A numerical model of cellular blebbing: a volume-conserving, fluid-structure interaction model of the entire cell

Microfluidic guillotine reveals multiple timescales and mechanical modes of wound response in Stentor coeruleus

Background

Wound healing is one of the defining features of life and is seen not only in tissues but also within individual cells. Understanding wound response at the single-cell level is critical for determining fundamental cellular functions needed for cell repair and survival. This understanding could also enable the engineering of single-cell wound repair strategies in emerging synthetic cell research. One approach is to examine and adapt self-repair mechanisms from a living system that already demonstrates robust capacity to heal from large wounds. Towards this end, Stentor coeruleus, a single-celled free-living ciliate protozoan, is a unique model because of its robust wound healing capacity. This capacity allows one to perturb the wounding conditions and measure their effect on the repair process without immediately causing cell death, thereby providing a robust platform for probing the self-repair mechanism.

Results

Here we used a microfluidic guillotine and a fluorescence-based assay to probe the timescales of wound repair and of mechanical modes of wound response in Stentor. We found that Stentor requires ~ 100–1000 s to close bisection wounds, depending on the severity of the wound. This corresponds to a healing rate of ~ 8–80 μm²/s, faster than most other single cells reported in the literature. Further, we characterized three distinct mechanical modes of wound response in Stentor: contraction, cytoplasm retrieval, and twisting/pulling. Using chemical perturbations, active cilia were found to be important for only the twisting/pulling mode. Contraction of myonemes, a major contractile fiber in Stentor, was surprisingly not important for the contraction mode and was of low importance for the others.

Conclusions

While events local to the wound site have been the focus of many single-cell wound repair studies, our results suggest that large-scale mechanical behaviors may be of greater importance to single-cell wound repair than previously thought. The work here advances our understanding of the wound response in Stentor and will lay the foundation for further investigations into the underlying components and molecular mechanisms involved.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12915-021-00970-0.

A mathematical model for bleb regulation in zebrafish primordial germ cells

Blebs are cell protrusions generated by local membrane-cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, e.g. primordial germ cells of the zebrafish. While blebs occur randomly at each part of the membrane in unpolarized cells, a polarization process guarantees the occurrence of blebs at a preferential site and thereby facilitates migration toward a specified direction. Little is known about the factors involved in the controlled and directed bleb generation, yet recent studies revealed the influence of an intracellular flow and the stabilizing role of the membrane-cortex linker molecule Ezrin. Based on this information, we develop and analyse a coupled bulk-surface model describing a potential cellular mechanism by which a bleb could be induced at a controlled site. The model rests upon intracellular Darcy flow and a diffusion-advection-reaction system, describing the temporal evolution from a homogeneous to a strongly anisotropic Ezrin distribution. We prove the well-posedness of the mathematical model and show that simulations qualitatively correspond to experimental observations, suggesting that indeed the interaction of an intracellular flow with membrane proteins can be the cause of the Ezrin redistribution accompanying bleb formation.

A Reverse-Osmosis Model of Apoptotic Shrinkage

The standard theory of apoptotic volume decrease (AVD) posits activation of potassium and/or chloride channels, causing an efflux of ions and osmotic loss of water. However, in view of the multitude of possible channels that are known to support apoptosis, a model based on specific signaling to a channel presents certain problems. We propose another mechanism of apoptotic dehydration based on cytoskeletal compression. As is well known, cytoskeleton is not strong enough to expel a substantial amount of water against an osmotic gradient. It is possible, however, that an increase in intracellular pressure may cause an initial small efflux of water, and that will create a small concentration gradient of ions, favoring their exit. If the channels are open, some ions will exit the cell, relieving the osmotic gradient; in this way, the process will be able to continue. Calculations confirm the possibility of such a mechanism. An increase in membrane permeability for water or ions may also result in dehydration if accompanied even by a constant cytoskeletal pressure. We review the molecular processes that may lead to apoptotic dehydration in the context of this model.

Cellular Blebs and Membrane Invaginations Are Coupled through Membrane Tension Buffering

Bleb-type cellular protrusions play key roles in a range of biological processes. It was recently found that bleb growth is facilitated by a local supply of membrane from tubular invaginations, but the interplay between the expanding bleb and the membrane tubes remains poorly understood. On the one hand, the membrane area stored in tubes may serve as a reservoir for bleb expansion. On the other hand, the sequestering of excess membrane in stabilized invaginations may effectively increase the cell membrane tension, which suppresses spontaneous protrusions. Here, we investigate this duality through physical modeling and in vivo experiments. In agreement with observations, our model describes the transition into a tube-flattening mode of bleb expansion while also predicting that the blebbing rate is impaired by elevating the concentration of the curved membrane proteins that form the tubes. We show both theoretically and experimentally that the stabilizing effect of tubes could be counterbalanced by the cortical myosin contractility. Our results largely suggest that proteins able to induce membrane tubulation, such as those containing N-BAR domains, can buffer the effective membrane tension-a master regulator of all cell deformations.

Microparticles as autoantigens in systemic lupus erythematosus

Systemic lupus erythematosus (SLE) is a prototypic autoimmune disease characterized by the production of antibodies to components of the cell nucleus (antinuclear antibodies or ANAs) and the formation of immune complexes with nuclear antigens. These complexes can drive pathogenesis by depositing in the tissue to incite inflammation or induce cytokine production by cells of the innate immune system. While ANAs can bind to purified nuclear molecules, nuclear autoantigens in vivo most likely exist attached to other molecules or embedded in larger structures. Among these structures, microparticles (MPs) are membrane bound vesicles that are released from dead and dying cells by a blebbing process; MPs can also be released during activation of platelets. The presence of MPs in the blood or tissue culture media can be assayed by flow cytometry on the basis of light scattering as well as binding of marker antibodies to identify the cell of origin. As shown by biochemical analyses, MPs contain an ensemble of intracellular components including nuclear, cytoplasmic and membrane molecules. Because of the display of these molecules on the particle surface or in an otherwise accessible form, ANAs, including anti-DNA, can bind to particles. Levels of MPs are increased in the blood of patients with SLE, with flow cytometry demonstrating the presence of IgG-containing particles. In addition to forming immune complexes, MPs can directly stimulate immune responses. Together, these findings suggest an important role of particles in the pathogenesis of SLE and their utility as biomarkers.

Interaction and fusion dynamics between cellular blebs

Membrane blebbing, as a mechanism for cells to regulate their internal pressure and membrane tension, is believed to play important roles in processes such as cell migration, spreading and apoptosis. However, the fundamental question of how different blebs interact with each other during their life cycles remains largely unclear. Here, we report a combined theoretical and experimental investigation to examine how the growth and retraction of a cellular bleb are influenced by neighboring blebs as well as the fusion dynamics between them. Specifically, a boundary integral model was developed to describe the shape evolution of cell membrane during the blebbing/retracting process. We showed that a drop in the intracellular pressure will be induced by the formation of a bleb whose retraction then restores the pressure level. Consequently, the volume that a second bleb can reach was predicted to heavily depend on its initial weakened size and the time lag with respect to the first bleb, all in quantitative agreement with our experimental observations. In addition, it was found that as the strength of membrane-cortex adhesion increases, the possible coalescence of two neighboring blebs changes from smooth fusion to abrupt coalescence and eventually to no fusion at all. Phase diagrams summarizing the dependence of such transition on key physical factors, such as the intracellular pressure and bleb separation, were also obtained.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

A computational model of amoeboid cell motility in the presence of obstacles

Locomotion of amoeboid cells is mediated by finger-like protrusions of the cell body, known as pseudopods, which grow, bifurcate, and retract in a dynamic fashion. Pseudopods are the primary mode of locomotion for many cells within the human body, such as leukocytes, embryonic cells, and metastatic cancer cells. Amoeboid motility is a complex and multiscale process, which involves bio-molecular reactions, cell deformation, and cytoplasmic and extracellular fluid motion. Additionally, cells within the human body are subject to a confined 3D environment known as the extra-cellular matrix (ECM), which resembles a fluid-filled porous medium. In this article, we present a 3D, multiphysics computational approach coupling fluid mechanics, solid mechanics, and a pattern formation model to simulate locomotion of amoeboid cells through a porous matrix composed of a viscous fluid and an array of finite-sized spherical obstacles. The model combines reaction-diffusion of activator/inhibitors, extreme deformation of the cell, pseudopod dynamics, cytoplasmic and extracellular fluid motion, and fully resolved extracellular matrix. A surface finite-element method is used to obtain the cell deformation and activator/inhibitor concentrations, while the fluid motion is solved using a combined finite-volume and spectral method. The immersed-boundary methods are used to couple the cell deformation, obstacles, and fluid. The model is able to recreate squeezing and weaving motion of cells through the matrix. We study the influence of matrix porosity, obstacle size, and cell deformability on the motility behavior. It is found that below certain values of these parameters, cell motion is completely inhibited. Phase diagrams are presented depicting such motility limits. Interesting dynamics seen in the presence of obstacles but absent in unconfined medium, such as freezing or cell arrest, probing, doubling-back, and tug-of-war are predicted. Furthermore, persistent unidirectional motion of cells that is often observed in an unconfined medium is shown to be lost in presence of obstacles, and is attributed to an alteration of the pseudopod dynamics. The same mechanism, however, allows the cell to find a new direction to penetrate further into the matrix without being stuck in one place. The results and analysis presented here show a strong coupling between cell deformability and ECM properties, and provide new fluid mechanical insights on amoeboid motility in confined medium.

High-Voltage, Multiphasic, Nanosecond Pulses to Modulate Cellular Responses

Nanosecond electric pulses are an effective power source in plasma medicine and biological stimulation, in which biophysical responses are governed by peak power and not energy. While uniphasic nanosecond pulse generators are widely available, the recent discovery that biological effects can be uniquely modulated by reversing the polarity of nanosecond duration pulses calls for the development of a multimodal pulse generator. This paper describes a method to generate nanosecond multiphasic pulses for biomedical use, and specifically demonstrates its ability to cancel or enhance cell swelling and blebbing. The generator consists of a series of the fundamental module, which includes a capacitor and a MOSFET switch. A positive or a negative phase pulse module can be produced based on how the switch is connected. Stacking the modules in series can increase the voltage up to 5 kV. Multiple stacks in parallel can create multiphase outputs. As each stack is independently controlled and charged, multiphasic pulses can be created to produce flexible and versatile pulse waveforms. The circuit topology can be used for high-frequency uniphasic or biphasic nanosecond burst pulse production, creating numerous opportunities for the generator in electroporation applications, tissue ablation, wound healing, and nonthermal plasma generation.

A combined experimental and theoretical investigation on cellular blebbing

Although accumulating evidence has demonstrated the important role of membrane blebbing in various cellular processes, the fundamental question of how the initiation/evolution of blebs are influenced by physical factors like membrane-cortex interactions and intracellular pressure remains unclear. Here, we report a combined modeling and experimental study to address this outstanding issue. Specifically, boundary integral method was used to track the motion of membrane (in 3D) during blebbing while possible rupture of the bilayer-cortex adhesion has also been taken into account. We showed that, for a given differential pressure across the cell membrane, the size of the weakened cortex must be over a critical value for blebbing to occur and the steady-state volume of a bleb is proportional to its initial growth rate, all in good agreement with recent experiments. The predicted shape evolution of blebs also matches well with our observations. Finally, a blebbing map, summarizing the essential physics involved, was obtained which exhibits three distinct regimes: no bleb formation corresponding to a low intracellular pressure or a small weakened cortex region; bleb formed with a fixed width when the disrupted cortex zone is very large; and a growing bleb resulted from progressive membrane-cortex detachment under intermediate weakened cortex size.

Coupling schemes for the FSI forward prediction challenge: Comparative study and validation

This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental fluid-structure interaction benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit, and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy. Copyright © 2016 John Wiley & Sons, Ltd.

Cell Surface Mechanochemistry and the Determinants of Bleb Formation, Healing, and Travel Velocity

Blebs are pressure-driven cell protrusions implicated in cellular functions such as cell division, apoptosis, and cell motility, including motility of protease-inhibited cancer cells. Because of their mechanical nature, blebs inform us about general cell-surface mechanics, including membrane dynamics, pressure propagation throughout the cytoplasm, and the architecture and dynamics of the actin cortex. Mathematical models including detailed fluid dynamics have previously been used to understand bleb expansion. Here, we develop mathematical models in two and three dimensions on longer timescales that recapitulate the full bleb life cycle, including both expansion and healing by cortex reformation, in terms of experimentally accessible biophysical parameters such as myosin contractility, osmotic pressure, and turnover of actin and ezrin. The model provides conditions under which blebbing occurs, and naturally gives rise to traveling blebs. The model predicts conditions under which blebs travel or remain stationary, as well as the bleb traveling velocity, a quantity that has remained elusive in previous models. As previous studies have used blebs as reporters of membrane tension and pressure dynamics within the cell, we have used our system to investigate various pressure equilibration models and dynamic, nonuniform membrane tension to account for the shape of a traveling bleb. We also find that traveling blebs tend to expand in all directions unless otherwise constrained. One possible constraint could be provided by spatial heterogeneity in, for example, adhesion density.

Intracellular Pressure Dynamics in Blebbing Cells

Blebs are pressure-driven protrusions that play an important role in cell migration, particularly in three-dimensional environments. A bleb is initiated when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol toward the area of detachment and local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic model of the cytoplasm that leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this discrepancy, a dynamic computational model of the cell was developed that includes mechanics of and the interactions among the cytoplasm, the actin cortex, the cell membrane, and the cytoskeleton. The model results quantify the relationship among cytoplasmic rheology, pressure, and bleb expansion dynamics, and provide a more detailed picture of intracellular pressure dynamics. This study shows the elastic response of the cytoplasm relieves pressure and limits bleb size, and that both permeability and elasticity of the cytoplasm determine bleb expansion time. Our model with a poroelastic cytoplasm shows that pressure disturbances from bleb initiation propagate faster than the timescale of bleb expansion and that pressure equilibrates slower than the timescale of bleb expansion. The multiple timescales in intracellular pressure dynamics explain the apparent discrepancy in the interpretation of experimental results.

Physical view on migration modes

Cellular motility is essential for many processes such as embryonic development, wound healing processes, tissue assembly and regeneration, immune cell trafficing and diseases such as cancer. The migration efficiency and the migratory potential depend on the type of migration mode. The previously established migration modes such as epithelial (non-migratory) and mesenchymal (migratory) as well as amoeboid (squeezing motility) relay mainly on phenomenological criteria such as cell morphology and molecular biological criteria such as gene expression. However, the physical view on the migration modes is still not well understood. As the process of malignant cancer progression such as metastasis depends on the migration of single cancer cells and their migration mode, this review focuses on the different migration strategies and discusses which mechanical prerequisites are necessary to perform a special migration mode through a 3-dimensional microenvironment. In particular, this review discusses how cells can distinguish and finally switch between the migration modes and what impact do the physical properties of cells and their microenvironment have on the transition between the novel migration modes such as blebbing and protrusive motility.

Bleb Nucleation through Membrane Peeling

We study the nucleation of blebs, i.e., protrusions arising from a local detachment of the membrane from the cortex of a cell. Based on a simple model of elastic linkers with force-dependent kinetics, we show that bleb nucleation is governed by membrane peeling. By this mechanism, the growth or shrinkage of a detached membrane patch is completely determined by the linker kinetics, regardless of the energetic cost of the detachment. We predict the critical nucleation radius for membrane peeling and the corresponding effective energy barrier. These may be typically smaller than those predicted by classical nucleation theory, implying a much faster nucleation. We also perform simulations of a continuum stochastic model of membrane-cortex adhesion to obtain the statistics of bleb nucleation times as a function of the stress on the membrane. The determinant role of membrane peeling changes our understanding of bleb nucleation and opens new directions in the study of blebs.

Vesiculation of healthy and defective red blood cells

Vesiculation of mature red blood cells (RBCs) contributes to removal of defective patches of the erythrocyte membrane. In blood disorders, which are related to defects in proteins of the RBC membrane, vesiculation of the plasma membrane is intensified. Several hypotheses have been proposed to explain RBC vesiculation but the exact underlying mechanisms and what determines the sizes of the vesicles are still not completely understood. In this work, we apply a two-component coarse-grained molecular dynamics RBC membrane model to study how RBC vesiculation is controlled by the membrane spontaneous curvature and by lateral compression of the membrane. Our simulation results show that the formation of small homogeneous vesicles with a diameter less than 40 nm can be attributed to a large spontaneous curvature of membrane domains. On the other hand, compression on the membrane can cause the formation of vesicles with heterogeneous composition and with sizes comparable with the size of the cytoskeleton corral. When spontaneous curvature and lateral compression are simultaneously considered, the compression on the membrane tends to facilitate formation of vesicles originating from curved membrane domains. We also simulate vesiculation of RBCs with membrane defects connected to hereditary elliptocytosis (HE) and to hereditary spherocytosis (HS). When the vertical connectivity between the lipid bilayer and the membrane skeleton is elevated, as in normal RBCs, multiple vesicles are shed from the compressed membrane with diameters similar to the cytoskeleton corral size. In HS RBCs, where the connectivity between the lipid bilayer and the cytoskeleton is reduced, larger-size vesicles are released under the same compression ratio as in normal RBCs. Lastly, we find that vesicles released from HE RBCs can contain cytoskeletal filaments due to fragmentation of the membrane skeleton while vesicles released from the HS RBCs are depleted of cytoskeletal filaments.

Membrane shrinkage and cortex remodelling are predicted to work in harmony to retract blebs

Numerous cell types undergo an oscillatory form of dynamics known as blebbing, whereby pressure-driven spherical protrusions of membrane (known as blebs) expand and contract over the cell's surface. Depending on the cell line, blebs play important roles in many different phenomena including mitosis and locomotion. The expansion phase of cellular blebbing has been mathematically modelled in detail. However, the active processes occurring during the retraction phase are not so well characterized. It is thought that blebs retract because a cortex reforms inside, and adheres to, the bleb membrane. This cortex is retracted into the cell and the attached bleb membrane follows. Using a computational model of a cell's membrane, cortex and interconnecting adhesions, we demonstrate that cortex retraction alone cannot account for bleb retraction and suggest that the mechanism works in tandem with membrane shrinking. Further, an emergent hysteresis loop is observed in the intracellular pressure, which suggests a potential mechanism through which a secondary bleb can be initiated as a primary bleb contracts.

Volume Changes During Active Shape Fluctuations in Cells

Cells modify their volume in response to changes in osmotic pressure but it is usually assumed that other active shape variations do not involve significant volume fluctuations. Here we report experiments demonstrating that water transport in and out of the cell is needed for the formation of blebs, commonly observed protrusions in the plasma membrane driven by cortex contraction. We develop and simulate a model of fluid-mediated membrane-cortex deformations and show that a permeable membrane is necessary for bleb formation which is otherwise impaired. Taken together, our experimental and theoretical results emphasize the subtle balance between hydrodynamics and elasticity in actively driven cell morphological changes.

A comprehensive mathematical framework for modeling intestinal smooth muscle cell contraction with applications to intestinal edema

The contraction of intestinal smooth muscle cells (ISMCs) involves many coordinated biochemical and mechanical processes. In this work, we present a framework for modeling ISMC contractility that begins with chemical models of calcium dynamics, continues with myosin light chain phosphorylation and force generation, and ends with a cell model of the ISMC undergoing contraction-relaxation. The motivation for developing this comprehensive framework is to study the effects of edema (excess fluid build-up in the muscle tissue) on ISMC contractility. The hypothesis is that more fluid equates to dilution of an external stimulis, eventually leading to reduced contractility. We compare our results to experimental data collected from normal versus edematous intestinal muscle tissue.

Cellular blebs: pressure-driven, axisymmetric, membrane protrusions

Blebs are cellular protrusions that are used by cells for multiple purposes including locomotion. A mechanical model for the problem of pressure-driven blebs based on force and moment balances of an axisymmetric shell model is proposed. The formation of a bleb is initiated by weakening the shell over a small region, and the deformation of the cellular membrane from the cortex is obtained during inflation. However, simply weakening the shell leads to an area increase of more than 4%, which is physically unrealistic. Thus, the model is extended to include a reconfiguration process that allows large blebs to form with small increases in area. It is observed that both geometric and biomechanical constraints are important in this process. In particular, it is shown that although blebs are driven by a pressure difference across the cellular membrane, it is not the limiting factor in determining bleb size.

Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions

The molecular requirements and morphology of migrating cells can vary depending on matrix geometry; therefore, predicting the optimal migration strategy or the effect of experimental perturbation is difficult. We present a model of cell motility that encompasses actin-polymerization-based protrusions, actomyosin contractility, variable actin-plasma membrane linkage leading to membrane blebbing, cell-extracellular-matrix adhesion and varying extracellular matrix geometries. This is used to explore the theoretical requirements for rapid migration in different matrix geometries. Confined matrix geometries cause profound shifts in the relationship of adhesion and contractility to cell velocity; indeed, cell-matrix adhesion is dispensable for migration in discontinuous confined environments. The model is challenged to predict the effect of different combinations of kinase inhibitors and integrin depletion in vivo, and in confined matrices based on in vitro two-dimensional measurements. Intravital imaging is used to verify bleb-driven migration at tumour margins, and the predicted response to single and combinatorial manipulations.

The role and regulation of blebs in cell migration

Blebs are cellular protrusions that have been shown to be instrumental for cell migration in development and disease. Bleb expansion is driven by hydrostatic pressure generated in the cytoplasm by the contractile actomyosin cortex. The mechanisms of bleb formation thus fundamentally differ from the actin polymerization-based mechanisms responsible for lamellipodia expansion. In this review, we summarize recent findings relevant for the mechanics of bleb formation and the underlying molecular pathways. We then review the processes involved in determining the type of protrusion formed by migrating cells, in particular in vivo, in the context of embryonic development. Finally, we discuss how cells utilize blebs for their forward movement in the presence or absence of strong substrate attachment.

Cell migration with multiple pseudopodia: temporal and spatial sensing models

Cell migration triggered by pseudopodia (or "false feet") is the most used method of locomotion. A 3D finite element model of a cell migrating over a 2D substrate is proposed, with a particular focus on the mechanical aspects of the biological phenomenon. The decomposition of the deformation gradient is used to reproduce the cyclic phases of protrusion and contraction of the cell, which are tightly synchronized with the adhesion forces at the back and at the front of the cell, respectively. First, a steady active deformation is considered to show the ability of the cell to simultaneously initiate multiple pseudopodia. Here, randomness is considered as a key aspect, which controls both the direction and the amplitude of the false feet. Second, the migration process is described through two different strategies: the temporal and the spatial sensing models. In the temporal model, the cell "sniffs" the surroundings by extending several pseudopodia and only the one that receives a positive input will become the new leading edge, while the others retract. In the spatial model instead, the cell senses the external sources at different spots of the membrane and only protrudes one pseudopod in the direction of the most attractive one.

Continuum modeling of a neuronal cell under blast loading

Traumatic brain injuries have recently been put under the spotlight as one of the most important causes of accidental brain dysfunctions. Significant experimental and modeling efforts are thus underway to study the associated biological, mechanical and physical mechanisms. In the field of cell mechanics, progress is also being made at the experimental and modeling levels to better characterize many of the cell functions, including differentiation, growth, migration and death. The work presented here aims to bridge both efforts by proposing a continuum model of a neuronal cell submitted to blast loading. In this approach, the cytoplasm, nucleus and membrane (plus cortex) are differentiated in a representative cell geometry, and different suitable material constitutive models are chosen for each one. The material parameters are calibrated against published experimental work on cell nanoindentation at multiple rates. The final cell model is ultimately subjected to blast loading within a complete computational framework of fluid-structure interaction. The results are compared to the nanoindentation simulation, and the specific effects of the blast wave on the pressure and shear levels at the interfaces are identified. As a conclusion, the presented model successfully captures some of the intrinsic intracellular phenomena occurring during the cellular deformation under blast loading that potentially lead to cell damage. It suggests, more particularly, that the localization of damage at the nucleus membrane is similar to what has already been observed at the overall cell membrane. This degree of damage is additionally predicted to be worsened by a longer blast positive phase duration. In conclusion, the proposed model ultimately provides a new three-dimensional computational tool to evaluate intracellular damage during blast loading.

'Run-and-tumble' or 'look-and-run'? A mechanical model to explore the behavior of a migrating amoeboid cell

Single cell migration constitutes a fundamental phenomenon involved in many biological events. Amoeboid cells are single cell organisms that migrate in a cyclic manner like worms. In this paper, we propose a 3D finite element model of an amoeboid cell migrating over a 2D surface. In particular, we focus on the mechanical aspect of the problem. The cell is able to generate cyclic active deformations, such as protrusion and contraction, in any direction. The progression of the cell is governed by a tight synchronization between the adhesion forces, which are alternatively applied at the front and at the rear edges of the cell, and the protrusion-contraction phases of the cell body. Finally, two important aspects have been taken into account: (1) the external stimuli in response to which the cell migrates (e.g. need to feed, morphogenetic events, normal or abnormal environment cues), (2) the heterogeneity of the 2D substrate (e.g. obstacles, rugosity, slippy regions) for which two distinct approaches have been evaluated: the 'run-and-tumble' strategy and the 'look-and-run' strategy. Overall, the results show a good agreement with respect to the experimental observations and the data from the literature (e.g. velocity and strains). Therefore, the present model helps, on one hand, to better understand the intimate relationship between the deformation modes of a cell and the adhesion strength that is required by the cell to crawl over a substrate, and, on the other hand, to put in evidence the crucial role played by mechanics during the migration process.

A computational model of bleb formation

Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused on cells that use blebbing for migrating through 3D fibrous matrices. In particular, metastatic cancer cells have been shown to use blebs for motility. A dynamic computational model of the cell is presented that includes mechanics of and the interactions between the intracellular fluid, the actin cortex and the cell membrane. The computational model is used to explore the relative roles in bleb formation time of cytoplasmic viscosity and drag between the cortex and the cytosol. A regime of values for the drag coefficient and cytoplasmic viscosity values that match bleb formation timescales is presented. The model results are then used to predict the Darcy permeability and the volume fraction of the cortex.

Computer simulation of cytoskeleton-induced blebbing in lipid membranes

Blebs are balloon-shaped membrane protrusions that form during many physiological processes. Using computer simulation of a particle-based model for self-assembled lipid bilayers coupled to an elastic meshwork, we investigated the phase behavior and kinetics of blebbing. We found that blebs form for large values of the ratio between the areas of the bilayer and the cytoskeleton. We also found that blebbing can be induced when the cytoskeleton is subject to a localized ablation or a uniform compression. The results obtained are qualitatively in agreement with the experimental evidence and the model opens up the possibility to study the kinetics of bleb formation in detail.

A POROELASTIC MODEL FOR CELL CRAWLING INCLUDING MECHANICAL COUPLING BETWEEN CYTOSKELETAL CONTRACTION AND ACTIN POLYMERIZATION

Much is known about the biophysical mechanisms involved in cell crawling, but how these processes are coordinated to produce directed motion is not well understood. Here, we propose a new hypothesis whereby local cytoskeletal contraction generates fluid flow through the lamellipodium, with the pressure at the front of the cell facilitating actin polymerization which pushes the leading edge forward. The contraction, in turn, is regulated by stress in the cytoskeleton. To test this hypothesis, finite element models for a crawling cell are presented. These models are based on nonlinear poroelasticity theory, modified to include the effects of active contraction and growth, which are regulated by mechanical feedback laws. Results from the models agree reasonably well with published experimental data for cell speed, actin flow, and cytoskeletal deformation in migrating fish epidermal keratocytes. The models also suggest that oscillations can occur for certain ranges of parameter values.

Apoptotic volume decrease as a geometric determinant for cell dismantling into apoptotic bodies

Apoptosis is a mode of cell death through which cells are dismantled and cell remains are packed into small, membrane-bound, sealed vesicles called apoptotic bodies, which are easy to erase by phagocytosis by neighbouring and immune system cells. The end point of the process is to cleanly eliminate damaged or unnecessary cells without disrupting the surrounding tissue or eliciting an inflammatory response. The apoptotic process involves a series of specific events including deoxyribonucleic acid and nuclear fragmentation, protease-driven cleavage of specific substrates, which inhibits key survival functions and reorganizes the cell's structure, externalization of molecules involved in phagocytosis, membrane blebbing and cell shrinkage. Apoptotic volume decrease (AVD) leading to cell shrinkage is a core event in the course of apoptosis, the biological meaning of which has not been clearly ascertained. In this article we argue that volume loss is a geometrical requisite for cell dismantling into apoptotic bodies. This is derived from the cell's volume-to-surface ratio. Indeed, package of the original cell volume into smaller membrane-sealed vesicles requires that either cell membrane surface increase or cell volume decrease. In this sense, AVD provides a reservoir of membrane surface for apoptotic body formation. The strategic situation of AVD in the time course of apoptosis is also discussed in the context of apoptotic body formation.