Intracellular Pressure Dynamics in Blebbing Cells

Biophysical modeling identifies an optimal hybrid amoeboid-mesenchymal phenotype for maximal T cell migration speeds

Despite recent experimental progress in characterizing cell migration mechanics, our understanding of the mechanisms governing rapid cell movement remains limited. To effectively limit tumor growth, antitumoral T cells need to rapidly migrate to find and kill cancer cells. To investigate the upper limits of cell speed, we developed a new hybrid stochastic-mean field model of bleb-based cell motility. We first examined the potential for adhesion-free bleb-based migration and show that cells migrate inefficiently in the absence of adhesion-based forces, i.e., cell swimming. While no cortical contractility oscillations are needed for cells to swim in viscoelastic media, high-to-low cortical contractility oscillations are necessary for cell swimming in viscous media. This involves a high cortical contractility phase with multiple bleb nucleation events, followed by an intracellular pressure buildup recovery phase at low cortical tensions, resulting in modest net cell motion. However, our model suggests that cells can employ a hybrid bleb- and adhesion-based migration mechanism for rapid cell motility and identifies conditions for optimality. The model provides a momentum-conserving mechanism underlying rapid single-cell migration and identifies factors as design criteria for engineering T cell therapies to improve movement in mechanically complex environments.

Benefits and challenges of reconstituting the actin cortex

The cell's ability to change shape is a central feature in many cellular processes, including cytokinesis, motility, migration, and tissue formation. The cell constructs a network of contractile proteins underneath the cell membrane to form the cortex, and the reorganization of these components directly contributes to cellular shape changes. The desire to mimic these cell shape changes to aid in the creation of a synthetic cell has been increasing. Therefore, membrane-based reconstitution experiments have flourished, furthering our understanding of the minimal components the cell uses throughout these processes. Although biochemical approaches increased our understanding of actin, myosin II, and actin-associated proteins, using membrane-based reconstituted systems has further expanded our understanding of actin structures and functions because membrane-cortex interactions can be analyzed. In this review, we highlight the recent developments in membrane-based reconstitution techniques. We examine the current findings on the minimal components needed to recapitulate distinct actin structures and functions and how they relate to the cortex's impact on cellular mechanical properties. We also explore how co-processing of computational models with wet-lab experiments enhances our understanding of these properties. Finally, we emphasize the benefits and challenges inherent to membrane-based, reconstitution assays, ranging from the advantage of precise control over the system to the difficulty of integrating these findings into the complex cellular environment.

Two-phase kinetics and cell cortex elastic behavior in Xenopus gastrula cell-cell adhesion

Morphogenetic movements during animal development involve repeated making and breaking of cell-cell contacts. Recent biophysical models of cell-cell adhesion integrate adhesion molecule interactions and cortical cytoskeletal tension modulation, describing equilibrium states for established contacts. We extend this emerging unified concept of adhesion to contact formation kinetics, showing that aggregating Xenopus embryonic cells rapidly achieve Ca2+-independent low-contact states. Subsequent transitions to cadherin-dependent high-contact states show rapid decreases in contact cortical F-actin levels but slow contact area growth. We developed a biophysical model that predicted contact growth quantitatively from known cellular and cytoskeletal parameters, revealing that elastic resistance to deformation and cytoskeletal network turnover are essential determinants of adhesion kinetics. Characteristic time scales of contact growth to low and high states differ by an order of magnitude, being at a few minutes and tens of minutes, respectively, thus providing insight into the timescales of cell-rearrangement-dependent tissue movements.

Modeling the dynamics of actin and myosin during bleb stabilization

The actin cortex is very dynamic during migration of eukaryotes. In cells that use blebs as leading-edge protrusions, the cortex reforms beneath the cell membrane (bleb cortex) and completely disassembles at the site of bleb initiation. Remnants of the actin cortex at the site of bleb nucleation are referred to as the actin scar. We refer to the combined process of cortex reformation along with the degradation of the actin scar during bleb-based cell migration as bleb stabilization. The molecular factors that regulate the dynamic reorganization of the cortex are not fully understood. Myosin motor protein activity has been shown to be necessary for blebbing, with its major role associated with pressure generation to drive bleb expansion. Here, we examine the role of myosin in regulating cortex dynamics during bleb stabilization. Analysis of microscopy data from protein localization experiments in Dictyostelium discoideum cells reveals a rapid formation of the bleb's cortex with a delay in myosin accumulation. In the degrading actin scar, myosin is observed to accumulate before active degradation of the cortex begins. Through a combination of mathematical modeling and data fitting, we identify that myosin helps regulate the equilibrium concentration of actin in the bleb cortex during its reformation by increasing its dissasembly rate. Our modeling and analysis also suggests that cortex degradation is driven primarily by an exponential decrease in actin assembly rate rather than increased myosin activity. We attribute the decrease in actin assembly to the separation of the cell membrane from the cortex after bleb nucleation.

Robotic Intracellular Pressure Measurement Using Micropipette Electrode

Intracellular pressure, a key physical parameter of the intracellular environment, has been found to regulate multiple cell physiological activities and impact cell micromanipulation results. The intracellular pressure may reveal the mechanism of these cells' physiological activities or improve the micro-manipulation accuracy for cells. The involvement of specialized and expensive devices and the significant damage to cell viability that the current intracellular pressure measurement methods cause significantly limit their wide applications. This paper proposes a robotic intracellular pressure measurement method using a traditional micropipette electrode system setup. First, the measured resistance of the micropipette inside the culture medium is modeled to analyze its variation trend when the pressure inside the micropipette increases. Then, the concentration of KCl solution filled inside the micropipette electrode that is suitable for intracellular pressure measurement is determined according to the tested electrode resistance-pressure relationship; 1 mol/L KCl solution is our final choice. Further, the measurement resistance of the micropipette electrode inside the cell is modeled to measure the intracellular pressure through the difference in key pressure before and after the release of the intracellular pressure. Based on the above work, a robotic measurement procedure of the intracellular pressure is established based on a traditional micropipette electrode system. The experimental results on porcine oocytes demonstrate that the proposed method can operate on cells at an average speed of 20~40 cells/day with measurement efficiency comparable to the related work. The average repeated error of the relationship between the measured electrode resistance and the pressure inside the micropipette electrode is less than 5%, and no observable intracellular pressure leakage was found during the measurement process, both guaranteeing the measurement accuracy of intracellular pressure. The measured results of the porcine oocytes are in accordance with those reported in related work. Moreover, a 90% survival rate of operated oocytes was obtained after measurement, proving limited damage to cell viability. Our method does not rely on expensive instruments and is conducive to promotion in daily laboratories.

T cell cytoskeletal forces shape synapse topography for targeted lysis via membrane curvature bias of perforin

Cytotoxic T lymphocytes (CTLs) lyse target cells by delivering lytic granules that contain the pore former perforin to the cytotoxic immunological synapse. Here, we establish that opposing cytoskeletal forces drive lytic granule polarization and simultaneously shape T cell synapse topography to enhance target perforation. At the cell rear, actomyosin contractility drives the anterograde movement of lytic granules toward the nucleus. At the synapse, dynein-derived forces induce negatively curved membrane pockets to which granules are transported around the nucleus. These highly concave degranulation pockets are located directly opposite positively curved bulges on the target cell membrane. We identify a curvature bias in the action of perforin, which preferentially perforates positively curved tumor cell membrane. Together, these findings demonstrate murine and human T cell-mediated cytotoxicity to be a highly tuned mechano-biochemical system, in which the forces that polarize lytic granules locally bend the synaptic membrane to favor the unidirectional perforation of the target cell.

The Pressure Dependence of the Stability of the G-quadruplex Formed by d(TGGGGT)

The G-quadruplex (GQ), a tetrahelix formed by guanine-rich nucleic acid sequences, is a potential drug target for several diseases. Monomolecular GQs are stabilized by guanine tetrads and non-guanine regions that form loops. Hydrostatic pressure destabilizes the folded, monomolecular GQ structures. In this communication, we present data on the effect of pressure on the conformational stability of the tetramolecular GQ, d[5′-TGGGGT-3′]₄. This molecule does not have loops linking the tetrads; thus, its physical properties presumably reflect those of the tetrads alone. Understanding the properties of the tetrads will aid in understanding the contribution of the other structural components to the stability of GQ DNA. By measuring UV light absorption, we have studied the effect of hydrostatic pressure on the thermal stability of the tetramolecular d[5′-TGGGGT-3′]₄ in the presence of sodium ions. Our data show that, unlike monomolecular GQ, the temperature at which d[5′-TGGGGT-3′]₄ dissociates to form the constituent monomers is nearly independent of pressure up to 200 MPa. This implies that there is no net molar volume difference (∆V) between the GQ and the unfolded random-coil states. This finding further suggests that the large negative ∆V values for the unfolding of monomolecular GQ are due to the presence of the loop regions in those structures.

A role for myosin II clusters and membrane energy in cortex rupture for Dictyostelium discoideum

Blebs, pressure driven protrusions of the cell membrane, facilitate the movement of eukaryotic cells such as the soil amoeba Dictyostelium discoideum, white blood cells and cancer cells. Blebs initiate when the cell membrane separates from the underlying cortex. A local rupture of the cortex, has been suggested as a mechanism by which blebs are initiated. However, much clarity is still needed about how cells inherently regulate rupture of the cortex in locations where blebs are expected to form. In this work, we examine the role of membrane energy and the motor protein myosin II (myosin) in facilitating the cell driven rupture of the cortex. We perform under-agarose chemotaxis experiments, using Dictyostelium discoideum cells, to visualize the dynamics of myosin and calculate changes in membrane energy in the blebbing region. To facilitate a rapid detection of blebs and analysis of the energy and myosin distribution at the cell front, we introduce an autonomous bleb detection algorithm that takes in discrete cell boundaries and returns the coordinate location of blebs with its shape characteristics. We are able to identify by microscopy naturally occurring gaps in the cortex prior to membrane detachment at sites of bleb nucleation. These gaps form at positions calculated to have high membrane energy, and are associated with areas of myosin enrichment. Myosin is also shown to accumulate in the cortex prior to bleb initiation and just before the complete disassembly of the cortex. Together our findings provide direct spatial and temporal evidence to support cortex rupture as an intrinsic bleb initiation mechanism and suggests that myosin clusters are associated with regions of high membrane energy where its contractile activity leads to a rupture of the cortex at points of maximal energy.

A Reduced 1D Stochastic Model of Bleb-driven Cell Migration

Blebs are pressure-driven protrusions that have been observed in cells undergoing apoptosis, cytokinesis, or migration, including tumour cells that use blebs to escape their organs of origin. Here, we present a minimal 1D model of bleb-driven cell motion that combines a simple mechanical model with turnover kinetics of the actin cortex and adhesions between the membrane and the cortex. The deterministic version of this model is used to study the properties of individual blebbing events. We further introduce stochastic turnover of the adhesions, which allows for spontaneous initiation of repeated blebbing events, thus leading to sustained cell travel. We explore how the main parameters of the system control the properties of the blebbing events and the speed of cell travel. Finally, we derive a further simplification by deriving a Langevin approximation to this stochastic model.

Effects of the Laplace pressure on the cells during cytokinesis

The Laplace pressure is one of the most fundamental regulators that determine cell shape and function, and thus has been receiving widespread attention. Here, we systemically investigate the effect of the Laplace pressure on the shape and function of the cells during cytokinesis. We find that the Laplace pressure during cytokinesis can directly control the distribution and size of cell blebbing and adjust the symmetry of cell division by virtue of changing the characteristics of cell blebbing. Further, we demonstrate that the Laplace pressure changes the structural uniformity of cell boundary to regulate the symmetry of cell division. Our findings provide further insights as to the important role of the Laplace pressure in regulating the symmetry of cell division during cytokinesis.

Lymphocyte egress signal sphingosine-1-phosphate promotes ERM-guided, bleb-based migration

Ezrin, radixin, and moesin (ERM) family proteins regulate cytoskeletal responses by tethering the plasma membrane to the underlying actin cortex. Mutations in ERM proteins lead to severe combined immunodeficiency, but the function of these proteins in T cells remains poorly defined. Using mice in which T cells lack all ERM proteins, we demonstrate a selective role for these proteins in facilitating S1P-dependent egress from lymphoid organs. ERM-deficient T cells display defective S1P-induced migration in vitro, despite normal responses to standard protein chemokines. Analysis of these defects revealed that S1P promotes a fundamentally different mode of migration than chemokines, characterized by intracellular pressurization and bleb-based motility. ERM proteins facilitate this process, controlling directional migration by limiting blebbing to the leading edge. We propose that the distinct modes of motility induced by S1P and chemokines are specialized to allow T cell migration across lymphatic barriers and through tissue stroma, respectively.

Cell nucleus as a microrheological probe to study the rheology of the cytoskeleton

Mechanical properties of the cell are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. The development of microfluidic technologies has enabled measuring the cell's mechanical properties at high throughput so that mechanical phenotyping can be applied to large samples in reasonable timescales. These studies typically measure the stiffness of the cell as the only mechanical biomarker and do not disentangle the rheological contributions of different structural components of the cell, including the cell cortex, the interior cytoplasm and its immersed cytoskeletal structures, and the nucleus. Recent advancements in high-speed fluorescent imaging have enabled probing the deformations of the cell cortex while also tracking different intracellular components in rates applicable to microfluidic platforms. We present a, to our knowledge, novel method to decouple the mechanics of the cell cortex and the cytoplasm by analyzing the correlation between the cortical deformations that are induced by external microfluidic flows and the nucleus displacements, induced by those cortical deformations, i.e., we use the nucleus as a high-throughput microrheological probe to study the rheology of the cytoplasm, independent of the cell cortex mechanics. To demonstrate the applicability of this method, we consider a proof-of-concept model consisting of a rigid spherical nucleus centered in a spherical cell. We obtain analytical expressions for the time-dependent nucleus velocity as a function of the cell deformations when the interior cytoplasm is modeled as a viscous, viscoelastic, porous, and poroelastic material and demonstrate how the nucleus velocity can be used to characterize the linear rheology of the cytoplasm over a wide range of forces and timescales/frequencies.

Nonlinear Elastic and Inelastic Properties of Cells

Mechanical forces play an important role in various physiological processes, such as morphogenesis, cytokinesis, and migration. Thus, in order to illuminate mechanisms underlying these physiological processes, it is crucial to understand how cells deform and respond to external mechanical stimuli. During recent decades, the mechanical properties of cells have been studied extensively using diverse measurement techniques. A number of experimental studies have shown that cells are far from linear elastic materials. Cells exhibit a wide variety of nonlinear elastic and inelastic properties. Such complicated properties of cells are known to emerge from unique mechanical characteristics of cellular components. In this review, we introduce major cellular components that largely govern cell mechanical properties and provide brief explanations of several experimental techniques used for rheological measurements of cell mechanics. Then, we discuss the representative nonlinear elastic and inelastic properties of cells. Finally, continuum and discrete computational models of cell mechanics, which model both nonlinear elastic and inelastic properties of cells, will be described.

Computational estimates of mechanical constraints on cell migration through the extracellular matrix

Cell migration through a three-dimensional (3D) extracellular matrix (ECM) underlies important physiological phenomena and is based on a variety of mechanical strategies depending on the cell type and the properties of the ECM. By using computer simulations of the cell’s mid-plane, we investigate two such migration mechanisms—‘push-pull’ (forming a finger-like protrusion, adhering to an ECM node, and pulling the cell body forward) and ‘rear-squeezing’ (pushing the cell body through the ECM by contracting the cell cortex and ECM at the cell rear). We present a computational model that accounts for both elastic deformation and forces of the ECM, an active cell cortex and nucleus, and for hydrodynamic forces and flow of the extracellular fluid, cytoplasm, and nucleoplasm. We find that relations between three mechanical parameters—the cortex’s contractile force, nuclear elasticity, and ECM rigidity—determine the effectiveness of cell migration through the dense ECM. The cell can migrate persistently even if its cortical contraction cannot deform a near-rigid ECM, but then the contraction of the cortex has to be able to sufficiently deform the nucleus. The cell can also migrate even if it fails to deform a stiff nucleus, but then it has to be able to sufficiently deform the ECM. Simulation results show that nuclear stiffness limits the cell migration more than the ECM rigidity. Simulations show the rear-squeezing mechanism of motility results in more robust migration with larger cell displacements than those with the push-pull mechanism over a range of parameter values. Additionally, results show that the rear-squeezing mechanism is aided by hydrodynamics through a pressure gradient.

Computational simulations of two different mechanisms of 3D cell migration in an extracellular matrix are presented. One mechanism represents a mesenchymal mode, characterized by finger-like actin protrusions, while the second mode is more amoeboid in that rear contraction of the cortex propels the cell forward. In both mechanisms, the cell generates a thin actin protrusion on the cortex that attaches to an ECM node. The cell is then either pulled (mesenchymal) or pushed (amoeboid) forward. Results show both mechanisms result in successful migration over a range of simulated parameter values as long as the contractile tension of the cortex exceeds either the nuclear stiffness or ECM stiffness, but not necessarily both. However, the distance traveled by the amoeboid migration mode is more robust to changes in parameter values, and is larger than in simulations of the mesenchymal mode. Additionally, cells experience a favorable fluid pressure gradient when migrating in the amoeboid mode, and an adverse fluid pressure gradient in the mesenchymal mode.

Focal adhesion kinase is activated by microtubule-depolymerizing agents and regulates membrane blebbing in human endothelial cells

Microtubule‐depolymerizing agents can selectively disrupt tumor vessels via inducing endothelial membrane blebbing. However, the mechanism regulating blebbing is largely unknown. IMB5046 is a newly discovered microtubule‐depolymerizing agent. Here, the functions of focal adhesion kinase (FAK) during IMB5046‐induced blebbing and the relevant mechanism are studied. We found that IMB5046 induced membrane blebbing and reassembly of focal adhesions in human vascular endothelial cells. Both FAK inhibitor and knock‐down expression of FAK inhibited IMB5046‐induced blebbing. Mechanism study revealed that IMB5046 induced the activation of FAK via GEF‐H1/ Rho/ ROCK/ MLC2 pathway. cRGD peptide, a ligand of integrin, also blocked IMB5046‐induced blebbing. After activation, FAK further promoted the phosphorylation of MLC2. This positive feedback loop caused more intensive actomyosin contraction and continuous membrane blebbing. FAK inhibitor blocked membrane blebbing via inhibiting actomyosin contraction, and stimulated stress fibre formation via promoting the phosphorylation of HSP27. Conclusively, these results demonstrate that FAK is a molecular switch controlling endothelial blebbing and stress fibre formation. Our study provides a new molecular mechanism for microtubule‐depolymerizing agents to be used as vascular disrupting agents.

Differences in creep response of GBM cells migrating in confinement

Using a microfluidic platform to apply negative aspiration pressure (–20, –25, –30, –35 and –40 cm H₂O), we compared the differences in creep responses of Glioblastoma Multiforme (GBM) cells while migrating in confinement and at a stationary state on a 2D substrate. Cells were either migrating in a channel of 5 x 5 μm cross-section or stationary at the entrance to the channel. In response to aspiration pressure, we found actively migrating GBM cells exhibited a higher stiffness than stationary cells. Additionally, migrating cells absorbed more energy elastically with a relatively small dissipative energy loss. At elevated negative pressure loads up to – 30 cm H₂O, we observed a linear increase in elastic deformation and a higher distribution in elastic storage than energy loss, and the response plateaued at further increasing negative pressure loads. To explore the underlying cause, we carried out immuno-cytochemical studies of these cells and found a polarized actin and myosin distribution at the front and posterior ends of the migrating cells, whereas the distribution of the stationary group demonstrated no specific regional differences. These differences in creep response and cytoskeletal protein distribution demonstrate the importance of a migrating cell’s kinematic state to the mechanism of cell migration.

Potential Hydrodynamic Cytoplasmic Transfer between Mammalian Cells: Cell-Projection Pumping

We earlier reported cytoplasmic fluorescence exchange between cultured human fibroblasts (Fibs) and malignant cells (MCs). Others report similar transfer via either tunneling nanotubes (TNTs) or shed membrane vesicles, and this changes the phenotype of recipient cells. Our time-lapse microscopy showed most exchange was from Fibs into MCs, with less in the reverse direction. Although TNTs were seen, we were surprised transfer was not via TNTs but was instead via fine and often branching cell projections that defied direct visual resolution because of their size and rapid movement. Their structure was revealed nonetheless by their organellar cargo and the grooves they formed indenting MCs, which was consistent with holotomography. Discrete, rapid, and highly localized transfer events evidenced against a role for shed vesicles. Transfer coincided with rapid retraction of the cell projections, suggesting a hydrodynamic mechanism. Increased hydrodynamic pressure in retracting cell projections normally returns cytoplasm to the cell body. We hypothesize "cell-projection pumping" (CPP), in which cytoplasm in retracting cell projections partially equilibrates into adjacent recipient cells via microfusions that form temporary intercellular cytoplasmic continuities. We tested plausibility for CPP by combined mathematical modeling, comparison of predictions from the model with experimental results, and then computer simulations based on experimental data. The mathematical model predicted preferential CPP into cells with lower cell stiffness, expected from equilibration of pressure toward least resistance. Predictions from the model were satisfied when Fibs were cocultured with MCs and fluorescence exchange was related to cell stiffness by atomic force microscopy. When transfer into 5000 simulated recipient MCs or Fibs was studied in computer simulations, inputting experimental cell stiffness and donor cell fluorescence values generated transfers to simulated recipient cells similar to those seen by experiment. We propose CPP as a potentially novel mechanism in mammalian intercellular cytoplasmic transfer and communication.

Advances in geometric techniques for analyzing blebbing in chemotaxing Dictyostelium cells

We present a technical platform that allows us to monitor and measure cortex and membrane dynamics during bleb-based chemotaxis. Using D. discoideum cells expressing LifeAct-GFP and crawling under agarose containing RITC-dextran, we were able to simultaneously visualize the actin cortex and the cell membrane throughout bleb formation. Using these images, we then applied edge detect to generate points on the cell boundary with coordinates in a coordinate plane. Then we fitted these points to a curve with known x and y coordinate functions. The result was to parameterize the cell outline. With the parameterization, we demonstrate how to compute data for geometric features such as cell area, bleb area and edge curvature. This allows us to collect vital data for the analysis of blebbing.

Distinct relaxation timescales of neurites revealed by rate-dependent indentation, relaxation and micro-rheology tests

Although the dynamic response of neurites is believed to play crucial roles in processes like axon outgrowth and formation of the neural network, the dynamic mechanical properties of such protrusions remain poorly understood. In this study, by using AFM (atomic force microscopy) indentation, we systematically examined the dynamic behavior of well-developed neurites on primary neurons under different loading modes (step loading, oscillating loading and ramp loading). Interestingly, the response was found to be strongly rate-dependent, with an apparent initial and long-term elastic modulus around 800 and 80 Pa, respectively. To better analyze the measurement data and extract information of key interest, the finite element simulation method (FEM) was also conducted where the neurite was treated as a viscoelastic solid consisting of multiple characteristic relaxation times. It was found that a minimum of three relaxation timescales, i.e. ∼0.01, 0.1 and 1 seconds, are needed to explain the observed relaxation curve as well as fit simulation results to the indentation and rheology data under different loading rates and driving frequencies. We further demonstrated that these three characteristic relaxation times likely originate from the thermal fluctuations of the microtubule, membrane relaxation and cytosol viscosity, respectively. By identifying key parameters describing the time-dependent behavior of neurites, as well as revealing possible physical mechanisms behind, this study could greatly help us understand how neural cells perform their biological duties over a wide spectrum of timescales.

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.

Living Matter: Mesoscopic Active Materials

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with "dead," nonactive matter is presented. This field of research is increasingly denoted as "biological physics" where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function. These include locomotion (cell motility and migration) forces that give rise to cell division, the growth and form of cellular assemblies in development, the beating of heart cells, and the effects of mechanical perturbations such as shear flow (in the bloodstream) or adhesion to other cells or tissues. An introduction to the fundamental concepts and theory with selected experimental examples related to the authors' own research is presented, including red-blood-cell membrane fluctuations, motion of the nucleus within an egg cell, self-contracting acto-myosin gels, and structure and beating of heart cells (cardiomyocytes), including how they can be driven by an oscillating, mechanical probe.

Spontaneous buckling of contractile poroelastic actomyosin sheets

Shape transitions in developing organisms can be driven by active stresses, notably, active contractility generated by myosin motors. The mechanisms generating tissue folding are typically studied in epithelia. There, the interaction between cells is also coupled to an elastic substrate, presenting a major difficulty for studying contraction induced folding. Here we study the contraction and buckling of active, initially homogeneous, thin elastic actomyosin networks isolated from bounding surfaces. The network behaves as a poroelastic material, where a flow of fluid is generated during contraction. Contraction starts at the system boundaries, proceeds into the bulk, and eventually leads to spontaneous buckling of the sheet at the periphery. The buckling instability resulted from system self-organization and from the spontaneous emergence of density gradients driven by the active contractility. The buckling wavelength increases linearly with sheet thickness. Our system offers a well-controlled way to study mechanically induced, spontaneous shape transitions in active matter.

Active matter composed of filaments and molecular motors can contract. Here, the authors report the spontaneous out-of-plane buckling of reconstituted contracting poroelastic actomyosin sheets in the absence of external cues.

Intracellular Pressure: A Driver of Cell Morphology and Movement

Intracellular pressure, generated by actomyosin contractility and the directional flow of water across the plasma membrane, can rapidly reprogram cell shape and behavior. Recent work demonstrates that cells can generate intracellular pressure with a range spanning at least two orders of magnitude; significantly, pressure is implicated as an important regulator of cell dynamics, such as cell division and migration. Changes to intracellular pressure can dictate the mechanisms by which single human cells move through three-dimensional environments. In this review, we chronicle the classic as well as recent evidence demonstrating how intracellular pressure is generated and maintained in metazoan cells. Furthermore, we highlight how this potentially ubiquitous physical characteristic is emerging as an important driver of cell morphology and behavior.

Going with the Flow: Water Flux and Cell Shape during Cytokinesis

Cell shape changes during cytokinesis in eukaryotic cells have been attributed to contractile forces from the actomyosin ring and the actomyosin cortex. Here we propose an additional mechanism where active pumping of ions and water at the cell poles and the division furrow can also achieve the same type of shape change during cytokinesis without myosin contraction. We develop a general mathematical model to examine shape changes in a permeable object subject to boundary fluxes. We find that hydrodynamic flows in the cytoplasm and the relative drag between the cytoskeleton network phase and the water phase also play a role in determining the cell shape during cytokinesis. Forces from the actomyosin contractile ring and cortex do contribute to the cell shape, and can work together with water permeation to facilitate cytokinesis. To influence water flow, we osmotically shock the cell during cell division, and find that the cell can actively adapt to osmotic changes and complete division. Depolymerizing the actin cytoskeleton during cytokinesis also does not affect the contraction speed. We also explore the role of membrane ion channels and pumps in setting up the spatially varying water flux.

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.

A free-boundary model of a motile cell explains turning behavior

To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell.

To understand shapes and movements of simple motile cells, we systematically explore minimal models describing a cell as a two-dimensional actin-myosin gel with a free boundary. The models account for actin-myosin contraction balanced by viscous stresses in the actin gel and uniform adhesion. The myosin contraction causes the lamellipodial boundary to retract. Actin protrusion at the boundary counters the retraction, and the balance of protrusion and retraction shapes the cell. The models reproduce a variety of motile shapes observed experimentally. The analysis shows that the mechanical state of a cell depends on a small number of parameters. We find that when the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectory. Scanning model parameters shows that the contractile mechanism of motility supports robust cell turning behavior in conditions where deformable actin gel and fast protrusion destabilize the axial symmetry of a moving cell.

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at leastC 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

BioFlow: a non-invasive, image-based method to measure speed, pressure and forces inside living cells

Cell motility is governed by a complex molecular machinery that converts physico-chemical cues into whole-cell movement. Understanding the underlying biophysical mechanisms requires the ability to measure physical quantities inside the cell in a simple, reproducible and preferably non-invasive manner. To this end, we developed BioFlow, a computational mechano-imaging method and associated software able to extract intracellular measurements including pressure, forces and velocity everywhere inside freely moving cells in two and three dimensions with high spatial resolution in a non-invasive manner. This is achieved by extracting the motion of intracellular material observed using fluorescence microscopy, while simultaneously inferring the parameters of a given theoretical model of the cell interior. We illustrate the power of BioFlow in the context of amoeboid cell migration, by modelling the intracellular actin bulk flow of the parasite Entamoeba histolytica using fluid dynamics, and report unique experimental measures that complement and extend both theoretical estimations and invasive experimental measures. Thanks to its flexibility, BioFlow is easily adaptable to other theoretical models of the cell, and alleviates the need for complex or invasive experimental conditions, thus constituting a powerful tool-kit for mechano-biology studies. BioFlow is open-source and freely available via the Icy software.

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.