Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure

Research progress on the regulatory role of cell membrane surface tension in cell behavior

Cell membrane surface tension has emerged as a pivotal biophysical factor governing cell behavior and fate. This review systematically delineates recent advances in techniques for cell membrane surface tension quantification, mechanosensing mechanisms, and regulatory roles of cell membrane surface tension in modulating major cellular processes. Micropipette aspiration, tether pulling, and newly developed fluorescent probes enable the measurement of cell membrane surface tension with spatiotemporal precision. Cells perceive cell membrane surface tension via conduits including mechanosensitive ion channels, curvature-sensing proteins (e.g. BAR domain proteins), and cortex-membrane attachment proteins (e.g. ERM proteins). Through membrane receptors like integrins, cells convert mechanical cues into biochemical signals. This conversion triggers cytoskeletal remodeling and extracellular matrix interactions in response to environmental changes. Elevated cell membrane surface tension suppresses cell spreading, migration, and endocytosis while facilitating exocytosis. Moreover, reduced cell membrane surface tension promotes embryonic stem cell differentiation and cancer cell invasion, underscoring cell membrane surface tension as a regulator of cell plasticity. Outstanding questions remain regarding cell membrane surface tension regulatory mechanisms and roles in tissue development/disease in vivo. Emerging tools to manipulate cell membrane surface tension with high spatiotemporal control in combination with omics approaches will facilitate the elucidation of cell membrane surface tension-mediated effects on signaling networks across various cell types/states. This will accelerate the development of cell membrane surface tension-based biomarkers and therapeutics for regenerative medicine and cancer. Overall, this review provides critical insights into cell membrane surface tension as a potent orchestrator of cell function, with broader impacts across mechanobiology.

Inhomogeneous Canham-Helfrich Abscission in Catenoid Necks under Critical Membrane Mosaicity

The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous to neck formation in cellular membranes. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution of necking forces is determined by the equilibrium mechanical equations and the boundary conditions as considered in the axisymmetric setting compatible with the necking process. To establish the role played by mechanical inhomogeneity, we focus on the catenoid, a surface of zero mean curvature. Analytic solutions are shown to exist for the spontaneous curvature and the constrictive forces in terms of the border radii. Our theoretical analysis shows that the inhomogeneous distribution of spontaneous curvature in a mosaic-like neck constrictional forces potentially contributes to the membrane scission under minimized work in living cells.

Constriction of Actin Rings by Passive Crosslinkers

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.

Intercellular Receptor-ligand Binding: Effect of Protein-membrane Interaction

Gaining insights into the intercellular receptor-ligand binding is of great importance for understanding numerous physiological and pathological processes, and stimulating new strategies in drug design and discovery. In contrast to the in vitro protein interaction in solution, the anchored receptor and ligand molecules interact with membrane in situ, which affects the intercellular receptor-ligand binding. Here, we review theoretical, simulation and experimental works regarding the regulatory effects of protein-membrane interactions on intercellular receptor-ligand binding mainly from the following aspects: membrane fluctuations, membrane curvature, glycocalyx, and lipid raft. In addition, we discuss biomedical significances and possible research directions to advance the field and highlight the importance of understanding of coupling effects of these factors in pharmaceutical development.

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.

Non-equilibrium conditions inside rock pores drive fission, maintenance and selection of coacervate protocells

Key requirements for the first cells on Earth include the ability to compartmentalize and evolve. Compartmentalization spatially localizes biomolecules from a dilute pool and an evolving cell, which, as it grows and divides, permits mixing and propagation of information to daughter cells. Complex coacervate microdroplets are excellent candidates as primordial cells with the ability to partition and concentrate molecules into their core and support primitive and complex biochemical reactions. However, the evolution of coacervate protocells by fusion, growth and fission has not yet been demonstrated. In this work, a primordial environment initiated the evolution of coacervate-based protocells. Gas bubbles inside heated rock pores perturb the coacervate protocell distribution and drive the growth, fusion, division and selection of coacervate microdroplets. Our findings provide a compelling scenario for the evolution of membrane-free coacervate microdroplets on the early Earth, induced by common gas bubbles within heated rock pores.

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.

Genetic requirements for cell division in a genomically minimal cell

Genomically minimal cells, such as JCVI-syn3.0, offer a platform to clarify genes underlying core physiological processes. Although this minimal cell includes genes essential for population growth, the physiology of its single cells remained uncharacterized. To investigate striking morphological variation in JCVI-syn3.0 cells, we present an approach to characterize cell propagation and determine genes affecting cell morphology. Microfluidic chemostats allowed observation of intrinsic cell dynamics that result in irregular morphologies. A genome with 19 genes not retained in JCVI-syn3.0 generated JCVI-syn3A, which presents morphology similar to that of JCVI-syn1.0. We further identified seven of these 19 genes, including two known cell division genes, ftsZ and sepF, a hydrolase of unknown substrate, and four genes that encode membrane-associated proteins of unknown function, which are required together to restore a phenotype similar to that of JCVI-syn1.0. This result emphasizes the polygenic nature of cell division and morphology in a genomically minimal cell.

Mechanochemical Regulation of Cell Adhesion by Incorporation of Synthetic Polymers to Plasma Membranes

Chemical control of cell-cell interactions using synthetic materials is useful for a wide range of biomedical applications. Herein, we report a method to regulate cell adhesion and dispersion by introducing repulsive forces to live cell membranes. To induce repulsion, we tethered amphiphilic polymers, such as cholesterol-modified poly(ethylene glycol) (PEG-CLS), to cell membranes. We found that the repulsive forces introduced by these tethered polymers induced cell detachment from a substrate and allowed cell dispersion in a suspension, modulated the speed of cell migration, and improved the separation of cells from tissues. Our analyses showed that coating the cells with tethered polymers most likely generated two distinct repulsive forces, lateral tension and steric repulsion, on the surface, which were tuned by altering the polymer size and density. We modeled how these two forces are generated in kinetically distinctive manners to explain the various responses of cells to the coating. Collectively, our observations demonstrate mechanochemical regulation of cell adhesion and dispersion by simply adding polymers to cells without genetic manipulation or chemical synthesis in the cells, which may contribute to the optimization of chemical coating strategies to regulate various types of cell-cell interacting systems.

Computational studies of shape control of charged deformable nanocontainers

Biological matter is often compartmentalized by soft membranes that dynamically change their shape in response to chemical and mechanical cues. Deformable soft-matter-based nanoscale membranes or nanocontainers that mimic this behavior can be used as drug-delivery carriers that can adapt to evolving physiological conditions, or as dynamic building blocks for the design of novel hierarchical materials via assembly engineering. Here, we connect the intrinsic features of charged deformable nanocontainers such as their size, charge, surface tension, and elasticity with their equilibrium shapes for a wide range of solution conditions using molecular dynamics simulations. These links identify the fundamental mechanisms that establish the chemical and materials design control strategies for modulating the equilibrium shape of these nanocontainers. We show that flexible nanocontainers of radii ranging from 10-20 nm exhibit sphere-to-rod-to-disc shape transitions yielding rods and discs over a wide range of aspect ratio λ (0.3 < λ < 5). The shape transitions can be controlled by tuning salt and/or surfactant concentration as well as material elastic parameters. The shape changes are driven by reduction in the global electrostatic energy and are associated with dramatic changes in local surface elastic energy distributions. To illustrate the shape transition mechanisms, exact analytical calculations for idealized spheroidal nanocontainers in salt-free conditions are performed. Explicit counterion simulations near nanocontainers and associated Manning model calculations provide an assessment of the stability of observed shape deformations in the event of ion condensation.

Mechanical conditions for stable symmetric cell constriction

Cell constriction is a decisive step for division in many cells. However, its physical pathway remains poorly understood, calling for a quantitative analysis of the forces required in different cytokinetic scenarios. Using a model cell composed by a flexible membrane (actin cortex and cell membrane) that encloses the cytoplasm, we study the mechanical conditions necessary for stable symmetric constriction under radial equatorial forces using analytical and numerical methods. We deduce that stable symmetric constriction requires positive effective spontaneous curvature, while spontaneous constriction requires a spontaneous curvature higher than the characteristic inverse cell size. Surface tension reduction (for example by actin cortex growth and membrane trafficking) increases the stability and spontaneity of cellular constriction. A reduction of external pressure also increases stability and spontaneity. Cells with prolate lobes (elongated cells) require lower stabilization forces than oblate-shaped cells (discocytes). We also show that the stability and spontaneity of symmetric constriction increase as constriction progresses. Our quantitative results settle the physical requirements for stable cytokinesis, defining a quantitative framework to analyze the mechanical role of the different constriction machinery and cytokinetic pathways found in real cells, so contributing to a deeper quantitative understanding of the physical mechanism of the cell division process.

Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints

An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting, and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are visualized on the sphere and on cylindrical surfaces.

Polarity signaling ensures epidermal homeostasis by coupling cellular mechanics and genomic integrity

Epithelial homeostasis requires balanced progenitor cell proliferation and differentiation, whereas disrupting this equilibrium fosters degeneration or cancer. Here we studied how cell polarity signaling orchestrates epidermal self-renewal and differentiation. Using genetic ablation, quantitative imaging, mechanochemical reconstitution and atomic force microscopy, we find that mammalian Par3 couples genome integrity and epidermal fate through shaping keratinocyte mechanics, rather than mitotic spindle orientation. Par3 inactivation impairs RhoA activity, actomyosin contractility and viscoelasticity, eliciting mitotic failures that trigger aneuploidy, mitosis-dependent DNA damage responses, p53 stabilization and premature differentiation. Importantly, reconstituting myosin activity is sufficient to restore mitotic fidelity, genome integrity, and balanced differentiation and stratification. Collectively, this study deciphers a mechanical signaling network in which Par3 acts upstream of Rho/actomyosin contractility to promote intrinsic force generation, thereby maintaining mitotic accuracy and cellular fitness at the genomic level. Disturbing this network may compromise not only epidermal homeostasis but potentially also that of other self-renewing epithelia.

Many developing tissues require Par-driven polarization, but its role in mammalian tissue maintenance is unclear. Here, the authors show that in mouse epidermis, Par3 governs tissue homeostasis not via orientation of cell division but by coupling cell mechanics with mitotic accuracy and genome integrity.

Membrane curvature induces cardiolipin sorting

Cardiolipin is a cone-shaped lipid predominantly localized in curved membrane sites of bacteria and in the mitochondrial cristae. This specific localization has been argued to be geometry-driven, since the CL's conical shape relaxes curvature frustration. Although previous evidence suggests a coupling between CL concentration and membrane shape in vivo, no precise experimental data are available for curvature-based CL sorting in vitro. Here, we test this hypothesis in experiments that isolate the effects of membrane curvature in lipid-bilayer nanotubes. CL sorting is observed with increasing tube curvature, reaching a maximum at optimal CL concentrations, a fact compatible with self-associative clustering. Observations are compatible with a model of membrane elasticity including van der Waals entropy, from which a negative intrinsic curvature of -1.1 nm-1 is predicted for CL. The results contribute to understanding the physicochemical interplay between membrane curvature and composition, providing key insights into mitochondrial and bacterial membrane organization and dynamics.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

Phase interfaces within different vesicle shapes

Liquid droplets on flat surfaces generally exhibit a contact angle in a range from 0 to [Formula: see text], but the two-phase interface within a vesicle membrane is very fascinating due to the involved force balance along three bending interfaces. Giant lipid vesicles encapsulated with the poly(ethylene glycol)/dextran aqueous two-phase system are established recently, and the phase interfaces within vesicle membrane are very interesting as experimentally observed. The developed theoretical framework by a combination of the Helfrich curvature elastic theory for vesicle membranes and self-consistent field theory for polymers has been extended to explore aqueous two phases within vesicles. The intrinsic contact angle [Formula: see text] that represents the material parameter, is introduced to describe this phase interfaces within vesicles, especially the transitions from complete wetting to partial wetting, from partial wetting to complete dewetting. The dependence of intrinsic contact angles on the parameters, such as the interaction strengths between the polymers [Formula: see text] and between the membrane and polymer [Formula: see text], the volume fraction [Formula: see text], impermeability of the membrane to the enclosed polymers [Formula: see text] and membrane spontaneous curvature c ₀, are thoroughly investigated, as well as these wetting/dewetting transitions are extensively discussed in the present study.