Electromechanics and Volume Dynamics in Nonexcitable Tissue Cells

Cytoskeletal activation of NHE1 regulates mechanosensitive cell volume adaptation and proliferation

Mammalian cells rapidly respond to environmental changes by altering transmembrane water and ion fluxes, changing cell volume. Contractile forces generated by actomyosin have been proposed to mechanically regulate cell volume. However, our findings reveal a different mechanism in adherent cells, where elevated actomyosin activity increases cell volume in normal-like cells (NIH 3T3 and others) through interaction with the sodium-hydrogen exchanger isoform 1 (NHE1). This leads to a slow secondary volume increase (SVI) following the initial regulatory volume decrease during hypotonic shock. The active cell response is further confirmed by intracellular alkalinization during mechanical stretch. Moreover, cytoskeletal activation of NHE1 during SVI deforms the nucleus, causing immediate transcriptomic changes and ERK-dependent growth inhibition. Notably, SVI and its associated changes are absent in many cancer cell lines or cells on compliant substrates with reduced actomyosin activity. Thus, actomyosin acts as a sensory element rather than a force generator during adaptation to environmental challenges.

HepG2 cells undergo regulatory volume decrease by mechanically induced efflux of water and solutes

This study challenges the conventional belief that animal cell membranes lack a significant hydrostatic gradient, particularly under anisotonic conditions, as demonstrated in the human hepatoma cell line HepG2. The Boyle van't Hoff (BvH) relation describes volumetric equilibration to anisotonic conditions for many cells. However, the BvH relation is simple and does not include many cellular components such as the cytoskeleton and actin cortex, mechanosensitive channels, and ion pumps. Here we present alternative models that account for mechanical resistance to volumetric expansion, solute leakage, and active ion pumping. We found the BvH relation works well to describe hypertonic volume equilibration but not hypotonic volume equilibration. After anisotonic exposure and return isotonic conditions cell volumes were smaller than their initial isotonic volume, indicating solutes had leaked out of the cell during swelling. Finally, we observed HepG2 cells undergo regulatory volume decrease at both 20 °C and 4 °C, indicating regulatory volume decrease to be a relatively passive phenomenon and not driven by ion pumps. We determined the turgor-leak model, which accounts for mechanical resistance and solute leakage, best fits the observations found in the suite of experiments performed, while other models were rejected.

Confinement controls the directional cell responses to fluid forces

Our understanding of how fluid forces influence cell migration in confining environments remains limited. By integrating microfluidics with live-cell imaging, we demonstrate that cells in tightly-but not moderately-confined spaces reverse direction and move upstream upon exposure to fluid forces. This fluid force-induced directional change occurs less frequently when cells display diminished mechanosensitivity, experience elevated hydraulic resistance, or sense a chemical gradient. Cell reversal requires actin polymerization to the new cell front, as shown mathematically and experimentally. Actin polymerization is necessary for the fluid force-induced activation of NHE1, which cooperates with calcium to induce upstream migration. Calcium levels increase downstream, mirroring the subcellular distribution of myosin IIA, whose activation enhances upstream migration. Reduced lamin A/C levels promote downstream migration of metastatic tumor cells by preventing cell polarity establishment and intracellular calcium rise. This mechanism could allow cancer cells to evade high-pressure environments, such as the primary tumor.

Cell-Driven Fluid Dynamics: A Physical Model of Active Systemic Circulation

Active fluid circulation and transport are key functions of living organisms, which drive efficient delivery of oxygen and nutrients to various physiological compartments. Because fluid circulation occurs in a network, the systemic flux and pressure are not simple outcomes of any given component. Rather, they are emergent properties of network elements and network topology. Moreover, consistent pressure and osmolarity gradients across compartments such as the kidney, interstitium, and vessels are known. How these gradients and network properties are established and maintained is an unanswered question in systems physiology. Previous studies have shown that epithelial cells are fluid pumps that actively generate pressure and osmolarity gradients. Polarization and activity of ion exchangers that drive fluid flux in epithelial cells are affected by pressure and osmolarity gradients. Therefore, there is an unexplored coupling between the pressure and osmolarity in the circulating network. Here we develop a mathematical theory that integrates the influence of pressure and osmolarity on solute transport and explores both cell fluid transport and systemic circulation. This model naturally generates pressure and osmolarity gradients across physiological compartments, and demonstrates how systemic transport properties can depend on cell properties, and how the cell state can depend on systemic properties. When epithelial and endothelial pumps are considered together, we predict how pressures at various points in the network depend on the overall osmolarity of the system. The model can be improved by including physiological geometries and expanding solute species, and highlights the interplay of fluid properties with cell function in living organisms.

Should I shrink or should I grow: cell size changes in tissue morphogenesis

Cells change shape, move, divide, and die to sculpt tissues. Common to all these cell behaviours are cell size changes, which have recently emerged as key contributors to tissue morphogenesis. Cells can change their mass-the number of macromolecules they contain-or their volume-the space they encompass. Changes in cell mass and volume occur through different molecular mechanisms and at different timescales, slow for changes in mass and rapid for changes in volume. Therefore, changes in cell mass and cell volume, which are often linked, contribute to the development and shaping of tissues in different ways. Here, we review the molecular mechanisms by which cells can control and alter their size, and we discuss how changes in cell mass and volume contribute to tissue morphogenesis. The role that cell size control plays in developing embryos is only starting to be elucidated. Research on the signals that control cell size will illuminate our understanding of the cellular and molecular mechanisms that drive tissue morphogenesis.

How Merkel cells transduce mechanical stimuli: A biophysical model of Merkel cells

Merkel cells combine with Aβ afferents, producing slowly adapting type 1(SA1) responses to mechanical stimuli. However, how Merkel cells transduce mechanical stimuli into neural signals to Aβ afferents is still unclear. Here we develop a biophysical model of Merkel cells for mechanical transduction by incorporating main ingredients such as Ca2+ and K+ voltage-gated channels, Piezo2 channels, internal Ca2+ stores, neurotransmitters release, and cell deformation. We first validate our model with several experiments. Then we reveal that Ca2+ and K+ channels on the plasma membrane shape the depolarization of membrane potentials, further regulating the Ca2+ transients in the cells. We also show that Ca2+ channels on the plasma membrane mainly inspire the Ca2+ transients, while internal Ca2+ stores mainly maintain the Ca2+ transients. Moreover, we show that though Piezo2 channels are rapidly adapting mechanical-sensitive channels, they are sufficient to inspire sustained Ca2+ transients in Merkel cells, which further induce the release of neurotransmitters for tens of seconds. Thus our work provides a model that captures the membrane potentials and Ca2+ transients features of Merkel cells and partly explains how Merkel cells transduce the mechanical stimuli by Piezo2 channels.

Active shrinkage protects neurons following axonal transection

Trauma, vascular events, or neurodegenerative processes can lead to axonal injury and eventual transection (axotomy). Neurons can survive axotomy, yet the underlying mechanisms are not fully understood. Excessive water entry into injured neurons poses a particular risk due to swelling and subsequent death. Using in vitro and in vivo neurotrauma model systems based on laser transection and surgical nerve cut, we demonstrated that axotomy triggers actomyosin contraction coupled with calpain activity. As a consequence, neurons shrink acutely to force water out through aquaporin channels preventing swelling and bursting. Inhibiting shrinkage increased the probability of neuronal cell death by about 3-fold. These studies reveal a previously unrecognized cytoprotective response mechanism to neurotrauma and offer a fresh perspective on pathophysiological processes in the nervous system.

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.

Trans-epithelial fluid flow and mechanics of epithelial morphogenesis

Active fluid transport across epithelial monolayers is emerging as a major driving force of tissue morphogenesis in a variety of healthy and diseased systems, as well as during embryonic development. Cells use directional transport of ions and osmotic gradients to drive fluid flow across the cell surface, in the process also building up fluid pressure. The basic physics of this process is described by the osmotic engine model, which also underlies actin-independent cell migration. Recently, the trans-epithelial fluid flux and the hydraulic pressure gradient have been explicitly measured for a variety of cellular and tissue model systems across various species. For the kidney, it was shown that tubular epithelial cells behave as active mechanical fluid pumps: the trans-epithelial fluid flux depends on the hydraulic pressure difference across the epithelial layer. When a stall pressure is reached, the fluid flux vanishes. Hydraulic forces generated from active fluid pumping are important in tissue morphogenesis and homeostasis, and could also underlie multiple morphogenic events seen in other developmental contexts. In this review, we highlight findings that examined the role of trans-epithelial fluid flux and hydraulic pressure gradient in driving tissue-scale morphogenesis. We also review organ pathophysiology due to impaired fluid pumping and the loss of hydraulic pressure sensing at the cellular scale. Finally, we draw an analogy between cellular fluidic pumps and a connected network of water pumps in a city. The dynamics of fluid transport in an active and adaptive network is determined globally at the systemic level, and transport in such a network is best when each pump is operating at its optimal efficiency.

The interplay between physical cues and mechanosensitive ion channels in cancer metastasis

Physical cues have emerged as critical influencers of cell function during physiological processes, like development and organogenesis, and throughout pathological abnormalities, including cancer progression and fibrosis. While ion channels have been implicated in maintaining cellular homeostasis, their cell surface localization often places them among the first few molecules to sense external cues. Mechanosensitive ion channels (MICs) are especially important transducers of physical stimuli into biochemical signals. In this review, we describe how physical cues in the tumor microenvironment are sensed by MICs and contribute to cancer metastasis. First, we highlight mechanical perturbations, by both solid and fluid surroundings typically found in the tumor microenvironment and during critical stages of cancer cell dissemination from the primary tumor. Next, we describe how Piezo1/2 and transient receptor potential (TRP) channels respond to these physical cues to regulate cancer cell behavior during different stages of metastasis. We conclude by proposing alternative mechanisms of MIC activation that work in tandem with cytoskeletal components and other ion channels to bestow cells with the capacity to sense, respond and navigate through the surrounding microenvironment. Collectively, this review provides a perspective for devising treatment strategies against cancer by targeting MICs that sense aberrant physical characteristics during metastasis, the most lethal aspect of cancer.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

Effective Force Generation During Mammalian Cell Migration Under Different Molecular and Physical Mechanisms

We have developed much understanding of actin-driven cell migration and the forces that propel cell motility. However, fewer studies focused on estimating the effective forces generated by migrating cells. Since cells in vivo are exposed to complex physical environments with various barriers, understanding the forces generated by cells will provide insights into how cells manage to navigate challenging environments. In this work, we use theoretical models to discuss actin-driven and water-driven cell migration and the effect of cell shapes on force generation. The results show that the effective force generated by actin-driven cell migration is proportional to the rate of actin polymerization and the strength of focal adhesion; the energy source comes from the actin polymerization against the actin network pressure. The effective force generated by water-driven cell migration is proportional to the rate of active solute flux and the coefficient of external hydraulic resistance; the energy sources come from active solute pumping against the solute concentration gradient. The model further predicts that the actin network distribution is mechanosensitive and the presence of globular actin helps to establish a biphasic cell velocity in the strength of focal adhesion. The cell velocity and effective force generation also depend on the cell shape through the intracellular actin flow field.

A mechano-osmotic feedback couples cell volume to the rate of cell deformation

Mechanics has been a central focus of physical biology in the past decade. In comparison, how cells manage their size is less understood. Here we show that a parameter central to both the physics and the physiology of the cell, its volume, depends on a mechano-osmotic coupling. We found that cells change their volume depending on the rate at which they change shape, when they spontaneously spread are externally deformed. Cells undergo slow deformation at constant volume, while fast deformation leads to volume loss. We propose a mechano-sensitive pump and leak model to explain this phenomenon. Our model and experiments suggest that volume modulation depends on the state of the actin cortex and the coupling of ion fluxes to membrane tension. This mechano-osmotic coupling defines a membrane tension homeostasis module constantly at work in cells, causing volume fluctuations associated with fast cell shape changes, with potential consequences on cellular physiology.

The correlation between cell and nucleus size is explained by an eukaryotic cell growth model

In eukaryotes, the cell volume is observed to be strongly correlated with the nuclear volume. The slope of this correlation depends on the cell type, growth condition, and the physical environment of the cell. We develop a computational model of cell growth and proteome increase, incorporating the kinetics of amino acid import, protein/ribosome synthesis and degradation, and active transport of proteins between the cytoplasm and the nucleoplasm. We also include a simple model of ribosome biogenesis and assembly. Results show that the cell volume is tightly correlated with the nuclear volume, and the cytoplasm-nucleoplasm transport rates strongly influence the cell growth rate as well as the cell/nucleus volume ratio (C/N ratio). Ribosome assembly and the ratio of ribosomal proteins to mature ribosomes also influence the cell volume and the cell growth rate. We find that in order to regulate the cell growth rate and the cell/nucleus volume ratio, the cell must optimally control groups of kinetic and transport parameters together, which could explain the quantitative roles of canonical growth pathways. Finally, although not explicitly demonstrated in this work, we point out that it is possible to construct a detailed proteome distribution using our model and RNAseq data, provided that a quantitative cell division mechanism is known.

Hydrogen, Bicarbonate, and Their Associated Exchangers in Cell Volume Regulation

Cells lacking a stiff cell wall, e.g., mammalian cells, must actively regulate their volume to maintain proper cell function. On the time scale that protein production is negligible, water flow in and out of the cell determines the cell volume variation. Water flux follows hydraulic and osmotic gradients; the latter is generated by various ion channels, transporters, and pumps in the cell membrane. Compared to the widely studied roles of sodium, potassium, and chloride in cell volume regulation, the effects of proton and bicarbonate are less understood. In this work, we use mathematical models to analyze how proton and bicarbonate, combined with sodium, potassium, chloride, and buffer species, regulate cell volume upon inhibition of ion channels, transporters, and pumps. The model includes several common, widely expressed ion transporters and focuses on obtaining generic outcomes. Results show that the intracellular osmolarity remains almost constant before and after cell volume change. The steady-state cell volume does not depend on water permeability. In addition, to ensure the stability of cell volume and ion concentrations, cells need to develop redundant mechanisms to maintain homeostasis, i.e., multiple ion channels or transporters are involved in the flux of the same ion species. These results provide insights for molecular mechanisms of cell volume regulation with additional implications for water-driven cell migration.

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.

Bioelectric signaling: Reprogrammable circuits underlying embryogenesis, regeneration, and cancer

How are individual cell behaviors coordinated toward invariant large-scale anatomical outcomes in development and regeneration despite unpredictable perturbations? Endogenous distributions of membrane potentials, produced by ion channels and gap junctions, are present across all tissues. These bioelectrical networks process morphogenetic information that controls gene expression, enabling cell collectives to make decisions about large-scale growth and form. Recent progress in the analysis and computational modeling of developmental bioelectric circuits and channelopathies reveals how cellular collectives cooperate toward organ-level structural order. These advances suggest a roadmap for exploiting bioelectric signaling for interventions addressing developmental disorders, regenerative medicine, cancer reprogramming, and synthetic bioengineering.

The importance of water and hydraulic pressure in cell dynamics

All mammalian cells live in the aqueous medium, yet for many cell biologists, water is a passive arena in which proteins are the leading players that carry out essential biological functions. Recent studies, as well as decades of previous work, have accumulated evidence to show that this is not the complete picture. Active fluxes of water and solutes of water can play essential roles during cell shape changes, cell motility and tissue function, and can generate significant mechanical forces. Moreover, the extracellular resistance to water flow, known as the hydraulic resistance, and external hydraulic pressures are important mechanical modulators of cell polarization and motility. For the cell to maintain a consistent chemical environment in the cytoplasm, there must exist an intricate molecular system that actively controls the cell water content as well as the cytoplasmic ionic content. This system is difficult to study and poorly understood, but ramifications of which may impact all aspects of cell biology from growth to metabolism to development. In this Review, we describe how mammalian cells maintain the cytoplasmic water content and how water flows across the cell surface to drive cell movement. The roles of mechanical forces and hydraulic pressure during water movement are explored.

Detection of the mesenchymal-to-epithelial transition of invasive non-small cell lung cancer cells by their membrane undulation spectra

A cancer cell changes its state from being epithelial- to mesenchymal-like in a dynamic manner during tumor progression. For example, it is well known that mesenchymal-to-epithelial transition (MET) is essential for cancer cells to regain the capability of seeding on and then invading secondary/tertiary regions. However, there is no fast yet reliable method for detecting this transition. Here, we showed that membrane undulation of invasive cancer cells could be used as a novel marker for MET detection, both in invasive model cell lines and repopulated circulating tumor cells (rCTCs) from non-small cell lung cancer (NSCLC) patients. Specifically, using atomic force microscopy (AFM), it was found that the surface oscillation spectra of different cancer cells, after undergoing MET, all exhibited two distinct peaks from 0.001 to 0.007 Hz that are absent in the spectra before MET. In addition, by adopting the long short-term memory (LSTM) based recurrent neural network learning algorithm, we showed that the positions of recorded membrane undulation peaks can be used to predict the occurrence of MET in invasive NSCLC cells with high accuracy (>90% for model cell lines and >80% for rCTCs when benchmarking against the conventional bio-marker vimentin). These findings demonstrate the potential of our approach in achieving rapid MET detection with a much reduced cell sample size as well as quantifying changes in the mesenchymal level of tumor cells.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.