A three-dimensional viscoelastic model for cell deformation with experimental verification

Morphological assessment of oocyte quality during assisted reproductive technology cycle

Following the advancement of medically assisted reproduction (MAR) technology, and the rationale to extend the culture to the blastocyst stage, performing elective single embryo transfer (eSET), gamete quality and assessment have acquired large relevance in ART. Embryo quality is strictly correlated with gametes quality and culture conditions. Oocyte maturity assessment is therefore imperative for fertilization and embryo evolution. Mature oocytes at the metaphase II stage result in a higher fertilization rate compared to immature oocytes. Indeed, oocyte morphology evaluation represents an important and challenging task that may serve as a valuable prognostic tool for future embryo development and implantation potential. Different grading systems have been reported to assess human embryos, however, in many cases, it is still a major challenge to select the single embryo to transfer with the highest implantation potential. Further, eSET has conferred a challenge to embryologists, who must try to enhance embryo culture and selection to provide an adequate success rate, whilst reducing the overall number of embryos transferred. Above the standard morphological assessment, there are several invasive or non-invasive approaches for embryo selection such as preimplantation genetic testing, time-lapse technology, proteomics and metabolomics, as well as oxygen utilization and analysis of oxidative stress in culture medium. This short review is not designed to be a comprehensive review of all possible features that may influence oocyte quality. It does give, however, a brief overview and describes the prognostic value of the morphological characteristics of human oocytes on their developmental capacity following ART treatments.

Analyzing force measurements of multi-cellular clusters comprising indeterminate geometries

Multi-cellular biomimetic models often comprise heterogenic geometries. Therefore, quantification of their mechanical properties-which is crucial for various biomedical applications-is a challenge. Due to its simplicity, linear fitting is traditionally used in analyzing force-displacement data of parallel compression measurements of multi-cellular clusters, such as tumor spheroids. However, the linear assumption would be artificial when the contact geometry is not planar. We propose here the integrated elasticity (IE) regression, which is based on extrapolation of established elastic theories for well-defined geometries, and is free, extremely simple to apply, and optimal for analyzing coarsely concave multi-cellular clusters. We studied here the quality of the data analysis in force measurements of tumor spheroids comprising different types of melanoma cells, using either the IE or the traditional linear regressions. The IE regression maintained excellent precision also when the contact geometry deviated from planarity (as shown by our image analysis). While the quality of the linear fittings was relatively satisfying, these predicted smaller elastic moduli as compared to the IE regression. This was in accordance with previous studies, in which the elastic moduli predicted by linear fits were smaller compared to those obtained by well-established methods. This suggests that linear regressions underestimate the elastic constants of bio-samples even in cases where the fitting precision seems satisfying, and highlights the need in alternative methods as the IE scheme. For comparison between different types of spheroids we further recommend to increase the soundness by regarding relative moduli, using universal reference samples.

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.

Interaction of magnetic fields with biogenic magnetic nanoparticles on cell membranes: Physiological consequences for organisms in health and disease

The interaction mechanisms between magnetic fields (MFs) and living systems, which remained hidden for more than a hundred years, continue to attract the attention of researchers from various disciplines: physics, biology, medicine, and life sciences. Revealing these mechanisms at the cellular level would allow to understand complex cell systems and could help to explain and predict cell responses to MFs, intervene in organisms' reactions to MFs of different strengths, directions, and spatial distributions. We suggest several new physical mechanisms of the MF impacts on endothelial and cancer cells by the MF interaction with chains of biogenic and non-biogenic magnetic nanoparticles on cell membranes. The revealed mechanisms can play a hitherto unexpected role in creating physiological responses of organisms to externally applied MFs. We have also a set of theoretical models that can predict how cells will individually and collectively respond to a MF exposure. The physiological sequences of the MF - cell interactions for organisms in health and disease are discussed. The described effects and their underlying mechanisms are general and should take place in a large family of biological effects of MFs. The results are of great importance for further developing novel approaches in cell biology, cell therapy and medicine.

Valve interstitial cells under impact load, a mechanobiology study

Understanding the relationship between mechanobiology and the biosynthetic activities of the valve interstitial cells (VICs) in health and disease under severe dynamic loading conditions is of particular interest. The purpose of this study is to further understand the mechanobiology of heart valve leaflet tissue and the VICs under impact forces. Two novel computational and experimental platforms were developed to study the effect of impact load on the VICs to monitor for apoptosis. The first objective was to design and develop an apparatus to experimentally study viability (apoptosis) of the porcine heart valve leaflet tissue VICs in the aortic position under controlled impact forces. Apoptosis was assessed based on terminal transferase dUTP nick end-labelling (TUNEL) assay. The second objective was to develop a computational platform to estimate the stress and strain fields in the vicinity of VICs when the tissue experiences impact forces. A nonlinear finite element (FE) model with an anisotropic, hyperelastic and heterogeneous material model for the matrix and cells was developed. Preliminary results confirm that interstitial cells are successfully resistant to impact loads up to 30 times more than normal physiological conditions. Additionally, the structure and composition of heart valve leaflet tissue provides a mechanical shield for VICs protecting them from excessive mechanical forces such as impact loads. Although, the entire tissue may experience excessive stresses, which may lead to structural damage, the stresses around and near VICs remain consistency low. Results of this study may be used for heart valve leaflet tissue-engineering, as well as further understanding the mechanobiology of the VICs in health and disease.

Nuclear size rectification: A potential new therapeutic approach to reduce metastasis in cancer

Research on metastasis has recently regained considerable interest with the hope that single cell technologies might reveal the most critical changes that support tumor spread. However, it is possible that part of the answer has been visible through the microscope for close to 200 years. Changes in nuclear size characteristically occur in many cancer types when the cells metastasize. This was initially discarded as contributing to the metastatic spread because, depending on tumor types, both increases and decreases in nuclear size could correlate with increased metastasis. However, recent work on nuclear mechanics and the connectivity between chromatin, the nucleoskeleton, and the cytoskeleton indicate that changes in this connectivity can have profound impacts on cell mobility and invasiveness. Critically, a recent study found that reversing tumor type-dependent nuclear size changes correlated with reduced cell migration and invasion. Accordingly, it seems appropriate to now revisit possible contributory roles of nuclear size changes to metastasis.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Non-invasive oocyte quality assessment

Oocyte quality is perhaps the most important limiting factor in female fertility; however, the current methods of determining oocyte competence are only marginally capable of predicting a successful pregnancy. We aim to review the predictive value of non-invasive techniques for the assessment of human oocytes and their related cells and biofluids that pertain to their developmental competence. Investigation of the proteome, transcriptome, and hormonal makeup of follicular fluid, as well as cumulus-oocyte complexes are currently underway; however, prospective randomized non-selection-controlled trials of the future are needed before determining their prognostic value. The biological significance of polar body morphology and genetics are still unknown and the subject of debate. The predictive utility of zygotic viscoelasticity for embryo development has been demonstrated, but similar studies performed on oocytes have yet to be conducted. Metabolic profiling of culture media using human oocytes are also limited and may require integration of automated, high-throughput targeted metabolomic assessments in real time with microfluidic platforms. Light exposure to oocytes can be detrimental to subsequent development and utilization of time-lapse imaging and morphometrics of oocytes is wanting. Polarized light, Raman microspectroscopy, and coherent anti-Stokes Raman scattering are a few novel imaging tools that may play a more important role in future oocyte assessment. Ultimately, the integration of chemistry, genomics, microfluidics, microscopy, physics, and other biomedical engineering technologies into the basic studies of oocyte biology, and in testing and perfecting practical solutions of oocyte evaluation, are the future for non-invasive assessment of oocytes.

Simulations of dynamically cross-linked actin networks: Morphology, rheology, and hydrodynamic interactions

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.

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.

Substrate stiffness modulates the viscoelastic properties of MCF-7 cells

Cells sense stiffness of surrounding tissues and adapt their activity, proliferation, motility and mechanical properties based on such interactions. Cells probe the stiffness of the substrate by anchoring and pulling to their surroundings, transmitting force to the extracellular matrix and other cells, and respond to the resistance they sense, mainly through changes in their cytoskeleton. Cancer and other diseases alter stiffness of tissues, and the response of cancer cells to this stiffness can also be affected. In the present study we show that MCF-7 breast cancer cells seeded on polyacrylamide gels have the ability to detect the stiffness of the substrate and alter their mechanical properties in response. MCF-7 cells plated on soft substrates display lower stiffness and viscosity when compared to those seeded on stiffer gels or glass. These differences can be associated with differences in the morphology and cytoskeleton organisation, since cells seeded on soft substrates have a round morphology, while cells seeded on stiffer substrates acquire a flat and spread morphology with formation of actin filaments, similar to that observed when seeded on glass. These findings show that MCF-7 cells can detect the stiffness of the surrounding microenvironment and thus, modify their mechanical properties.

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.

Stem Cell Mechanobiology and the Role of Biomaterials in Governing Mechanotransduction and Matrix Production for Tissue Regeneration

Mechanobiology has underpinned many scientific advances in understanding how biophysical and biomechanical cues regulate cell behavior by identifying mechanosensitive proteins and specific signaling pathways within the cell that govern the production of proteins necessary for cell-based tissue regeneration. It is now evident that biophysical and biomechanical stimuli are as crucial for regulating stem cell behavior as biochemical stimuli. Despite this, the influence of the biophysical and biomechanical environment presented by biomaterials is less widely accounted for in stem cell-based tissue regeneration studies. This Review focuses on key studies in the field of stem cell mechanobiology, which have uncovered how matrix properties of biomaterial substrates and 3D scaffolds regulate stem cell migration, self-renewal, proliferation and differentiation, and activation of specific biological responses. First, we provide a primer of stem cell biology and mechanobiology in isolation. This is followed by a critical review of key experimental and computational studies, which have unveiled critical information regarding the importance of the biophysical and biomechanical cues for stem cell biology. This review aims to provide an informed understanding of the intrinsic role that physical and mechanical stimulation play in regulating stem cell behavior so that researchers may design strategies that recapitulate the critical cues and develop effective regenerative medicine approaches.

Mechanobiology of Epithelia From the Perspective of Extracellular Matrix Heterogeneity

Understanding the complexity of the extracellular matrix (ECM) and its variability is a necessary step on the way to engineering functional (bio)materials that serve their respective purposes while relying on cell adhesion. Upon adhesion, cells receive messages which contain both biochemical and mechanical information. The main focus of mechanobiology lies in investigating the role of this mechanical coordination in regulating cellular behavior. In recent years, this focus has been additionally shifted toward cell collectives and the understanding of their behavior as a whole mechanical continuum. Collective cell phenomena very much apply to epithelia which are either simple cell-sheets or more complex three-dimensional structures. Researchers have been mostly using the organization of monolayers to observe their collective behavior in well-defined experimental setups in vitro. Nevertheless, recent studies have also reported the impact of ECM remodeling on epithelial morphogenesis in vivo. These new concepts, combined with the knowledge of ECM biochemical complexity are of key importance for engineering new interactive materials to support both epithelial remodeling and homeostasis. In this review, we summarize the structure and heterogeneity of the ECM before discussing its impact on the epithelial mechanobiology.

Mechanics of the cell: Interaction mechanisms and mechanobiological models

The importance of cell mechanics has long been recognized for the cell development and function. Biomechanics plays an important role in cell metabolism, regulation of mechanotransduction pathways and also modulation of nuclear response. The mechanical properties of the cell are likely determined by, among many others, the cytoskeleton elasticity, membrane tension and cell-substrate adhesion. This coordinated but complex mechanical interplay is required however, for the cell to respond to and influence in a reciprocal manner the chemical and mechanical signals from the extracellular matrix (ECM). In an effort to better and more fully understand the cell mechanics, the role of nuclear mechanics has emerged as an important contributor to the overall cellular mechanics. It is not too difficult to appreciate the physical connection between the nucleus and the cytoskeleton network that may be connected to the ECM through the cell membrane. Transmission of forces from ECM through this connection is essential for a wide range of cellular behaviors and functions such as cytoskeletal reorganization, nuclear movement, cell migration and differentiation. Unlike the cellular mechanics that can be measured using a number of biophysical techniques that were developed in the past few decades, it still remains a daunting challenge to probe the nuclear mechanics directly. In this paper, we therefore aim to provide informative description of the cell membrane and cytoskeleton mechanics, followed by unique computational modeling efforts to elucidate the nucleus-cytoskeleton coupling. Advances in our knowledge of complete cellular biomechanics and mechanotransduction may lead to clinical relevance and applications in mechano-diseases such as atherosclerosis, stem cell-based therapies, and the development of tissue engineered products.

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.

Cell-substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

During the process of tissue formation and regeneration, cells migrate collectively while remaining connected through intercellular adhesions. However, the roles of cell-substrate and cell-cell mechanical interactions in regulating collective cell migration are still unclear. In this study, we employ a newly developed finite element cellular model to study collective cell migration by exploring the effects of mechanical feedback between cell and substrate and mechanical signal transmission between adjacent cells. Our viscoelastic model of cells consists many triangular elements and is of high resolution. Cadherin adhesion between cells is modeled explicitly as linear springs at subcellular level. In addition, we incorporate a mechano-chemical feedback loop between cell-substrate mechanics and Rac-mediated cell protrusion. Our model can reproduce a number of experimentally observed patterns of collective cell migration during wound healing, including cell migration persistence, separation distance between cell pairs and migration direction. Moreover, we demonstrate that cell protrusion determined by the cell-substrate mechanics plays an important role in guiding persistent and oriented collective cell migration. Furthermore, this guidance cue can be maintained and transmitted to submarginal cells of long distance through intercellular adhesions. Our study illustrates that our finite element cellular model can be employed to study broad problems of complex tissue in dynamic changes at subcellular level.

Migration of the 3T3 Cell with a Lamellipodium on Various Stiffness Substrates—Tensegrity Model

Changes in mechanical stimuli and the physiological environment are sensed by the cell. Thesechanges influence the cell’s motility patterns. The cell’s directional migration is dependent on the substrate stiffness. To describe such behavior of a cell, a tensegrity model was used. Cells with an extended lamellipodium were modeled. The internal elastic strain energy of a cell attached to the substrates with different stiffnesses was evaluated. The obtained results show that on the stiffer substrate, the elastic strain energy of the cell adherent to this substrate decreases. Therefore, the substrate stiffness is one of the parameters that govern the cell’s directional movement.

Correlating nuclear morphology and external force with combined atomic force microscopy and light sheet imaging separates roles of chromatin and lamin A/C in nuclear mechanics

Nuclei are often under external stress, be it during migration through tight constrictions or compressive pressure by the actin cap, and the mechanical properties of nuclei govern their subsequent deformations. Both altered mechanical properties of nuclei and abnormal nuclear morphologies are hallmarks of a variety of disease states. Little work, however, has been done to link specific changes in nuclear shape to external forces. Here, we utilize a combined atomic force microscope and light sheet microscope to show SKOV3 nuclei exhibit a two-regime force response that correlates with changes in nuclear volume and surface area, allowing us to develop an empirical model of nuclear deformation. Our technique further decouples the roles of chromatin and lamin A/C in compression, showing they separately resist changes in nuclear volume and surface area, respectively; this insight was not previously accessible by Hertzian analysis. A two-material finite element model supports our conclusions. We also observed that chromatin decompaction leads to lower nuclear curvature under compression, which is important for maintaining nuclear compartmentalization and function. The demonstrated link between specific types of nuclear morphological change and applied force will allow researchers to better understand the stress on nuclei throughout various biological processes.

Correlating nuclear morphology and external force with combined atomic force microscopy and light sheet imaging separates roles of chromatin and lamin A/C in nuclear mechanics

Nuclei are often under external stress, be it during migration through tight constrictions or compressive pressure by the actin cap, and the mechanical properties of nuclei govern their subsequent deformations. Both altered mechanical properties of nuclei and abnormal nuclear morphologies are hallmarks of a variety of disease states. Little work, however, has been done to link specific changes in nuclear shape to external forces. Here, we utilize a combined atomic force microscope and light sheet microscope to show SKOV3 nuclei exhibit a two-regime force response that correlates with changes in nuclear volume and surface area, allowing us to develop an empirical model of nuclear deformation. Our technique further decouples the roles of chromatin and lamin A/C in compression, showing they separately resist changes in nuclear volume and surface area, respectively; this insight was not previously accessible by Hertzian analysis. A two-material finite element model supports our conclusions. We also observed that chromatin decompaction leads to lower nuclear curvature under compression, which is important for maintaining nuclear compartmentalization and function. The demonstrated link between specific types of nuclear morphological change and applied force will allow researchers to better understand the stress on nuclei throughout various biological processes.

Modeling of Cell Nuclear Mechanics: Classes, Components, and Applications

Cell nuclei are paramount for both cellular function and mechanical stability. These two roles of nuclei are intertwined as altered mechanical properties of nuclei are associated with altered cell behavior and disease. To further understand the mechanical properties of cell nuclei and guide future experiments, many investigators have turned to mechanical modeling. Here, we provide a comprehensive review of mechanical modeling of cell nuclei with an emphasis on the role of the nuclear lamina in hopes of spurring future growth of this field. The goal of this review is to provide an introduction to mechanical modeling techniques, highlight current applications to nuclear mechanics, and give insight into future directions of mechanical modeling. There are three main classes of mechanical models-schematic, continuum mechanics, and molecular dynamics-which provide unique advantages and limitations. Current experimental understanding of the roles of the cytoskeleton, the nuclear lamina, and the chromatin in nuclear mechanics provide the basis for how each component is subsequently treated in mechanical models. Modeling allows us to interpret assay-specific experimental results for key parameters and quantitatively predict emergent behaviors. This is specifically powerful when emergent phenomena, such as lamin-based strain stiffening, can be deduced from complimentary experimental techniques. Modeling differences in force application, geometry, or composition can additionally clarify seemingly conflicting experimental results. Using these approaches, mechanical models have informed our understanding of relevant biological processes such as migration, nuclear blebbing, nuclear rupture, and cell spreading and detachment. There remain many aspects of nuclear mechanics for which additional mechanical modeling could provide immediate insight. Although mechanical modeling of cell nuclei has been employed for over a decade, there are still relatively few models for any given biological phenomenon. This implies that an influx of research into this realm of the field has the potential to dramatically shape both future experiments and our current understanding of nuclear mechanics, function, and disease.

Protein corona impact on nanoparticle-cell interactions: toward an energy-based model of endocytosis

Upon incubation of nanoparticles in biological fluids, a new layer called the protein corona is formed on their surface affecting the interactions between nanoparticles and targeted cells during the endocytosis process. In the present study, a mathematical model based on the diffusion of membrane mobile receptors is proposed. Opposing the endocytosis proceeding, membrane bending and tension energies are named as resistant energy. Also, the binding energy and free-energy associated with the configurational entropy are collectively termed promoter energy. Utilizing this model, endocytosis of gold nanoparticle (GNP) is simulated to explore the biological media effect. The results reveal that there exists a nanoparticle size of 60 nm at which, the endocytosis time is at a minimum. It has been illustrated that, although for sufficiently small particles of diameter 30nm, membrane tension has a negligible contribution (<10%) in the resistant energy, it noticeably increases the endocytosis processing time for large particles. Therefore, we report several parametric studies to provide a better insight into the effects of biological media on the ingestion of nanoparticles. Through a detailed analysis of the engulfment of the nanoparticles, it is shown that the nanoparticle radius corresponding to the quickest possible ingestion time is affected in the presence of corona. Moreover, it is found that the formation of this layer does not only affect the endocytosis time but also can lead to incomplete engulfment by decreasing the ligand density on the nanoparticle surface. Use of the proposed model can play a significant role in advancing the design of nanoparticles in targeted drug delivery applications.

Localized Axolemma Deformations Suggest Mechanoporation as Axonal Injury Trigger

Traumatic brain injuries are a leading cause of morbidity and mortality worldwide. With almost 50% of traumatic brain injuries being related to axonal damage, understanding the nature of cellular level impairment is crucial. Experimental observations have so far led to the formulation of conflicting theories regarding the cellular primary injury mechanism. Disruption of the axolemma, or alternatively cytoskeletal damage has been suggested mainly as injury trigger. However, mechanoporation thresholds of generic membranes seem not to overlap with the axonal injury deformation range and microtubules appear too stiff and too weakly connected to undergo mechanical breaking. Here, we aim to shed a light on the mechanism of primary axonal injury, bridging finite element and molecular dynamics simulations. Despite the necessary level of approximation, our models can accurately describe the mechanical behavior of the unmyelinated axon and its membrane. More importantly, they give access to quantities that would be inaccessible with an experimental approach. We show that in a typical injury scenario, the axonal cortex sustains deformations large enough to entail pore formation in the adjoining lipid bilayer. The observed axonal deformation of 10–12% agree well with the thresholds proposed in the literature for axonal injury and, above all, allow us to provide quantitative evidences that do not exclude pore formation in the membrane as a result of trauma. Our findings bring to an increased knowledge of axonal injury mechanism that will have positive implications for the prevention and treatment of brain injuries.

Microtubule disruption changes endothelial cell mechanics and adhesion

The interest in studying the mechanical and adhesive properties of cells has increased in recent years. The cytoskeleton is known to play a key role in cell mechanics. However, the role of the microtubules in shaping cell mechanics is not yet well understood. We have employed Atomic Force Microscopy (AFM) together with confocal fluorescence microscopy to determine the role of microtubules in cytomechanics of Human Umbilical Vein Endothelial Cells (HUVECs). Additionally, the time variation of the adhesion between tip and cell surface was studied. The disruption of microtubules by exposing the cells to two colchicine concentrations was monitored as a function of time. Already, after 30 min of incubation the cells stiffened, their relaxation times increased (lower fluidity) and the adhesion between tip and cell decreased. This was accompanied by cytoskeletal rearrangements, a reduction in cell area and changes in cell shape. Over the whole experimental time, different behavior for the two used concentrations was found while for the control the values remained stable. This study underlines the role of microtubules in shaping endothelial cell mechanics.

A mathematical model of tumor-endothelial interactions in a 3D co-culture

Intravasation and extravasation of cancer cells through blood/lymph vessel endothelium are essential steps during metastasis. Successful invasion requires coordinated tumor-endothelial crosstalk, utilizing mechanochemical signaling to direct cytoskeletal rearrangement for transmigration of cancer cells. However, mechanisms underlying physical interactions are difficult to observe due to the lack of experimental models easily combined with theoretical models that better elucidate these pathways. We have previously demonstrated that an engineered 3D in vitro endothelial-epithelial co-culture system can be used to isolate both molecular and physical tumor-endothelial interactions in a platform that is easily modeled, quantified, and probed for experimental investigation. Using this platform with mathematical modeling, we show that breast metastatic cells display unique behavior with the endothelium, exhibiting a 3.2-fold increase in interaction with the endothelium and a 61-fold increase in elongation compared to normal breast epithelial cells. Our mathematical model suggests energetic favorability for cellular deformation prior to breeching endothelial junctions, expending less energy as compared to undeformed cells, which is consistent with the observed phenotype. Finally, we show experimentally that pharmacological inhibition of the cytoskeleton can disrupt the elongatation and alignment of metastatic cells with endothelial tubes, reverting to a less invasive phenotype.

Visco-Node-Pore Sensing: A Microfluidic Rheology Platform to Characterize Viscoelastic Properties of Epithelial Cells

Viscoelastic properties of cells provide valuable information regarding biological or clinically relevant cellular characteristics. Here, we introduce a new, electronic-based, microfluidic platform-visco-node-pore sensing (visco-NPS)-which quantifies cellular viscoelastic properties under periodic deformation. We measure the storage (G') and loss (G″) moduli (i.e., elasticity and viscosity, respectively) of cells. By applying a wide range of deformation frequencies, our platform quantifies the frequency dependence of viscoelastic properties. G' and G″ measurements show that the viscoelastic properties of malignant breast epithelial cells (MCF-7) are distinctly different from those of non-malignant breast epithelial cells (MCF-10A). With its sensitivity, visco-NPS can dissect the individual contributions of different cytoskeletal components to whole-cell mechanical properties. Moreover, visco-NPS can quantify the mechanical transitions of cells as they traverse the cell cycle or are initiated into an epithelial-mesenchymal transition. Visco-NPS identifies viscoelastic characteristics of cell populations, providing a biophysical understanding of cellular behavior and a potential for clinical applications.

Architecture-Dependent Anisotropic Hysteresis in Smooth Muscle Cells

Cells within mechanically dynamic tissues like arteries are exposed to ever-changing forces and deformations. In some pathologies, like aneurysms, complex loads may alter how cells transduce forces, driving maladaptive growth and remodeling. Here, we aimed to determine the dynamic mechanical properties of vascular smooth muscle cells (VSMCs) under biaxial load. Using cellular micro-biaxial stretching microscopy, we measured the large-strain anisotropic stress-strain hysteresis of VSMCs and found that hysteresis is strongly dependent on load orientation and actin organization. Most notably, under some cyclic loads, we found that VSMCs with elongated in-vivo-like architectures display a hysteresis loop that is reverse to what is traditionally measured in polymers, with unloading stresses greater than loading stresses. This reverse hysteresis could not be replicated using a quasilinear viscoelasticity model, but we developed a Hill-type active fiber model that can describe the experimentally observed hysteresis. These results suggest that cells in highly organized tissues, like arteries, can have strongly anisotropic responses to complex loads, which could have important implications in understanding pathological mechanotransduction.

A coupled approach for fluid saturated poroelastic media and immersed solids for modeling cell-tissue interactions

In this paper, we propose a finite element-based immersed method to treat the mechanical coupling between a deformable porous medium model (PM) and an immersed solid model (ISM). The PM is formulated as a homogenized, volume-coupled two-field model, comprising a nearly incompressible solid phase that interacts with an incompressible Darcy-Brinkman flow. The fluid phase is formulated with respect to the Lagrangian finite element mesh, following the solid phase deformation. The ISM is discretized with an independent Lagrangian mesh and may behave arbitrarily complex (it may, eg, be compressible, grow, and perform active deformations). We model two distinct types of interactions, namely, (1) the immersed fluid-structure interaction (FSI) between the ISM and the fluid phase in the PM and (2) the immersed structure-structure interaction (SSI) between the ISM and the solid phase in the PM. Within each time step, we solve both FSI and SSI, employing strongly coupled partitioned schemes. This novel finite element method establishes a main building block of an evolving computational framework for modeling and simulating complex biomechanical problems, with focus on key phenomena during cell migration. Cell movement is strongly influenced by mechanical interactions between the cell body and the surrounding tissue, ie, the extracellular matrix (ECM). In this context, the PM represents the ECM, ie, a fibrous scaffold of structural proteins interacting with interstitial flow, and the ISM represents the cell body. The FSI models the influence of fluid drag, and the SSI models the force transmission between cell and ECM at adhesions sites.

Mechanical stability of the cell nucleus - roles played by the cytoskeleton in nuclear deformation and strain recovery

Extracellular forces transmitted through the cytoskeleton can deform the cell nucleus. Large nuclear deformations increase the risk of disrupting the integrity of the nuclear envelope and causing DNA damage. The mechanical stability of the nucleus defines its capability to maintain nuclear shape by minimizing nuclear deformation and allowing strain to be minimized when deformed. Understanding the deformation and recovery behavior of the nucleus requires characterization of nuclear viscoelastic properties. Here, we quantified the decoupled viscoelastic parameters of the cell membrane, cytoskeleton, and the nucleus. The results indicate that the cytoskeleton enhances nuclear mechanical stability by lowering the effective deformability of the nucleus while maintaining nuclear sensitivity to mechanical stimuli. Additionally, the cytoskeleton decreases the strain energy release rate of the nucleus and might thus prevent shape change-induced structural damage to chromatin.

Human mesenchymal stem cell basal membrane bending on gratings is dependent on both grating width and curvature

The topography of the extracellular substrate provides physical cues to elicit specific downstream biophysical and biochemical effects in cells. An example of such a topographical substrate is periodic gratings, where the dimensions of the periodic gratings influence cell morphology and directs cell differentiation. We first develop a novel sample preparation technique using Spurr's resin to allow for cross-sectional transmission electron microscopy imaging of cells on grating grooves, and observed that the plasma membrane on the basal surface of these cells can deform and bend into grooves between the gratings. We postulate that such membrane bending is an important first step in eliciting downstream effects. Thus, we use a combination of image analysis and mathematical modeling to explain the extent of bending of basal membrane into grooves. We show that the extent to which the basal membrane bends into grooves depends on both groove width and angle of the grating ridge. Our model predicts that the basal membrane will bend into grooves when they are wider than 1.9 µm in width. The existence of such a threshold may provide an explanation for how the width of periodic gratings may bring about cellular downstream effects, such as cell proliferation or differentiation.

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.

Structural Characterization and Statistical-Mechanical Model of Epidermal Patterns

In proliferating epithelia of mammalian skin, cells of irregular polygon-like shapes pack into complex, nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct space (correlation function) and Fourier space (structure factor) of the cell centroids in the early stages of embryonic development show structural directional dependence (statistical anisotropy), which is a reflection of the fact that cells are stretched, which promotes uniaxial growth along the epithelial plane. In the late stages, the patterns tend toward statistically isotropic states, as cells attain global polarization and epidermal growth shifts to produce the skin's outer stratified layers. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-range soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. In contrast with many vertex-based models, our statistical-mechanical model does not explicitly incorporate information about the cell shapes and interfacial energy between cells; nonetheless, our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments, as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. The array of structural descriptors that we deploy enable us to distinguish between normal, mechanically deformed, and pathological skin tissues. Our statistical-mechanical model enables one to generate tissue microstructure at will for further analysis. We also discuss ways in which our model might be extended to better understand morphogenesis (in particular the emergence of planar cell polarity), wound healing, and disease-progression processes in skin, and how it could be applied to the design of synthetic tissues.

An integrated enhancement and reconstruction strategy for the quantitative extraction of actin stress fibers from fluorescence micrographs

BACKGROUND

The stress fibers are prominent organization of actin filaments that perform important functions in cellular processes such as migration, polarization, and traction force generation, and whose collective organization reflects the physiological and mechanical activities of the cells. Easily visualized by fluorescence microscopy, the stress fibers are widely used as qualitative descriptors of cell phenotypes. However, due to the complexity of the stress fibers and the presence of other actin-containing cellular features, images of stress fibers are relatively challenging to quantitatively analyze using previously developed approaches, requiring significant user intervention. This poses a challenge for the automation of their detection, segmentation, and quantitative analysis.

RESULT

Here we describe an open-source software package, SFEX (Stress Fiber Extractor), which is geared for efficient enhancement, segmentation, and analysis of actin stress fibers in adherent tissue culture cells. Our method made use of a carefully chosen image filtering technique to enhance filamentous structures, effectively facilitating the detection and segmentation of stress fibers by binary thresholding. We subdivided the skeletons of stress fiber traces into piecewise-linear fragments, and used a set of geometric criteria to reconstruct the stress fiber networks by pairing appropriate fiber fragments. Our strategy enables the trajectory of a majority of stress fibers within the cells to be comprehensively extracted. We also present a method for quantifying the dimensions of the stress fibers using an image gradient-based approach. We determine the optimal parameter space using sensitivity analysis, and demonstrate the utility of our approach by analyzing actin stress fibers in cells cultured on various micropattern substrates.

CONCLUSION

We present an open-source graphically-interfaced computational tool for the extraction and quantification of stress fibers in adherent cells with minimal user input. This facilitates the automated extraction of actin stress fibers from fluorescence images. We highlight their potential uses by analyzing images of cells with shapes constrained by fibronectin micropatterns. The method we reported here could serve as the first step in the detection and characterization of the spatial properties of actin stress fibers to enable further detailed morphological analysis.

Relaxation of a simulated lipid bilayer vesicle compressed by an atomic force microscope

Using coarse-grained molecular dynamics simulations, we study the relaxation of bilayer vesicles, uniaxially compressed by an atomic force microscope cantilever. The relaxation time exhibits a strong force dependence. Force-compression curves are very similar to recent experiments wherein giant unilamellar vesicles were compressed in a nearly identical manner.

Atomic force microscopy indentation and inverse analysis for non-linear viscoelastic identification of breast cancer cells

Breast cancer cells (MCF-7 and MCF-10A) are studied through indentation with spherical borosilicate glass particles in atomic force microscopy (AFM) contact mode in fluid. Their mechanical properties are obtained by analyzing the recorded reaction force-time response. The analysis is based on comparing experimental data with predictions from finite element (FE) simulation. Here, FE modeling is employed to simulate the AFM indentation experiment which is neither a displacement nor a force controlled test. This approach is expected to overcome many underlying problems of the widely used models such as Hertz contact model due to its capability to capture the contact behaviors between the spherical indentor and the cell, account for cell geometry, and incorporate with large strain theory. In this work, a non-linear viscoelastic (NLV) model in which the viscoelastic part is described by Prony series terms is used for the constitutive model of the cells. The time-dependent material parameters are extracted through an inverse analysis with the use of a surrogate model based on a Kriging estimator. The purpose is to automatically extract the NLV properties of the cells with a more efficient process compared to the iterative inverse technique that has been mostly applied in the literature. The method also allows the use of FE modeling in the analysis of a large amount of experimental data. The NLV parameters are compared between MCF-7 and MCF-10A and MCF-10A treated and untreated with the drug Cytochalasin D to examine the possibility of using relaxation properties as biomarkers for distinguishing these types of breast cancer cells. The comparisons indicate that malignant cells (MCF-7) are softer and exhibit more relaxation than benign cells (MCF-10A). Disrupting the cytoskeleton using the drug Cytochalasin D also results in a larger amount of relaxation in the cell's response. In addition, relaxation properties indicate larger differences as compared to the elastic moduli like instantaneous shear modulus. These results may be useful for disease diagnosing purposes.

Complex wavefront reconstruction from multiple-image planes produced by a focus tunable lens

We propose, through simulations and experiments, a wavefront reconstruction technique using a focus-tunable lens and a phase-retrieval technique. A collimated beam illuminates a complex object (amplitude and phase), and a diffuser then modulates the outgoing wavefront. Finally the diffracted complex field reaches the focus-tunable lens, and a CMOS camera positioned at a fixed plane registers the subjective speckle distribution produced by the lens (one pattern for each focal length). We have demonstrated that a tunable lens can replace the translation stage used in the conventional single-beam, multiple-intensity reconstruction algorithm. In other words, through iterations with a modified version of this algorithm, the speckle images produced by different focal lengths can be successfully employed to recover the initial complex object. With no movable elements, (speckle) image sampling can be performed at high frame rates, which is suitable for dynamical reconstruction applications.

Combining AFM and acoustic probes to reveal changes in the elastic stiffness tensor of living cells

Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young's modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell's cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell's shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.

Sub-cellular force microscopy in single normal and cancer cells

This work investigates the biomechanical properties of sub-cellular structures of breast cells using atomic force microscopy (AFM). The cells are modeled as a triple-layered structure where the Generalized Maxwell model is applied to experimental data from AFM stress-relaxation tests to extract the elastic modulus, the apparent viscosity, and the relaxation time of sub-cellular structures. The triple-layered modeling results allow for determination and comparison of the biomechanical properties of the three major sub-cellular structures between normal and cancerous cells: the up plasma membrane/actin cortex, the mid cytoplasm/nucleus, and the low nuclear/integrin sub-domains. The results reveal that the sub-domains become stiffer and significantly more viscous with depth, regardless of cell type. In addition, there is a decreasing trend in the average elastic modulus and apparent viscosity of the all corresponding sub-cellular structures from normal to cancerous cells, which becomes most remarkable in the deeper sub-domain. The presented modeling in this work constitutes a unique AFM-based experimental framework to study the biomechanics of sub-cellular structures.

An Atomic Force Microscope Study Revealed Two Mechanisms in the Effect of Anticancer Drugs on Rate-Dependent Young's Modulus of Human Prostate Cancer Cells

Mechanical properties of cells have been recognized as a biomarker for cellular cytoskeletal organization. As chemical treatments lead to cell cytoskeletal rearrangements, thereby, modifications of cellular mechanical properties, investigating cellular mechanical property variations provides insightful knowledge to effects of chemical treatments on cancer cells. In this study, the effects of eight different anticancer drugs on the mechanical properties of human prostate cancer cell (PC-3) are investigated using a recently developed control-based nanoindentation measurement (CNM) protocol on atomic force microscope (AFM). The CNM protocol overcomes the limits of other existing methods to in-liquid nanoindentation measurement of live cells on AFM, particularly for measuring mechanical properties of live cells. The Young's modulus of PC-3 cells treated by the eight drugs was measured by varying force loading rates over three orders of magnitude, and compared to the values of the control. The results showed that the Young's modulus of the PC-3 cells increased substantially by the eight drugs tested, and became much more pronounced as the force load rate increased. Moreover, two distinct trends were clearly expressed, where under the treatment of Disulfiram, paclitaxel, and MK-2206, the exponent coefficient of the frequency- modulus function remained almost unchanged, while with Celebrex, BAY, Totamine, TPA, and Vaproic acid, the exponential rate was significantly increased.

Cell shape-dependent shear stress on adherent cells in a micro-physiologic system as revealed by FEM

Flow-induced shear stress on adherent cells leads to biochemical signaling and mechanical responses of the cells. To determine the flow-induced shear stress on adherent cells cultured in a micro-scaled reaction chamber, we developed a suitable finite element method model. The influence of the most important parameters-cell shape, cell density, shear modulus and fluid velocity-was investigated. Notably, the cell shape strongly influences the resulting shear stress. Long and smooth cells undergo lower shear stress than more rounded cells. Changes in the curvature of the cells lead to stress peaks and single cells experience higher shear stress values than cells of a confluent monolayer. The computational results of the fluid flow simulation were validated experimentally. We also analyzed the influence of flow-induced shear stress on the metabolic activity and shape of L929, a mouse fibroblast cell line, experimentally. The results indicate that threshold stress values for continuous flow conditions cannot be transferred to quasi static flow conditions interrupted by short fluid exchange events.

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.

Probing cellular mechanoadaptation using cell-substrate de-adhesion dynamics: experiments and model

Physical properties of the extracellular matrix (ECM) are known to regulate cellular processes ranging from spreading to differentiation, with alterations in cell phenotype closely associated with changes in physical properties of cells themselves. When plated on substrates of varying stiffness, fibroblasts have been shown to exhibit stiffness matching property, wherein cell cortical stiffness increases in proportion to substrate stiffness up to 5 kPa, and subsequently saturates. Similar mechanoadaptation responses have also been observed in other cell types. Trypsin de-adhesion represents a simple experimental framework for probing the contractile mechanics of adherent cells, with de-adhesion timescales shown to scale inversely with cortical stiffness values. In this study, we combine experiments and computation in deciphering the influence of substrate properties in regulating de-adhesion dynamics of adherent cells. We first show that NIH 3T3 fibroblasts cultured on collagen-coated polyacrylamide hydrogels de-adhere faster on stiffer substrates. Using a simple computational model, we qualitatively show how substrate stiffness and cell-substrate bond breakage rate collectively influence de-adhesion timescales, and also obtain analytical expressions of de-adhesion timescales in certain regimes of the parameter space. Finally, by comparing stiffness-dependent experimental and computational de-adhesion responses, we show that faster de-adhesion on stiffer substrates arises due to force-dependent breakage of cell-matrix adhesions. In addition to illustrating the utility of employing trypsin de-adhesion as a biophysical tool for probing mechanoadaptation, our computational results highlight the collective interplay of substrate properties and bond breakage rate in setting de-adhesion timescales.

Indentation quantification for in-liquid nanomechanical measurement of soft material using an atomic force microscope: rate-dependent elastic modulus of live cells

In this paper, a control-based approach to replace the conventional method to achieve accurate indentation quantification is proposed for nanomechanical measurement of live cells using atomic force microscope. Accurate indentation quantification is central to probe-based nanomechanical property measurement. The conventional method for in-liquid nanomechanical measurement of live cells, however, fails to accurately quantify the indentation as effects of the relative probe acceleration and the hydrodynamic force are not addressed. As a result, significant errors and uncertainties are induced in the nanomechanical properties measured. In this paper, a control-based approach is proposed to account for these adverse effects by tracking the same excitation force profile on both a live cell and a hard reference sample through the use of an advanced control technique, and by quantifying the indentation from the difference of the cantilever base displacement in these two measurements. The proposed control-based approach not only eliminates the relative probe acceleration effect with no need to calibrate the parameters involved, but it also reduces the hydrodynamic force effect significantly when the force load rate becomes high. We further hypothesize that, by using the proposed control-based approach, the rate-dependent elastic modulus of live human epithelial cells under different stress conditions can be reliably quantified to predict the elasticity evolution of cell membranes, and hence can be used to predict cellular behaviors. By implementing the proposed approach, the elastic modulus of HeLa cells before and after the stress process were quantified as the force load rate was changed over three orders of magnitude from 0.1 to 100 Hz, where the amplitude of the applied force and the indentation were at 0.4-2 nN and 250-450 nm, respectively. The measured elastic modulus of HeLa cells showed a clear power-law dependence on the load rate, both before and after the stress process. Moreover, the elastic modulus of HeLa cells was substantially reduced by two to five times due to the stress process. Thus, our measurements demonstrate that the control-based protocol is effective in quantifying and characterizing the evolution of nanomechanical properties during the stress process of live cells.

Resiliency of the plasma membrane and actin cortex to large-scale deformation

The tight coupling between the plasma membrane and actin cortex allows cells to rapidly change shape in response to mechanical cues and during physiological processes. Mechanical properties of the membrane are critical for organizing the actin cortex, which ultimately governs the conversion of mechanical information into signaling. The cortex has been shown to rapidly remodel on timescales of seconds to minutes, facilitating localized deformations and bundling dynamics that arise during the exertion of mechanical forces and cellular deformations. Here, we directly visualized and quantified the time-dependent deformation and recovery of the membrane and actin cortex of HeLa cells in response to externally applied loads both on- and off-nucleus using simultaneous confocal and atomic force microscopy. The local creep-like deformation of the membrane and actin cortex depends on both load magnitude and duration and does not appear to depend on cell confluency. The membrane and actin cortex rapidly recover their initial shape after prolonged loading (up to 10 min) with large forces (up to 20 nN) and high aspect ratio deformations. Cytoplasmic regions surrounding the nucleus are shown to be more resistant to long-term creep than nuclear regions. These dynamics are highly regulated by actomyosin contractility and an intact actin cytoskeleton. Results suggest that in response to local deformations, the nucleus does not appear to provide significant resistance or play a major role in cell shape recovery. The membrane and actin cortex clearly possess remarkable mechanical stability, critical for the transduction of mechanical deformation into long term biochemical signals and cellular remodeling.

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to compute the biophysical stimuli generated within a cell under mechanical loading. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of atomic force microscopy indentation was performed and results showed a force/indentation simulation with the range of experimental results. A parametric analysis of both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age) was performed. Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain as compared with young cells, but the difference, surprisingly, is very small and may not be measurable experimentally. Ageing is predicted to have a more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models; correspondence between computed and measured force/displacement behaviours provides a high-level validation of the model. Regarding the effect of ageing, the models suggest only small, although possibly physiologically significant, differences in internal biophysical stimuli between normal and aged cells.

A multi-structural single cell model of force-induced interactions of cytoskeletal components

Several computational models based on experimental techniques and theories have been proposed to describe cytoskeleton (CSK) mechanics. Tensegrity is a prominent model for force generation, but it cannot predict mechanics of individual CSK components, nor explain the discrepancies from the different single cell stimulating techniques studies combined with cytoskeleton-disruptors. A new numerical concept that defines a multi-structural 3D finite element (FE) model of a single-adherent cell is proposed to investigate the biophysical and biochemical differences of the mechanical role of each cytoskeleton component under loading. The model includes prestressed actin bundles and microtubule within cytoplasm and nucleus surrounded by the actin cortex. We performed numerical simulations of atomic force microscopy (AFM) experiments by subjecting the cell model to compressive loads. The numerical role of the CSK components was corroborated with AFM force measurements on U2OS-osteosarcoma cells and NIH-3T3 fibroblasts exposed to different cytoskeleton-disrupting drugs. Computational simulation showed that actin cortex and microtubules are the major components targeted in resisting compression. This is a new numerical tool that explains the specific role of the cortex and overcomes the difficulty of isolating this component from other networks in vitro. This illustrates that a combination of cytoskeletal structures with their own properties is necessary for a complete description of cellular mechanics.