Shape and Dynamics of Adhesive Cells: Mechanical Response of Open Systems

Quantitative comparison of cell-cell detachment force in different experimental setups

We compare three different setups for measuring cell-cell adhesion. We show that the measured strength depends on the type of setup that is used. For identical cells different assays measure different detachment forces. This can be understood from the fact that cell-cell detachment is a global property of the system. We also analyse the role of external force and line tension on contact angle and cell-cell detachment. Comparison with the experiments suggest that viscous forces play an important role in the process. We dedicate this article to Fyl Pincus who for many of us is an example to be followed not only for outstanding science but also for a marvelous human behavior.

Electric field-mediated adhesive dynamics of cells inside bio-functionalised microchannels offers important cues for active control of cell-substrate adhesion

Adhesive dynamics of cells plays a critical role in determining different biophysical processes orchestrating health and disease in living systems. While the rolling of cells on functionalised substrates having similarity with biophysical pathways appears to be extensively discussed in the literature, the effect of an external stimulus in the form of an electric field on the same remains underemphasized. Here, we bring out the interplay of fluid shear and electric field on the rolling dynamics of adhesive cells in biofunctionalised micro-confinements. Our experimental results portray that an electric field, even restricted to low strengths within the physiologically relevant regimes, can significantly influence the cell adhesion dynamics. We quantify the electric field-mediated adhesive dynamics of the cells in terms of two key parameters, namely, the voltage-altered rolling velocity and the frequency of adhesion. The effect of the directionality of the electric field with respect to the flow direction is also analysed by studying cellular migration with electrical effects acting both along and against the flow. Our experiment, on one hand, demonstrates the importance of collagen functionalisation in the adhesive dynamics of cells through micro channels, while on the other hand, it reveals how the presence of an axial electric field can lead to significant alteration in the kinetic rate of bond breakage, thereby modifying the degree of cell-substrate adhesion and quantifying in terms of the adhesion frequency of the cells. Proceeding further forward, we offer a simple theoretical explanation towards deriving the kinetics of cellular bonding in the presence of an electric field, which corroborates favourably with our experimental outcome. These findings are likely to offer fundamental insights into the possibilities of local control of cellular adhesion via electric field mediated interactions, bearing critical implications in a wide variety of medical conditions ranging from wound healing to cancer metastasis.

Curvature-dependent adhesion of vesicles

The morphology and motion behavior of a cell are highly influenced by its external biological, chemical, and physical stimuli, and geometric confinement. In this paper, it is revealed that the mean curvature of the substrate significantly influences the adhesion of vesicles. By employing the variational method and investigating the Helfrich free energy, the configuration of axisymmetric vesicles adhered to curved spherical substrates is obtained theoretically. Moreover, numerical simulations based on the finite element method are also carried out to investigate the adhesion of vesicles on curved substrates with complex shapes. It is found that for a fixed area of a vesicle, its total free energy depends mainly on the mean curvature of the adhesion region but is insensitive to the specific shape of the substrate, and the total free energy monotonically decreases with the increase in the mean curvature. In addition, possible biological significances of the curvature-dependent adhesion, such as the shape of the cell and antibiofouling, are discussed. This study may deepen our understanding of the underlying mechanisms of adhesion in cellular activities.

Electromechanical model for object roughness perception during finger sliding

Touch allows us to gather abundant information in the world around us. However, how sensory cells embedded in the fingers convey texture information into their firing patterns is still poorly understood. Here, we develop an electromechanical model for roughness perception by incorporating main ingredients such as voltage-gated ion channels, active ion pumps, mechanosensitive channels, and cell deformation. The model reveals that sensory cells can convey texture wavelengths into the period of their firing patterns as the finger slides across object surfaces, but they can only convey a limited range of texture wavelengths. We also show that an increase in sliding speed broadens the decoding wavelength range at the cost of reduction of lower perception limits. Thus, a smaller sliding speed and a bigger contact force may be needed to successfully discern a smooth surface, consistent with previous psychophysical observations. Moreover, we show that cells with slowly adapting mechanosensitive channels can still fire action potentials under static loadings, indicating that slowly adapting mechanosensitive channels may contribute to the perception of coarse textures under static touch. Our work thus provides a new theoretical framework to study roughness perception and may have important implications for the design of electronic skin, artificial touch, and haptic interfaces.

Intercellular water exchanges trigger soliton-like waves in multicellular systems

Oscillations and waves are ubiquitous in living cellular systems. Generations of these spatio-temporal patterns are generally attributed to some mechanochemical feedbacks. Here, we treat cells as open systems, i.e., water and ions can pass through the cell membrane passively or actively, and reveal a new origin of wave generation. We show that osmotic shocks above a shock threshold will trigger self-sustained cell oscillations and result in long-range waves propagating without decrement, a phenomenon that is analogous to the excitable medium. The travelling wave propagates along intercellular osmotic pressure gradient and its wave speed scales with the magnitude of intercellular water flows. Furthermore, we also find that the travelling wave exhibits several hallmarks of solitary waves. Together, our findings predict a new mechanism of wave generation in living multicellular systems. The ubiquity of intercellular water exchanges implies that this mechanism may be relevant to a broad class of systems.

Endocytosis and exocytosis protect cells against severe membrane tension variations

The ability of cells to regulate their shape and volume is critical for many cell functions. How endocytosis and exocytosis, as important ways of membrane trafficking, affect cellular volume regulation is still unclear. Here, we develop a theoretical framework to study the dynamics of cell volume, endocytosis, and exocytosis in response to osmotic shocks and mechanical loadings. This model can not only explain observed dynamics of endocytosis and exocytosis during osmotic shocks but also predict the dynamics of endocytosis and exocytosis during cell compressions. We find that a hypotonic shock stimulates exocytosis, while a hypertonic shock stimulates endocytosis; and exocytosis in turn allows cells to have a dramatic change in cell volume but a small change in membrane tension during hyposmotic swelling, protecting cells from rupture under high tension. In addition, we find that cell compressions with various loading speeds induce three distinct dynamic modes of endocytosis and exocytosis. Finally, we show that increasing endocytosis and exocytosis rates reduce the changes in cell volume and membrane tension under fast cell compression, whereas they enhance the changes in cell volume and membrane tension under slow cell compression. Together, our findings reveal critical roles of endocytosis and exocytosis in regulating cell volume and membrane tension.

Modelling Nuclear Morphology and Shape Transformation: A Review

As one of the most important cellular compartments, the nucleus contains genetic materials and separates them from the cytoplasm with the nuclear envelope (NE), a thin membrane that is susceptible to deformations caused by intracellular forces. Interestingly, accumulating evidence has also indicated that the morphology change of NE is tightly related to nuclear mechanotransduction and the pathogenesis of diseases such as cancer and Hutchinson–Gilford Progeria Syndrome. Theoretically, with the help of well-designed experiments, significant progress has been made in understanding the physical mechanisms behind nuclear shape transformation in different cellular processes as well as its biological implications. Here, we review different continuum-level (i.e., energy minimization, boundary integral and finite element-based) approaches that have been developed to predict the morphology and shape change of the cell nucleus. Essential gradients, relative advantages and limitations of each model will be discussed in detail, with the hope of sparking a greater research interest in this important topic in the future.

Mechanical properties of external confinement modulate the rounding dynamics of cells

Many studies have demonstrated that mitotic cells can round up against external impediments. However, how the stiffness of external confinement affects the dynamics of rounding force/pressure and cell volume remains largely unknown. Here, we develop a theoretical framework to study the rounding of adherent cells confined between a substrate and a cantilever. We show that the rounding force and pressure increase exclusively with the effective confinement on the cell, which is related to the cantilever stiffness and the separation between cantilever and substrate. Remarkably, an increase of cantilever stiffness from 0.001 to 1 N/m can lead to a 100-fold change in rounding force. This model also predicts an active role of confinement stiffness in regulating the dynamics of cell volume and hydrostatic pressure. We find that the dynamic changes of cellular volume and hydrostatic pressure after osmotic shocks are opposite if the cantilever is soft, whereas the dynamic changes of cellular volume and pressure are the same if the cantilever is stiff. Taken together, this work demonstrates that confinement stiffness appears as a critical regulator in regulating the dynamics of rounding force and pressure. Our findings also indicate that the difference in cantilever stiffness need to be considered when comparing the measured rounding force and pressure from various experiments.

Effects of Geometric Confinement on Zero-Gravity Droplets between Two Parallel Planes

Investigation of geometric effects on confined droplets is important for the fundamental understanding of the ubiquitous wetting phenomena in nature as well as for a variety of practical applications. In this study, the effect of geometric confinement on the wetting behavior of a droplet confined between two parallel rigid planes was investigated. The closed solutions of the Young-Laplace equation were derived through an analytical method. These solutions are applicable for arbitrary values of the contact angles and the ratio of the size of the droplet to the separation of the planes. For completely nonwetting and wetting cases, an asymptotic method was employed, and the sophisticated analytical solutions of the Laplace pressure, droplet volume, surface energy, and capillary force were expressed as functions of the size and the separation of the droplet in a simple way. In order to check the applicability of the results, experiments were designed to counteract the gravity of the droplets. The asymptotic results not only quantitatively agree well with the theoretical and experimental results over a large range of the parameter space, but also provide a straightforward view for reflecting the effect of the geometric confinement on the wetting behaviors of droplets.

Durotaxis Index of 3T3 Fibroblast Cells Scales with Stiff-to-Soft Membrane Tension Polarity

Cell durotaxis is an essential process in tissue development. Although the role of cytoskeleton in cell durotaxis has been widely studied, whether cell volume and membrane tension are implicated in cell durotaxis remains unclear. By quantifying the volume distribution during cell durotaxis, we show that the volume of 3T3 fibroblast cells decreases by almost 40% as cells migrate toward stiffer regions of gradient gels. Inhibiting ion transporters that can reduce the amplitude of cell volume decrease significantly suppresses cell durotaxis. However, from the correlation analysis, we find that durotaxis index does not correlate with the cell volume decrease. It scales with the membrane tension difference in the direction of stiffness gradient. Because of the tight coupling between cell volume and membrane tension, inhibition of Na⁺/K⁺ ATPase and Na⁺/H⁺ exchanger results in smaller volume decrease and membrane tension difference. Collectively, our findings indicate that the polarization of membrane tension is a central regulator of cell durotaxis, and Na⁺/K⁺ ATPase and Na⁺/H⁺ exchanger can help to maintain the membrane tension polarity.

Emerging themes and unifying concepts underlying cell behavior regulation by the pericellular space

Cells reside in a complex three-dimensional (3D) microenvironment where physical, chemical, and architectural features of the pericellular space regulate important cellular functions like migration, differentiation, and morphogenesis. A major goal of tissue engineering is to identify which properties of the pericellular space orchestrate these emergent cell behaviors and how. In this review, we highlight recent studies at the interface of biomaterials and single cell biophysics that are lending deeper insight towards this goal. Advanced methods have enabled the decoupling of architectural and mechanical features of the microenvironment, revealing multiple mechanisms of adhesion and mechanosensing modulation by biomaterials. Such studies are revealing important roles for pericellular space degradability, hydration, and adhesion competition in cell shape, volume, and differentiation regulation. STATEMENT OF SIGNIFICANCE: Cell fate and function are closely regulated by the local extracellular microenvironment. Advanced methods at the interface of single cell biophysics and biomaterials have shed new light on regulators of cell-pericellular space interactions by decoupling more features of the complex pericellular milieu than ever before. These findings lend deeper mechanistic insight into how biomaterials can be designed to fine-tune outcomes like differentiation, migration, and collective morphogenesis.

Assembly structures and dynamics of active colloidal cells

Many types of active matter are deformable, such as epithelial cells and bacteria. To mimic the feature of deformability, we built a model called an active colloidal cell (ACC), i.e. a vesicle enclosed with self-propelled particles (SPPs), which as a whole can move actively. Based on the model, we then study the role of deformability in the assembly structures and dynamics of ACCs by Langevin dynamics simulation. We find that deformability weakens the self-trapping effect and hence suppresses the clustering and phase separation of the deformable soft ACCs (sACCs). Instead of forming a large compact cluster like ordinary SPPs, sACCs pack into a loose network or porous structure in the phase-separation region. The condensed phase is liquid-like, in which sACCs are strongly compressed and deformed but still keep high motility. The interface between the gas and the condensed phases is blurry and unstable, and the effective interfacial energy is very low. Our work gives new insights into the role of deformability in the assembly of active matter and also provides a reference for further studies on different types of deformable active matter.

Controlling Cellular Volume via Mechanical and Physical Properties of Substrate

The mechanical and physical properties of substrate play a crucial role in regulating many cell functions and behaviors. However, how these properties affect cell volume is still unclear. Here, we show that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable cell volume decrease (up to 50%), and the dynamic cell spreading process is also accompanied by dramatic cell volume decrease. Further, studies of ion channel inhibition and osmotic shock suggest that these volume decreases are due to the efflux of water and ions. We also show that disrupting cortex contractility leads to bigger cell volume. Collectively, these results reveal the "mechanism of adhesion-induced compression of cells," i.e., stronger interaction between cell and substrate leads to higher actomyosin contractility, expels water and ions, and thus decreases cell volume.

Tuning interfacial patterns of molecular bonds via surface morphology

Many studies have demonstrated that the mechanical properties of the extracellular matrix can significantly influence the morphology, strength and lifetime of focal adhesions. However, how the morphology of the contact surface affects the pattern formation of the molecular bonds still remains largely unknown. Here, by simplifying the cell and extracellular matrix to two opposing elastic bodies and considering the lateral diffusion as well as the bonding/debonding of molecular bonds, we study the clustering behavior of receptor-ligand bonds between curved surfaces and the phase diagrams of cluster patterns. We reveal the important role of surface morphology and bond kinetics in regulating the patterns of bond clusters. We further investigate the segregation dynamics of the interfacial bonds under various loading speeds, and we show that the average interfacial stress is rate-dependent while the rupture stress is rate-independent. Finally, we demonstrate that programmable patterning of bond clusters can be achieved through the designed surface morphology.

A mathematical model of cellular swelling in Neuromyelitis optica

Neuromyelitis Optica (NMO) is a severe neuro-inflammatory disease of the central nervous system characterized by predominant damage to the optic nerve and of the spinal cord. The pathogenic antibody found in the majority of patients targets the AQP4 channels on astrocytic endfeet and causes the cells to swell. Although, the pathophysiology of the disease is broadly known, there are no specific targeted treatments for this process clinically available nor accurate prognostic markers both during attacks and for predicting long term neuronal damage. This lack is, in part, due to the rarity of the disease and its relatively recent pathogenic clarity. Hence, the ability to mathematically model the progress of the condition to test prospective therapies in silico would be a step forward. This paper combines state of the art models of cellular metabolism and cytotoxic oedema in neurons and astrocytes and augments it with a detailed characterization of water transport across the cellular membrane. In particular, we capture the process of perforation of the cell through the human complement cascade and resulting water and ionic fluxes. Simulating NMO by injecting its antibody and human complement into the extracellular space showed a 25% increase of the astrocytic volume after 12 h from onset. Most of the volume change occurred during the first 30 min of simulation with a peak volume change of 38%. The model was further adapted to simulate the therapeutic potential of CD59. It was found that there is a threshold of CD59 concentration that can prevent the swelling of astrocytes. Since the astrocyte volume changes mostly during the first hour, further experimental work should focus on this time scale to provide data for further model refinement and validation.