Model of human immunodeficiency virus budding and self-assembly: role of the cell membrane

Theoretical Studies on Assembly, Physical Stability, and Dynamics of Viruses

All matter must 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 that are 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 viral capsid, its assembly and stability, and the entry and exit of viral particles and their genomes can be explained using fundamental physics theories.

HIV-1 diverts cortical actin for particle assembly and release

Enveloped viruses assemble and bud from the host cell membranes. Any role of cortical actin in these processes have often been a source of debate. Here, we assessed if cortical actin was involved in HIV-1 assembly in infected CD4 T lymphocytes. Our results show that preventing actin branching not only increases HIV-1 particle release but also the number of individual HIV-1 Gag assembly clusters at the T cell plasma membrane. Indeed, in infected T lymphocytes and in in vitro quantitative model systems, we show that HIV-1 Gag protein prefers areas deficient in F-actin for assembling. Finally, we found that the host factor Arpin, an inhibitor of Arp2/3 branched actin, is recruited at the membrane of infected T cells and it can associate with the viral Gag protein. Altogether, our data show that, for virus assembly and particle release, HIV-1 prefers low density of cortical actin and may favor local actin debranching by subverting Arpin.

Self-assembly of polyhedral bilayer vesicles from Piezo ion channels

Piezo ion channels underlie many forms of mechanosensation in vertebrates and have been found to bend the membrane into strongly curved dome shapes. We develop a methodology describing the self-assembly of lipids and Piezo proteins into polyhedral bilayer vesicles. We validate this methodology for bilayer vesicles formed from bacterial mechanosensitive channels of small conductance, for which experiments found a polyhedral arrangement of proteins with snub cube symmetry and a well-defined characteristic vesicle size. On this basis, we calculate the self-assembly diagram for polyhedral bilayer vesicles formed from Piezo proteins. We find that the radius of curvature of the Piezo dome provides a critical control parameter for the self-assembly of Piezo vesicles, with high abundances of Piezo vesicles with octahedral, icosahedral, and snub cube symmetry with increasing Piezo dome radius of curvature.

Rapid formation of human immunodeficiency virus-like particles

Understanding the molecular mechanisms involved in the assembly of viruses is essential for discerning how viruses transmit from cell to cell and host to host. Although molecular aspects of assembly have been studied for many viruses, we still have little information about these events in real time. Enveloped viruses such as HIV that assemble at, and bud from, the plasma membrane have been studied in some detail using live cell fluorescence imaging techniques; however, these approaches provide little information about the real-time morphological changes that take place as viral components come together to form individual virus particles. Here we used correlative scanning ion conductance microscopy and fluorescence confocal microscopy to measure the topological changes, together with the recruitment of fluorescently labeled viral proteins such as Gag and Vpr, during the assembly and release of individual HIV virus-like particles (VLPs) from the top, nonadherent surfaces of living cells. We show that 1) labeling of viral proteins with green fluorescent protein affects particle formation, 2) the kinetics of particle assembly on different plasma membrane domains can vary, possibly as a consequence of differences in membrane biophysical properties, and 3) VLPs budding from the top, unimpeded surface of cells can reach full size in 20 s and disappear from the budding site in 0.5 to 3 min from the moment curvature is initially detected, significantly faster than has been previously reported.

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.

Piezo's membrane footprint and its contribution to mechanosensitivity

Piezo1 is an ion channel that gates open when mechanical force is applied to a cell membrane, thus allowing cells to detect and respond to mechanical stimulation. Molecular structures of Piezo1 reveal a large ion channel with an unusually curved shape. This study analyzes how such a curved ion channel interacts energetically with the cell membrane. Through membrane mechanical calculations, we show that Piezo1 deforms the membrane shape outside the perimeter of the channel into a curved 'membrane footprint'. This membrane footprint amplifies the sensitivity of Piezo1 to changes in membrane tension, rendering it exquisitely responsive. We assert that the shape of the Piezo channel is an elegant example of molecular form evolved to optimize a specific function, in this case tension sensitivity. Furthermore, the predicted influence of the membrane footprint on Piezo gating is consistent with the demonstrated importance of membrane-cytoskeletal attachments to Piezo gating.

Immature HIV-1 lattice assembly dynamics are regulated by scaffolding from nucleic acid and the plasma membrane

The packaging and budding of Gag polyprotein and viral RNA is a critical step in the HIV-1 life cycle. High-resolution structures of the Gag polyprotein have revealed that the capsid (CA) and spacer peptide 1 (SP1) domains contain important interfaces for Gag self-assembly. However, the molecular details of the multimerization process, especially in the presence of RNA and the cell membrane, have remained unclear. In this work, we investigate the mechanisms that work in concert between the polyproteins, RNA, and membrane to promote immature lattice growth. We develop a coarse-grained (CG) computational model that is derived from subnanometer resolution structural data. Our simulations recapitulate contiguous and hexameric lattice assembly driven only by weak anisotropic attractions at the helical CA-SP1 junction. Importantly, analysis from CG and single-particle tracking photoactivated localization (spt-PALM) trajectories indicates that viral RNA and the membrane are critical constituents that actively promote Gag multimerization through scaffolding, while overexpression of short competitor RNA can suppress assembly. We also find that the CA amino-terminal domain imparts intrinsic curvature to the Gag lattice. As a consequence, immature lattice growth appears to be coupled to the dynamics of spontaneous membrane deformation. Our findings elucidate a simple network of interactions that regulate the early stages of HIV-1 assembly and budding.

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.

Simulations show that virus assembly and budding are facilitated by membrane microdomains

For many viruses, assembly and budding occur simultaneously during virion formation. Understanding the mechanisms underlying this process could promote biomedical efforts to block viral propagation and enable use of capsids in nanomaterials applications. To this end, we have performed molecular dynamics simulations on a coarse-grained model that describes virus assembly on a fluctuating lipid membrane. Our simulations show that the membrane can promote association of adsorbed subunits through dimensional reduction, but it also introduces thermodynamic and kinetic effects that can inhibit complete assembly. We find several mechanisms by which membrane microdomains, such as lipid rafts, reduce these effects, and thus, enhance assembly. We show how these predicted mechanisms can be experimentally tested. Furthermore, the simulations demonstrate that assembly and budding depend crucially on the system dynamics via multiple timescales related to membrane deformation, protein diffusion, association, and adsorption onto the membrane.

Shape and energy of a membrane bud induced by protein coats or viral protein assembly

Intracellular transport vesicles and enveloped virus production is mediated by the polymerization of proteins that form bi-dimensional curved and rigid structures, or "coats", on a membrane. Using the classical framework of fluid membrane elasticity, we compute numerically the shape and the mechanical energy of the membrane deformation induced by a coat at different stage of growth. We furthermore derive analytical approximate expressions for the membrane shape and energy. They are found to be very accurate when compared to numerical calculations. These analytical expressions should be useful when building a relevant model of coat polymerization kinetics. We also discuss some consequences of the membrane energy features on the coat assembly process, showing that at high tension a kinetically arrested state of incomplete assembly could exist.

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.

Influence of fluctuating membranes on self-assembly of patchy colloids

A coarse-grained computational model is used to investigate the effect of a fluid membrane on patchy-particle assembly into biologically relevant structures motivated by viral cores and clathrin. For cores, we demonstrate a nonmonotonic dependence of the promotion of assembly on membrane stiffness. If the membrane is significantly deformable, cores are enveloped in buds, although this effect is suppressed for very flexible membranes. In the less deformable regime, we observe no marked enhancement for cores, even for strong adhesion to the surface. For clathrinlike particles, we again observe the formation of buds, whose morphology depends on membrane flexibility.

Mechanisms of budding of nanoscale particles through lipid bilayers

We examine the budding of a nanoscale particle through a lipid bilayer using molecular dynamics simulations, free energy calculations, and an elastic theory, with the aim of determining the extent to which equilibrium elasticity theory can describe the factors that control the mechanism and efficiency of budding. The particle is a smooth sphere which experiences attractive interactions to the lipid head groups. Depending on the parameters, we observe four classes of dynamical trajectories: particle adhesion to the membrane, stalled partially wrapped states, budding followed by scission, and membrane rupture. In most regions of parameter space we find that the elastic theory agrees nearly quantitatively with the simulated phase behavior as a function of adhesion strength, membrane bending rigidity, and particle radius. However, at parameter values near the transition between particle adhesion and budding, we observe long-lived partially wrapped states which are not captured by existing elastic theories. These states could constrain the accessible system parameters for those enveloped viruses or drug delivery vehicles which rely on exo- or endocytosis for membrane transport.