Kinetics of virus entry by endocytosis

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.

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.

Synthesis, Self-Assembly and In Vitro Cellular Uptake Kinetics of Nanosized Drug Carriers Based on Aggregates of Amphiphilic Oligomers of N-Vinyl-2-pyrrolidone

Development of nanocarrier-based drug delivery systems is a major breakthrough in pharmacology, promising targeted delivery and reduction in drug toxicity. On the cellular level, encapsulation of a drug substantially affects the endocytic processes due to nanocarrier–membrane interaction. In this study we synthesized and characterized nanocarriers assembled from amphiphilic oligomers of N-vinyl-2-pyrrolidone with a terminal thiooctadecyl group (PVP-OD). It was found that the dissolution free energy of PVP-OD depends linearly on the molecular mass of its hydrophilic part up to M¯n = 2 × 10⁴, leading to an exponential dependence of critical aggregation concentration (CAC) on the molar mass. A model hydrophobic compound (DiI dye) was loaded into the nanocarriers and exhibited slow release into the aqueous phase on a scale of 18 h. Cellular uptake of the loaded nanocarriers and that of free DiI were compared in vitro using glioblastoma (U87) and fibroblast (CRL2429) cells. While the uptake of both DiI/PVP-OD nanocarriers and free DiI was inhibited by dynasore, indicating a dynamin-dependent endocytic pathway as a major mechanism, a decrease in the uptake rate of free DiI was observed in the presence of wortmannin. This suggests that while macropinocytosis plays a role in the uptake of low-molecular components, this pathway might be circumvented by incorporation of DiI into nanocarriers.

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.

Virology from the perspective of theoretical colloid and interface science

Viral infections occur at very different length and time scales and include various processes, which can often be described using the models developed and/or employed in colloid and interface science. Bearing in mind the currently active COVID-19, I discuss herein the models aimed at viral transmission via respiratory droplets and the contact of virions with the epithelium. In a more general context, I outline the models focused on penetration of virions via the cellular membrane, initial stage of viral genome replication, and formation of viral capsids in cells. In addition, the models related to a new generation of drug delivery vehicles, for example, lipid nanoparticles with size about 100-200 nm, are discussed as well. Despite the high current interest in all these processes, their understanding is still limited, and this area is open for new theoretical studies.

Chemodynamic features of nanoparticles: Application to understanding the dynamic life cycle of SARS-CoV-2 in aerosols and aqueous biointerfacial zones

We review concepts involved in describing the chemodynamic features of nanoparticles and apply the framework to gain physicochemical insights into interactions between SARS-CoV-2 virions and airborne particulate matter (PM). Our analysis is highly pertinent given that the World Health Organisation acknowledges that SARS-CoV-2 may be transmitted by respiratory droplets, and the US Center for Disease Control and Prevention recognises that airborne transmission of SARS-CoV-2 can occur. In our theoretical treatment, the virion is assimilated to a core-shell nanoparticle, and contributions of various interaction energies to the virion-PM association (electrostatic, hydrophobic, London-van der Waals, etc.) are generically included. We review the limited available literature on the physicochemical features of the SARS-CoV-2 virion and identify knowledge gaps. Despite the lack of quantitative data, our conceptual framework qualitatively predicts that virion-PM entities are largely able to maintain equilibrium on the timescale of their diffusion towards the host cell surface. Comparison of the relevant mass transport coefficients reveals that virion biointernalization demand by alveolar host cells may be greater than the diffusive supply. Under such conditions both the free and PM-sorbed virions may contribute to the transmitted dose. This result points to the potential for PM to serve as a shuttle for delivery of virions to host cell targets. Thus, our critical review reveals that the chemodynamics of virion-PM interactions may play a crucial role in the transmission of COVID-19, and provides a sound basis for explaining reported correlations between episodes of air pollution and outbreaks of COVID-19.

Virions and respiratory droplets in air: Diffusion, drift, and contact with the epithelium

Some infections, including e.g. influenza and currently active COVID 19, may be transmitted via air during sneezing, coughing, and talking. This pathway occurs via diffusion and gravity-induced drift of single virions and respiratory droplets consisting primarily of water, including small fraction of nonvolatile matter, and containing virions. These processes are accompanied by water evaporation resulting in reduction of the droplet size. The manifold of information concerning these steps is presented in textbooks and articles not related to virology and the focus is there frequently on biologically irrelevant conditions and/or droplet sizes. In this brief review, we systematically describe the behavior of virions and virion-carrying droplets in air with emphasis on various regimes of diffusion, drift, and evaporation, and estimate the rates of all these steps under virologically relevant conditions. In addition, we discuss the kinetic aspects of the first steps of infection after attachment of virions or virion-carrying droplets to the epithelium, i.e., virion diffusion in the mucus and periciliary layers, penetration into the cells, and the early stage of replication. The presentation is oriented to virologists who are interested in the corresponding physics and to physicists who are interested in application of the physics to virology.

Intracellular RNA delivery by lipid nanoparticles: Diffusion, degradation, and release

Various RNAs (siRNAs, miRNAs, or mRNAs) can be delivered into cells by lipid nanoparticles (LNPs) of 50-150 nm in diameter. The subsequent RNA release from LNPs may occur via various scenarios. Herein, two related kinetic models are proposed. The first model takes into account that LNPs are often porous so that RNA molecules diffuse in and detach from nanopores. The analysis is focused on RNA diffusion from a pore. The analytical expression obtained for the RNA escape rate constant is used to identify the difference in the release of siRNAs, miRNAs, and mRNAs. The key message here is that the mRNA diffusion from pores appears to be too slow, and accordingly the mRNA release seems to occur primarily via degradation of LNPs. The second coarse-grained model describes the diffusion-mediated release of RNA from a LNP in the situation when this process is accompanied by the LNP degradation at the lipid-solution interface. The corresponding kinetics are shown in detail at different relative rates of the RNA diffusion and LNP degradation. Potentially, this can help to interpret drug plasma levels after various dosing regimens.

A Theoretical Analysis of Receptor-Mediated Endocytosis of Nanoparticles in Wall Shear Flow

This study theoretically investigates receptor–ligand-mediated endocytosis of nanoparticles (NPs) in wall shear flow. The endocytosis is modeled as a birth–death process and relationships between coefficients in the model and the wall shear rate have been derived to deal with the effects of the shear flow. Model predictions show that flow-induced alteration in bond formation rates does not affect the endocytosis significantly, and the suppression of hydrodynamic load on endocytosis is eminent only when diameters of NPs are large (around 700[Formula: see text]nm) and the shear rate is sufficiently high. In the latter case, it is shown that the hydrodynamic load suppresses the initial attachment of NPs to cells more than the following internalization. The model also predicts that shear-promoted expression of certain ligands can lead to observable increase in the number of endocytozed NPs in typical flow-chamber experiments, and the promotion can also cause selective endocytosis of NPs by cells at high shear rate regions if the ligand surface density on NPs or the original expression of receptors on cells in the absence of flow is low.

The role of the encapsulated cargo in microcompartment assembly

Bacterial microcompartments are large, roughly icosahedral shells that assemble around enzymes and reactants involved in certain metabolic pathways in bacteria. Motivated by microcompartment assembly, we use coarse-grained computational and theoretical modeling to study the factors that control the size and morphology of a protein shell assembling around hundreds to thousands of molecules. We perform dynamical simulations of shell assembly in the presence and absence of cargo over a range of interaction strengths, subunit and cargo stoichiometries, and the shell spontaneous curvature. Depending on these parameters, we find that the presence of a cargo can either increase or decrease the size of a shell relative to its intrinsic spontaneous curvature, as seen in recent experiments. These features are controlled by a balance of kinetic and thermodynamic effects, and the shell size is assembly pathway dependent. We discuss implications of these results for synthetic biology efforts to target new enzymes to microcompartment interiors.

Membrane Deformation Induces Clustering of Norovirus Bound to Glycosphingolipids in a Supported Cell-Membrane Mimic

Quartz crystal microbalance with dissipation monitoring and total internal reflection fluorescence microscopy have been used to investigate binding of norovirus-like particles (noroVLPs) to a supported (phospho)lipid bilayer (SLB) containing a few percent of H or B type 1 glycosphingolipid (GSL) receptors. Although neither of these GSLs spontaneously form domains, noroVLPs were observed to form micron-sized clusters containing typically up to about 30 VLP copies, especially for B type 1, which is a higher-affinity receptor. This novel finding is explained by proposing a model implying that VLP-induced membrane deformation promotes VLP clustering, a hypothesis that was further supported by observing that functionalized gold nanoparticles were able to locally induce SLB deformation. Because similar effects are likely possible also at cellular membranes, our findings are interesting beyond a pure biophysicochemical perspective as they shed new light on what may happen during receptor-mediated uptake of viruses as well as nanocarriers in drug delivery.

Kinetics of lipid-nanoparticle-mediated intracellular mRNA delivery and function

mRNA delivery into cells forms the basis for one of the new and promising ways to treat various diseases. Among suitable carriers, lipid nanoparticles (LNPs) with a size of about 100 nm are now often employed. Despite high current interest in this area, the understanding of the basic details of LNP-mediated mRNA delivery and function is limited. To clarify the kinetics of mRNA release from LNPs, the author uses three generic models implying (i) exponential, (ii) diffusion-controlled, and (iii) detachment-controlled kinetic regimes, respectively. Despite the distinct differences in these kinetics, the associated transient kinetics of mRNA translation to the corresponding protein and its degradation are shown to be not too sensitive to the details of the mRNA delivery by LNPs (or other nanocarriers). In addition, the author illustrates how this protein may temporarily influence the expression of one gene or a few equivalent genes. The analysis includes positive or negative regulation of the gene transcription via the attachment of the protein without or with positive or negative feedback in the gene expression. Stable, bistable, and oscillatory schemes have been scrutinized in this context.

Multivalent ligand-receptor-mediated interaction of small filled vesicles with a cellular membrane

The ligand-receptor-mediated contacts of small sub-100-nm-sized lipid vesicles (or nanoparticles) with the cellular membrane are of interest in the contexts of cell-to-cell communication, endocytosis of membrane-coated virions, and drug (RNA) delivery. In all these cases, the interior of vesicles is filled by biologically relevant content. Despite the diversity of such systems, the corresponding ligand-receptor interaction possesses universal features. One of them is that the vesicle-membrane contacts can be accompanied by the redistribution of ligands and receptors between the contact and contact-free regions. In particular, the concentrations of ligands and receptors may become appreciably higher in the contact regions and their composition may there be different compared to that in the suspended state in the solution. A statistical model presented herein describes the corresponding distribution of various ligands and receptors and allows one to calculate the related change of the free energy with variation of the vesicle-engulfment extent. The results obtained are used to clarify the necessary conditions for the vesicle-assisted pathway of drug delivery.

Interaction of Virus-Like Particles with Vesicles Containing Glycolipids: Kinetics of Detachment

Many viruses interact with their host cells via glycosphingolipids (GSLs) and/or glycoproteins present on the outer cell membrane. This highly specific interaction includes virion attachment and detachment. The residence time determined by the detachment is particularly interesting, since it is directly related to internalization and infection as well as to virion egress and spreading. In an attempt to deepen the understanding of virion detachment kinetics, we have used total internal reflection fluorescence (TIRF) microscopy to probe the interaction between individual fluorescently labeled GSL-containing lipid vesicles and surface-bound virus-like particles (VLPs) of a norovirus genotype II.4 strain. The distribution of the VLP-vesicle residence time was investigated for seven naturally occurring GSLs, all of which are candidates for the not yet identified receptor(s) mediating norovirus entry into host cells. As expected for interactions involving multiple GSL binding sites at a viral capsid, the detachment kinetics displayed features typical for a broad activation-energy distribution for all GSLs. Detailed inspection of these distributions revealed significant differences among the different GSLs. The results are discussed in terms of strength of the interaction, vesicle size, as well as spatial distribution and clustering of GSLs in the vesicle membrane.