sheets of micrometer-scale lateral dimension, which is consistent with our multimodal bioimaging results for primary human keratinocytes, human lung epithelial cells, and murine macrophages.

Morphology transition in lipid vesicles due to in-plane order and topological defects

Complex morphologies in lipid membranes typically arise due to chemical heterogeneity, but in the tilted gel phase, complex shapes can form spontaneously even in a membrane containing only a single lipid component. We explore this phenomenon via experiments and coarse-grained simulations on giant unilamellar vesicles of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine. When cooled from the untilted L(α) liquid-crystalline phase into the tilted gel phase, vesicles deform from smooth spheres to disordered, highly crumpled shapes. We propose that this shape evolution is driven by nucleation of complex membrane microstructure with topological defects in the tilt orientation that induce nonuniform membrane curvature. Coarse-grained simulations demonstrate this mechanism and show that kinetic competition between curvature change and defect motion can trap vesicles in deeply metastable, defect-rich structures.

Microphysical derivation of the Canham-Helfrich free-energy density

The Canham-Helfrich free-energy density for a lipid bilayer has drawn considerable attention. Aside from the mean and Gaussian curvatures, this free-energy density involves a spontaneous mean-curvature that encompasses information regarding the preferred, natural shape of the lipid bilayer. We use a straightforward microphysical argument to derive the Canham-Helfrich free-energy density. Our derivation (1) provides a justification for the common assertion that spontaneous curvature originates primarily from asymmetry between the leaflets comprising a bilayer and (2) furnishes expressions for the splay and saddle-splay moduli in terms of derivatives of the underlying potential.

Surface-structure-regulated penetration of nanoparticles across a cell membrane

The cell uptake rate of nanoparticles (NPs) coated with mixed hydrophilic/hydrophobic ligands is known to be strongly influenced by the ligand pattern on the nanoparticle surface. To help reveal the physical mechanism behind this intriguing phenomenon, here we perform dissipative particle dynamics simulations to analyze the evolution of free energy as the ligand-coated NPs pierce through a lipid bilayer. Four characteristic ligand patterns are considered: striated NPs with alternating hydrophilic and hydrophobic groups compared to NPs with randomly mixed ligands at the same hydrophilic to hydrophobic ratio, as well as NPs coated with homogeneous hydrophilic or hydrophobic ligands. The free energy analysis indicates that among the four ligand patterns under study, the striated NP encounters the lowest energy barrier during translocation across the membrane. Further analysis reveals that the translocation of the striated NP is facilitated by the constraint of its rotational degree of freedom by the anisotropic ligand pattern, which prevented the free energy of the system from sinking to a deeper valley as the NP passes through the hydrophobic core of the bilayer. Finally, the critical forces required for almost instant penetration of these patterned NPs across the bilayer are calculated and shown to be consistent with the free energy analysis. These findings provide useful guidelines for the molecular design of patterned NPs for controllable cell penetrability.

Fluid membranes can drive linear aggregation of adsorbed spherical nanoparticles

Using computer simulations, we show that lipid membranes can mediate linear aggregation of spherical nanoparticles binding to it for a wide range of biologically relevant bending rigidities. This result is in net contrast with the isotropic aggregation of nanoparticles on fluid interfaces or the expected clustering of isotropic insertions in biological membranes. We present a phase diagram indicating where linear aggregation is expected and compute explicitly the free-energy barriers associated with linear and isotropic aggregation. Finally, we provide simple scaling arguments to explain this phenomenology.

Two-component coarse-grained molecular-dynamics model for the human erythrocyte membrane

We present a two-component coarse-grained molecular-dynamics model for simulating the erythrocyte membrane. The proposed model possesses the key feature of combing the lipid bilayer and the erythrocyte cytoskeleton, thus showing both the fluidic behavior of the lipid bilayer and the elastic properties of the erythrocyte cytoskeleton. In this model, three types of coarse-grained particles are introduced to represent clusters of lipid molecules, actin junctions, and band-3 complexes, respectively. The proposed model facilitates simulations that span large length scales (approximately micrometers) and timescales (approximately milliseconds). By tuning the interaction potential parameters, we were able to control the diffusivity and bending rigidity of the membrane model. We studied the membrane under shearing and found that at a low shear strain rate, the developed shear stress was due mainly to the spectrin network, whereas the viscosity of the lipid bilayer contributed to the resulting shear stress at higher strain rates. In addition, we investigated the effects of a reduced spectrin network connectivity on the shear modulus of the membrane.