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While cells offer numerous inspiring examples in which membrane morphology and function are controlled by interactions with viruses or proteins, we still lack design principles for controlling membrane morphology in synthetic systems. With experiments and simulations, we show that spherical nanoparticles binding to lipid-bilayer membrane vesicles results in a remarkably rich set of collective morphologies that are controllable via the particle binding energy. We separately study cationic and anionic particles, where the adhesion is tuned by addition of oppositely charged lipids to the vesicles. When the binding energy is weak relative to a characteristic membrane-bending energy, vesicles adhere to one another and form a soft solid gel, a novel and useful platform for controlled release. With larger binding energy, a transition from partial to complete wrapping of the nanoparticles causes a remarkable vesicle destruction process culminating in rupture, nanoparticle-membrane tubules, and an apparent inversion of the vesicles. These findings help unify the diverse phenomena observed previously. They also open the door to a new class of vesicle-based, closed-cell gels that are more than 99% water and can encapsulate and release on demand, and show how to drive intentional membrane remodeling for shape-responsive systems.

Virus coat proteins of small isometric plant viruses readily assemble into symmetric, icosahedral cages encapsulating noncognate cargo, provided the cargo meets a minimal set of chemical and physical requirements. While this capability has been intensely explored for certain virus-enabled nanotechnologies, additional applications require lower symmetry than that of an icosahedron. Here, we show that the coat proteins of an icosahedral virus can efficiently assemble around metal nanorods into spherocylindrical closed shells with hexagonally close-packed bodies and icosahedral caps. Comparison of chiral angles and packing defects observed by in situ atomic force microscopy with those obtained from molecular dynamics models offers insight into the mechanism of growth, and the influence of stresses associated with intrinsic curvature and assembly pathways.

The precise control of assembly and packing of proteins and colloids on curved surfaces has fundamental implications in nanotechnology. In this paper, we describe dynamical simulations of the self-assembly of conical subunits around a spherocylindrical template, and a continuum theory for the bending energy of a triangular lattice with spontaneous curvature on a surface with arbitrary curvature. We find that assembly depends sensitively on mismatches between subunit spontaneous curvature and the mean curvature of the template, as well as anisotropic curvature of the template (mismatch between the two principal curvatures). Our simulations predict assembly morphologies that closely resemble those observed in experiments in which virus capsid proteins self-assemble around metal nanorods. Below a threshold curvature mismatch, our simulations identify a regime of optimal assembly leading to complete, symmetrical particles. Outside of this regime we observe defective particles, whose morphologies depend on the degree of curvature mismatch. To learn how assembly is affected by the nonuniform curvature of a spherocylinder, we also study the simpler cases of assembly around spherical and cylindrical cores. Our results show that both the intrinsic (Gaussian) and extrinsic (mean) curvatures of a template play significant roles in guiding the assembly of anisotropic subunits, providing a rich design space for the formation of nanoscale materials.

During the life cycle of a virus, viral proteins and other components self-assemble to form an ordered protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article, we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly and thus should be taken into account in models that are used to estimate interaction parameters from experimental data.

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., Author summary 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.

We study the flow properties of red blood cells in confined channels, when the channel width is comparable to the cell size. We focus on the case of intermediate concentrations when hydrodynamic interactions between cells play a dominant role. This regime is different to the case of low concentration in which the cells behave as hydrodynamically isolated. In this last case, the dynamic behavior is entirely controlled by the interplay between the interaction with the wall and the elastic response of the cell membrane. Our results highlight the different fluid properties when collective flow is present. The cells acquire a characteristic slipper shape, and parachute shapes are only observed at very large capillary numbers. We have characterized the spatial ordering and the layering by means of a pairwise correlation function. Focusing effects are observed at the core of the channel instead of at the lateral position typical of the single-train case. These results indicate that at these intermediate concentrations we observed at the microscale the first steps of the well-known macroscopic Fahraeus-Lindqvist effect. The rheological properties of the suspension are studied by means of the effective viscosity, with an expected shear-thinning behavior. Two main differences are obtained with respect to the single-train case. First, a large magnitude of the viscosity is obtained indicating a high resistance to flow. Secondly, the shear-thinning behavior is obtained at larger values of the capillary number respect to the single-train case. These results suggest that the phenomena of ordering in space and orientation occur at higher values of the capillary number.

Biological membranes are complex structures whose mechanics are usually described at a mesoscopic level, such as the Helfrich bending theory. In this article, we present the phase-field methods, a useful tool for studying complex membrane problems which can be applied to very different phenomena. We start with an overview of the general theory of elasticity, paying special attention to its derivation from a molecular scale. We then study the particular case of membrane elasticity, explicitly obtaining the Helfrich bending energy. Within the framework of this theory, we derive a phase-field model for biological membranes and explore its physical basis and interpretation in terms of membrane elasticity. We finally explain three examples of applications of these methods to membrane related problems. First, the case of vesicle pearling and tubulation, when lipidic vesicles are exposed to the presence of hydrophobic polymers that anchor to the membrane, inducing a shape instability. Finally, we study the behavior of red blood cells while flowing in narrow microchannels, focusing on the importance of membrane elasticity to the cell flow capabilities.

We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high confinement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.

We study the focusing of red blood cells and vesicles in pressure-driven flows in highly confined microchannels (10–30 μm), identifying the control parameters that dictate the cell distribution along the channel. Our results show that an increase in the flow velocity leads to a sharper cell distribution in a lateral position of the channel. This position depends on the channel width, with cells flowing at outer (closer to the walls) positions in thicker channels. We also study the relevance of the object shape, exploring the different behaviour of red blood cells and different vesicles. We also analyze the implications of these phenomena in the cell suspension rheology, highlighting the crucial role of the wall confinement in the rheological properties of the suspension.

Red blood cells are highly sensitive to changes in the relative areas of the two lipid leaflets of the cell membrane. Expansion of the outer leaflet forces the membrane to bend, leading to the deformation of the biconcave discocyte into increasingly spiculated shapes, in a well-defined series of cell shapes known as the discoechinocyte transition. We explore the first stages of this transition by means of an elastic membrane energy model that accounts for the bilayer and cytoskeleton contributions. The morphological evolution is explained in terms of the elastic response of these membrane components. Our results highlight the importance of the cytoskeleton as a stabilizing component and how it determines the strong sequential character of the development of different morphologies. In general, cells develop undulations around the cell contour prior to the growth of out-of-plane bumps; this was found to be due to the high energetic penalty relative to a limited area-difference benefit.

Application of force to echinocytes during atomic force microscopy measurements was shown to be able to convert the cells to stable discocyte shapes. The echinocyte shape is associated with a relative excess of the area of the outer leaflet of the cell membrane; the AFM measurements are therefore associated with a change in the relative areas of the inner and outer membrane leaflets. It was hypothesized that localised damage in the lipid bilayer that is caused by an AFM tip can permit the lipids to flip-flop between the two membrane leaflets, thus changing their relative areas. The conditions in which AFM measurements on cells could induce shape changes were investigated both experimentally and by modelling. The relative area change of the membrane leaflets, attributed here to lipid movement, was characterised in terms of the membrane energy levels; membrane energy was calculated using a version of the area-difference-elasticity model that was applied to predetermined shapes, rather than being used to generate shapes as solutions found at the energy minima. Shapes were generated by rotation of Cassini ovals with a superimposed undulation in order to generate spikes similar to those of the echinocytes. The membrane energy was considered as a function of the membrane curvature, the area difference between the two membrane leaflets, and the deformation of the cytoskeleton. This led to the conclusions that the minimisation of the membrane energy causes the lipid translocation, with the relaxation of the cytoskeleton being a significant driving force.

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Phase-field models have been extensively used to study interfacial phenomena, from solidification to vesicle dynamics. In this article, we analyze a phase-field model that captures the relevant physical features that characterize biological membranes. We show that the Helfrich theory of elasticity of membranes can be applied to phase-field models, allowing to derive the expressions of the stress tensor, lateral stress profile and elastic moduli. We discuss the relevance and interpretations of these magnitudes from a phase-field perspective. Taking the sharp-interface limit we show that the membrane macroscopic equilibrium equation can be derived from the equilibrium condition of the phase-field interface. We also study two dynamic models that describe the behaviour of a membrane. From the study of the relaxational behaviour of the membrane we characterize the relevant dynamics of each model, and discuss their applications.