Dynamics of particle uptake at cell membranes

Nonequilibrium Dynamic Phase Diagram for Transmembrane Transport of Active Particles

In recent years, there has been considerable push toward the biomedical applications with active particles, which have great potential to revolutionize disease diagnostics and therapy. The direct penetration of active particles through the cell membrane leads to more efficient intracellular delivery than previously considered endocytosis processes but may cause membrane disruption. Understanding fundamental behaviors of cell membranes in response to such extreme impacts by active particles is crucial to develop active particle-based biomedical technologies and manage health and safety issues in this emerging field. Unfortunately, the physical principles underlying the nonequilibrium behaviors from endocytosis to direct penetration remain elusive, and experiments are challenging. Here, we present a computed dynamic phase diagram for transmembrane transport of active particles and identify four characteristic dynamic phases in endocytosis and direct penetration according to the particle activity and membrane tension. The boundaries dividing these phases are analytically obtained with theoretical models, elucidating the nonequilibrium physics and criteria for the transition between different phases. Furthermore, we numerically and experimentally show three distinct dynamic regimes related to the interplay between necking and wrapping during the endocytosis process of active particles, which strikingly contrast the regimes for passive particles. Overall, these findings could be useful for sharpening the understanding of basic principles underlying biological issues related to the safe and efficient biomedical applications of such emerging matters.

Effective cell membrane tension protects red blood cells against malaria invasion

A critical step in how malaria parasites invade red blood cells (RBCs) is the wrapping of the membrane around the egg-shaped merozoites. Recent experiments have revealed that RBCs can be protected from malaria invasion by high membrane tension. While cellular and biochemical aspects of parasite actomyosin motor forces during the malaria invasion have been well studied, the important role of the biophysical forces induced by the RBC membrane-cytoskeleton composite has not yet been fully understood. In this study, we use a theoretical model for lipid bilayer mechanics, cytoskeleton deformation, and membrane-merozoite interactions to systematically investigate the influence of effective RBC membrane tension, which includes contributions from the lipid bilayer tension, spontaneous tension, interfacial tension, and the resistance of cytoskeleton against shear deformation on the progression of membrane wrapping during the process of malaria invasion. Our model reveals that this effective membrane tension creates a wrapping energy barrier for a complete merozoite entry. We calculate the tension threshold required to impede the malaria invasion. We find that the tension threshold is a nonmonotonic function of spontaneous tension and undergoes a sharp transition from large to small values as the magnitude of interfacial tension increases. We also predict that the physical properties of the RBC cytoskeleton layer-particularly the resting length of the cytoskeleton-play key roles in specifying the degree of the membrane wrapping. We also found that the shear energy of cytoskeleton deformation diverges at the full wrapping state, suggesting the local disassembly of the cytoskeleton is required to complete the merozoite entry. Additionally, using our theoretical framework, we predict the landscape of myosin-mediated forces and the physical properties of the RBC membrane in regulating successful malaria invasion. Our findings on the crucial role of RBC membrane tension in inhibiting malaria invasion can have implications for developing novel antimalarial therapeutic or vaccine-based strategies.

Physicochemical Properties and Route of Systemic Delivery Control the In Vivo Dynamics and Breakdown of Radiolabeled Gold Nanostars

The in vivo dynamics of nanoparticles requires a mechanistic understanding of multiple factors. Here, for the first time, the surprising breakdown of functionalized gold nanostars (F-AuNSs) conjugated with antibodies and 64 Cu radiolabels in vivo and in artificial lysosomal fluid ex vivo, is shown. The short-term biodistribution of F-AuNSs is driven by the route of systemic delivery (intravenous vs intraperitoneal) and long-term fate is controlled by the tissue type in vivo. In vitro studies including endocytosis pathways, intracellular trafficking, and opsonization, are combined with in vivo studies integrating a milieu of spectroscopy and microcopy techniques that show F-AuNSs dynamics is driven by their physicochemical properties and route of delivery. F-AuNSs break down into sub-20 nm broken nanoparticles as early as 7 days postinjection. Martini coarse-grained simulations are performed to support the in vivo findings. Simulations suggest that shape, size, and charge of the broken nanoparticles, and composition of the lipid membrane depicting various tissues govern the interaction of the nanoparticles with the membrane, and the rate of translocation across the membrane to ultimately enable tissue clearance. The fundamental study addresses critical gaps in the knowledge regarding the fate of nanoparticles in vivo that remain a bottleneck in their clinical translation.

Wrapping dynamics and critical conditions for active nonspherical nanoparticle uptake

The cellular uptake of self-propelled nonspherical nanoparticles (NPs) or viruses by cell membrane is crucial in many biological processes, but its universal dynamics have yet to be elucidated. In this study, using the Onsager variational principle, we obtain a general wrapping equation for nonspherical self-propelled nanoparticles. Two analytical critical conditions are theoretically found, indicating a continuous full uptake for prolate particles and a snapthrough full uptake for oblate particles. They precisely capture the full uptake critical boundaries in the phase diagrams numerically constructed in terms of active force, aspect ratio, adhesion energy density, and membrane tension. It is found that enhancing activity (active force), reducing effective dynamic viscosity, increasing adhesion energy density, and decreasing membrane tension can significantly improve the wrapping efficiency of the self-propelled nonspherical nanoparticles. These results give a panoramic view of the uptake dynamics of active nonspherical nanoparticles, and may offer instructions for designing an effective active NP-based vehicle for controlled drug delivery.

Force-induced wrapping phase transition in activated cellular uptake

Intracellular pathogens, including all viruses and many bacteria, enter a host cell through either passive endocytosis or active self-propulsion. Though the cellular uptake of passive particles via endocytic process has been studied extensively, little work has been done on the active entry of self-propelled pathogens, such as Listeria monocytogenes. Here, we present a theoretical model to investigate the adhesive wrapping of a self-propelled particle by a plasma membrane, and find a type of first-order wrapping transition from a small partial wrapping state to a large partial wrapping state triggered by the active force. The phase diagram displays more complex behaviors compared with the passive wrapping mediated merely by adhesion. We also find that a tubular protrusion can be formed if the active force exceeds a force barrier. These results may provide a useful guidance to the study of activity-driven cellular entry of active particles into cells.

Emerging Diamond Quantum Sensing in Bio-Membranes

Bio-membranes exhibit complex but unique mechanical properties as communicative regulators in various physiological and pathological processes. Exposed to a dynamic micro-environment, bio-membranes can be seen as an intricate and delicate system. The systematical modeling and detection of their local physical properties are often difficult to achieve, both quantitatively and precisely. The recent emerging diamonds hosting quantum defects (i.e., nitrogen-vacancy (NV) center) demonstrate intriguing optical and spin properties, together with their outstanding photostability and biocompatibility, rendering them ideal candidates for biological applications. Notably, the extraordinary spin-based sensing enable the measurements of localized nanoscale physical quantities such as magnetic fields, electrical fields, temperature, and strain. These nanoscale signals can be optically read out precisely by simple optical microscopy systems. Given these exclusive properties, NV-center-based quantum sensors can be widely applied in exploring bio-membrane-related features and the communicative chemical reaction processes. This review mainly focuses on NV-based quantum sensing in bio-membrane fields. The attempts of applying NV-based quantum sensors in bio-membranes to investigate diverse physical and chemical events such as membrane elasticity, phase change, nanoscale bio-physical signals, and free radical formation are fully overviewed. We also discuss the challenges and future directions of this novel technology to be utilized in bio-membranes.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

Membrane area gain and loss during cytokinesis

In cytokinesis of animal cells, the cell is symmetrically divided into two. Since the cell's volume is conserved, the projected area has to increase to allow for the change of shape. Here we aim to predict how membrane gain and loss adapt during cytokinesis. We work with a kinetic model in which membrane turnover depends on membrane tension and cell shape. We apply this model to a series of calculated vesicle shapes as a proxy for the shape of dividing cells. We find that the ratio of kinetic turnover parameters changes nonmonotonically with cell shape, determined by the dependence of exocytosis and endocytosis on membrane curvature. Our results imply that controlling membrane turnover will be crucial for the successful division of artificial cells.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

Competing pathways for the invagination of clathrin-coated membranes

Clathrin-mediated endocytosis is the major pathway by which eukaryotic cells take up extracellular material, but it is still elusive which physical pathways are being taken during membrane invagination. From a continuum point of view, it can be driven by increases in coat stiffness, preferred curvature or line tension. Here we develop a comprehensive theoretical framework that can be solved analytically and that predicts the consequences of these different scenarios. We find that for the case of increasing stiffness or preferred curvature, curvature will be acquired gradually with growth, while for increasing line tension, the lattice must have grown to a certain size before a flat-to-curved transition can occur. At low membrane tension, the critical value for coat stiffness is 30 kBT, for preferred curvature it is 200 nm, and for line tension it is 6 pN. For high membrane tension, critical coat stiffness is 150 kBT and critical preferred curvature is 70 nm. In the mixed case when a coat with finite rigidity but increasing line tension is considered, a cup-to-sphere transition can occur for a line tension of 6 pN. The flat-to-curved and the cup-to-sphere transitions driven by line tension are both suppressed by high membrane tension.