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

Making the cut: Multiscale simulation of membrane remodeling

Biological membranes are dynamic heterogeneous materials, and their shape and organization are tightly coupled to the properties of the proteins in and around them. However, the length scales of lipid and protein dynamics are far below the size of membrane-bound organelles, much less an entire cell. Therefore, multiscale modeling approaches are often necessary to build a comprehensive picture of the interplay of these factors, and have provided critical insights into our understanding of membrane dynamics. Here, we review computational methods for studying membrane remodeling, as well as passive and active examples of protein-driven membrane remodeling. As the field advances towards the modeling of key aspects of organelles and whole cells - an increasingly accessible regime of study - we summarize here recent successes and offer comments on future trends.

Deciphering Müller cell heterogeneity signatures in diabetic retinopathy across species: an integrative single-cell analysis

Diabetic retinopathy (DR), a leading cause of visual impairment, demands a profound comprehension of its cellular mechanisms to formulate effective therapeutic strategies. Our study presentes a comprehensive single-cell analysis elucidating the intricate landscape of Müller cells within DR, emphasizing their nuanced involvement. Utilizing scRNA-seq data from both Sprague-Dawley rat models and human patients, we delineated distinct Müller cell clusters and their corresponding gene expression profiles. These findings were further validated through differential gene expression analysis utilizing human transcriptomic data. Notably, certain Müller cell clusters displayed upregulation of the Rho gene, implying a phagocytic response to damaged photoreceptors within the DR microenvironment. This phenomenon was consistently observed across species. Additionally, the co-expression patterns of RHO and PDE6G within Müller cell clusters provided compelling evidence supporting their potential role in maintaining retinal integrity during DR. Our results offer novel insights into the cellular dynamics of DR and underscore Müller cells as promising therapeutic targets for preserving vision in retinal disorders induced by diabetes.

Role of Shape in Particle-Lipid Membrane Interactions: From Surfing to Full Engulfment

Understanding and manipulating the interactions between foreign bodies and cell membranes during endo- and phagocytosis is of paramount importance, not only for the fate of living cells but also for numerous biomedical applications. This study aims to elucidate the role of variables such as anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength in this essential process using a minimal experimental biomimetic system comprising giant unilamellar vesicles and rod-like particles with different curvatures and aspect ratios. We find that the particle wrapping process is dictated by the balance between the elastic free energy penalty and adhesion free energy gain, leading to two distinct engulfment pathways, tip-first and side-first, emphasizing the significance of the particle orientation in determining the pathway. Moreover, our experimental results are consistent with theoretical predictions in a state diagram, showcasing how to control the wrapping pathway from surfing to partial to complete wrapping by the interplay between membrane tension and adhesive strength. At moderate particle concentrations, we observed the formation of rod clusters, which exhibited cooperative and sequential wrapping. Our study contributes to a comprehensive understanding of the mechanistic intricacies of endocytosis by highlighting how the interplay between the anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength can influence the engulfment pathway.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

A minimal cell model for lamellipodia-based cellular dynamics and migration

One ubiquitous cellular structure for performing various tasks, such as spreading and migration over external surfaces, is the sheet-like protrusion called a lamellipodium, which propels the leading edge of the cell. Despite the detailed knowledge about the many components of this cellular structure, it is not yet fully understood how these components self-organize spatiotemporally to form lamellipodia. We review here recent theoretical works where we have demonstrated that membrane-bound protein complexes that have intrinsic curvature and recruit the protrusive forces of the cytoskeleton result in a simple, yet highly robust, organizing feedback mechanism that organizes the cytoskeleton and the membrane. This self-organization mechanism accounts for the formation of flat lamellipodia at the leading edge of cells spreading over adhesive substrates, allowing for the emergence of a polarized, motile 'minimal cell' model. The same mechanism describes how lamellipodia organize to drive robust engulfment of particles during phagocytosis and explains in simple physical terms the spreading and migration of cells over fibers and other curved surfaces. This Review highlights that despite the complexity of cellular composition, there might be simple general physical principles that are utilized by the cell to drive cellular shape dynamics.

Geometry-induced patterns through mechanochemical coupling

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.

Theoretical model of membrane protrusions driven by curved active proteins

Eukaryotic cells intrinsically change their shape, by changing the composition of their membrane and by restructuring their underlying cytoskeleton. We present here further studies and extensions of a minimal physical model, describing a closed vesicle with mobile curved membrane protein complexes. The cytoskeletal forces describe the protrusive force due to actin polymerization which is recruited to the membrane by the curved protein complexes. We characterize the phase diagrams of this model, as function of the magnitude of the active forces, nearest-neighbor protein interactions and the proteins' spontaneous curvature. It was previously shown that this model can explain the formation of lamellipodia-like flat protrusions, and here we explore the regimes where the model can also give rise to filopodia-like tubular protrusions. We extend the simulation with curved components of both convex and concave species, where we find the formation of complex ruffled clusters, as well as internalized invaginations that resemble the process of endocytosis and macropinocytosis. We alter the force model representing the cytoskeleton to simulate the effects of bundled instead of branched structure, resulting in shapes which resemble filopodia.

Entry of microparticles into giant lipid vesicles by optical tweezers

Entry of micro- or nanosized objects into cells or vesicles made of lipid membranes occurs in many processes such as entry of viruses into host cells, microplastics pollution, drug delivery, or biomedical imaging. Here we investigate the microparticle crossing of lipid membranes in giant unilamellar vesicles in the absence of strong binding interactions (e.g., streptavidin-biotin binding). In these conditions, we observe that organic and inorganic particles can always penetrate inside the vesicles provided an external piconewton force is applied and for relatively low membrane tensions. In the limit of vanishing adhesion, we identify the role of the membrane area reservoir and show that a force minimum exists when the particle size is comparable to the bendocapillary length.

Actomyosin-Driven Division of a Synthetic Cell

One of the major challenges of bottom-up synthetic biology is rebuilding a minimal cell division machinery. From a reconstitution perspective, the animal cell division apparatus is mechanically the simplest and therefore attractive to rebuild. An actin-based ring produces contractile force to constrict the membrane. By contrast, microbes and plant cells have a cell wall, so division requires concerted membrane constriction and cell wall synthesis. Furthermore, reconstitution of the actin division machinery helps in understanding the physical and molecular mechanisms of cytokinesis in animal cells and thus our own cells. In this review, we describe the state-of-the-art research on reconstitution of minimal actin-mediated cytokinetic machineries. Based on the conceptual requirements that we obtained from the physics of the shape changes involved in cell division, we propose two major routes for building a minimal actin apparatus capable of division. Importantly, we acknowledge both the passive and active roles that the confining lipid membrane can play in synthetic cytokinesis. We conclude this review by identifying the most pressing challenges for future reconstitution work, thereby laying out a roadmap for building a synthetic cell equipped with a minimal actin division machinery.

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.

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.

Driven Engulfment of Janus Particles by Giant Vesicles in and out of Thermal Equilibrium

The interaction between Janus colloids and giant lipid vesicles was experimentally investigated to elucidate the dynamics and mechanisms related to microparticle engulfment by lipid vesicles. Janus (Pt–SiO₂ and Pt–MF, where MF is melamine formaldehyde) colloids do not spontaneously adhere to POPC or DOPC bilayers, but by applying external forces via centrifugation we were able to force the contact between the particles and the membranes, which may result in a partial engulfment state of the particle. Surface properties of the Janus colloids play a crucial role in the driven particle engulfment by vesicles. Engulfment of the silica and platinum regions of the Janus particles can be observed, whereas the polymer (MF) region does not show any affinity towards the lipid bilayer. By using fluorescence microscopy, we were able to monitor the particle orientation and measure the rotational dynamics of a single Janus particle engulfed by a vesicle. By adding hydrogen peroxide to the solution, particle self-propulsion was used to perform an active transport of a giant vesicle by a single active particle. Finally, we observe that partially engulfed particles experience a membrane curvature-induced force, which pushes the colloids towards the bottom where the membrane curvature is the lowest.

Cholesterol plays a decisive role in tetraspanin assemblies during bilayer deformations

The tetraspanin family plays key roles in many physiological processes, such as, tumour invasion, cell motility, virus infection, cell attachment and entry. Tetraspanins function as molecular scaffolds organized in microdomains with interesting downstream cellular consequences. However, despite their relevance in human physiology, the precise mechanisms of their various functions remain elusive. In particular, the full-length CD81 tetraspanin has interesting cholesterol-related properties that modulate its activity in cells. In this work, we study the opening transition of CD81 under different conditions. We propose that such conformational change is a collaborative process enhanced by simultaneous interactions between multiple identical CD81 tetraspanins. With molecular dynamics simulations we describe the crucial role of a ternary lipid bilayer with cholesterol in CD81 conformational dynamics, observing two emergent properties: first, clusters of CD81 collectively segregate one tetraspanin while favouring one opening transition, second, cumulative cholesterol sequestering by CD81 tetraspanins inhibits large membrane deformations due to local density variations.