Passive deformations and active motions of leukocytes

The purpose of this paper is to review the development of continuum mechanics models of single leukocytes in both passive deformations and active motions and to indicate some future directions. Models of passive deformations describe the overall rheological behavior of single leukocytes under externally applied forces and predict the average mechanical properties from experimental data. Various "apparent" viscoelastic coefficients are obtained depending on the models assumed and the types of test used. Models of spontaneous motions postulate active driving mechanisms which must be derived internally from the cell itself and probably have different bases for different kind of motions. For pseudopod protrusion on leukocytes, energy transduction from chemical potential to mechanical work associated with actin polymerization at the tip of the projection is assumed to supply the motive power. For pseudopod retraction, active contraction due to actin-myosin interaction is assumed to be the driving force. The feasibility of the hypotheses are tested via numerical examples and comparison of the theoretical results with experimental measurements.     

Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress

Cultured vascular endothelial cells undergo significant morphological changes when subjected to sustained fluid shear stress. The cells elongate and align in the direction of applied flow. Accompanying this shape change is a reorganization at the intracellular level. The cytoskeletal actin filaments reorient in the direction of the cells' long axis. How this external stimulus is transmitted to the endothelial cytoskeleton still remains unclear. In this article. we present a theoretical model accounting for the cytoskeletal reorganization under the influence of fluid shear stress. We develop a system of integro-partial-differential equations describing the dynamics of actin filaments, the actin-binding proteins, and the drift of transmembrane proteins due to the fluid shear forces applied on the plasma membrane. Numerical simulations of the equations show that under certain conditions, initially randomly oriented cytoskeletal actin filaments reorient in structures parallel to the externally applied fluid shear forces. Thus, the model suggests a mechanism by which shear forces acting on the cell membrane can be transmitted to the entire cytoskeleton via molecular interactions alone.     

Fluid‐driven interfacial instabilities and turbulence in bacterial biofilms

Biofilms are thin layers of bacteria embedded within a slime matrix that live on surfaces. They are ubiquitous in nature and responsible for many medical and dental infections, industrial fouling and are also evident in ancient fossils. A biofilm structure is shaped by growth, detachment and response to mechanical forces acting on them. The main contribution to biofilm versatility in response to physical forces is the matrix that provides a platform for the bacteria to grow. The interaction between biofilm structure and hydrodynamics remains a fundamental question concerning biofilm dynamics. Here, we document the appearance of ripples and wrinkles in biofilms grown from three species of bacteria when subjected to high‐velocity fluid flows. Linear stability analysis suggested that the ripples were Kelvin–Helmholtz Instabilities. The analysis also predicted a strong dependence of the instability formation on biofilm viscosity explaining the different surface corrugations observed. Turbulence through Kelvin–Helmholtz instabilities occurring at the interface demonstrated that the biofilm flows like a viscous liquid under high flow velocities applied within milliseconds. Biofilm fluid‐like behavior may have important implications for our understanding of how fluid flow influences biofilm biology since turbulence will likely disrupt metabolite and signal gradients as well as community stratification.     

Fluid flows and forces in development: functions, features and biophysical principles

Throughout morphogenesis, cells experience intracellular tensile and contractile forces on microscopic scales. Cells also experience extracellular forces, such as static forces mediated by the extracellular matrix and forces resulting from microscopic fluid flow. Although the biological ramifications of static forces have received much attention, little is known about the roles of fluid flows and forces during embryogenesis. Here, we focus on the microfluidic forces generated by cilia-driven fluid flow and heart-driven hemodynamics, as well as on the signaling pathways involved in flow sensing. We discuss recent studies that describe the functions and the biomechanical features of these fluid flows. These insights suggest that biological flow determines many aspects of cell behavior and identity through a specific set of physical stimuli and signaling pathways.     

Effects of extracellular fiber architecture on cell membrane shear stress in a 3D fibrous matrix

Interstitial fluid flow has been shown to affect the organization and behavior of cells in 3D environments in vivo and in vitro, yet the forces driving such responses are not clear. Due to the complex architecture of the extracellular matrix (ECM) and the difficulty of measuring fluid flow near cells embedded in it, the levels of shear stress experienced by cells in this environment are typically estimated using bulk-averaged matrix parameters such as hydraulic permeability. While this is useful for estimating average stresses, it cannot yield insight into how local matrix fiber architecture-which is cell-controlled in the immediate pericellular environment-affects the local stresses imposed on the cell surface. To address this, we used computational fluid dynamics to study flow through an idealized mesh constructed of a cubic lattice of fibers simulating a typical in vitro collagen gel. We found that, in such high porosity matrices, the fibers strongly affect the flow fields near the cell, with peak shear stresses up to five times higher than those predicted by the Brinkman equation. We also found that minor remodeling of the fibers near the cell surface had major effects on the shear stress profile on the cell. These findings demonstrate the importance of fiber architecture to the fluid forces on a cell embedded in a 3D matrix, and also show how small modifications in the local ECM can lead to large changes in the mechanical environment of the cell.     

MECHANICAL STRESS AND CELL WALL ORIENTATION IN PLANTS. II. THE APPLICATION OF CONTROLLED DIRECTIONAL STRESS TO GROWING PLANTS; WITH A DISCUSSION ON THE NATURE OF THE WOUND REACTION

This paper describes an attempt to present living stem tissue with defined mechanical stress in a spatial configuration which can be easily interpreted in section. We have applied compressive stress to a growing Coleus internode in vivo, using stainless-steel spring-clips which act through a double-edged glass interface of known area. We have found that cambial activity consisting of cell division and enlargement continues even under applied compressive stress ranging up to 20 atm. Tissue reactions to applied stress are discussed in terms of the equilibration of forces propagating through the tissue before, during, and after the presentation of externally applied stress.     

Mechanical state of airway smooth muscle at very short lengths.

Although the shortening of smooth muscle at physiological lengths is dominated by an interaction between external forces (loads) and internal forces, at very short lengths, internal forces appear to dominate the mechanical behavior of the active tissue. We tested the hypothesis that, under conditions of extreme shortening and low external force, the mechanical behavior of isolated canine tracheal smooth muscle tissue can be understood as a structure in which the force borne and exerted by the cross bridge and myofilament array is opposed by radially disposed connective tissue in the presence of an incompressible fluid matrix (cellular and extracellular). Strips of electrically stimulated tracheal muscle were allowed to shorten maximally under very low afterload, and large longitudinal sinusoidal vibrations (34 Hz, 1 s in duration, and up to 50% of the muscle length before vibration) were applied to highly shortened (active) tissue strips to produce reversible cross-bridge detachment. During the vibration, peak muscle force fell exponentially with successive forced elongations. After the episode, the muscle either extended itself or exerted a force against the tension transducer, depending on external conditions. The magnitude of this effect was proportional to the prior muscle stiffness and the amplitude of the vibration, indicating a recoil of strained connective tissue elements no longer opposed by cross-bridge forces. This behavior suggests that mechanical behavior at short lengths is dominated by tissue forces within a tensegrity-like structure made up of connective tissue, other extracellular matrix components, and active contractile elements.     

Cell shape controls rheotaxis in small parasitic bacteria

Mycoplasmas, a group of small parasitic bacteria, adhere to and move across host cell surfaces. The role of motility across host cell surfaces in pathogenesis remains unclear. Here, we used optical microscopy to visualize rheotactic behavior in three phylogenetically distant species of Mycoplasma using a microfluidic chamber that enabled the application of precisely controlled fluid flow. We show that directional movements against fluid flow occur synchronously with the polarized cell orienting itself to be parallel against the direction of flow. Analysis of depolarized cells revealed that morphology itself functions as a sensor to recognize rheological properties that mimic those found on host-cell surfaces. These results demonstrate the vital role of cell morphology and motility in responding to mechanical forces encountered in the native environment.     

Traction Forces of Endothelial Cells under Slow Shear Flow

Endothelial cells are constantly exposed to fluid shear stresses that regulate vascular morphogenesis, homeostasis, and disease. The mechanical responses of endothelial cells to relatively high shear flow such as that characteristic of arterial circulation has been extensively studied. Much less is known about the responses of endothelial cells to slow shear flow such as that characteristic of venous circulation, early angiogenesis, atherosclerosis, intracranial aneurysm, or interstitial flow. Here we used a novel, to our knowledge, microfluidic technique to measure traction forces exerted by confluent vascular endothelial cell monolayers under slow shear flow. We found that cells respond to flow with rapid and pronounced increases in traction forces and cell-cell stresses. These responses are reversible in time and do not involve reorientation of the cell body. Traction maps reveal that local cell responses to slow shear flow are highly heterogeneous in magnitude and sign. Our findings unveil a low-flow regime in which endothelial cell mechanics is acutely responsive to shear stress.     

Shear-Induced Unfolding of Lysozyme Monitored In Situ

Conformational changes due to externally applied physiochemical parameters, including pH, temperature, solvent composition, and mechanical forces, have been extensively reported for numerous proteins. However, investigations on the effect of fluid shear flow on protein conformation remain inconclusive despite its importance not only in the research of protein dynamics but also for biotechnology applications where processes such as pumping, filtration, and mixing may expose protein solutions to changes in protein structure. By combining particle image velocimetry and Raman spectroscopy, we have successfully monitored reversible, shear-induced structural changes of lysozyme in well-characterized flows. Shearing of lysozyme in water altered the protein's backbone structure, whereas similar shear rates in glycerol solution affected the solvent exposure of side-chain residues located toward the exterior of the lysozyme α-domain. The results demonstrate the importance of measuring conformational changes in situ and of quantifying fluid stresses by the three-dimensional shear tensor to establish reversible unfolding or misfolding transitions occurring due to flow exposure.     

Fluid-Flow Induced Wall Shear Stress and Epithelial Ovarian Cancer Peritoneal Spreading

Epithelial ovarian cancer (EOC) is usually discovered after extensive metastasis have developed in the peritoneal cavity. The ovarian surface is exposed to peritoneal fluid pressures and shear forces due to the continuous peristaltic motions of the gastro-intestinal system, creating a mechanical micro-environment for the cells. An in vitro experimental model was developed to expose EOC cells to steady fluid flow induced wall shear stresses (WSS). The EOC cells were cultured from OVCAR-3 cell line on denuded amniotic membranes in special wells. Wall shear stresses of 0.5, 1.0 and 1.5 dyne/cm² were applied on the surface of the cells under conditions that mimic the physiological environment, followed by fluorescent stains of actin and β-tubulin fibers. The cytoskeleton response to WSS included cell elongation, stress fibers formation and generation of microtubules. More cytoskeletal components were produced by the cells and arranged in a denser and more organized structure within the cytoplasm. This suggests that WSS may have a significant role in the mechanical regulation of EOC peritoneal spreading.     

Microstructural strain near osteocyte lacuna in cortical bone in vitro

Mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Two proposed mechanical signals are stress-generated fluid flow forces acting on cells and bone matrix deformation itself. A prominent current theory is that bone cells are more responsive to fluid flow than to mechanical strain. Recent experiments support this conclusion: bone cells increase their production of osteopontin (OPN) mRNA, prostaglandin (PGE(2)), and nitric oxide (NO) in response to fluid flow in contrast to cells stimulated by mechanical strain levels similar to those measured in vivo. However, when cells are subjected to substrate strains levels many times greater than those measured in vivo, increased biological activity again results. We assert that it is neither fluid flow nor matrix deformation per se, but rather the resulting cell deformation that causes cell biological response. Machined specimens of undamaged bovine cortical bone were subjected to increasing levels of macroscopic strain while observed under an optical microscope at 220X. Continuum level strain was measured using a standard foil strain gauge attached to the back of the specimen and ranged from 500 to 6,000 microstrain. Images of the specimen surface at each strain level were captured. To determine the level of osteocyte deformation that results from fluid flow in vitro, MLO-Y4 cells were cultured on collagen coated 190 cm2 plastic sheets and subjected to steady fluid flow at 16 dynes/cm(2). Images representing the initial undisturbed cell configuration and the configuration of the cells after ten minutes of fluid flow were acquired from a videotape of the flow experiment. The captured unloaded vs. loaded image pairs were analyzed to determine the local deformation and strain fields using a digital stereoimaging system. When subjected to a nominal continuum strain level approximately equal to that measured in humans in vivo during rigorous activity (2,000 microstrain), the local, osteocyte level strains can be as high as 12,000 to 15,000 microstrain (1.2% to 1.5%). Average osteocyte strains due to fluid flow in vitro increase from 7,972 microstrains after 16 seconds of flow to 22,856 microstrains after 64 seconds of flow. In contrast, maximum strains measured in vivo are approximately 1,800 microstrain in humans and up to 3,000 microstrain in other species. These data may help to explain why bone cells are more sensitive to fluid flow than substrate strain; fluid forces result in cell deformations much higher than those considered to be "physiological".     

Regulation of tumor invasion by interstitial fluid flow

The importance of the tumor microenvironment in cancer progression is undisputed, yet the significance of biophysical forces in the microenvironment remains poorly understood. Interstitial fluid flow is a nearly ubiquitous and physiologically relevant biophysical force that is elevated in tumors because of tumor-associated angiogenesis and lymphangiogenesis, as well as changes in the tumor stroma. Not only does it apply physical forces to cells directly, but interstitial flow also creates gradients of soluble signals in the tumor microenvironment, thus influencing cell behavior and modulating cell-cell interactions. In this paper, we highlight our current understanding of interstitial fluid flow in the context of the tumor, focusing on the physical changes that lead to elevated interstitial flow, how cells sense flow and how they respond to changes in interstitial flow. In particular, we emphasize that interstitial flow can directly promote tumor cell invasion through a mechanism known as autologous chemotaxis, and indirectly support tumor invasion via both biophysical and biochemical cues generated by stromal cells. Thus, interstitial fluid flow demonstrates how important biophysical factors are in cancer, both by modulating cell behavior and coupling biophysical and biochemical signals.     

Signaling through the phosphatidylinositol 3-kinase regulates mechanotaxis induced by local low magnetic forces in Entamoeba histolytica

In micro-organisms, as well as in metazoan cells, cellular polarization and directed migration are finely regulated by external stimuli, including mechanical stresses. The mechanisms sustaining the transduction of such external stresses into intracellular biochemical signals remain mainly unknown. Using an external magnetic tip, we generated a magnetic field gradient that allows migration analysis of cells submitted to local low-intensity magnetic forces (50 pN). We applied our system to the amoeba Entamoeba histolytica. Indeed, motility and chemotaxis are key activities that allow this parasite to invade and destroy the human tissues during amoebiasis. The magnetic force was applied either inside the cytoplasm or externally at the rear pole of the amoeba. We observed that the application of an intracellular force did not affect cell polarization and migration, whereas the application of the force at the rear pole of the cell induced a persistent polarization and strongly directional motion, almost directly opposed to the magnetic force. This phenomenon was completely abolished when phosphatidylinositol 3-kinase activity was inhibited by wortmanin. This result demonstrated that the applied mechanical stimulus was transduced and amplified into an intracellular biochemical signal, a process that allows such low-intensity force to strongly modify the migration behavior of the cell.     

Differentiation of stem/progenitor cells into vascular cells in response to fluid mechanical forces

Vascular functions are regulated not only by chemical mediators, such as hormones, cytokines, and neurotransmitters, but by mechanical hemodynamic forces generated by blood flow and blood pressure. The mechanical force-mediated regulation is based on the ability of vascular cells, including endothelial cells and smooth muscle cells, to recognize fluid mechanical forces, i.e., the shear stress produced by flowing blood and the cyclic strain generated by blood pressure, and to transmit the signals into the cell interior, where they trigger cell responses that involve changes in cell morphology, cell function, and gene expression. Recent studies have revealed that immature cells, such as endothelial progenitor cells (EPCs) and embryonic stem (ES) cells, as well as adult vascular cells, respond to fluid mechanical forces. Shear stress and cyclic strain promote the proliferation and differentiation of EPCs and ES cells into vascular cells and enhance their ability to form new vessels. Even more recently, attempts have been made to apply fluid mechanical forces to EPCs and ES cells cultured on polymer tubes and develop tissue-engineered blood vessel grafts that have a structure and function similar to that of blood vessels in vivo. This review summarizes the current state of knowledge concerning the mechanobiological responses of stem/progenitor cells and its potential applications to tissue engineering.     

Prediction of fluid forces acting on a hand model in unsteady flow conditions

The aim of this study was to develop a method to predict fluid forces acting on the human hand in unsteady flow swimming conditions. A mechanical system consisting of a pulley and chain mechanism and load cell was constructed to rotate a hand model in fluid flows. To measure the angular displacement of the hand model a potentiometer was attached to the axis of the rotation. The hand model was then fixed at various angles about the longitudinal axis of the hand model and rotated at different flow velocities in a swimming flume for 258 different trials to approximate a swimmer's stroke in unsteady flow conditions. Pressures were taken from 12 transducers embedded in the hand model at a sampling frequency of 200Hz. The resultant fluid force acting on the hand model was then determined on the basis of the kinetic and kinematic data taken from the mechanical system at the frequency of 200Hz. A stepwise regression analysis was applied to acquire higher order polynomial equations that predict the fluid force acting on the accelerating hand model from the 12 pressure values. The root mean square (RMS) difference between the resultant fluid force measured and that predicted from the single best-fit polynomial equation across all trials was 5N. The method developed in the present study accurately predicted the fluid forces acting on the hand model.     

Mechanotransduction in embryonic vascular development

A plethora of biochemical signals provides spatial and temporal cues that carefully orchestrate the complex process of vertebrate embryonic development. The embryonic vasculature develops not only in the context of these biochemical cues, but also in the context of the biomechanical forces imparted by blood flow. In the mature vasculature, different blood flow regimes induce distinct genetic programs, and significant progress has been made toward understanding how these forces are perceived by endothelial cells and transduced into biochemical signals. However, it cannot be assumed that paradigms that govern the mature vasculature are pertinent to the developing embryonic vasculature. The embryonic vasculature can respond to the mechanical forces of blood flow, and these responses are critical in vascular remodeling, certain aspects of sprouting angiogenesis, and maintenance of arterial–venous identity. Here, we review data regarding mechanistic aspects of endothelial cell mechanotransduction, with a focus on the response to shear stress, and elaborate upon the multifarious effects of shear stress on the embryonic vasculature. In addition, we discuss emerging predictive vascular growth models and highlight the prospect of combining signaling pathway information with computational modeling. We assert that correlation of precise measurements of hemodynamic parameters with effects on endothelial cell gene expression and cell behavior is required for fully understanding how blood flow-induced loading governs normal vascular development and shapes congenital cardiovascular abnormalities.     

Control of microtubule assembly by extracellular matrix and externally applied strain

A number of studies have suggested that externally applied mechanical forces and alterations in the intrinsic cell-extracellular matrix (ECM) force balance equivalently induce changes in cell phenotype. However, this possibility has never been directly tested. To test this hypothesis, we directly investigated the response of the microtubule (MT) cytoskeleton in smooth muscle cells to both mechanical signals and alterations in the ECM. A tensile force that resulted in a positive 10% step change in substrate strain increased MT mass by 34 +/- 10% over static controls, independent of the cell adhesion ligand and tyrosine phosphorylation. Conversely, a compressive force that resulted in a negative 10% step change in substrate strain decreased MT mass by 40 +/- 6% over static controls. In parallel, increasing the density of the ECM ligand fibronectin from 50 to 1,000 ng/cm(2) in the absence of any applied force increased the amount of polymeric tubulin in the cell from 59 +/- 11% to 81 +/- 13% of the total cellular tubulin. These data are consistent with a model in which MT assembly is, in part, controlled by forces imposed on these structures, and they suggest a novel control point for MT assembly by altering the intrinsic cell-ECM force balance and applying external mechanical forces.     

Biorheological views of endothelial cell responses to mechanical stimuli

Vascular endothelial cells are located at the innermost layer of the blood vessel wall and are always exposed to three different mechanical forces: shear stress due to blood flow, hydrostatic pressure due to blood pressure and cyclic stretch due to vessel deformation. It is well known that endothelial cells respond to these mechanical forces and change their shapes, cytoskeletal structures and functions. In this review, we would like to mainly focus on the effects of shear stress and hydrostatic pressure on endothelial cell morphology. After applying fluid shear stress, cultured endothelial cells show marked elongation and orientation in the flow direction. In addition, thick stress fibers of actin filaments appear and align along the cell long axis. Thus, endothelial cell morphology is closely related to the cytoskeletal structure. Further, the dynamic course of the morphological changes is shown and the related events such as changes in mechanical stiffness and functions are also summarized. When endothelial cells were exposed to hydrostatic pressure, they exhibited a marked elongation and orientation in a random direction, together with development of centrally located, thick stress fibers. Pressured endothelial cells also exhibited a multilayered structure with less expression of VE-cadherin unlike under control conditions. Simultaneous loading of hydrostatic pressure and shear stress inhibited endothelial cell multilayering and induced elongation and orientation of endothelial cells with well-developed VE-cadherin in a monolayer, which suggests that for a better understanding of vascular endothelial cell responses one has to take into consideration the combination of the different mechanical forces such as exist under in vivo mechanical conditions.