How does a virus bud?

Comparing Multifunctional Viral and Eukaryotic Proteins for Generating Scission Necks in Membranes

Deterministic formation of membrane scission necks by protein machinery with multiplexed functions is critical in biology. A microbial example is M2 viroporin, a proton pump from the influenza A virus that is multiplexed with membrane remodeling activity to induce budding and scission in the host membrane during viral maturation. In comparison, the dynamin family constitutes a class of eukaryotic proteins implicated in mitochondrial fission, as well as various budding and endocytosis pathways. In the case of Dnm1, the mitochondrial fission protein in yeast, the membrane remodeling activity is multiplexed with mechanoenzyme activity to create fission necks. It is not clear why these functions are combined in these scission processes, which occur in drastically different compositions and solution conditions. In general, direct experimental access to changing neck sizes induced by individual proteins or peptide fragments is challenging due to the nanoscale dimensions and influence of thermal fluctuations. Here, we use a mechanical model to estimate the size of scission necks by leveraging small-angle X-ray scattering structural data of protein-lipid systems under different conditions. The influence of interfacial tension, lipid composition, and membrane budding morphology on the size of the induced scission necks is systematically investigated using our data and molecular dynamic simulations. We find that the M2 budding protein from the influenza A virus has robust pH-dependent membrane activity that induces nanoscopic necks within the range of spontaneous hemifission for a broad range of lipid compositions. In contrast, the sizes of scission necks generated by mitochondrial fission proteins strongly depend on lipid composition, which suggests a role for mechanical constriction.

Mechanics of diffusion-mediated budding and implications for virus replication and infection

Budding allows virus replication and macromolecular secretion in cells through the formation of a membrane protrusion (bud) that evolves into an envelope. The largest energetic barrier to bud formation is membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are the main promotors of adhesion and can accommodate membrane bending thanks to an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane from remote regions to gather on the bud surface, thus, diffusivity controls the kinetics. This paper proposes a simple model to describe diffusion-mediated budding unravelling important size limitations and size-dependent kinetics. The predicted optimal virion radius, giving the fastest budding, is validated against experiments for coronavirus, HIV, flu and hepatitis. Assuming exponential replication of virions and hereditary size, the model can predict the size distribution of a virus population. This is verified against experiments for SARS-CoV-2. All the above comparisons rely on the premise that budding poses the tightest size constraint. This is true in most cases, as demonstrated in this paper, where the proposed model is extended to describe virus infection via receptor- and clathrin-mediated endocytosis, and via membrane fusion.

A proposed mathematical description of in vivo nanoparticle delivery

Nanoparticles are promising vehicles for the precise delivery of molecular therapies to diseased sites. Nanoparticles interact with a series of tissues and cells before they reach their target, which causes less than 1% of administered nanoparticles to be delivered to these target sites. Researchers have been studying the nano-bio interactions that mediate nanoparticle delivery to develop guidelines for designing nanoparticles with enhanced delivery properties. In this review article, we describe these nano-bio interactions with a series of mathematical equations that quantitatively define the nanoparticle delivery process. We employ a compartment model framework to describe delivery where nanoparticles are either (1) at the site of administration, (2) in the vicinity of target cells, (3) internalized by the target cells, or (4) sequestered away in off-target sites or eliminated from the body. This framework explains how different biological processes govern nanoparticle transport between these compartments, and the role of intercompartmental transport rates in determining the final nanoparticle delivery efficiency. Our framework provides guiding principles to engineer nanoparticles for improved targeted delivery.

Adhesive contact between cylindrical (Ebola) and spherical (SARS-CoV-2) viral particles and a cell membrane

A critical event during the process of cell infection by a viral particle is attachment, which is driven by adhesive interactions and resisted by bending and tension. The biophysics of this process has been studied extensively, but the additional role of externally applied force or displacement has generally been neglected. In this work, we study the adhesive force-displacement response of viral particles against a cell membrane. We have built two models: one in which the viral particle is cylindrical (say, representative of a filamentous virus such as Ebola) and another in which it is spherical (such as SARS-CoV-2 and Zika). Our interest is in initial adhesion, in which case deformations are small, and the mathematical model for the system can be simplified considerably. The parameters that characterize the process combine into two dimensionless groups that represent normalized membrane bending stiffness and tension. In the limit where bending dominates, for sufficiently large values of normalized bending stiffness, there is no adhesion between viral particles and the cell membrane without applied force. (The zero external force contact width and pull-off force are both zero.) For large values of normalized membrane tension, the adhesion between virus and cell membrane is weak but stable. (The contact width at zero external force has a small value.) Our results for pull-off force and zero force contact width help to quantify conditions that could aid the development of therapies based on denying the virus entry into the cell by blocking its initial adhesion.

Gaussian curvature and the budding kinetics of enveloped viruses

The formation of a membrane-enveloped virus starts with the assembly of a curved layer of capsid proteins lining the interior of the plasma membrane (PM) of the host cell. This layer develops into a spherical shell (capsid) enveloped by a lipid-rich membrane. In many cases, the budding process stalls prior to the release of the virus. Recently, Brownian dynamics simulations of a coarse-grained model system reproduced protracted pausing and stalling, which suggests that the origin of pausing/stalling is to be found in the physics of the budding process. Here, we propose that the pausing/stalling observed in the simulations can be understood as a purely kinetic phenomenon associated with the neck geometry. A geometrical potential energy barrier develops during the budding that must be overcome by capsid proteins diffusing along the membrane prior to incorporation into the capsid. The barrier is generated by a conflict between the positive Gauss curvature of the assembling capsid and the negative Gauss curvature of the neck region. A continuum theory description is proposed and is compared with the Brownian simulations of the budding of enveloped viruses.

Despite intense study, the life-cycle of the HIV-1 virus continues to pose mysteries. One of these is the fact that the assembly of an HIV-1 virus along the plasma membrane (PM) of the host cell—the budding process—stalls prior to release of the virus. Many other important viral pathogens with a surrounding lipid membrane envelope display similar stalling. Combining numerical and analytical methods, we demonstrate that the neck-like shape of the membrane that forms prior to release of the virus creates a barrier that blocks the proteins required for the assembly process from reaching the budding virus. An improved understanding of the physics of the blocking process could enable new strategies to combat enveloped viruses.

Why Enveloped Viruses Need Cores-The Contribution of a Nucleocapsid Core to Viral Budding

During the lifecycle of many enveloped viruses, a nucleocapsid core buds through the cell membrane to acquire an outer envelope of lipid membrane and viral glycoproteins. However, the presence of a nucleocapsid core is not required for assembly of infectious particles. To determine the role of the nucleocapsid core, we develop a coarse-grained computational model with which we investigate budding dynamics as a function of glycoprotein and nucleocapsid interactions, as well as budding in the absence of a nucleocapsid. We find that there is a transition between glycoprotein-directed budding and nucleocapsid-directed budding that occurs above a threshold strength of nucleocapsid interactions. The simulations predict that glycoprotein-directed budding leads to significantly increased size polydispersity and particle polymorphism. This polydispersity can be explained by a theoretical model accounting for the competition between bending energy of the membrane and the glycoprotein shell. The simulations also show that the geometry of a budding particle leads to a barrier to subunit diffusion, which can result in a stalled, partially budded state. We present a phase diagram for this and other morphologies of budded particles. Comparison of these structures against experiments could establish bounds on whether budding is directed by glycoprotein or nucleocapsid interactions. Although our model is motivated by alphaviruses, we discuss implications of our results for other enveloped viruses.

Entry of nanoparticles into cells: the importance of nanoparticle properties

Knowledge of the interactions between nanoparticles (NPs) and cell membranes is of great importance for the design of safe and efficient nanomedicines.

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.

Mechanisms of virus assembly

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.

Probing the Effect of Random Adhesion Energy on Receptor-Mediated Endocytosis With a Semistochastic Model

The cellular uptake of a particle through receptor-mediated endocytosis involves specific binding between ligands on the particle surface and diffusive receptors on the cell membrane. Since the rupture force of these specific bonds is generally random, the same can be the associated adhesion energy. To probe the effect of this randomness, we present a semistochastic model of receptor-mediated endocytosis, in which the adhesion energy between particle and membrane is regarded as a stochastic parameter obeying Boltzmann's distribution. It is shown that the so-called speed factor varies and that the rate of uptake is much lower than that from a previous deterministic model. It is also found that a spontaneous curvature can significantly increase the rate of uptake for particles of certain sizes. When constraining the random adhesion energy, we find that the rate of uptake can substantially increase. This work suggests that adhesion energy may be actively regulated during receptor-mediated endocytosis to improve the efficiency. By adopting random adhesion energy in the analysis, the physical picture of endocytosis implicated by the current work can be fundamentally different from that by a previous deterministic model.

Dynamics of self-assembly of model viral capsids in the presence of a fluctuating membrane

A coarse-grained computational model is used to investigate the effect of a fluctuating fluid membrane on the dynamics of patchy-particle assembly into virus capsid-like cores. Results from simulations for a broad range of parameters are presented, showing the effect of varying interaction strength, membrane stiffness, and membrane viscosity. Furthermore, the effect of hydrodynamic interactions is investigated. Attraction to a membrane may promote assembly, including for subunit interaction strengths for which it does not occur in the bulk, and may also decrease single-core assembly time. The membrane budding rate is strongly increased by hydrodynamic interactions. The membrane deformation rate is important in determining the finite-time yield. Higher rates may decrease the entropic penalty for assembly and help guide subunits toward each other but may also block partial cores from being completed. For increasing subunit interaction strength, three regimes with different effects of the membrane are identified.

Theoretical studies on assembly, physical stability and dynamics of viruses

All matter has to obey the general laws of physics and living matter is not an exception. Viruses have not only learnt how to cope with them, but have managed to use them for their own survival. In this chapter we will review some of the exciting physics behind viruses and discuss simple physical models that can shed some light on different aspects of the viral life cycle and viral properties. In particular, we will focus on how the structure and shape of the capsid, its assembly and stability, and the entry and exit of viral particles and their genomes can be understood using fundamental physics theories.

Modeling receptor-mediated endocytosis via mechanics of cell adhesion

A mathematical 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 particle size effects in receptor mediated endocytosis. The model predicted an optimal particle size for the smallest wrapping time, as well as a minimum and a maximum particle size for successful wrapping. The results showed 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 some further progresses on modeling a spontaneous membrane curvature induced by clathrin or caveolin coats at the inner membrane leaflet as well as simultaneous entry of many particles into cells. It is found that a spontaneous membrane curvature narrows the particle size range for successful wrapping and there exists an optimal particle density for maximum particle adsorptivity.

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.

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.

Cellular Biophysics: Bacterial Endospore, Membranes and Random Fluctuation

Purposeful motion of biological processes can be driven by Brownian motion of macromolecular complexes with one-sided binding biasing movement in one direction: a Brownian ratchet, now proposed to explain membrane motion during a phagocytosis-like process in bacteria.

Mechanics of receptor-mediated endocytosis

Most viruses and bioparticles endocytosed by cells have characteristic sizes in the range of tens to hundreds of nanometers. The process of viruses entering and leaving animal cells is mediated by the binding interaction between ligand molecules on the viral capid and their receptor molecules on the cell membrane. How does the size of a bioparticle affect receptor-mediated endocytosis? Here, we study how a cell membrane containing diffusive mobile receptors wraps around a ligand-coated cylindrical or spherical particle. It is shown that particles in the size range of tens to hundreds of nanometers can enter or exit cells via wrapping even in the absence of clathrin or caveolin coats, and an optimal particles size exists for the smallest wrapping time. This model can also be extended to include the effect of clathrin coat. The results seem to show broad agreement with experimental observations.

A statistical-thermodynamic model of viral budding

We present a simple statistical thermodynamic model for budding of viral nucleocapsids at the cell membrane. The membrane is modeled as a flexible lipid bilayer embedding linker (spike) proteins, which serve to anchor and thus wrap the membrane around the viral capsids. The free energy of a single bud is expressed as a sum of the bending energy of its membrane coat, the spike-mediated capsid-membrane adhesion energy, and the line energy associated with the bud's rim, all depending on the extent of wrapping (i.e., bud size), and density of spikes in the curved membrane. This self-energy is incorporated into a simple free energy functional for the many-bud system, allowing for different spike densities, and hence entropy, in the curved (budding) and planar membrane regions, as well as for the configurational entropy of the polydisperse bud population. The equilibrium spike densities in the coexisting, curved and planar, membrane regions are calculated as a function of the membrane bending energy and the spike-mediated adhesion energy, for different spike and nucleocapsid concentrations in the membrane plane, as well as for several values of the bud's rim energy. We show that complete budding (full wrapping of nucleocapsids) can only take place if the adhesion energy exceeds a certain, critical, bending free energy. Whenever budding takes place, the spike density in the mature virions is saturated, i.e., all spike adhesion sites are occupied. The rim energy plays an important role in determining the size distribution of buds. The fraction of fully wrapped buds increases as this energy increases, resulting eventually in an all-or-nothing mechanism, whereby nucleocapsids at the plasma membrane are either fully enveloped or completely naked (just touching the membrane). We also find that at low concentrations all capsids arriving at the membrane get tightly and fully enveloped. Beyond a certain concentration, corresponding approximately to a stoichiometric spike/capsid ratio, newly arriving capsids cannot be fully wrapped; i.e., the budding yield decreases.

The alphaviruses: gene expression, replication, and evolution

The alphaviruses are a genus of 26 enveloped viruses that cause disease in humans and domestic animals. Mosquitoes or other hematophagous arthropods serve as vectors for these viruses. The complete sequences of the +/- 11.7-kb plus-strand RNA genomes of eight alphaviruses have been determined, and partial sequences are known for several others; this has made possible evolutionary comparisons between different alphaviruses as well as comparisons of this group of viruses with other animal and plant viruses. Full-length cDNA clones from which infectious RNA can be recovered have been constructed for four alphaviruses; these clones have facilitated many molecular genetic studies as well as the development of these viruses as expression vectors. From these and studies involving biochemical approaches, many details of the replication cycle of the alphaviruses are known. The interactions of the viruses with host cells and host organisms have been exclusively studied, and the molecular basis of virulence and recovery from viral infection have been addressed in a large number of recent papers. The structure of the viruses has been determined to about 2.5 nm, making them the best-characterized enveloped virus to date. Because of the wealth of data that has appeared, these viruses represent a well-characterized system that tell us much about the evolution of RNA viruses, their replication, and their interactions with their hosts. This review summarizes our current knowledge of this group of viruses.

The alphaviruses: gene expression, replication, and evolution

The alphaviruses are a genus of 26 enveloped viruses that cause disease in humans and domestic animals. Mosquitoes or other hematophagous arthropods serve as vectors for these viruses. The complete sequences of the +/- 11.7-kb plus-strand RNA genomes of eight alphaviruses have been determined, and partial sequences are known for several others; this has made possible evolutionary comparisons between different alphaviruses as well as comparisons of this group of viruses with other animal and plant viruses. Full-length cDNA clones from which infectious RNA can be recovered have been constructed for four alphaviruses; these clones have facilitated many molecular genetic studies as well as the development of these viruses as expression vectors. From these and studies involving biochemical approaches, many details of the replication cycle of the alphaviruses are known. The interactions of the viruses with host cells and host organisms have been exclusively studied, and the molecular basis of virulence and recovery from viral infection have been addressed in a large number of recent papers. The structure of the viruses has been determined to about 2.5 nm, making them the best-characterized enveloped virus to date. Because of the wealth of data that has appeared, these viruses represent a well-characterized system that tell us much about the evolution of RNA viruses, their replication, and their interactions with their hosts. This review summarizes our current knowledge of this group of viruses.