Finite-element modeling of viscoelastic cells during high-frequency cyclic strain

Atomic Force Microscopy for the Study of Cell Mechanics in Pharmaceutics

Cell mechanics is gaining attraction in drug screening, but the applicable methods have not yet become part of the standardized norm. This review presents the current state of the art for atomic force microscopy, which is the most widely available method. The field is first motivated as a new way of tracking pharmaceutical effects, followed by a basic introduction targeted at pharmacists on how to measure cellular stiffness. The review then moves on to the current state of the knowledge in terms of experimental results and supplementary methods such as fluorescence microscopy that can give relevant additional information. Finally, rheological approaches as well as the theoretical interpretations are presented before ending on additional methods and outlooks.

Computational simulation of applying mechanical vibration to mesenchymal stem cell for mechanical modulation toward bone tissue engineering

Evaluation of cell response to mechanical stimuli at in vitro conditions is known as one of the important issues for modulating cell behavior. Mechanical stimuli, including mechanical vibration and oscillatory fluid flow, act as important biophysical signals for the mechanical modulation of stem cells. In the present study, mesenchymal stem cell (MSC) consists of cytoplasm, nucleus, actin, and microtubule. Also, integrin and primary cilium were considered as mechanoreceptors. In this study, the combined effect of vibration and oscillatory fluid flow on the cell and its components were investigated using numerical modeling. The results of the FEM and FSI model showed that the cell response (stress and strain values) at the frequency of 30 H z mechanical vibration has the highest value. The achieved results on shear stress caused by the fluid flow on the cell showed that the cell experiences shear stress in the range of 0 . 1 - 10 Pa . Mechanoreceptors that bind separately to the cell surface, can be highly stimulated by hydrodynamic pressure and, therefore, can play a role in the mechanical modulation of MSCs at in vitro conditions. The results of this research can be effective in future studies to optimize the conditions of mechanical stimuli applied to the cell culture medium and to determine the mechanisms involved in mechanotransduction.

Data driven and cell specific determination of nuclei-associated actin structure

Quantitative and volumetric assessment of filamentous actin fibers (F-actin) remains challenging due to their interconnected nature, leading researchers to utilize threshold based or qualitative measurement methods with poor reproducibility. Here we introduce a novel machine learning based methodology for accurate quantification and reconstruction of nuclei-associated F-actin. Utilizing a Convolutional Neural Network (CNN), we segment actin filaments and nuclei from 3D confocal microscopy images and then reconstruct each fiber by connecting intersecting contours on cross-sectional slices. This allowed measurement of the total number of actin filaments and individual actin filament length and volume in a reproducible fashion. Focusing on the role of F-actin in supporting nucleocytoskeletal connectivity, we quantified apical F-actin, basal F-actin, and nuclear architecture in mesenchymal stem cells (MSCs) following the disruption of the Linker of Nucleoskeleton and Cytoskeleton (LINC) Complexes. Disabling LINC in mesenchymal stem cells (MSCs) generated F-actin disorganization at the nuclear envelope characterized by shorter length and volume of actin fibers contributing a less elongated nuclear shape. Our findings not only present a new tool for mechanobiology but introduce a novel pipeline for developing realistic computational models based on quantitative measures of F-actin.

A role for nuclear stretching and NPCs changes in the cytoplasmic-nuclear trafficking of YAP: An experimental and numerical modelling approach

Mechanical forces, acting on eukaryotic cells, are responsible for cell shape, cell proliferation, cell polarity, and cell differentiation thanks to two cells abilities known as mechanosensing and mechanotransduction. Mechanosensing consists of the ability of a cell to sense mechanical cues, while mechanotransduction is the capacity of a cell to respond to these signals by translating mechanical stimuli into biochemical ones. These signals propagate from the extracellular matrix to the nucleus with different well known physical connections, but how the mechanical signals are transduced into biochemical ones remains an open challenge. Recent findings showed that the cell-generated forces affect the translocation of transcription factors (TFs) from the cytoplasm to the nucleus. This mechanism is affected by the features of nuclear pore complexes. Owing to the complex patterns of strains and stresses of the nuclear envelope caused by cytoskeletal forces, it is likely that the morphology of NPC changes as cytoskeleton assemblies’ change. This may ultimately affect molecular transport through the nucleus, hence altering cell functions. Among the various TFs, Yes-associated protein (YAP), which is typically involved in cell proliferation, survival, and differentiation, is able to activate specific pathways when entrapped into the cell nucleus. Here, starting from experimental results, we develop a multiscale finite element (FE) model aimed to simulate the macroscopic cell spreading and consequent changes in the cell mechanical behaviour to be related to the NPCs changes and YAP nuclear transport.

In silico stress fibre content affects peak strain in cytoplasm and nucleus but not in the membrane for uniaxial substrate stretch

Existing in silico models for single cell mechanics feature limited representations of cytoskeletal structures that contribute substantially to the mechanics of a cell. We propose a micromechanical hierarchical approach to capture the mechanical contribution of actin stress fibres. For a cell-specific fibroblast geometry with membrane, cytoplasm and nucleus, the Mori-Tanaka homogenization method was employed to describe cytoplasmic inhomogeneities and constitutive contribution of actin stress fibres. The homogenization was implemented in a finite element model of the fibroblast attached to a substrate through focal adhesions. Strain in cell membrane, cytoplasm and nucleus due to uniaxial substrate stretch was assessed for different stress fibre volume fractions and different elastic modulus of the substrate. A considerable decrease of the peak strain with increasing stress fibre content was observed in cytoplasm and nucleus but not the membrane, whereas the peak strain in cytoplasm, nucleus and membrane increased for increasing elastic modulus of the substrate. Finite element mesh of reconstructed human fibroblast and intracellular strain distribution in cell subjected to substrate stretch.

A finite element model of an osteoblast to quantify the transduction of exogenous forces to cellular components

Encouraged by recent advances of biophysical and biochemical assays we introduce a 3D finite element model of an osteoblast, seeking an analogue between exogenous forces and intracellularly activated sensory mechanisms. The cell was reverse engineered and the dimensions of the internal cellular structures were based on literature data. The model was verified and validated against atomic force microscopy experiments and four loading scenarios were considered. The stress distributions developing on the main cellular components were calculated along with their corresponding strain values. The nucleus and mitochondria exhibited similar loading trends, with the mitochondria being stressed by an order of magnitude higher than the nucleus (e.g. 1.4 vs. 0.16 MPa). Equivalent stiffness was determined to increase by almost 50%, from the apex to the cell's periphery, as was the cell's elasticity, which was lowest when the load was exerted directly above the nucleus. The assessment of how extrinsic loads are propagated to a cell's internal structures is inherently a problem of high complexity. The findings presented in this study can provide important insight into biophysical and biochemical responses elicited in cells through mechanical stimulus. This was evident in both the nuclear and mitochondrial loading and would stipulate the important contribution of even more accurate models in the interpretation of cellular events. One Sentence Summary: The results of this numerical biomechanical study demonstrated that even minor extrinsic loads irrespective of the application site, are transduced by a fraction of the cytoskeleton to its internal structure (primarily to its mitochondria and secondary to the cell's nucleus), indicating mechanical stimulus as the dominant pathway to cell expression.

Nonlinear Elastic and Inelastic Properties of Cells

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

A NanoFE simulation-based surrogate machine learning model to predict mechanical functionality of protein networks from live confocal imaging

Sub-cellular mechanics plays a crucial role in a variety of biological functions and dysfunctions. Due to the strong structure-function relationship in cytoskeletal protein networks, light can be shed on their mechanical functionality by investigating their structures. Here, we present a data-driven approach employing a combination of confocal live imaging of fluorescent tagged protein networks, in silico mechanical experiments and machine learning to investigate this relationship. Our designed image processing and nanoFE mechanical simulation framework resolves the structure and mechanical behaviour of cytoskeletal networks and the developed gradient boosting surrogate models linking network structure to its functionality. In this study, for the first time, we perform mechanical simulations of Filamentous Temperature Sensitive Z (FtsZ) complex protein networks with realistic network geometry depicting its skeletal functionality inside organelles (here, chloroplasts) of the moss Physcomitrella patens. Training on synthetically produced simulation data enables predicting the mechanical characteristics of FtsZ network purely based on its structural features (R2⩾0.93), therefore allowing to extract structural principles enabling specific mechanical traits of FtsZ, such as load bearing and resistance to buckling failure in case of large network deformation.

Viscoelasticity in natural tissues and engineered scaffolds for tissue reconstruction

Viscoelasticity of living tissues plays a critical role in tissue homeostasis and regeneration, and its implication in disease development and progression is being recognized recently. In this review, we first explored the state of knowledge regarding the potential application of tissue viscoelasticity in disease diagnosis. In order to better characterize viscoelasticity with local resolution and non-invasiveness, emerging characterization methods have been developed with the potential to be supplemented to existing facilities. To understand cellular responses to matrix viscoelastic behaviors in vitro, hydrogels made of natural polymers have been developed and the relationships between their molecular structure and viscoelastic behaviors, are elucidated. Moreover, how cells perceive the viscoelastic microenvironment and cellular responses including cell attachment, spreading, proliferation, differentiation and matrix production, have been discussed. Finally, some future perspective on an integrated mechanobiological comprehension of the viscoelastic behaviors involved in tissue homeostasis, cellular responses and biomaterial design are highlighted. STATEMENT OF SIGNIFICANCE: Tissue- or organ-scale viscoelastic behavior is critical for homeostasis, and the molecular basis and cellular responses of viscoelastic materials at micro- or nano-scale are being recognized recently. We summarized the potential applications of viscoelasticity in disease diagnosis enabled by emerging non-invasive characterization technologies, and discussed the underlying mechanism of viscoelasticity of hydrogels and current understandings of cell regulatory functions of them. With a growing understanding of the molecular basis of hydrogel viscoelasticity and recognition of its regulatory functions on cell behaviors, it is important to bring the clinical insights on how these characterization technologies and engineered materials may contribute to disease diagnosis and treatment. This review explains the basics in characterizing viscoelasticity with our hope to bridge the gap between basic research and clinical applications.

Quantitative assessment of cell contractility using polarized light microscopy

Cell contractility regulates multiple cell behaviors which contribute to both normal and pathological processes. However, measuring cell contractility remains a technical challenge in complex biological samples. The current state of the art technologies employed to measure cell contractility have inherent limitations that greatly limit the experimental conditions under which they can be used. Here, we use quantitative polarization microscopy to extract information about cell contractility. We show that the optical retardance signal measured from the cell body is proportional to cell contractility in 2-dimensional and 3-dimensional platforms, and as such can be used as a straightforward, tractable methodology to assess cell contractility in a variety of systems. This label-free optical method provides a novel and flexible way to assess cellular forces of single cells and monolayers in several cell types, fixed or live, in addition to cells present in situ in mouse tumor tissue samples. This easily implementable and experimentally versatile method will significantly contribute to the cell mechanics field.

In-silico quest for bactericidal but non-cytotoxic nanopatterns

Nanopillar arrays that are bactericidal but not cytotoxic against the host cells could be used in implantable medical devices to prevent implant-associated infections. It is, however, unclear what heights, widths, interspacing, and shape should be used for the nanopillars to achieve the desired antibacterial effects while not hampering the integration of the device in the body. Here, we present an in-silico approach based on finite element modeling of the interactions between Staphylococcus aureus and nanopatterns on the one hand and osteoblasts and nanopatterns on the other hand to find the best design parameters. We found that while the height of the nanopillars seems to have little impact on the bactericidal behavior, shorter widths and larger interspacings substantially increase the bactericidal effects. The same combination of parameters could, however, also cause cytotoxicity. Our results suggest that a specific combination of height (120 nm), width (50 nm), and interspacing (300 nm) offers the bactericidal effects without cytotoxicity.

Endothelial cells on an aged subendothelial matrix display heterogeneous strain profiles in silico

Within the artery intima, endothelial cells respond to mechanical cues and changes in subendothelial matrix stiffness. Recently, we found that the aging subendothelial matrix stiffens heterogeneously and that stiffness heterogeneities are present on the scale of one cell length. However, the impacts of these complex mechanical micro-heterogeneities on endothelial cells have not been fully understood. Here, we simulate the effects of matrices that mimic young and aged vessels on single- and multi-cell endothelial cell models and examine the resulting cell basal strain profiles. Although there are limitations to the model which prohibit the prediction of intracellular strain distributions in alive cells, this model does introduce mechanical complexities to the subendothelial matrix material. More heterogeneous basal strain distributions are present in the single- and multi-cell models on the matrix mimicking an aged artery over those exhibited on the young artery. Overall, our data indicate that increased heterogeneous strain profiles in endothelial cells are displayed in silico when there is an increased presence of microscale arterial mechanical heterogeneities in the matrix.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

A numerical model suggests the interplay between nuclear plasticity and stiffness during a perfusion assay

Cell deformability is a necessary condition for a cell to be able to migrate, an ability that is vital both for healthy and diseased organisms. The nucleus being the largest and stiffest organelle, it often is a barrier to cell migration. It is thus essential to characterize its mechanical behaviour. First, we numerically investigate the visco-elasto-plastic properties of the isolated nucleus during a compression test. This simulation highlights the impact of the mechanical behaviour of the nuclear lamina and the nucleoplasm on the overall plasticity. Second, a whole cell model is developed to simulate a perfusion experiment to study the possible interactions between the cytoplasm and the nucleus. We analyze and discuss the role of the lamina for a wild-type cell model, and a lamin-deficient one, in which the Young's modulus of the lamina is set to 1% of its nominal value. This simulation suggests an interplay between the cytoplasm and the nucleoplasm, especially in the lamin-deficient cell, showing the need of a stiffer nucleoplasm to maintain nuclear plasticity.

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus [Formula: see text] on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of [Formula: see text], were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and [Formula: see text]140 KPa and (2) [Formula: see text], 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35[Formula: see text], 0.235[Formula: see text] and 0.6[Formula: see text]) than for FA attachment (0.0952[Formula: see text], 0.0472[Formula: see text] and 0.05[Formula: see text]). For increasing [Formula: see text], the largest maximum principal strain was 4.4[Formula: see text], 5[Formula: see text], 5.3[Formula: see text] and 5.3[Formula: see text] in the membrane, 9.5[Formula: see text], 1.1[Formula: see text], 1.2[Formula: see text] and 1.2[Formula: see text] in the cytosol, and 4.5[Formula: see text], 5.3[Formula: see text], 5.7[Formula: see text] and 5.7[Formula: see text] in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.

Promoter hypermethylation as a mechanism for Lamin A/C silencing in a subset of neuroblastoma cells

Nuclear lamins support the nuclear envelope and provide anchorage sites for chromatin. They are involved in DNA synthesis, transcription, and replication. It has previously been reported that the lack of Lamin A/C expression in lymphoma and leukaemia is due to CpG island promoter hypermethylation. Here, we provide evidence that Lamin A/C is silenced via this mechanism in a subset of neuroblastoma cells. Moreover, Lamin A/C expression can be restored with a demethylating agent. Importantly, Lamin A/C reintroduction reduced cell growth kinetics and impaired migration, invasion, and anchorage-independent cell growth. Cytoskeletal restructuring was also induced. In addition, the introduction of lamin Δ50, known as Progerin, caused senescence in these neuroblastoma cells. These cells were stiffer and developed a cytoskeletal structure that differed from that observed upon Lamin A/C introduction. Of relevance, short hairpin RNA Lamin A/C depletion in unmethylated neuroblastoma cells enhanced the aforementioned tumour properties. A cytoskeletal structure similar to that observed in methylated cells was induced. Furthermore, atomic force microscopy revealed that Lamin A/C knockdown decreased cellular stiffness in the lamellar region. Finally, the bioinformatic analysis of a set of methylation arrays of neuroblastoma primary tumours showed that a group of patients (around 3%) gives a methylation signal in some of the CpG sites located within the Lamin A/C promoter region analysed by bisulphite sequencing PCR. These findings highlight the importance of Lamin A/C epigenetic inactivation for a subset of neuroblastomas, leading to enhanced tumour properties and cytoskeletal changes. Additionally, these findings may have treatment implications because tumour cells lacking Lamin A/C exhibit more aggressive behaviour.

Effects of Frequency and Acceleration Amplitude on Osteoblast Mechanical Vibration Responses: A Finite Element Study

Bone cells are deformed according to mechanical stimulation they receive and their mechanical characteristics. However, how osteoblasts are affected by mechanical vibration frequency and acceleration amplitude remains unclear. By developing 3D osteoblast finite element (FE) models, this study investigated the effect of cell shapes on vibration characteristics and effect of acceleration (vibration intensity) on vibrational responses of cultured osteoblasts. Firstly, the developed FE models predicted natural frequencies of osteoblasts within 6.85-48.69 Hz. Then, three different levels of acceleration of base excitation were selected (0.5, 1, and 2 g) to simulate vibrational responses, and acceleration of base excitation was found to have no influence on natural frequencies of osteoblasts. However, vibration response values of displacement, stress, and strain increased with the increase of acceleration. Finally, stress and stress distributions of osteoblast models under 0.5 g acceleration in Z-direction were investigated further. It was revealed that resonance frequencies can be a monotonic function of cell height or bottom area when cell volumes and material properties were assumed as constants. These findings will be useful in understanding how forces are transferred and influence osteoblast mechanical responses during vibrations and in providing guidance for cell culture and external vibration loading in experimental and clinical osteogenesis studies.

Fluid-Structure Interactions Analysis of Shear-Induced Modulation of a Mesenchymal Stem Cell: An Image-Based Study

Although effects of biochemical modulation of stem cells have been widely investigated, only recent advances have been made in the identification of mechanical conditioning on cell signaling pathways. Experimental investigations quantifying the micromechanical environment of mesenchymal stem cells (MSCs) are challenging while computational approaches can predict their behavior due to in vitro stimulations. This study introduces a 3D cell-specific finite element model simulating large deformations of MSCs. Here emphasizing cell mechanical modulation which represents the most challenging multiphysics phenomena in sub-cellular level, we focused on an approach attempting to elicit unique responses of a cell under fluid flow. Fluorescent staining of MSCs was performed in order to visualize the MSC morphology and develop a geometrically accurate model of it based on a confocal 3D image. We developed a 3D model of a cell fixed in a microchannel under fluid flow and then solved the numerical model by fluid-structure interactions method. By imposing flow characteristics representative of vigorous in vitro conditions, the model predicts that the employed external flow induces significant localized effective stress in the nucleo-cytoplasmic interface and average cell deformation of about 40%. Moreover, it can be concluded that a lower strain level is made in the cell by the oscillatory flow as compared with steady flow, while same ranges of effective stress are recorded inside the cell in both conditions. The deeper understanding provided by this study is beneficial for better design of single cell in vitro studies.

Cell morphology and focal adhesion location alters internal cell stress

Extracellular mechanical cues have been shown to have a profound effect on osteogenic cell behaviour. However, it is not known precisely how these cues alter intracellular mechanics to initiate changes in cell behaviour. In this study, a combination of in vitro culture of MC3T3-E1 cells and finite-element modelling was used to investigate the effects of passive differences in substrate stiffness on intracellular mechanics. Cells on collagen-based substrates were classified based on the presence of cell processes and the dimensions of various cellular features were quantified. Focal adhesion (FA) density was quantified from immunohistochemical staining, while cell and substrate stiffnesses were measured using a live-cell atomic force microscope. Computational models of cell morphologies were developed using an applied contraction of the cell body to simulate active cell contraction. The results showed that FA density is directly related to cell morphology, while the effect of substrate stiffness on internal cell tension was modulated by both cell morphology and FA density, as investigated by varying the number of adhesion sites present in each morphological model. We propose that the cells desire to achieve a homeostatic stress state may play a role in osteogenic cell differentiation in response to extracellular mechanical cues.

Dissecting the contribution of actin and vimentin intermediate filaments to mechanical phenotype of suspended cells using high-throughput deformability measurements and computational modeling

Mechanical cell properties play an important role in many basic biological functions, including motility, adhesion, proliferation and differentiation. There is a growing body of evidence that the mechanical cell phenotype can be used for detection and, possibly, treatment of various diseases, including cancer. Understanding of pathological mechanisms requires investigation of the relationship between constitutive properties and major structural components of cells, i.e., the nucleus and cytoskeleton. While the contribution of actin und microtubules to cellular rheology has been extensively studied in the past, the role of intermediate filaments has been scarcely investigated up to now. Here, for the first time we compare the effects of drug-induced disruption of actin and vimentin intermediate filaments on mechanical properties of suspended NK cells using high-throughput deformability measurements and computational modeling. Although, molecular mechanisms of actin and vimentin disruption by the applied cytoskeletal drugs, Cytochalasin-D and Withaferin-A, are different, cell softening in both cases can be attributed to reduction of the effective density and stiffness of filament networks. Our experimental data suggest that actin and vimentin deficient cells exhibit, in average, 41% and 20% higher deformability in comparison to untreated control. 3D Finite Element simulation is performed to quantify the contribution of cortical actin and perinuclear vimentin to mechanical phenotype of the whole cell. Our simulation provides quantitative estimates for decreased filament stiffness in drug-treated cells and predicts more than two-fold increase of the strain magnitude in the perinuclear vimentin layer of actin deficient cells relatively to untreated control. Thus, the mechanical function of vimentin becomes particularly essential in motile and proliferating cells that have to dynamically remodel the cortical actin network. These insights add functional cues to frequently observed overexpression of vimentin in diverse types of cancer and underline the role of vimentin targeting drugs, such as Withaferin-A, as a potent cancerostatic supplement.