A kinematic model of stretch-induced stress fiber turnover and reorientation

Cell orientation under stretch: A review of experimental findings and mathematical modelling

The key role of electro-chemical signals in cellular processes had been known for many years, but more recently the interplay with mechanics has been put in evidence and attracted substantial research interests. Indeed, the sensitivity of cells to mechanical stimuli coming from the microenvironment turns out to be relevant in many biological and physiological circumstances. In particular, experimental evidence demonstrated that cells on elastic planar substrates undergoing periodic stretches, mimicking native cyclic strains in the tissue where they reside, actively reorient their cytoskeletal stress fibres. At the end of the realignment process, the cell axis forms a certain angle with the main stretching direction. Due to the importance of a deeper understanding of mechanotransduction, such a phenomenon was studied both from the experimental and the mathematical modelling point of view. The aim of this review is to collect and discuss both the experimental results on cell reorientation and the fundamental features of the mathematical models that have been proposed in the literature.

An ex vivo culture model of kidney podocyte injury reveals mechanosensitive, synaptopodin-templating, sarcomere-like structures

Chronic kidney diseases are widespread and incurable. The biophysical mechanisms underlying them are unclear, in part because material systems for reconstituting the microenvironment of relevant kidney cells are limited. A critical question is how kidney podocytes (glomerular epithelial cells) regenerate foot processes of the filtration apparatus following injury. Recently identified sarcomere-like structures (SLSs) with periodically spaced myosin IIA and synaptopodin appear in injured podocytes in vivo. We hypothesized that SLSs template synaptopodin in the initial stages of recovery in response to microenvironmental stimuli and tested this hypothesis by developing an ex vivo culture system that allows control of the podocyte microenvironment. Results supported our hypothesis. SLSs in podocytes that migrated from isolated kidney glomeruli presented periodic synaptopodin-positive clusters that nucleated peripheral, foot process-like extensions. SLSs were mechanoresponsive to actomyosin inhibitors and substrate stiffness. Results suggest SLSs as mechanobiological mediators of podocyte recovery and as potential targets for therapeutic intervention.

Thermodynamically-motivated chemo-mechanical models and multicellular simulation to provide new insight into active cell and tumour remodelling

Computational models can shape our understanding of cell and tissue remodelling, from cell spreading, to active force generation, adhesion, and growth. In this mini-review, we discuss recent progress in modelling of chemo-mechanical cell behaviour and the evolution of multicellular systems. In particular, we highlight recent advances in (i) free-energy based single cell models that can provide new fundamental insight into cell spreading, cancer cell invasion, stem cell differentiation, and remodelling in disease, and (ii) mechanical agent-based models to simulate large numbers of discrete interacting cells in proliferative tumours. We describe how new biological understanding has emerged from such theoretical models, and the trade-offs and constraints associated with current approaches. Ultimately, we aim to make a case for why theory should be integrated with an experimental workflow to optimise new in-vitro studies, to predict feedback between cells and their microenvironment, and to deepen understanding of active cell behaviour.

Biomechanical regulation of planar cell polarity in endothelial cells

Cell polarity refers to the uneven distribution of certain cytoplasmic components in a cell with a spatial order. The planar cell polarity (PCP), the cell aligns perpendicular to the polar plane, in endothelial cells (ECs) has become a research hot spot. The planar polarity of ECs has a positive significance on the regulation of cardiovascular dysfunction, pathological angiogenesis, and ischemic stroke. The endothelial polarity is stimulated and regulated by biomechanical force. Mechanical stimuli promote endothelial polarization and make ECs produce PCP to maintain the normal physiological and biochemical functions. Here, we overview recent advances in understanding the interplay and mechanism between PCP and ECs function involved in mechanical forces, with a focus on PCP signaling pathways and organelles in regulating the polarity of ECs. And then showed the related diseases caused by ECs polarity dysfunction. This study provides new ideas and therapeutic targets for the treatment of endothelial PCP-related diseases.

A Mechanistic Motor-Clutch Model That Explains Cell Shape Dynamics to Cyclic Stretch

Many cells in the body experience cyclic mechanical loading, which can impact cellular processes and morphology. In vitro studies often report that cells reorient in response to cyclic stretch of their substrate. To explore cellular mechanisms involved in this reorientation, a computational model was developed by adapting previous computational models of the actin–myosin–integrin motor-clutch system developed by others. The computational model predicts that under most conditions, actin bundles align perpendicular to the direction of applied cyclic stretch, but under specific conditions, such as low substrate stiffness, actin bundles align parallel to the direction of stretch. The model also predicts that stretch frequency impacts the rate of reorientation and that proper myosin function is critical in the reorientation response. These computational predictions are consistent with reports from the literature and new experimental results presented here. The model suggests that the impact of different stretching conditions (stretch type, amplitude, frequency, substrate stiffness, etc.) on the direction of cell alignment can largely be understood by considering their impact on cell–substrate detachment events, specifically whether detachments preferentially occur during stretching or relaxing of the substrate.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

Constrained Mixture Models of Soft Tissue Growth and Remodeling - Twenty Years After

Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or clinical intervention. Such approaches also can be used to design improved tissue engineered constructs to repair, replace, or regenerate tissues. Focusing on blood vessels as archetypes of soft tissues, this paper reviews a constrained mixture theory introduced twenty years ago and explores its usage since by contrasting simulations of diverse vascular conditions. The discussion is framed within the concept of mechanical homeostasis, with consideration of solid-fluid interactions, inflammation, and cell signaling highlighting both past accomplishments and future opportunities as we seek to understand better the evolving composition, geometry, and material behaviors of soft tissues under complex conditions.

Progress in the mechanical modulation of cell functions in tissue engineering

In mammals, mechanics at multiple stages-nucleus to cell to ECM-underlie multiple physiological and pathological functions from its development to reproduction to death. Under this inspiration, substantial research has established the role of multiple aspects of mechanics in regulating fundamental cellular processes, including spreading, migration, growth, proliferation, and differentiation. However, our understanding of how these mechanical mechanisms are orchestrated or tuned at different stages to maintain or restore the healthy environment at the tissue or organ level remains largely a mystery. Over the past few decades, research in the mechanical manipulation of the surrounding environment-known as substrate or matrix or scaffold on which, or within which, cells are seeded-has been exceptionally enriched in the field of tissue engineering and regenerative medicine. To do so, traditional tissue engineering aims at recapitulating key mechanical milestones of native ECM into a substrate for guiding the cell fate and functions towards specific tissue regeneration. Despite tremendous progress, a big puzzle that remains is how the cells compute a host of mechanical cues, such as stiffness (elasticity), viscoelasticity, plasticity, non-linear elasticity, anisotropy, mechanical forces, and mechanical memory, into many biological functions in a cooperative, controlled, and safe manner. High throughput understanding of key cellular decisions as well as associated mechanosensitive downstream signaling pathway(s) for executing these decisions in response to mechanical cues, solo or combined, is essential to address this issue. While many reports have been made towards the progress and understanding of mechanical cues-particularly, substrate bulk stiffness and viscoelasticity-in regulating the cellular responses, a complete picture of mechanical cues is lacking. This review highlights a comprehensive view on the mechanical cues that are linked to modulate many cellular functions and consequent tissue functionality. For a very basic understanding, a brief discussion of the key mechanical players of ECM and the principle of mechanotransduction process is outlined. In addition, this review gathers together the most important data on the stiffness of various cells and ECM components as well as various tissues/organs and proposes an associated link from the mechanical perspective that is not yet reported. Finally, beyond addressing the challenges involved in tuning the interplaying mechanical cues in an independent manner, emerging advances in designing biomaterials for tissue engineering are also explored.

Mechanosensitive myosin II but not cofilin primarily contributes to cyclic cell stretch-induced selective disassembly of actin stress fibers

Cells adapt to applied cyclic stretch (CS) to circumvent chronic activation of proinflammatory signaling. Currently, the molecular mechanism of the selective disassembly of actin stress fibers (SFs) in the stretch direction, which occurs at the early stage of the cellular response to CS, remains controversial. Here, we suggest that the mechanosensitive behavior of myosin II, a major cross-linker of SFs, primarily contributes to the directional disassembly of the actomyosin complex SFs in bovine vascular smooth muscle cells and human U2OS osteosarcoma cells. First, we identified that CS with a shortening phase that exceeds in speed the inherent contractile rate of individual SFs leads to the disassembly. To understand the biological basis, we investigated the effect of expressing myosin regulatory light-chain mutants and found that SFs with less actomyosin activities disassemble more promptly upon CS. We consequently created a minimal mathematical model that recapitulates the salient features of the direction-selective and threshold-triggered disassembly of SFs to show that disassembly or, more specifically, unbundling of the actomyosin bundle SFs is enhanced with sufficiently fast cell shortening. We further demonstrated that similar disassembly of SFs is inducible in the presence of an active LIM-kinase-1 mutant that deactivates cofilin, suggesting that cofilin is dispensable as opposed to a previously proposed mechanism.

A Fully Integrated Arduino-Based System for the Application of Stretching Stimuli to Living Cells and Their Time-Lapse Observation: A Do-It-Yourself Biology Approach

Mechanobiology has nowadays acquired the status of a topic of fundamental importance in a degree in Biological Sciences. It is inherently a multidisciplinary topic where biology, physics and engineering competences are required. A course in mechanobiology should include lab experiences where students can appreciate how mechanical stimuli from outside affect living cell behaviour. Here we describe all the steps to build a cell stretcher inside an on-stage cell incubator. This device allows exposing living cells to a periodic mechanical stimulus similar to what happens in physiological conditions such as, for example, in the vascular system or in the lungs. The reaction of the cells to the periodic mechanical stretching represents a prototype of a mechanobiological signal integrated by living cells. We also provide the theoretical and experimental aspects related to the calibration of the stretcher apparatus at a level accessible to researchers not used to dealing with topics like continuum mechanics and analysis of deformations. We tested our device by stretching cells of two different lines, U87-MG and Balb-3T3 cells, and we analysed and discussed the effect of the periodic stimulus on both cell reorientation and migration. We also discuss the basic aspects related to the quantitative analysis of the reorientation process and of cell migration. We think that the device we propose can be easily reproduced at low-cost within a project-oriented course in the fields of biology, biotechnology and medical engineering.

Finite Element Simulations of Mechanical Behaviour of Endothelial Cells

Biomechanical models based on the finite element method have already shown their potential in the simulation of the mechanical behaviour of cells. For instance, development of atherosclerosis is accelerated by damage of the endothelium, a monolayer of endothelial cells on the inner surface of arteries. Finite element models enable us to investigate mechanical factors not only at the level of the arterial wall but also at the level of individual cells. To achieve this, several finite element models of endothelial cells with different shapes are presented in this paper. Implementing the recently proposed bendotensegrity concept, these models consider the flexural behaviour of microtubules and incorporate also waviness of intermediate filaments. The suspended and adherent cell models are validated by comparison of their simulated force-deformation curves with experiments from the literature. The flat and dome cell models, mimicking natural cell shapes inside the endothelial layer, are then used to simulate their response in compression and shear which represent typical loads in a vascular wall. The models enable us to analyse the role of individual cytoskeletal components in the mechanical responses, as well as to quantify the nucleus deformation which is hypothesized to be the quantity decisive for mechanotransduction.

Modeling the mechanics of fibrous-porous scaffolds for skeletal muscle regeneration

The scaffolds for skeletal muscle regeneration are designed to mimic the structure, stiffness, and strains applied to the muscle under physiologic conditions. The external strains are also used to stimulate myogenesis of the (stem) cells seeded on the scaffold. The time- and location-dependent mechanics inside the scaffold determine the microenvironment for the seeded cells. Here, fibrous-porous cylindrical scaffolds under the action of external cyclic strains are considered. The scaffold mechanics are described as two-phase (poroelastic) where the solid phase is associated with the fibers and the fluid phase is associated with the liquid-containing pores. In response to an applied cyclic strain, pressure oscillates and fluid moves radially toward and away from the axis of the scaffold. We compute the directions and magnitudes of the radial gradients of the poroelastic characteristics (solid-phase displacement, strain, and velocity; fluid-phase pressure and velocity; relative fluid-solid-phase velocity) determined by the boundary conditions and geometry of the scaffold. Several kinds of the external cyclic strain are analyzed and the resulting poroelastic functions are found. The poroelastic characteristics are obtained in closed form which is convenient for further consideration of myogenesis of the seeded cells and ultimately for the design of the scaffolds for skeletal muscle regeneration. Graphical abstract.

Endothelial Cells Morphology in Response to Combined WSS and Biaxial CS: Introduction of Effective Strain Ratio

Introduction

Endothelial cells (ECs) morphology strongly depends on the imposed mechanical stimuli. These mechanical stimuli include wall shear stress (WSS) and biaxial cyclic stretches (CS). Under combined loading, the effect of CS is not as simple as pure CS. The present study investigates the morphological response of ECs to the realistic mechanical stimuli.

Methods

The cell population is theoretically studied using our previous validated model. The mechanical stimuli on ECs are described using four parameters; WSS magnitude (0 to 2.0 Pa), WSS angle (- 50° to 50°), and biaxial CS in two perpendicular directions (0 to 10%). The morphology of ECs is reported using four parameters; average shape index (SI) and orientation angle (OA) of the cell population as well as the standard deviation (SD) of SI and OA as measures for scattering of cells' SI and OA from these average values.

Results

A new effective strain ratio (ESR) is defined as the ratio of the undesirable CS to the desirable one. The obtained results of the model, illustrated that the SI and OA of cells increase with absolute value of ESR. In addition, the scattering in the SI of cells decreases with the absolute value of ESR, which means that the cell shapes become more regular. It is shown that the angular irregularity of cells increases at higher ESR values.

Conclusions

The results indicated that, the defined ESR is a stand-alone parameter for describing the realistic mechanical loading on the ECs and their morphological response.

Computational modeling for cardiovascular tissue engineering: the importance of including cell behavior in growth and remodeling algorithms

Understanding cardiovascular growth and remodeling (G&R) is fundamental for designing robust cardiovascular tissue engineering strategies, which enable synthetic or biological scaffolds to transform into healthy living tissues after implantation. Computational modeling, particularly when integrated with experimental research, is key for advancing our understanding, predicting the in vivo evolution of engineered tissues, and efficiently optimizing scaffold designs. As cells are ultimately the drivers of G&R and known to change their behavior in response to mechanical cues, increasing efforts are currently undertaken to capture (mechano-mediated) cell behavior in computational models. In this selective review, we highlight some recent examples that are relevant in the context of cardiovascular tissue engineering and discuss the current and future biological and computational challenges for modeling cell-mediated G&R.

What factors determine the number of nonmuscle myosin II in the sarcomeric unit of stress fibers?

Actin stress fibers (SFs), a contractile apparatus in nonmuscle cells, possess a contractile unit that is apparently similar to the sarcomere of myofibrils in muscles. The function of SFs has thus often been addressed based on well-characterized properties of muscles. However, unlike the fixed number of myosin molecules in myofibrils, the number of nonmuscle myosin II (NMII) within the contractile sarcomeric unit in SFs is quite low and variable for some reason. Here we address what factors may determine the specific number of NMII in SFs. We suggest with a theoretical model that the number lies just in between the function of SFs for bearing cellular tension under static conditions and for promptly disintegrating upon forced cell shortening. We monitored shortening-induced disintegration of SFs in human osteosarcoma U2OS cells expressing mutants of myosin regulatory light chain that virtually regulates the interaction of NMII with actin filaments, and the behaviors observed were indeed consistent with the theoretical consequences. This situation-specific nature of SFs may allow nonmuscle cells to respond adaptively to mechanical stress to circumvent activation of pro-inflammatory signals as previously indicated, i.e., a behavior distinct from that of muscles that are basically specialized for exhibiting contractile activity.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Role of boundary conditions in determining cell alignment in response to stretch

The ability of cells to orient in response to mechanical stimuli is essential to embryonic development, cell migration, mechanotransduction, and other critical physiologic functions in a range of organs. Endothelial cells, fibroblasts, mesenchymal stem cells, and osteoblasts all orient perpendicular to an applied cyclic stretch when plated on stretchable elastic substrates, suggesting a common underlying mechanism. However, many of these same cells orient parallel to stretch in vivo and in 3D culture, and a compelling explanation for the different orientation responses in 2D and 3D has remained elusive. Here, we conducted a series of experiments designed specifically to test the hypothesis that differences in strains transverse to the primary loading direction give rise to the different alignment patterns observed in 2D and 3D cyclic stretch experiments ("strain avoidance"). We found that, in static or low-frequency stretch conditions, cell alignment in fibroblast-populated collagen gels correlated with the presence or absence of a restraining boundary condition rather than with compaction strains. Cyclic stretch could induce perpendicular alignment in 3D culture but only at frequencies an order of magnitude greater than reported to induce perpendicular alignment in 2D. We modified a published model of stress fiber dynamics and were able to reproduce our experimental findings across all conditions tested as well as published data from 2D cyclic stretch experiments. These experimental and model results suggest an explanation for the apparently contradictory alignment responses of cells subjected to cyclic stretch on 2D membranes and in 3D gels.

Cellular Microbiaxial Stretching to Measure a Single-Cell Strain Energy Density Function

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel-Gasser-Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

A multiscale approach for determining the morphology of endothelial cells at a coronary artery

The morphology of endothelial cells (ECs) may be an indication for determining atheroprone sites. Until now, there has been no clinical imaging technique to visualize the morphology of ECs in the arteries. The present study introduces a computational technique for determining the morphology of ECs. This technique is a multiscale simulation consisting of the artery scale and the cell scale. The artery scale is a fluid-structure interaction simulation. The input for the artery scale is the geometry of the coronary artery, that is, the dynamic curvature of the artery due to the cardiac motion, blood flow, blood pressure, heart rate, and the mechanical properties of the blood and the arterial wall, the measurements of which can be obtained for a specific patient. The results of the artery scale are wall shear stress (WSS) and cyclic strains as the mechanical stimuli of ECs. The cell scale is an inventive mass-and-spring model that is able to determine the morphological response of ECs to any combination of mechanical stimuli. The results of the multiscale simulation show the morphology of ECs at different locations of the coronary artery. The results indicate that the atheroprone sites have at least 1 of 3 factors: low time-averaged WSS, high angle of WSS, and high longitudinal strain. The most probable sites for atherosclerosis are located at the bifurcation region and lie on the myocardial side of the artery. The results also indicated that a higher dynamic curvature is a negative factor and a higher pulse pressure is a positive factor for protection against atherosclerosis.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Modeling Stem Cell Myogenic Differentiation

The process of stem cell myogenesis (transformation into skeletal muscle cells) includes several stages characterized by the expression of certain combinations of myogenic factors. The first part of this process is accompanied by cell division, while the second part is mainly associated with direct differentiation. The mechanical cues are known to enhance stem cell myogenesis, and the paper focuses on the stem cell differentiation under the condition of externally applied strain. The process of stem cell myogenic differentiation is interpreted as the interplay among transcription factors, targeted proteins and strain-generated signaling molecule, and it is described by a kinetic multi-stage model. The model parameters are optimally adjusted by using the available data from the experiment with adipose-derived stem cells subjected to the application of cyclic uniaxial strains of the magnitude of 10%. The modeling results predict the kinetics of the process of myogenic differentiation, including the number of cells in each stage of differentiation and the rates of differentiation from one stage to another for different strains from 4% to 16%. The developed model can help better understand the process of myogenic differentiation and the effects of mechanical cues on stem cell use in muscle therapies.

Biomechanics of cell reorientation in a three-dimensional matrix under compression

Although a number of studies have reported that cells cultured on a stretchable substrate align away from or perpendicular to the stretch direction, how cells sense and respond to compression in a three-dimensional (3D) matrix remains an open question. We analyzed the reorientation of human prostatic normal tissue fibroblasts (NAFs) and cancer-associated fibroblasts (CAFs) in response to 3D compression using a Fast Fourier Transform (FFT) method. Results show that NAFs align to specific angles upon compression while CAFs exhibit a random distribution. In addition, NAFs with enhanced contractile force induced by transforming growth factor β (TGF-β) behave in a similar way as CAFs. Furthermore, a theoretical model based on the minimum energy principle has been developed to provide insights into these observations. The model prediction is in agreement with the observed cell orientation patterns in several different experimental conditions, disclosing the important role of stress fibers and inherent cell contractility in cell reorientation.

Fibroblasts Slow Conduction Velocity in a Reconstituted Tissue Model of Fibrotic Cardiomyopathy

Myocardial function deteriorates over the course of fibrotic cardiomyopathy, due to electrophysiological and mechanical effects of myofibroblasts that are not completely understood. Although a range of experimental model systems and associated theoretical treatments exist at the levels of isolated cardiomyocytes and planar co-cultures of myofibroblasts and cardiomyocytes, interactions between these cell types at the tissue level are less clear. We studied these interactions through an engineered heart tissue (EHT) model of fibrotic myocardium and a mathematical model of the effects of cellular composition on EHT impulse conduction velocity. The EHT model allowed for modulation of cardiomyocyte and myofibroblast volume fractions, and observation of cell behavior in a three-dimensional environment that is more similar to native heart tissue than is planar cell culture. The cardiomyocyte and myofibroblast volume fractions determined the retardation of impulse conduction (spread of the action potential) in EHTs as measured by changes of the fluorescence of the Ca²⁺ probe, Fluo-2. Interpretation through our model showed retardation far in excess of predictions by homogenization theory, with conduction ceasing far below the fibroblast volume fraction associated with steric percolation. Results point to an important multiscale structural role of myofibroblasts in attenuating impulse conduction in fibrotic cardiomyopathy.

Efficient computational simulation of actin stress fiber remodeling

Understanding collagen and stress fiber remodeling is essential for the development of engineered tissues with good functionality. These processes are complex, highly interrelated, and occur over different time scales. As a result, excessive computational costs are required to computationally predict the final organization of these fibers in response to dynamic mechanical conditions. In this study, an analytical approximation of a stress fiber remodeling evolution law was derived. A comparison of the developed technique with the direct numerical integration of the evolution law showed relatively small differences in results, and the proposed method is one to two orders of magnitude faster.

A mechanical model for morphological response of endothelial cells under combined wall shear stress and cyclic stretch loadings

The shape and morphology of endothelial cells (ECs) lining the blood vessels are a good indicator for atheroprone and atheroprotected sites. ECs of blood vessels experience both wall shear stress (WSS) and cyclic stretch (CS). These mechanical stimuli influence the shape and morphology of ECs. A few models have been proposed for predicting the morphology of ECs under WSS or CS. In the present study, a mathematical cell population model is developed to simulate the morphology of ECs under combined WSS and CS conditions. The model considers the cytoskeletal filaments, cell-cell interactions, and cell-extracellular matrix interactions. In addition, the reorientation and polymerization of microfilaments are implemented in the model. The simulations are performed for different conditions: without mechanical stimuli, under pure WSS, under pure CS, and under combined WSS and CS. The results are represented as shape and morphology of ECs, shape index, and angle of orientation. The model is validated qualitatively and quantitatively with several experimental studies, and good agreement with experimental studies is achieved. To the best of our knowledge, it is the first model for predicting the morphology of ECs under combined WSS and CS condition. The model can be used to indicate the atheroprone regions of a patient's artery.

Heading in the Right Direction: Understanding Cellular Orientation Responses to Complex Biophysical Environments

The aim of cardiovascular regeneration is to mimic the biological and mechanical functioning of tissues. For this it is crucial to recapitulate the in vivo cellular organization, which is the result of controlled cellular orientation. Cellular orientation response stems from the interaction between the cell and its complex biophysical environment. Environmental biophysical cues are continuously detected and transduced to the nucleus through entwined mechanotransduction pathways. Next to the biochemical cascades invoked by the mechanical stimuli, the structural mechanotransduction pathway made of focal adhesions and the actin cytoskeleton can quickly transduce the biophysical signals directly to the nucleus. Observations linking cellular orientation response to biophysical cues have pointed out that the anisotropy and cyclic straining of the substrate influence cellular orientation. Yet, little is known about the mechanisms governing cellular orientation responses in case of cues applied separately and in combination. This review provides the state-of-the-art knowledge on the structural mechanotransduction pathway of adhesive cells, followed by an overview of the current understanding of cellular orientation responses to substrate anisotropy and uniaxial cyclic strain. Finally, we argue that comprehensive understanding of cellular orientation in complex biophysical environments requires systematic approaches based on the dissection of (sub)cellular responses to the individual cues composing the biophysical niche.

A biomechanical model for fluidization of cells under dynamic strain

Recent experiments have investigated the response of smooth muscle cells to transient stretch-compress (SC) and compress-stretch (CS) maneuvers. The results indicate that the transient SC maneuver causes a sudden fluidization of the cell while the CS maneuver does not. To understand this asymmetric behavior, we have built a biomechanical model to probe the response of stress fibers to the two maneuvers. The model couples the cross-bridge cycle of myosin motors with a viscoelastic Kelvin-Voigt element that represents the stress fiber. Simulation results point to the sensitivity of the myosin detachment rate to tension as the cause for the asymmetric response of the stress fiber to the CS and SC maneuvers. For the SC maneuver, the initial stretch increases the tension in the stress fiber and suppresses myosin detachment. The subsequent compression then causes a large proportion of the myosin population to disengage rapidly from actin filaments. This leads to the disassembly of the stress fibers and the observed fluidization. In contrast, the CS maneuver only produces a mild loss of myosin motors and no fluidization.

Rapid Quantification of 3D Collagen Fiber Alignment and Fiber Intersection Correlations with High Sensitivity

Metastatic cancers aggressively reorganize collagen in their microenvironment. For example, radially orientated collagen fibers have been observed surrounding tumor cell clusters in vivo. The degree of fiber alignment, as a consequence of this remodeling, has often been difficult to quantify. In this paper, we present an easy to implement algorithm for accurate detection of collagen fiber orientation in a rapid pixel-wise manner. This algorithm quantifies the alignment of both computer generated and actual collagen fiber networks of varying degrees of alignment within 5°°. We also present an alternative easy method to calculate the alignment index directly from the standard deviation of fiber orientation. Using this quantitative method for determining collagen alignment, we demonstrate that the number of collagen fiber intersections has a negative correlation with the degree of fiber alignment. This decrease in intersections of aligned fibers could explain why cells move more rapidly along aligned fibers than unaligned fibers, as previously reported. Overall, our paper provides an easier, more quantitative and quicker way to quantify fiber orientation and alignment, and presents a platform in studying effects of matrix and cellular properties on fiber alignment in complex 3D environments.

Tissue-specific mechanical and geometrical control of cell viability and actin cytoskeleton alignment

Different tissues have specific mechanical properties and cells of different geometries, such as elongated muscle cells and polygonal endothelial cells, which are precisely regulated during embryo development. However, the mechanisms that underlie these processes are not clear. Here, we built an in vitro model to mimic the cellular microenvironment of muscle by combining both mechanical stretch and geometrical control. We found that mechanical stretch was a key factor that determined the optimal geometry of myoblast C2C12 cells under stretch, whereas vascular endothelial cells and fibroblasts had no such dependency. We presented the first experimental evidence that can explain why myoblasts are destined to take the elongated geometry so as to survive and maintain parallel actin filaments along the stretching direction. The study is not only meaningful for the research on myogenesis but also has potential application in regenerative medicine.

Structural finite element analysis to explain cell mechanics variability

The ability to model the mechanical responses of different cell types presents many opportunities to tissue engineering research to further identify changes from physiological conditions to disease. Using a previously validated finite element cell model we aim to show how variation of the material properties of the intracellular components affects cell response after compression and shearing. A parametric study was performed to understand the key mechanical features from different cell types, focussing on specific cytoskeleton components and prestress. Results show that actin cortex does not have a mechanical role in resisting shearing loading conditions. The sensitivity analysis predicted that cell force to compression and shearing is highly affected by changes in cortex thickness, cortex Young's modulus and rigidity of the remaining cytoplasm. Variation of prestress affects mainly the response of cells under shear loads and the model defines a relationship between cell force and prestress depending on the specific loading conditions, which is in good agreement with in vitro experiments. The results are used to make predictions that can relate mechanical properties with cell phenotype to be used as guidelines for individual cytoskeletal structures for future modelling efforts of the structure-function relationships of living cells.

Simulation of the Mechanical Response of Cells on Micropost Substrates

Experimental studies where cells are seeded on micropost arrays in order to quantify their contractile behavior are becoming increasingly common. Interpretation of the data generated by this experimental technique is difficult, due to the complexity of the processes underlying cellular contractility and mechanotransduction. In the current study, a coupled framework that considers strain rate dependent contractility and remodeling of the cytoskeleton is used in tandem with a thermodynamic model of tension dependent focal adhesion formation to investigate the biomechanical response of cells adhered to micropost arrays. Computational investigations of the following experimental studies are presented: cell behavior on different sized arrays with a range of post stiffness; stress fiber and focal adhesion formation in irregularly shaped cells; the response of cells to deformations applied locally to individual posts; and the response of cells to equibiaxial stretching of micropost arrays. The predicted stress fiber and focal adhesion distributions; in addition to the predicted post tractions are quantitatively and qualitatively supported by previously published experimental data. The computational models presented in this study thus provide a framework for the design and interpretation of experimental micropost studies.

Effect of Static Pre-stretch Induced Surface Anisotropy on Orientation of Mesenchymal Stem Cells

Mechanical cues in the cellular environment play important roles in guiding various cell behaviors, such as cell alignment, migration, and differentiation. Previous studies investigated mechanical stretch guided cell alignment pre-dominantly with cyclic stretching whereby an external force is applied to stretch the substrate dynamically (i.e., cyclically) while the cells are attached onto the substrate. In contrast, we created a static pre-stretched anisotropic surface in which the cells were seeded subsequent to stretching the substrate. We hypothesized that the cell senses the physical environment through a more active mechanism, namely, even without external forces the cell can actively apply traction and sense an increased stiffness in the stretched direction and align in that direction. To test our hypothesis, we quantified the extent of pre-stretch induced anisotropy by employing the theory of small deformation superimposed on large and predicted the effective stiffness in the stretch direction as well as its perpendicular direction. We showed mesenchymal stem cells (MSC) aligned in the pre-stretched direction, and the cell alignment and morphology were dependent on the pre-stretch magnitude. In addition, the pre-stretched surface demonstrated an ability to promote early myoblast differentiation of the MSC. This study is the first report on MSC alignment on a statically pre-stretched surface. The cell orientation induced by the pre-stretch induced anisotropy could provide insight into tissue engineering applications involving cells that aligned in vivo in the absence of dynamic mechanical stimuli.

The role of mechanics in actin stress fiber kinetics

The dynamic responses of actin stress fibers within a cell's cytoskeleton are central to the development and maintenance of healthy tissues and organs. Disturbances to these underlie a broad range of pathologies. Because of the importance of these responses, extensive experiments have been conducted in vitro to characterize actin cytoskeleton dynamics of cells cultured upon two-dimensional substrata, and the first experiments have been conducted for cells within three-dimensional tissue models. Three mathematical models exist for predicting the dynamic behaviors observed. Surprisingly, despite differing viewpoints on how actin stress fibers are stabilized or destabilized, all of these models are predictive of a broad range of available experimental data. Coarsely, the models of Kaunas and co-workers adopt a strategy whereby mechanical stretch can hasten the depolymerization actin stress fibers that turn over constantly, while the models of Desphande and co-workers adopt a strategy whereby mechanical stress is required to activate the formation of stress fibers and subsequently stabilize them. In three-dimensional culture, elements of both approaches appear necessary to predict observed phenomena, as embodied by the model of Lee et al. After providing a critical review of existing models, we propose lines of experimentation that might be able to test the different principles underlying their kinetic laws.

AXIAL-SYMMETRIC MODELING AND KINEMATIC ANALYSIS OF SPREADING OF SPARSELY CULTURED FIBROBLASTS

Cell spreading plays an important role in the modulation of physiological functions such as inflammation and cancer metastasis. The Brownian ratchet model and Bell's model have been used to simulate actin dynamics and bond kinetics for focal adhesion dynamics, respectively. In the present study, these models were modified and two additional subcellular mechanisms, integrin and myosin kinetics, were incoporated. An integrin recruitment function was introduced to determine the size of a focal adhesion associated with the substrate stiffness. The relationship between myosin concentration and the actin protrusion velocity was described by a first-order differential equation. Subcellular processes, including cell protrusion, focal adhesion formation, and stress fiber formation, were integrated into an axial-symmetric biophysical model, while inputs to the model were kinematic data from time-lapse experiments. Numerical simulations of the model using the Gillespie algorithm showed that dynamics of cell spreading can be well described by the model.

Dynamic modeling of cell migration and spreading behaviors on fibronectin coated planar substrates and micropatterned geometries

An integrative cell migration model incorporating focal adhesion (FA) dynamics, cytoskeleton and nucleus remodeling, actin motor activity, and lamellipodia protrusion is developed for predicting cell spreading and migration behaviors. This work is motivated by two experimental works: (1) cell migration on 2-D substrates under various fibronectin concentrations and (2) cell spreading on 2-D micropatterned geometries. These works suggest (1) cell migration speed takes a maximum at a particular ligand density (∼1140 molecules/µm(2)) and (2) that strong traction forces at the corners of the patterns may exist due to combined effects exerted by actin stress fibers (SFs). The integrative model of this paper successfully reproduced these experimental results and indicates the mechanism of cell migration and spreading. In this paper, the mechanical structure of the cell is modeled as having two elastic membranes: an outer cell membrane and an inner nuclear membrane. The two elastic membranes are connected by SFs, which are extended from focal adhesions on the cortical surface to the nuclear membrane. In addition, the model also includes ventral SFs bridging two focal adhesions on the cell surface. The cell deforms and gains traction as transmembrane integrins distributed over the outer cell membrane bond to ligands on the ECM surface, activate SFs, and form focal adhesions. The relationship between the cell migration speed and fibronectin concentration agrees with existing experimental data for Chinese hamster ovary (CHO) cell migrations on fibronectin coated surfaces. In addition, the integrated model is validated by showing persistent high stress concentrations at sharp geometrically patterned edges. This model will be used as a predictive model to assist in design and data processing of upcoming microfluidic cell migration assays.

BIOMECHANICAL INVESTIGATION OF PULSATILE FLOW IN A THREE-DIMENSIONAL ATHEROSCLEROTIC CAROTID BIFURCATION MODEL

It is a well-established fact that atherosclerosis in carotid bifurcation depends on flow parameters such as wall shear stress, flow pulsatility, and blood pressure. However, it is still not clearly verified how atherosclerosis can become aggravated when plaque experiences a high level of shear stress during advance stages of this disease. In this paper, fluid and structural properties in idealistic geometries are analyzed by using fluid-structure interaction (FSI). From our results, the relationship among blood pressure, stenotic compression, and deformation was established. We show that a high level of compression occurs at the stenotic apex, and can potentially be responsible for plaque progression. Moreover, wall shear stress and deformation are significantly affected by the degree of stenosis. Finally, through analysis of the FSI-based simulation results, we can better understand the parameters that influence flow through a stenotic artery and plaque aggravation, and apply the knowledge for the enhancement of clinical research and prediction of treatment outcomes.

Physically-induced cytoskeleton remodeling of cells in three-dimensional culture

Characterizing how cells in three-dimensional (3D) environments or natural tissues respond to biophysical stimuli is a longstanding challenge in biology and tissue engineering. We demonstrate a strategy to monitor morphological and mechanical responses of contractile fibroblasts in a 3D environment. Cells responded to stretch through specific, cell-wide mechanisms involving staged retraction and reinforcement. Retraction responses occurred for all orientations of stress fibers and cellular protrusions relative to the stretch direction, while reinforcement responses, including extension of cellular processes and stress fiber formation, occurred predominantly in the stretch direction. A previously unreported role of F-actin clumps was observed, with clumps possibly acting as F-actin reservoirs for retraction and reinforcement responses during stretch. Responses were consistent with a model of cellular sensitivity to local physical cues. These findings suggest mechanisms for global actin cytoskeleton remodeling in non-muscle cells and provide insight into cellular responses important in pathologies such as fibrosis and hypertension.

Cyclic stretch reveals a mechanical role for intermediate filaments in a desminopathic cell model

Mechanics is now recognized as crucial in cell function. To date, the mechanical properties of cells have been inferred from experiments which investigate the roles of actin and microtubules ignoring the intermediate filaments (IFs) contribution. Here, we analyse myoblasts behaviour in the context of myofibrillar myopathy resulting from p.D399Y desmin mutation which disorganizes the desmin IF network in muscle cells. We compare the response of myoblasts expressing either mutated or wild-type desmin to cyclic stretch. Cells are cultivated on supports submitted to periodic uniaxial stretch of 20% elongation amplitude and 0.3 Hz frequency. We show that during stretching cycles, cells expressing mutated desmin reduce their mean amplitude both for the elongation and spreading area compared to those expressing wild-type desmin. Even more unexpected, the reorientation angles are altered in the presence of p.D399Y desmin. Yet, at rest, the whole set of those parameters are similar for the two cell populations. Thus, we demonstrate that IFs affect the mechanical properties and the dynamics of cell reorientation. Since these processes are known due to actin cytoskeleton, these results suggest the IFs implication in mechanics signal transduction. Further studies may lead to better understanding of their contribution to this process.

Microtubule dynamics regulate cyclic stretch-induced cell alignment in human airway smooth muscle cells

Microtubules are structural components of the cytoskeleton that determine cell shape, polarity, and motility in cooperation with the actin filaments. In order to determine the role of microtubules in cell alignment, human airway smooth muscle cells were exposed to cyclic uniaxial stretch. Human airway smooth muscle cells, cultured on type I collagen-coated elastic silicone membranes, were stretched uniaxially (20% in strain, 30 cycles/min) for 2 h. The population of airway smooth muscle cells which were originally oriented randomly aligned near perpendicular to the stretch axis in a time-dependent manner. However, when the cells treated with microtubule disruptors, nocodazole and colchicine, were subjected to the same cyclic uniaxial stretch, the cells failed to align. Lack of alignment was also observed for airway smooth muscle cells treated with a microtubule stabilizer, paclitaxel. To understand the intracellular mechanisms involved, we developed a computational model in which microtubule polymerization and attachment to focal adhesions were regulated by the preexisting tensile stress, pre-stress, on actin stress fibers. We demonstrate that microtubules play a central role in cell re-orientation when cells experience cyclic uniaxial stretching. Our findings further suggest that cell alignment and cytoskeletal reorganization in response to cyclic stretch results from the ability of the microtubule-stress fiber assembly to maintain a homeostatic strain on the stress fiber at focal adhesions. The mechanism of stretch-induced alignment we uncovered is likely involved in various airway functions as well as in the pathophysiology of airway remodeling in asthma.

Non-muscle myosin II induces disassembly of actin stress fibres independently of myosin light chain dephosphorylation

Dynamic remodelling of actin stress fibres (SFs) allows non-muscle cells to adapt to applied forces such as uniaxial cell shortening. However, the mechanism underlying rapid and selective disassembly of SFs oriented in the direction of shortening remains to be elucidated. Here, we investigated how myosin crossbridge cycling induced by MgATP is associated with SF disassembly. Moderate concentrations of MgATP, or [MgATP], induced SF contraction. Meanwhile, at [MgATP] slightly higher than the physiological level, periodic actin patterns emerged along the length of SFs and dispersed within seconds. The actin fragments were diverse in length, but comparable to those in characteristic sarcomeric units of SFs. These results suggest that MgATP-bound non-muscle myosin II dissociates from the individual actin filaments that constitute the sarcomeric units, resulting in unbundling-induced disassembly rather than end-to-end actin depolymerization. This rapid SF disassembly occurred independent of dephosphorylation of myosin light chain. In terms of effects on actin-myosin interactions, a rise in [MgATP] is functionally equivalent to a temporal decrease in the total number of actin-myosin crossbridges. Actin-myosin crossbridges are known to be reduced by an assisting load on myosin. Thus, the present study suggests that reducing the number of actin-myosin crossbridges promotes rapid and orientation-dependent disassembly of SFs after cell shortening.

Energy distribution in disordered elastic networks

Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed.

A novel platform for in situ investigation of cells and tissues under mechanical strain

The mechanical micro-environment influences cellular responses such as migration, proliferation, differentiation and apoptosis. Cells are subjected to mechanical stretching in vivo, e.g., epithelial cells during embryogenesis. Current methodologies do not allow high-resolution in situ observation of cells and tissues under applied strain, which may reveal intracellular dynamics and the origin of cell mechanosensitivity. A novel polydimethylsiloxane substrate was developed, capable of applying tensile and compressive strain (up to 45%) to cells and tissues while allowing in situ observation with high-resolution optics. The strain field of the substrate was characterized experimentally using digital image correlation, and the deformation was modeled by the finite element method, using a Mooney-Rivlin hyperelastic constitutive relation. The substrate strain was found to be uniform for >95% of the substrate area. As a demonstration of the system, mechanical strain was applied to single fibroblasts transfected with GFP-actin and whole transgenic Drosophila embryos expressing GFP in all neurons during live imaging. Three observations of biological responses due to applied strain are reported: (1) dynamic rotation of intact actin stress fibers in fibroblasts; (2) lamellipodia activity and actin polymerization in fibroblasts; (3) active axonal contraction in Drosophila embryo motor neurons. The novel platform may serve as an important tool in studying the mechanoresponse of cells and tissues, including whole embryos.