Mechanics of enveloped virus entry into host cells

Why does a cell function? New arguments in favor of quantum effects

In this study, the complexities of intracellular processes have been analyzed, including DNA folding, alternative splicing, mitochondrial function, and enzyme transport in lysosomes. Based on a previously proposed hypothesis (Levinthal's generalized paradox), a conclusion is made that all abovementioned processes cannot be realized with sufficient accuracy and in a realistic timeframe within the framework of classical physics. It is unclear why the cell functions at all. For the cell to function, its internal environment must be highly structured. In this regard, the cell shares similarities with computational devices (computers). In this study, quantum models of interactions between biologically important molecules were constructed, taking into account the long-range effects. One significant aspect of these models is the special role of the phase of the wavefunction, which serves as a controlling parameter. Experiments have been proposed that may confirm or refute these models.

Combination of spironolactone and DPP-4 inhibitors for treatment of SARS-CoV-2 infection: a literature review

Coronavirus disease 2019 (COVID-19) is still causing hospitalization and death, and vaccination appears to become less effective with each emerging variant. Spike, non-spike, and other possible unrecognized mutations have reduced the efficacy of recommended therapeutic approaches, including monoclonal antibodies, plasma transfusion, and antivirals. SARS-CoV-2 binds to angiotensin-converting enzyme 2 (ACE2) and probably dipeptidyl peptidase 4 (DPP-4) to initiate the process of endocytosis by employing host proteases such as transmembrane serine protease-2 (TMPRSS-2) and ADAM metallopeptidase domain 17 (ADAM17). Spironolactone reduces the amount of soluble ACE2 and antagonizes TMPRSS-2 and ADAM17. DPP-4 inhibitors play immunomodulatory roles and may block viral entry. The efficacy of treatment with a combination of spironolactone and DPP-4 inhibitors does not appear to be affected by viral mutations. Therefore, the combination of spironolactone and DPP-4 inhibitors might improve the clinical outcome for COVID-19 patients by decreasing the efficiency of SARS-CoV-2 entry into cells and providing better anti-inflammatory, antiproliferative, and antifibrotic effects than those achieved using current therapeutic approaches such as antivirals and monoclonal antibodies.

Two-component macrophage model for active phagocytosis with pseudopod formation

Macrophage phagocytosis is critical for the immune response, homeostasis regulation, and tissue repair. This intricate process involves complex changes in cell morphology, cytoskeletal reorganization, and various receptor-ligand interactions controlled by mechanical constraints. However, there is a lack of comprehensive theoretical and computational models that investigate the mechanical process of phagocytosis in the context of cytoskeletal rearrangement. To address this issue, we propose a novel coarse-grained mesoscopic model that integrates a fluid-like cell membrane and a cytoskeletal network to study the dynamic phagocytosis process. The growth of actin filaments results in the formation of long and thin pseudopods, and the initial cytoskeleton can be disassembled upon target entry and reconstructed after phagocytosis. Through dynamic changes in the cytoskeleton, our macrophage model achieves active phagocytosis by forming a phagocytic cup utilizing pseudopods in two distinct ways. We have developed a new algorithm for modifying membrane area to prevent membrane rupture and ensure sufficient surface area during phagocytosis. In addition, the bending modulus, shear stiffness, and cortical tension of the macrophage model are investigated through computation of the axial force for the tubular structure and micropipette aspiration. With this model, we simulate active phagocytosis at the cytoskeletal level and investigate the mechanical process during the dynamic interplay between macrophage and target particles.

Mathematical model for force and energy of virion-cell interactions during full engulfment in HIV: Impact of virion maturation and host cell morphology

Viral endocytosis involves elastic cell deformation, driven by chemical adhesion energy, and depends on physical interactions between the virion and cell membrane. These interactions are not easy to quantify experimentally. Hence, this study aimed to develop a mathematical model of the interactions of HIV particles with host cells and explore the effects of mechanical and morphological parameters during full virion engulfment. The invagination force and engulfment energy were described as viscoelastic and linear-elastic functions of radius and elastic modulus of virion and cell, ligand-receptor energy density and engulfment depth. The influence of changes in the virion-cell contact geometry representing different immune cells and ultrastructural membrane features and the decrease in virion radius and shedding of gp120 proteins during maturation on invagination force and engulfment energy was investigated. A low invagination force and high ligand-receptor energy are associated with high virion entry ability. The required invagination force was the same for immune cells of different sizes but lower for a local convex geometry of the cell membrane at the virion length scale. This suggests that localized membrane features of immune cells play a role in viral entry ability. The available engulfment energy decreased during virion maturation, indicating the involvement of additional biological or biochemical changes in viral entry. The developed mathematical model offers potential for the mechanobiological assessment of the invagination of enveloped viruses towards improving the prevention and treatment of viral infections.

Biomechanical Role of Epsin in Influenza A Virus Entry

Influenza A virus (IAV) utilizes clathrin-mediated endocytosis for cellular entry. Membrane-bending protein epsin is a cargo-specific adaptor for IAV entry. Epsin interacts with ubiquitinated surface receptors bound to IAVs via its ubiquitin interacting motifs (UIMs). Recently, epsin was shown to have membrane tension sensitivity via its amphiphilic H₀ helix. We hypothesize this feature is important as IAV membrane binding would bend the membrane and clinical isolates of IAVs contain filamentous IAVs that may involve more membrane bending. However, it is not known if IAV internalization might also depend on epsin's H₀ helix. We found that CALM, a structurally similar protein to epsin lacking UIMs shows weaker recruitment to IAV-containing clathrin-coated structures (CCSs) compared to epsin. Removal of the ENTH domain of epsin containing the N-terminus H₀ helix, which detects changes in membrane curvature and membrane tension, or mutations in the ENTH domain preventing the formation of H₀ helix reduce the ability of epsin to be recruited to IAV-containing CCSs, thereby reducing the internalization of spherical IAVs. However, internalization of IAVs competent in filamentous particle formation is not affected by the inhibition of H₀ helix formation in the ENTH domain of epsin. Together, these findings support the hypothesis that epsin plays a biomechanical role in IAV entry.

Role of Ligand Distribution in the Cytoskeleton-Associated Endocytosis of Ellipsoidal Nanoparticles

Nanoparticle (NP)–cell interaction mediated by receptor–ligand bonds is a crucial phenomenon in pathology, cellular immunity, and drug delivery systems, and relies strongly on the shape of NPs and the stiffness of the cell. Given this significance, a fundamental question is raised on how the ligand distribution may affect the membrane wrapping of non-spherical NPs under the influence of cytoskeleton deformation. To address this issue, in this work we use a coupled elasticity–diffusion model to systematically investigate the role of ligand distribution in the cytoskeleton-associated endocytosis of ellipsoidal NPs for different NP shapes, sizes, cytoskeleton stiffness, and the initial receptor densities. In this model, we have taken into account the effects of receptor diffusion, receptor–ligand binding, cytoskeleton and membrane deformations, and changes in the configuration entropy of receptors. By solving this model, we find that the uptake process can be significantly influenced by the ligand distribution. Additionally, there exists an optimal state of such a distribution, which corresponds to the fastest uptake efficiency and depends on the NP aspect ratio and cytoskeleton stiffness. We also find that the optimal distribution usually needs local ligand density to be sufficiently high at the large curvature region. Furthermore, the optimal state of NP entry into cells can tolerate slight changes to the corresponding optimal distribution of the ligands. The tolerance to such a change is enhanced as the average receptor density and NP size increase. These results may provide guidelines to control NP–cell interactions and improve the efficiency of target drug delivery systems.

How nanoparticles can induce dimerization and aggregation of cells in blood or lymph

By analogy with virions, the binding of biologically-inspired nanoparticles (NPs) with ligands to the cellular membrane containing receptors depends on the multivalent ligand-receptor interaction, membrane bending, and cytoskeleton deformation. The interplay of these factors results in the existence of the potential minimum and activation barrier on the pathway towards full absorption of a NP. Herein, I hypothesize and show theoretically that the interaction of a NP, bound to one cell, with another cell can stabilize the potential minimum and increase the corresponding activation barrier, i.e., NPs can mediate the formation of long-living pairs of cells and aggregates containing a few cells inside blood and lymphatic vessels.

Unraveling How Multivalency Triggers Shape Deformation of Sub-100 nm Lipid Vesicles

Multivalent ligand-receptor interactions are critical to the function of membrane-enveloped biological and biomimetic nanoparticles, yet resulting nanoparticle shape changes are rarely investigated. Using the localized surface plasmon resonance (LSPR) sensing technique, we tracked the attachment of biotinylated, sub-100 nm lipid vesicles to a streptavidin-functionalized supported lipid bilayer (SLB) and developed an analytical model to extract quantitative details about the vesicle-SLB contact region. The experimental results were supported by theoretical analyses of biotin-streptavidin complex formation and corresponding structural and energetic aspects of vesicle deformation. Our findings reveal how varying the surface densities of streptavidin receptors in the SLB and biotin ligands in the vesicles affects the extent of nanometer-scale vesicle deformation. We also identify conditions, i.e., a critical ligand density, at which appreciable vesicle deformation began, which provides insight into how the membrane bending energy partially counterposes the multivalent binding interaction energy. These findings are generalizable to various multivalent ligand-receptor systems.

Trajectories in nanotechnology: embracing complexity, seeking analogies

This account comprises personal reflections on the field of nanosystems primarily designed for the delivery of biologically active agents. It emphasises the colloidal nature of nanoparticles obeying the same physical laws that dictate the behaviour of disperse systems. Research reveals not only intrinsic complexities but a variety of possible trajectories in vivo and ex vivo, issues of stability, interactions and behaviour in a range of often constrained environments. Such are the variations in the chemical and physical nature of the nanosystems and the active agents they carry, their putative "targets" and the many biological systems and models in which they are employed, it is not possible to generalise. Stochastic events may exclude precise prediction or extrapolation of outcomes, but embracing and studying complexity lead to new insights, often aided by consideration of analogies in cognate areas. This is part of the process of illumination. Unexpected results provide the true essence and excitement of scientific endeavour. Simplification is perhaps its antithesis.

Independent Size and Fluorescence Emission Determination of Individual Biological Nanoparticles Reveals that Lipophilic Dye Incorporation Does Not Scale with Particle Size

Advancements in nanoparticle characterization techniques are critical for improving the understanding of how biological nanoparticles (BNPs) contribute to different cellular processes, such as cellular communication, viral infection, as well as various drug-delivery applications. Since BNPs are intrinsically heterogeneous, there is a need for characterization methods that are capable of providing information about multiple parameters simultaneously, preferably at the single-nanoparticle level. In this work, fluorescence microscopy was combined with surface-based two-dimensional flow nanometry, allowing for simultaneous and independent determination of size and fluorescence emission of individual BNPs. In this way, the dependence of the fluorescence emission of the commonly used self-inserting lipophilic dye 3,3'-dioctadecyl-5,5'-di(4-sulfophenyl)oxacarbocyanine (SP-DiO) could successfully be correlated with nanoparticle size for different types of BNPs, including synthetic lipid vesicles, lipid vesicles derived from cellular membrane extracts, and extracellular vesicles derived from human SH-SY5Y cell cultures; all vesicles had a radius, r, of ∼50 nm and similar size distributions. The results demonstrate that the dependence of fluorescence emission of SP-DiO on nanoparticle size varies significantly between the different types of BNPs, with the expected dependence on membrane area, r², being observed for synthetic lipid vesicles, while a significant weaker dependence on size was observed for BNPs with more complex composition. The latter observation is attributed to a size-dependent difference in membrane composition, which may influence either the optical properties of the dye and/or the insertion efficiency, indicating that the fluorescence emission of this type of self-inserting dye may not be reliable for determining size or size distribution of BNPs with complex lipid compositions.

Entry Dynamics of Single Ebola Virus Revealed by Force Tracing

Infections by the Ebola virus (EBOV) rapidly cause fatal hemorrhagic fever in humans. Viral entry into host cells is the most critical step in infection and an attractive target for therapeutic intervention. Herein, the invagination behavior and entry dynamics of filamentous Ebola virus-like particles (EBO-VLPs) were investigated using a force tracing technique based on atomic force microscopy and single-particle fluorescence tracking in real time. The filamentous EBOV-VLPs might enter cells in both horizontal and vertical modes, and the virus-receptor interactions during endocytic uptake were analyzed. In addition, molecular dynamics simulations and engulfment energy analysis further depicted EBO-VLP entry in the horizontal and vertical directions and suggested that internalization in the vertical direction requires a larger force and more time. This report provides useful information for further revealing the mechanism of viral infection, which is important for understanding viral pathogenesis.

Dynamics of particle uptake at cell membranes

Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While the shape of the free membrane does not play an important role for tensed and loose membranes, in the intermediate regime it leads to an important energy barrier. Here we show that this barrier is similar to but different from an effective line tension and suggest a simple analytical approximation for it. We then explore the rich dynamics of uptake for particles of different shapes and present the corresponding dynamical state diagrams. We also extend our model to include stochastic fluctuations, which facilitate uptake and lead to corresponding changes in the phase diagrams.

Intra- and intercellular transport of substances: Models and mechanisms

Non-equilibrium-statistical models of intracellular transport are built. The most significant features of these models are microscopic reversibility and the explicit considerations of the driving forces of the process - the ATP-ADP chemical potential difference. In this paper, water transport using contractile vacuoles, the transport and assembly of microtubules and microfilaments, the protein distribution within a cell, the transport of neurotransmitters from the synaptic cleft and the transport of substances between cells using plasmodesmata are discussed. Endocytosis and phagocytosis models are considered, and transport tasks and information transfer mechanisms inside the cell are explored. Based on an analysis of chloroplast movement, it was concluded that they have a complicated method of influencing each other in the course of their movements. The role of quantum effects in sorting and control transport mechanisms is also discussed. It is likely that quantum effects play a large role in these processes, otherwise reliable molecular recognition would be impossible, which would lead to very low intracellular transport efficiency.

Intermittency of Deformation and the Elastic Limit of an Icosahedral Virus under Compression

Viruses undergo mesoscopic morphological changes as they interact with host interfaces and in response to chemical cues. The dynamics of these changes, over the entire temporal range relevant to virus processes, are unclear. Here, we report on creep compliance experiments on a small icosahedral virus under uniaxial constant stress. We find that even at small stresses, well below the yielding point and generally thought to induce a Hookean response, strain continues to develop in time via sparse, randomly distributed, relatively rapid plastic events. The intermittent character of mechanical compliance only appears above a loading threshold, similar to situations encountered in granular flows and the plastic deformation of crystalline solids. The threshold load is much smaller for the empty capsids of the brome mosaic virus than for the wild-type virions. The difference highlights the involvement of RNA in stabilizing the assembly interface. Numerical simulations of spherical crystal deformation suggest intermittency is mediated by lattice defect dynamics and identify the type of compression-induced defect that nucleates the transition to plasticity.

Stochastic modeling of nanoparticle internalization and expulsion through receptor-mediated transcytosis

Receptor-mediated transcytosis (RMT) is a fundamental mechanism for the transcellular transport of nanoparticles. RMT is a complex process, during which the nanoparticles actively interact with the membrane and the membrane profile undergoes extreme deformations for particle internalization and expulsion. In this work, we developed a stochastic model to study the endocytosis and exocytosis of nanoparticles across soft membranes. The model is based on the combination of a stochastic particle binding model with a membrane model, and accounts for both clathrin-mediated endocytosis for internalization and actin-mediated exocytosis for expulsion. Our results showed that nanoparticles must have certain avidity with enough ligand density and ligand-receptor binding affinity to be taken up, while too high avidity limited the particle release from the cell surface. We further explored the functional roles of actin during exocytosis, which has been a topic under active debate. Our simulations indicated that the membrane compression due to the actin induced tension tended to break the ligand-receptor bonds and to shrink the fusion pore. Therefore, an intermediate tension promoted the fusion pore expansion and nanoparticle release, while high tension prohibits particle release. Our model provides new and critical mechanistic insights into RMT, and represents a powerful platform for aiding the rational design of nanocarriers for controlled drug delivery.

Computational Models for Trapping Ebola Virus Using Engineered Bacteria

The outbreak of the Ebola virus in recent years has resulted in numerous research initiatives to seek new solutions to contain the virus. A number of approaches that have been investigated include new vaccines to boost the immune system. An alternative post-exposure treatment is presented in this paper. The proposed approach for clearing the Ebola virus can be developed through a microfluidic attenuator, which contains the engineered bacteria that traps Ebola flowing through the blood onto its membrane. The paper presents the analysis of the chemical binding force between the virus and a genetically engineered bacterium considering the opposing forces acting on the attachment point, including hydrodynamic tension and drag force. To test the efficacy of the technique, simulations of bacterial motility within a confined area to trap the virus were performed. More than 60 percent of the displaced virus could be collected within 15 minutes. While the proposed approach currently focuses on in vitro environments for trapping the virus, the system can be further developed into a future treatment system whereby blood can be cycled out of the body into a microfluidic device that contains the engineered bacteria to trap viruses.

Stochastic simulations of nanoparticle internalization through transferrin receptor dependent clathrin-mediated endocytosis

BACKGROUND

Receptor dependent clathrin-mediated endocytosis (CME) is one of the most important endocytic pathways for the internalization of bioparticles into cells. During CME, the ligand-receptor interactions, development of clathrin-coated pit (CCP) and membrane evolution all act together to drive the internalization of bioparticles. In this work, we develop a stochastic computational model to investigate the CME based on the Metropolis Monte Carlo simulations.

METHODS

The model is based on the combination of a stochastic particle binding model with a membrane model. The energetic costs of membrane bending, CCP formation and ligand-receptor interactions are systematically linked together.

RESULTS

We implement our model to investigate the effects of particle size, ligand density and membrane stiffness on the overall process of CME from the drug delivery perspectives. Consistent with some experiments, our results show that the intermediate particle size and ligand density favor the particle internalization. Moreover, our results show that it is easier for a particle to enter a cell with softer membrane.

CONCLUSIONS

The model presented here is able to provide mechanistic insights into CME and can be readily modified to include other important factors, such as actins. The predictions from the model will aid in the therapeutic design of intracellular/transcellular drug delivery and antiviral interventions.

Effects of ligand distribution on receptor-diffusion-mediated cellular uptake of nanoparticles

Biophysical-factor-dependent cellular uptake of nanoparticles (NPs) through receptor-diffusion-mediated endocytosis bears significance in pathology, cellular immunity and drug-delivery systems. Advanced nanotechnology of NP synthesis provides methods for modifying NP surface with different ligand distributions. However, no report discusses effects of ligand distribution on NP surface on receptor-diffusion-mediated cellular uptake. In this article, we used a statistical dynamics model of receptor-diffusion-mediated endocytosis to examine ligand-distribution-dependent cellular uptake dynamics by considering that ligand-receptor complexes drive engulfing to overcome resistance to membrane deformation and changes in configuration entropy of receptors. Results showed that cellular internalization of NPs strongly depended on ligand distribution and that cellular-uptake efficiency of NPs was high when ligand distribution was within a range around uniform distribution. This feature of endocytosis ensures robust infection ability of viruses to enter host cells. Interestingly, results also indicated that optimal ligand distribution associated with highest cellular-uptake efficiency slightly depends on distribution pattern of ligands and density of receptors, and the optimal distribution becomes uniform when receptor density is sufficiently large. Position of initial contact point is also a factor affecting dynamic wrapping. This study explains why most enveloped viruses present almost homogeneous ligand distribution and is useful in designing controlled-release drug-delivery systems.

Kinetics of receptor-mediated endocytosis of elastic nanoparticles

It is now widely recognized that mechanical properties play critical roles in the cell uptake of nanomaterials. Here we conduct a theoretical study on the kinetics of receptor-mediated endocytosis of elastic nanoparticles that is limited by receptor diffusion, specifically focusing on how the uptake rate depends on the nanoparticle stiffness and size, membrane tension and binding strength between membrane receptors and ligands grafted on the nanoparticle surface. It is shown that, while soft nanoparticles are energetically less prone to full wrapping than stiff ones, the wrapping of the former is kinetically faster than that of the latter. Spherical and cylindrical elastic nanoparticles show dramatic differences in the effect of stiffness on the uptake rate. Additional theoretical analysis is performed to investigate the role of the stochastic receptor-ligand binding in the endocytosis of elastic nanoparticles. The relation between the uptake efficiency and uptake proneness is discussed. This study provides new insight into the elasticity effects on cell uptake and may serve as a design guideline for the controlled endocytosis and diagnostics delivery.

Comparative protein profiling of B16 mouse melanoma cells susceptible and non-susceptible to alphavirus infection: Effect of the tumor microenvironment

Alphavirus vectors are promising tools for cancer treatment. However, relevant entry mechanisms and interactions with host cells are still not clearly understood. The first step toward a more effective therapy is the identification of novel intracellular alterations that could be associated with cancer aggressiveness and could affect the therapeutic potential of these vectors. In this study, we observed that alphaviruses efficiently infected B16 mouse melanoma tumors/tumor cells in vivo, whereas their transduction efficiency in B16 cells under in vitro conditions was blocked. Therefore, we further aimed to understand the mechanisms pertaining to the differential transduction efficacy of alphaviruses in B16 tumor cells under varying growth conditions. We hypothesized that the tumor microenvironment might alter gene expression in B16 cells, leading to an up-regulation of the expression of virus-binding receptors or factors associated with virus entry and replication. To test our hypothesis, we performed a proteomics analysis of B16 cells cultured in vitro and of B16 cells isolated from tumors, and we identified 277 differentially regulated proteins. A further in-depth analysis to identify the biological and molecular functions of the detected proteins revealed a set of candidate genes that could affect virus infectivity. Importantly, we observed a decrease in the expression of interferon α (IFN-α) in tumor-isolated cells that resulted in the suppression of several IFN-regulated genes, thereby abrogating host cell antiviral defense. Additionally, differences in the expression of genes that regulate cytoskeletal organization caused significant alterations in cell membrane elasticity. Taken together, our findings demonstrated favorable intracellular conditions for alphavirus transduction/replication that occurred during tumor transformation. These results pave the way for optimizing the development of strategies for the application of alphaviral vectors as a potent cancer therapy.

Target shape dependence in a simple model of receptor-mediated endocytosis and phagocytosis

Phagocytosis and receptor-mediated endocytosis are vitally important particle uptake mechanisms in many cell types, ranging from single-cell organisms to immune cells. In both processes, engulfment by the cell depends critically on both particle shape and orientation. However, most previous theoretical work has focused only on spherical particles and hence disregards the wide-ranging particle shapes occurring in nature, such as those of bacteria. Here, by implementing a simple model in one and two dimensions, we compare and contrast receptor-mediated endocytosis and phagocytosis for a range of biologically relevant shapes, including spheres, ellipsoids, capped cylinders, and hourglasses. We find a whole range of different engulfment behaviors with some ellipsoids engulfing faster than spheres, and that phagocytosis is able to engulf a greater range of target shapes than other types of endocytosis. Further, the 2D model can explain why some nonspherical particles engulf fastest (not at all) when presented to the membrane tip-first (lying flat). Our work reveals how some bacteria may avoid being internalized simply because of their shape, and suggests shapes for optimal drug delivery.

Multiscale modeling of virus replication and spread

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.

On the modeling of endocytosis in yeast

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Results of experiments on endocytosis in yeast show general agreement that 1) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it, and 2) the large-scale membrane deformation is tubular in shape. In contrast, there are three competing proposals for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: 1) initiation, where clathrin interacts with the membrane via adaptor proteins; 2) elongation, where the membrane is then further deformed by polymerizing actin filaments; and 3) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed.

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.

Membrane-wrapping contributions to malaria parasite invasion of the human erythrocyte

The blood stage malaria parasite, the merozoite, has a small window of opportunity during which it must successfully target and invade a human erythrocyte. The process of invasion is nonetheless remarkably rapid. To date, mechanistic models of invasion have focused predominantly on the parasite actomyosin motor contribution to the energetics of entry. Here, we have conducted a numerical analysis using dimensions for an archetypal merozoite to predict the respective contributions of the host-parasite interactions to invasion, in particular the role of membrane wrapping. Our theoretical modeling demonstrates that erythrocyte membrane wrapping alone, as a function of merozoite adhesive and shape properties, is sufficient to entirely account for the first key step of the invasion process, that of merozoite reorientation to its apex and tight adhesive linkage between the two cells. Next, parasite-induced reorganization of the erythrocyte cytoskeleton and release of parasite-derived membrane can also account for a considerable energetic portion of actual invasion itself, through membrane wrapping. Thus, contrary to the prevailing dogma, wrapping by the erythrocyte combined with parasite-derived membrane release can markedly reduce the expected contributions of the merozoite actomyosin motor to invasion. We therefore propose that invasion is a balance between parasite and host cell contributions, evolved toward maximal efficient use of biophysical forces between the two cells.

Coupled elasticity-diffusion model for the effects of cytoskeleton deformation on cellular uptake of cylindrical nanoparticles

Molecular dynamic simulations and experiments have recently demonstrated how cylindrical nanoparticles (CNPs) with large aspect ratios penetrate animal cells and inevitably deform cytoskeletons. Thus, a coupled elasticity-diffusion model was adopted to elucidate this interesting biological phenomenon by considering the effects of elastic deformations of cytoskeleton and membrane, ligand-receptor binding and receptor diffusion. The mechanism by which the binding energy drives the CNPs with different orientations to enter host cells was explored. This mechanism involved overcoming the resistance caused by cytoskeleton and membrane deformations and the change in configurational entropy of the ligand-receptor bonds and free receptors. Results showed that deformation of the cytoskeleton significantly influenced the engulfing process by effectively slowing down and even hindering the entry of the CNPs. Additionally, the engulfing depth was determined quantitatively. CNPs preferred or tended to vertically attack target cells until they were stuck in the cytoskeleton as implied by the speed of vertically oriented CNPs that showed much faster initial engulfing speeds than horizontally oriented CNPs. These results elucidated the most recent molecular dynamics simulations and experimental observations on the cellular uptake of carbon nanotubes and phagocytosis of filamentous Escherichia coli bacteria. The most efficient engulfment showed the stiffness-dependent optimal radius of the CNPs. Cytoskeleton stiffness exhibited more significant influence on the optimal sizes of the vertical uptake than the horizontal uptake.

Ultrafast Tracking of a Single Live Virion During the Invagination of a Cell Membrane

The first step in most viral infections is the penetration of the cell membrane via endocytosis. However, the underlying mechanism of this important process has not been quantitatively characterized; for example, the velocity and force of a single virion during invagination remain unknown. Here, the endocytosis of a single live virion (Singapore grouper iridovirus, SGIV) through the apical membranes of a host cell is monitored by developing and using a novel ultrafast (at the microsecond level) tracking technique: force tracing. For the first time, these results unambiguously reveal that the maximum velocity during the cell entry of a single SGIV by membrane invagination is approximately 200 nm s(-1), the endocytic force is approximately 60.8 ± 18.5 pN, and the binding energy density increases with the engulfment depth. This report utilizing high temporospatial resolution (subnanometer and microsecond levels) approaches provides new insight into the dynamic process of viral infection via endocytosis and the mechanism of membrane invagination at the single-particle level.

Kinetics of virus entry by endocytosis

Entry of virions into the host cells is either endocytotic or fusogenic. In both cases, it occurs via reversible formation of numerous relatively weak bonds resulting in wrapping of a virion by the host membrane with subsequent membrane rupture or scission. The corresponding kinetic models are customarily focused on the formation of bonds and do not pay attention to the energetics of the whole process, which is crucially dependent, especially in the case of endocytosis, on deformation of actin filaments forming the cytoskeleton of the host cell. The kinetic model of endocytosis, proposed by the author, takes this factor into account and shows that the whole process can be divided into a rapid initial transient stage and a long steady-state stage. The entry occurs during the latter stage and can be described as a first-order reaction. Depending on the details of the dependence of the grand canonical potential on the number of bonds, the entry can be limited either by the interplay of bond formation and membrane rupture (or scission) or by reaching a maximum of this potential.

DEPENDENCE OF ENDOCYTOSIS CAUSED BY DEPLETION EFFECTS ON THE ASPECT RATIO OF COLLOIDAL PARTICLE

In colloidal suspensions containing large and small particles, a peculiar attractive force caused by entropy appears, this force can cause aggregation of large particles. With the concentration of small particles increasing, the large particles can be endocytosed by vesicle. A continuum model is developed to investigate the equilibrium mechanics between a biomembrane and an enveloped colloidal particle with different aspect ratios. The results show that the endocytosis of colloidal particle depends on the aspect ratio of colloidal particle. For a spherical colloidal particle (aspect ratio is zero), the entropy provides sufficient favorable energy to drive its engulfment; however, at a high aspect ratio, the entropy is not sufficient to overcome the resistance from the biomembrane and causes endocytosis.

Force generation by endocytic actin patches in budding yeast

Membrane deformation during endocytosis in yeast is driven by local, templated assembly of a sequence of proteins including polymerized actin and curvature-generating coat proteins such as clathrin. Actin polymerization is required for successful endocytosis, but it is not known by what mechanisms actin polymerization generates the required pulling forces. To address this issue, we develop a simulation method in which the actin network at the protein patch is modeled as an active gel. The deformation of the gel is treated using a finite-element approach. We explore the effects and interplay of three different types of force driving invagination: 1), forces perpendicular to the membrane, generated by differences between actin polymerization rates at the edge of the patch and those at the center; 2), the inherent curvature of the coat-protein layer; and 3), forces parallel to the membrane that buckle the coat protein layer, generated by an actomyosin contractile ring. We find that with optimistic estimates for the stall stress of actin gel growth and the shear modulus of the actin gel, actin polymerization can generate almost enough force to overcome the turgor pressure. In combination with the other mechanisms, actin polymerization can the force over the critical value.

Dynamic interfacial behavior of viscoelastic aqueous hyaluronic acid: effects of molecular weight, concentration and interfacial velocity

An aqueous hyaluronic acid (HA(aq)) pericellular coat, when mediating the tactile aspect of cellular contact inhibition, has three tasks: interface formation, mechanical signal transmission and interface separation. To quantify the interfacial adhesive behavior of HA(aq), we induce simultaneous interface formation and separation between HA(aq) and a model hydrophobic, hysteretic Si-SAM surface. While surface tension γ remains essentially constant, interface formation and separation depend greatly on concentration (5 ≤ C ≤ 30 mg mL(-1)), molecular weight (6 ≤ MW ≤ 2000 kDa) and interfacial velocity (0 ≤ V ≤ 3 mm s(-1)), each of which affect shear elastic and loss moduli G′ and G′′, respectively. Viscoelasticity dictates the mode of interfacial motion: wetting-dewetting, capillary necking, or rolling. Wetting-dewetting is quantified using advancing and receding contact angles θ(A) and θ(R), and the hysteresis between them, yielding data landscapes for each C above the [MW, V] plane. The landscape sizes, shapes, and curvatures disclose the interplay, between surface tension and viscoelasticity, which governs interfacial dynamics. Gel point coordinates modulus G and angular frequency ω appear to predict wetting-dewetting (G < 75 ω0.2), capillary necking (75 ω0.2 < G < 200 ω0.075) or rolling (G > 200ω0.075). Dominantly dissipative HA(aq) sticks to itself and distorts irreversibly before separating, while dominantly elastic HA(aq) makes contact and separates with only minor, reversible distortion. We propose the dimensionless number (G′V)/(ω(r)γ), varying from 10(-5) to 10(3) in this work, as a tool to predict the mode of interface formation-separation by relating interfacial kinetics with bulk viscoelasticity. Cellular contact inhibition may be thus aided or compromised by physiological or interventional shifts in [C, MW, V], and thus in (G′V)/(ω(r)γ), which affect both mechanotransduction and interfacial dynamics. These observations, understood in terms of physical properties, may be broadened to probe interfacial dynamics of other viscoelastic aqueous biopolymers.

Physical aspects of the initial phase of endocytosis

The endocytotic mechanism of entry of virions into cells includes wrapping of a virion by the host membrane with subsequent formation of a vesicle covering a virion. The energy along this pathway depends on the ligand-receptor interaction and deformation of the cell membrane and underlying actin cytoskeleton. The available models describe the cytoskeleton deformation by using the conventional continuum theory of elasticity and predict that this factor often controls the repulsive part of the virion-cell interaction. This approach is, however, debatable because the size of virions is smaller than or comparable to the length scale characterizing the cytoskeleton structure. The author shows that the continuum theory appreciably (up to one order of magnitude) overestimates the cytoskeleton-deformation energy and that the scale of this energy is comparable to that of cell membrane bending.

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.

Depletion effect and biomembrane budding

Depletion effects are well known to lead to phase separation in microsystems consisting of large and small particles with short-range repulsive interactions that act over macromolecular length scales. The equilibrium mechanics between an enveloped colloidal particle and a biomembrane caused by entropy is investigated by using a continuum model. We show that the favorable contact energy stems from entropy, which is sufficient to drive engulfment of the colloidal particle, and deformation of the biomembrane determines the resistance to the engulfment of the colloidal particle. The engulfment process depends on the ratio of the radii of the larger particle and smaller particles and the bending rigidity. The results show insights into the effects of depletion on biomembrane budding and nanoparticle transportation by a vesicle.

Multiscale perspectives of virus entry via endocytosis

Most viruses take advantage of endocytic pathways to gain entry into host cells and initiate infections. Understanding of virus entry via endocytosis is critically important for the design of antiviral strategies. Virus entry via endocytosis is a complex process involving hundreds of cellular proteins. The entire process is dictated by events occurring at multiple time and length scales. In this review, we discuss and evaluate the available means to investigate virus endocytic entry, from both experimental and theoretical/numerical modeling fronts, and highlight the importance of multiscale features. The complexity of the process requires investigations at a systems biology level, which involves the combination of different experimental approaches, the collaboration of experimentalists and theorists across different disciplines, and the development of novel multiscale models.

On resistance to virus entry into host cells

In this article, we adopt a continuum model from Sun and Wirtz (2006. Biophys. J. 90:L10-L12) to show that, for the enveloped virus entry into host cells, the binding energy of the receptor-ligand complex can drive the engulfment of the viral particle to overcome the resistance alternatively dominated by the membrane deformation and cytoskeleton deformation at a different engulfing stage. This is contrary to the conclusions by Sun and Wirtz that the cytoskeleton deformation is always dominant. This discrepancy occurs because the energy of membrane deformation in their article is incorrect. Such an unfortunate small error has led to a severe underestimation of the contribution from membrane deformation to the total energy of the system, which then led them to improperly conclude that the cytoskeleton deformation plays the dominant role in the virus entry into host cell. By using the correct energy expression, our conclusion is justified by energy comparisons under a large range of virus sizes and Young's moduli of cytoskeleton. We even find that a critical radius of virus exists, beyond which the resistance to the virus engulfment becomes dominated by the membrane deformation during the whole stage, contrary to the point of view of Sun and Wirtz.

Encapsulation of a polyelectrolyte chain by an oppositely charged spherical surface

Using the ground state dominance approximation and a variational theory, we study the encapsulation of a polyelectrolyte chain by an oppositely charged spherical surface. The electrostatic attraction between the polyelectrolyte and the surface and the entropy loss of the encapsulated polyelectrolyte chain dictate the optimum conditions for encapsulation. Two scenarios of encapsulation are identified: entropy-dominated and adsorption-dominated encapsulation. In the entropy-dominated encapsulation regime, the polyelectrolyte chain is delocalized, and the optimum radius of the encapsulating sphere decreases with increasing the attraction. In the adsorption-dominated encapsulation regime, the polyelectrolyte chain is strongly localized near the surface, and the optimum radius increases with increasing the attraction. After identifying a universal encapsulation parameter, the dependencies of the optimum radius on the salt concentration, surface charge density, polymer charge density, and polymer length are explored.

Endocytosis at the nanoscale

Endocytosis is a fundamental process in which eukaryotic cells internalise molecules and macromolecules via deformation of the membrane and generation of membrane-bound carriers. Functional aspects are not only limited to uptake of nutrients, but also play a primary role in evolutionary conserved processes such as the regulation of plasma membrane protein activity (i.e. signal-transducing receptors, small-molecule transporters and ion channels), cell motility and mitosis. The macromolecular nature of the material transported by endocytosis makes this route one of the most important targets for nanomedicine. Indeed, many nanoparticle formulations have been customised to enter cells through endocytosis and deliver the cargo within the cell. In this critical review, we present an overview of the biology of endocytosis and discuss its implications in cell internalisation of nanoparticles. We discuss how nanoparticle size, shape and surface chemistry can control this process effectively. Finally, we discuss different drug delivery strategies on how to evade lysosomal degradation to promote effective release of the cargo (376 references).

VISUALIZING SOFT MATTER: MESOSCOPIC SIMULATIONS OF MEMBRANES, VESICLES AND NANOPARTICLES

Biological membranes have properties and behavior that emerge from the propagation of the molecular characteristics of their components across many scales. Artificial smart materials, such as drug delivery vehicles and nanoparticles, often rely on modifying naturally-occurring soft matter, such as polymers and lipid vesicles, so that they possess useful behavior. Mesoscopic simulations allow in silico experiments to be easily and cheaply performed on complex, soft materials requiring as input only the molecular structure of the constituents at a coarse-grained level. They can therefore act as a guide to experimenters prior to performing costly assays. Additionally, mesoscopic simulations provide the only currently feasible window on the length and time scales relevant to important biophysical processes such as vesicle fusion. We describe here recent work using Dissipative Particle Dynamics simulations to explore the structure and behavior of amphiphilic membranes, the fusion of vesicles, and the interactions between rigid nanoparticles and soft surfaces.

Wrapping and Internalization of Nanoparticles by Lipid Bilayers: a Computer Simulation Study

Endocytosis is a basic pathway for nanoparticles to enter or leave cells. However, because of the complexity of the cell membrane, the mechanism of endocytosis is largely elusive. By dissipative particle dynamics (DPD), we investigate the wrapping and internalization processes of different particles (e.g., spheres and ellipsoids) by a lipid vesicle. It is found that rotation is possibly an important mechanism in the particle internalization process under a strong adhesive interaction, which can adjust the configuration of the nanoparticle to the lipid bilayer and facilitate the progress of the wrapping. Furthermore, the fission behaviour of the vesicle and the wrapped particle is also observed when the lipid domain is considered in the system. These simulation results give an insight into the nature of endocytosis.

Virus-inspired design principles of nanoparticle-based bioagents

The highly effectiveness and robustness of receptor-mediated viral invasion of living cells shed lights on the biomimetic design of nanoparticle(NP)-based therapeutics. Through thermodynamic analysis, we elucidate that the mechanisms governing both the endocytic time of a single NP and the cellular uptake can be unified into a general energy-balance framework of NP-membrane adhesion and membrane deformation. Yet the NP-membrane adhesion strength is a globally variable quantity that effectively regulates the NP uptake rate. Our analysis shows that the uptake rate interrelatedly depends on the particle size and ligand density, in contrast to the widely reported size effect. Our model predicts that the optimal radius of NPs for maximal uptake rate falls in the range of 25–30 nm, and optimally several tens of ligands should be coated onto NPs. These findings are supported by both recent experiments and typical viral structures, and serve as fundamental principles for the rational design of NP-based nanomedicine.

Variable nanoparticle-cell adhesion strength regulates cellular uptake

In receptor-mediated endocytosis, cells exercise biochemical control over the mechanics of adhesion to engulf foreign particles, featuring a variable adhesion strength. Here we present a thermodynamic model with which we elucidate that the variable adhesion strength critically governs the cellular uptake, yielding an uptake phase diagram in the space of ligand density and particle size. We identify from the diagram an endocytosed phase with markedly high uptake, encompassed by a lower and an upper phase boundary that are set, respectively, by the enthalpic and entropic limits of the adhesion strength. The phase diagram may provide useful guidance to the rational design of nanoparticle-based therapeutic and diagnostic agents.

Organization of cellular receptors into a nanoscale junction during HIV-1 adhesion

The fusion of the human immunodeficiency virus type 1 (HIV-1) with its host cell is the target for new antiretroviral therapies. Viral particles interact with the flexible plasma membrane via viral surface protein gp120 which binds its primary cellular receptor CD4 and subsequently the coreceptor CCR5. However, whether and how these receptors become organized at the adhesive junction between cell and virion are unknown. Here, stochastic modeling predicts that, regarding binding to gp120, cellular receptors CD4 and CCR5 form an organized, ring-like, nanoscale structure beneath the virion, which locally deforms the plasma membrane. This organized adhesive junction between cell and virion, which we name the viral junction, is reminiscent of the well-characterized immunological synapse, albeit at much smaller length scales. The formation of an organized viral junction under multiple physiopathologically relevant conditions may represent a novel intermediate step in productive infection.

The entry of human immunodeficiency virus (HIV) into cells is the target for new therapies preventing HIV infection. While intermediate steps of viral entry have been characterized, the progression between these steps and how they result in productive infection are not well understood. By using stochastic modeling, we examine the initial interaction of a single viral particle with a flexible plasma membrane populated with viral receptors. The model predicts the formation of an organized receptor ultrastructure beneath the viral particle, which we name viral junction and which may contribute to productive viral infection. The organization of the viral junction depends on receptor density, CD4 bond stability, membrane mechanical flexibility, as well as viral protein organization and density.

Effects of Virus Size and Cell Stiffness on Forces, Work, and Pressures Driving Membrane Invagination in a Receptor-Mediated Endocytosis

A continuum model based on the contact mechanics theory was developed and used for evaluating virus indentation forces at the early stage of membrane invagination, as well as the work of the virus indentation forces and virus-cell contact pressures in a receptor-mediated endocytosis, depending on the virus size and virus/cell stiffnesses. The model indicated that early virus indentation forces are in the order of 1–10 pN and for a given extent of virus engulfment, they increase linearly with the elastic modulus of the host cell and also with the square of the virus radius. The work of invagination at the initial phase of virus endocytosis is in the order of tens of zeptojoules and peak virus-cell contact pressures at this stage are in the order of hundreds of Pascals to several kPa. For a given extent of virus engulfment, peak and average contact pressures increase linearly with the elastic modulus of the host cell but interestingly, they are negligibly affected by the virus size. The present model may be useful in the fields of cellular biomechanics, virology and nanodrug delivery to evaluate mechanical factors during the early phase of membrane invagination.

The tethered infinitesimal tori and spheres algorithm: a versatile calculator for axisymmetric problems in equilibrium membrane mechanics

Constrained minimization of energy functionals is a central part, and usually the difficult part, of solving problems in the equilibrium mechanics of biological and biomimetic membranes. The inherent difficulties of the conventional variational-calculus approach prevents the numerical calculation involved from being made routine in the analyses of experimental results. We have developed a simulated annealing-based computational technique for routinizing the task of constrained minimization of energy functionals governing whole, or small patches of whole, fluid membranes with axisymmetry, spherical topology, and no domains of inhomogeneity. In this article, we describe the essential principles of the technique and apply it to five examples to demonstrate its versatility. It gives membrane shapes that are automatically stable to axisymmetric perturbations. Presently, it can account for constraints on 1), the membrane area or the effective membrane tension; 2), the enclosed volume or the effective pressure difference across the membrane thickness; and 3), the axial end-to-end distance or the applied axial point force.

Mechanisms of receptor/coreceptor-mediated entry of enveloped viruses

Enveloped viruses enter host cells either through endocytosis, or by direct fusion of the viral envelope and the membrane of the host cell. However, some viruses, such as HIV-1, HSV-1, and Epstein-Barr can enter a cell through either mechanism, with the choice of pathway often a function of the ambient physical chemical conditions, such as temperature and pH. We develop a stochastic model that describes the entry process at the level of binding of viral glycoprotein spikes to cell membrane receptors and coreceptors. In our model, receptors attach the cell membrane to the viral membrane, while subsequent binding of coreceptors enables fusion. The model quantifies the competition between fusion and endocytotic entry pathways. Relative probabilities for each pathway are computed numerically, as well as analytically in the high viral spike density limit. We delineate parameter regimes in which fusion or endocytosis is dominant. These parameters are related to measurable and potentially controllable quantities such as membrane bending rigidity and receptor, coreceptor, and viral spike densities. Experimental implications of our mechanistic hypotheses are proposed and discussed.

Size and shape effects on diffusion and absorption of colloidal particles near a partially absorbing sphere: implications for uptake of nanoparticles in animal cells

A mechanics model describing how a cell membrane with diffusive mobile receptors wraps around a ligand-coated cylindrical or spherical particle has been recently developed to model the role of particle size in receptor-mediated endocytosis. The results show that particles in the size range of tens to hundreds of nanometers can enter cells even in the absence of clathrin or caveolin coats. Here we report further progress on modeling the effects of size and shape in diffusion, interaction, and absorption of finite-sized colloidal particles near a partially absorbing sphere. Our analysis indicates that, from the diffusion and interaction point of view, there exists an optimal hydrodynamic size of particles, typically in the nanometer regime, for the maximum rate of particle absorption. Such optimal size arises as a result of balance between the diffusion constant of the particles and the interaction energy between the particles and the absorbing sphere relative to the thermal energy. Particles with a smaller hydrodynamic radius have larger diffusion constant but weaker interaction with the sphere while larger particles have smaller diffusion constant but stronger interaction with the sphere. Since the hydrodynamic radius is also determined by the particle shape, an optimal hydrodynamic radius implies an optimal size as well as an optimal aspect ratio for a nonspherical particle. These results show broad agreement with experimental observations and may have general implications on interaction between nanoparticles and animal cells.