Response of an actin filament network model under cyclic stretching through a coarse grained Monte Carlo approach

Mechanical stretch leads to increased caveolin-1 content and mineralization potential in extracellular vesicles from vascular smooth muscle cells

BACKGROUND

Hypertension-induced mechanical stress on vascular smooth muscle cells (VSMCs) is a known risk factor for vascular remodeling, including vascular calcification. Caveolin-1 (Cav-1), an integral structural component of plasma membrane invaginations, is a mechanosensitive protein that is required for the formation of calcifying extracellular vesicles (EVs). However, the role of mechanics in Cav-1-induced EV formation from VSMCs has not been reported.

RESULTS

Exposure of VSMCs to 10% mechanical stretch (0.5 Hz) for 72 h resulted in Cav-1 translocation into non-caveolar regions of the plasma membrane and subsequent redistribution of Cav-1 from the VSMCs into EVs. Inhibition of Rho-A kinase (ROCK) in mechanically-stimulated VSMCs exacerbated the liberation of Cav-1 positive EVs from the cells, suggesting a potential involvement of actin stress fibers in this process. The mineralization potential of EVs was measured by incubating the EVs in a high phosphate solution and measuring light scattered by the minerals at 340 nm. EVs released from stretched VSMCs showed higher mineralization potential than the EVs released from non-stretched VSMCs. Culturing VSMCs in pro-calcific media and exposure to mechanical stretch increased tissue non-specific alkaline phosphatase (ALP), an important enzyme in vascular calcification, activity in EVs released from the cells, with cyclic stretch further elevating EV ALP activity compared to non-stretched cells.

CONCLUSION

Our data demonstrate that mechanical stretch alters Cav-1 trafficking and EV release, and the released EVs have elevated mineralization potential.

A machine learning approach to predict cellular mechanical stresses in response to chemical perturbation

Mechanical stresses generated at the cell-cell level and cell-substrate level have been suggested to be important in a host of physiological and pathological processes. However, the influence various chemical compounds have on the mechanical stresses mentioned above is poorly understood, hindering the discovery of novel therapeutics, and representing a barrier in the field. To overcome this barrier, we implemented two approaches: 1) monolayer boundary predictor and 2) discretized window predictor utilizing either stepwise linear regression or quadratic support vector machine machine learning model to predict the dose-dependent response of tractions and intercellular stresses to chemical perturbation. We used experimental traction and intercellular stress data gathered from samples subject to 0.2 or 2 μg/mL drug concentrations along with cell morphological properties extracted from the bright-field images as predictors to train our model. To demonstrate the predictive capability of our machine learning models, we predicted tractions and intercellular stresses in response to 0 and 1 μg/mL drug concentrations which were not utilized in the training sets. Results revealed the discretized window predictor trained just with four samples (292 images) to best predict both intercellular stresses and tractions using the quadratic support vector machine and stepwise linear regression models, respectively, for the unseen sample images.

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.

Rapid prediction of protein natural frequencies using graph neural networks

Natural vibrational frequencies of proteins help to correlate functional shifts with sequence or geometric variations that lead to negligible changes in protein structures, such as point mutations related to disease lethality or medication effectiveness. Normal mode analysis is a well-known approach to accurately obtain protein natural frequencies. However, it is not feasible when high-resolution protein structures are not available or time consuming to obtain. Here we provide a machine learning model to directly predict protein frequencies from primary amino acid sequences and low-resolution structural features such as contact or distance maps. We utilize a graph neural network called principal neighborhood aggregation, trained with the structural graphs and normal mode frequencies of more than 34 000 proteins from the protein data bank. combining with existing contact/distance map prediction tools, this approach enables an end-to-end prediction of the frequency spectrum of a protein given its primary sequence.

We present a computational framework based on graph neural networks (GNNs) to predict the natural frequencies of proteins from primary amino acid sequences and contact/distance maps.

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.

Cell stretchers and the LINC complex in mechanotransduction

How cells respond to mechanical forces from the surrounding environment is critical for cell survival and function. The LINC complex is a central component in the mechanotransduction pathway that transmits mechanical information from the cell surface to the nucleus. Through LINC complex functionality, the nucleus is able to respond to mechanical stress by altering nuclear structure, chromatin organization, and gene expression. The use of specialized devices that apply mechanical strain to cells have been central to investigating how mechanotransduction occurs, how cells respond to mechanical stress, and the role of the LINC complexes in these processes. A large variety of designs have been reported for these devices, with the most common type being cell stretchers. Here we highlight some of the salient features of cell stretchers and suggest some key parameters that should be considered when using these devices. We provide a brief overview of how the LINC complexes contribute to the cellular responses to mechanical strain. And finally, we suggest that stretchers may be a useful tool to study aging.

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.

Genomics models in radiotherapy: From mechanistic to machine learning

Machine learning (ML) provides a broad framework for addressing high-dimensional prediction problems in classification and regression. While ML is often applied for imaging problems in medical physics, there are many efforts to apply these principles to biological data toward questions of radiation biology. Here, we provide a review of radiogenomics modeling frameworks and efforts toward genomically guided radiotherapy. We first discuss medical oncology efforts to develop precision biomarkers. We next discuss similar efforts to create clinical assays for normal tissue or tumor radiosensitivity. We then discuss modeling frameworks for radiosensitivity and the evolution of ML to create predictive models for radiogenomics.

Tumor-on-a-chip for integrating a 3D tumor microenvironment: chemical and mechanical factors

Tumor progression, including metastasis, is significantly influenced by factors in the tumor microenvironment (TME) such as mechanical force, shear stress, chemotaxis, and hypoxia. At present, most cancer studies investigate tumor metastasis by conventional cell culture methods and animal models, which are limited in data interpretation. Although patient tissue analysis, such as human patient-derived xenografts (PDX), can provide important clinical relevant information, they may not be feasible for functional studies as they are costly and time-consuming. Thus, in vitro three-dimensional (3D) models are rapidly being developed that mimic TME and allow functional investigations of metastatic mechanisms and drug responses. One of those new 3D models is tumor-on-a-chip technology that provides a powerful in vitro platform for cancer research, with the ability to mimic the complex physiological architecture and precise spatiotemporal control. Tumor-on-a-chip technology can provide integrated features including 3D scaffolding, multicellular culture, and a vasculature system to simulate dynamic flow in vivo. Here, we review a select set of recent achievements in tumor-on-a-chip approaches and present potential directions for tumor-on-a-chip systems in the future for areas including mechanical and chemical mimetic systems. We also discuss challenges and perspectives in both biological factors and engineering methods for tumor-on-a-chip progress. These approaches will allow in the future for the tumor-on-a-chip systems to test therapeutic approaches for individuals through using their cancerous cells gathered through approaches like biopsies, which then will contribute toward personalized medicine treatments for improving their outcomes.

Bioreactor With Electrically Deformable Curved Membranes for Mechanical Stimulation of Cell Cultures

Physiologically relevant in vitro models of stretchable biological tissues, such as muscle, lung, cardiac and gastro-intestinal tissues, should mimic the mechanical cues which cells are exposed to in their dynamic microenvironment in vivo. In particular, in order to mimic the mechanical stimulation of tissues in a physiologically relevant manner, cell stretching is often desirable on surfaces with dynamically controllable curvature. Here, we present a device that can deform cell culture membranes without the current need for external pneumatic/fluidic or electrical motors, which typically make the systems bulky and difficult to operate. We describe a modular device that uses elastomeric membranes, which can intrinsically be deformed by electrical means, producing a dynamically tuneable curvature. This approach leads to compact, self-contained, lightweight and versatile bioreactors, not requiring any additional mechanical equipment. This was obtained via a special type of dielectric elastomer actuator. The structure, operation and performance of early prototypes are described, showing preliminary evidence on their ability to induce changes on the spatial arrangement of the cytoskeleton of fibroblasts dynamically stretched for 8 h.

Time dependence of cellular responses to dynamic and complex strain fields

Exposing cells to an unconventional sequence of physical cues can reveal subtleties of cellular sensing and response mechanisms. We investigated the mechanoresponse of cyclically stretched fibroblasts under a spatially non-uniform strain field which was subjected to repeated changes in stretching directions over 55 h. A polydimethylsiloxane microfluidic stretcher array optimized for complex staining procedures and imaging was developed to generate biologically relevant strain and strain gradient amplitudes. We demonstrated that cells can successfully reorient themselves repeatedly, as the main cyclical stretching direction is consecutively switched between two perpendicular directions every 11 h. Importantly, from one reorientation to the next, the extent to which cells reorient themselves perpendicularly to the local strain direction progressively decreases, while their tendency to align perpendicularly to the strain gradient direction increases. We demonstrate that these results are consistent with our finding that cellular responses to strains and strain gradients occur on two distinct time scales, the latter being slower. Overall, our results reveal the absence of major irreversible cellular changes that compromise the ability to sense and reorient to changing strain directions under the conditions of this experiment. On the other hand, we show how the history of strain field dynamics can influence the cellular realignment behavior, due to the interplay of complex time-dependent responses.

Mechanical stretch implications for vascular endothelial cells: Altered extracellular matrix synthesis and remodeling in pathological conditions

AIMS

Cardiovascular diseases such as hypertension, thrombosis and atherosclerosis are responses to mechanical forces applied to the endothelium. Endothelial cells respond to hemodynamic mechanical forces such as cellular mechanical stretching. We investigated the expression of glycosaminoglycans, proteoglycans and other extracellular matrix molecules in endothelial cells subjected to various mechanical stimuli.

MAIN METHODS

Endothelial cells were subjected to mechanical stretch in a vacuum system FlexCell™ to 5% (physiological condition) and 15% (pathological condition), for 4 h or 24 h. Culture plates not subjected to strain were used as controls. Subsequently, ECs were subjected to immunofluorescence, real-time PCR, PCR array, glycosaminoglycans biosynthesis using metabolic radiolabeling with ³⁵S-sulfate and cell behavior assays (adhesion, migration and capillary tube formation).

KEY FINDINGS

Mechanical stretch induced changes in endothelial cell morphology. Pathological consequences of mechanical stretch included inhibited migration in 2-fold and capillary-like tube formation in 2-fold, when compared to physiological condition after 4 h of ECs exposure; it also reduced total sulfated glycosaminoglycans synthesis thereabout 1.5-fold. Pathological mechanical stretch conditions induced higher expression after 24 h of ECs exposure to mechanical stretch of syndecan-4 (3.5-fold), perlecan (9.1-fold), decorin (5.7-fold), adhesive proteins as fibronectin (5.6-fold) and collagen III α1 (2.2-fold) and growth factors, including VEGF-A (7.3-fold) and TGFβ-1 (14.6-fold) and TGFβ-3 (4.3-fold).

SIGNIFICANCE

Exposure of endothelial cells to mechanical stretch influenced remodeling of the extracellular matrix as well as cell-matrix interactions. These studies improve understanding of how vascular biology is affected by mechanical forces and how these molecules behave in cardiovascular diseases.

Myofibrils in Cardiomyocytes Tend to Assemble Along the Maximal Principle Stress Directions

The mechanisms underlying the spatial organization of self-assembled myofibrils in cardiac tissues remain incompletely understood. By modeling cells as elastic solids under active cytoskeletal contraction, we found a good correlation between the predicted maximal principal stress directions and the in vitro myofibril orientations in individual cardiomyocytes. This implies that actomyosin fibers tend to assemble along the maximal tensile stress (MTS) directions. By considering the dynamics of focal adhesion and myofibril formation in the model, we showed that different patterns of myofibril organizations in mature versus immature cardiomyocytes can be explained as the consequence of the different levels of force-dependent remodeling of focal adhesions. Further, we applied the mechanics model to cell pairs and showed that the myofibril organizations can be regulated by a combination of multiple factors including cell shape, cell-substrate adhesions, and cell-cell adhesions. This mechanics model can guide the rational design in cardiac tissue engineering where recapitulating in vivo myofibril organizations is crucial to the contractile function of the heart.

Cellular orientation is guided by strain gradients

The strain-induced reorientation response of cyclically stretched cells has been well characterized in uniform strain fields. In the present study, we comprehensively analyse the behaviour of human fibroblasts subjected to a highly non-uniform strain field within a polymethylsiloxane microdevice. Our results indicate that the strain gradient amplitude and direction regulate cell reorientation through a coordinated gradient avoidance response. We provide critical evidence that strain gradient is a key physical cue that can guide cell organization. Specifically, our work suggests that cells are able to pinpoint the location under the cell of multiple physical cues and integrate this information (strain and strain gradient amplitudes and directions), resulting in a coordinated response. To gain insight into the underlying mechanosensing processes, we studied focal adhesion reorganization and the effect of modulating myosin-II contractility. The extracted focal adhesion orientation distributions are similar to those obtained for the cell bodies, and their density is increased by the presence of stretching forces. Moreover, it was found that the myosin-II activity promoter calyculin-A has little effect on the cellular response, while the inhibitor blebbistatin suppresses cell and focal adhesion alignment and reduces focal adhesion density. These results confirm that similar internal structures involved in sensing and responding to strain direction and amplitude are also key players in strain gradient mechanosensing and avoidance.

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.

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.

Shielding of the Geomagnetic Field Alters Actin Assembly and Inhibits Cell Motility in Human Neuroblastoma Cells

Accumulating evidence has shown that absence of the geomagnetic field (GMF), the so-called hypomagnetic field (HMF) environment, alters the biological functions in seemingly non-magnetosensitive cells and organisms, which indicates that the GMF could be sensed by non-iron-rich and non-photo-sensing cells. The underlying mechanisms of the HMF effects on those cells are closely related to their GMF sensation but remain poorly understood so far. Previously, we found that the HMF represses expressions of genes associated with cell migration and cytoskeleton assembly in human neuroblastoma cells (SH-SY5Y cell line). Here, we measured the HMF-induced changes on cell morphology, adhesion, motility and actin cytoskeleton in SH-SY5Y cells. The HMF inhibited cell adhesion and migration accompanied with a reduction in cellular F-actin amount. Moreover, following exposure to the HMF, the number of cell processes was reduced and cells were smaller in size and more round in shape. Furthermore, disordered kinetics of actin assembly in vitro were observed during exposure to the HMF, as evidenced by the presence of granule and meshed products. These results indicate that elimination of the GMF affects assembly of the motility-related actin cytoskeleton, and suggest that F-actin is a target of HMF exposure and probably a mediator of GMF sensation.

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.

FSI SIMULATION OF A HEALTHY CORONARY BIFURCATION FOR STUDYING THE MECHANICAL STIMULI OF ENDOTHELIAL CELLS UNDER DIFFERENT PHYSIOLOGICAL CONDITIONS

Atherosclerosis is a world-spread and well-known disease. This disease strongly relates to the endothelial cells (ECs) function. Normally, the endothelial cells align in the flow direction in the atheroprotected sites; however, in the case of atheroprone sites these cells orient randomly. The mechanical stimuli such as wall shear stress and strains could determine the morphology and function of the endothelial cells. In the present study, we numerically simulated the left main coronary artery (LCA) and its branches to left anterior descending (LAD) and left circumflex coronary (LCX) artery using fluid–structure interaction (FSI) modeling. The results were presented as longitudinal and circumferential strains of ECs as well as wall shear stress. Wide ranges of heart rate, cardiac motion, systolic and diastolic pressures were considered and their effects on mechanical stimuli were described in detail. The results showed that these factors could greatly influence the risk of atherosclerosis and the location of atherosclerotic lesions.

Understanding emergent functions in self-assembled fibrous networks

Understanding self-assembly processes of nanoscale building blocks and characterizing their properties are both imperative for designing new hierarchical, network materials for a wide range of structural, optoelectrical, and transport applications. Although the characterization and choices of these material building blocks have been well studied, our understanding of how to precisely program a specific morphology through self-assembly still must be significantly advanced. In the recent study by Xie et al (2015 Nanotechnology 26 205602), the self-assembly of end-functionalized nanofibres is investigated using a coarse-grained molecular model and offers fundamental insight into how to control the structural morphology of nanofibrous networks. Varying nanoscale networks are observed when the molecular interaction strength is changed and the findings suggest that self-assembly through the tuning of molecular interactions is a key strategy for designing nanostructured networks with specific topologies.

Structurally governed cell mechanotransduction through multiscale modeling

Mechanotransduction has been divided into mechanotransmission, mechanosensing, and mechanoresponse, although how a cell performs all three functions using the same set of structural components is still highly debated. Here, we bridge the gap between emerging molecular and systems-level understandings of mechanotransduction through a multiscale model linking these three phases. Our model incorporates a discrete network of actin filaments and associated proteins that responds to stretching through geometric relaxation. We assess three potential activating mechanisms at mechanosensitive crosslinks as inputs to a mixture model of molecular release and benchmark each using experimental data of mechanically-induced Rho GTPase FilGAP release from actin-filamin crosslinks. Our results suggest that filamin-FilGAP mechanotransduction response is best explained by a bandpass mechanism favoring release when crosslinking angles fall outside of a specific range. Our model further investigates the difference between ordered versus disordered networks and finds that a more disordered actin network may allow a cell to more finely tune control of molecular release enabling a more robust response.

Mesoscale modelling of environmentally responsive hydrogels: emerging applications

We review recent advances in mesoscale computational modeling, focusing on dissipative particle dynamics, used to probe stimuli-sensitive behavior of hydrogels.

A coupled fiber-matrix model demonstrates highly inhomogeneous microstructural interactions in soft tissues under tensile load

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

Mechanoregulation of h2-calponin gene expression and the role of Notch signaling

The essential role of mechanical signals in regulating the function of living cells is universally observed. However, how mechanical signals are transduced in cells to regulate gene expression is largely unknown. We previously demonstrated that the gene encoding h2-calponin (Cnn2) is sensitively regulated by mechanical tension. In the present study, mouse genomic DNA containing the Cnn2 promoter was cloned, and a nested set of 5' truncations was studied. Transcriptional activity of the Cnn2 promoter-reporter constructs was examined in transfected NIH/3T3, HEK293, and C2C12 cells for their responses to the stiffness of culture substrate. The results showed significant transcriptional activities of the -1.00- and -1.24-kb promoter constructs, whereas the -0.61-kb construct was inactive. The -1.38-, -1.57-, and -2.12-kb constructs showed higher transcriptional activity, whereas only the -1.57- and -2.12-kb constructs exhibited repression of expression when the host cells were cultured on low stiffness substrate. Internal deletion of the segment between -1.57 and -1.38 kb in the -2.12-kb promoter construct abolished the low substrate stiffness-induced repression. Site-specific deletion or mutation of an HES-1 transcription factor binding site in this region also abolished this repression effect. The level of HES-1 increased in cells cultured under a low tension condition, corresponding to the down-regulation of h2-calponin. h2-Calponin gene expression is further affected by the treatment of cells with Notch inhibitor and activator, suggesting an upstream signaling mechanism.

Form-finding model shows how cytoskeleton network stiffness is realized

In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network’s stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein’s relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.

Mechanics of a fiber network within a non-fibrillar matrix: model and comparison with collagen-agarose co-gels

While collagen is recognized as the predominant mechanical component of soft connective tissues, the role of the non-fibrillar matrix (NFM) is less well understood. Even model systems, such as the collagen-agarose co-gel, can exhibit complex behavior, making it difficult to identify relative contributions of specific tissue constituents. In the present study, we developed a two-component microscale model of collagen-agarose tissue analogs and used it to elucidate the interaction between collagen and NFM in uniaxial tension. Collagen fibers were represented with Voronoi networks, and the NFM was modeled as a neo-Hookean solid. Model predictions of total normal stress and Poisson's ratio matched experimental observations well (including high Poisson's values of ~3), and the addition of NFM led to composition-dependent decreases in volume change and increases in fiber stretch. Because the NFM was more resistant to volume change than the fiber network, extension of the composite led to pressurization of the NFM. Within a specific range of parameter values (low shear modulus and moderate Poisson's ratio), the magnitude of the reaction force decreased relative to this pressurization component resulting in a negative (compressive) NFM stress in the loading direction, even though the composite tissue was in tension.