Experimental and computational investigation of the role of stress fiber contractility in the resistance of osteoblasts to compression

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

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

Image-derived modeling of nucleus strain amplification associated with chromatin heterogeneity

Beyond the critical role of cell nuclei in gene expression and DNA replication, they also have a significant influence on cell mechanosensation and migration. Nuclear stiffness can impact force transmission and, furthermore, act as a physical barrier to translocation across tight spaces. As such, it is of wide interest to accurately characterize nucleus mechanical behavior. In this study, we present a computational investigation of the in situ deformation of a heterogeneous chondrocyte nucleus. A methodology is developed to accurately reconstruct a three-dimensional finite-element model of a cell nucleus from confocal microscopy. By incorporating the reconstructed nucleus into a chondrocyte model embedded in pericellular and extracellular matrix, we explore the relationship between spatially heterogeneous nuclear DNA content, shear stiffness, and resultant shear strain. We simulate an externally applied extracellular matrix shear deformation and compute intranuclear strain distributions, which are directly compared with corresponding experimentally measured distributions. Simulations suggest that the mechanical behavior of the nucleus is highly heterogeneous, with a nonlinear relationship between experimentally measured grayscale values and corresponding local shear moduli (μn). Three distinct phases are identified within the nucleus: a low-stiffness mRNA-rich interchromatin phase (0.17 kPa ≤ μn ≤ 0.63 kPa), an intermediate-stiffness euchromatin phase (1.48 kPa ≤ μn ≤ 2.7 kPa), and a high-stiffness heterochromatin phase (3.58 kPa ≤ μn ≤ 4.0 kPa). Our simulations also indicate that disruption of the nuclear envelope associated with lamin A/C depletion significantly increases nuclear strain in regions of low DNA concentration. We further investigate a phenotypic shift of chondrocytes to fibroblast-like cells, a signature for osteoarthritic cartilage, by increasing the contractility of the actin cytoskeleton to a level associated with fibroblasts. Peak nucleus strains increase by 35% compared to control, with the nucleus becoming more ellipsoidal. Our findings may have broad implications for current understanding of how local DNA concentrations and associated strain amplification can impact cell mechanotransduction and drive cell behavior in development, migration, and tumorigenesis.

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.

Influence of multi-axial dynamic constraint on cell alignment and contractility in engineered tissues

In this study an experimental rig is developed to investigate the influence of tissue constraint and cyclic loading on cell alignment and active cell force generation in uniaxial and biaxial engineered tissues constructs. Addition of contractile cells to collagen hydrogels dramatically increases the measured forces in uniaxial and biaxial constructs under dynamic loading. This increase in measured force is due to active cell contractility, as is evident from the decreased force after treatment with cytochalasin D. Prior to dynamic loading, cells are highly aligned in uniaxially constrained tissues but are uniformly distributed in biaxially constrained tissues, demonstrating the importance of tissue constraints on cell alignment. Dynamic uniaxial stretching resulted in a slight increase in cell alignment in the centre of the tissue, whereas dynamic biaxial stretching had no significant effect on cell alignment. Our active modelling framework accurately predicts our experimental trends and suggests that a slightly higher (3%) total SF formation occurs at the centre of a biaxial tissue compared to the uniaxial tissue. However, high alignment of SFs and lateral compaction in the case of the uniaxially constrained tissue results in a significantly higher (75%) actively generated cell contractile stress, compared to the biaxially constrained tissue. These findings have significant implications for engineering of contractile tissue constructs.

Transient active force generation and stress fibre remodelling in cells under cyclic loading

The active cytoskeleton is known to play an important mechanistic role in cellular structure, spreading, and contractility. Contractility is actively generated by stress fibres (SF), which continuously remodel in response to physiological dynamic loading conditions. The influence of actin-myosin cross-bridge cycling on SF remodelling under dynamic loading conditions has not previously been uncovered. In this study, a novel SF cross-bridge cycling model is developed to predict transient active force generation in cells subjected to dynamic loading. Rates of formation of cross-bridges within SFs are governed by the chemical potentials of attached and unattached myosin heads. This transient cross-bridge cycling model is coupled with a thermodynamically motivated framework for SF remodelling to analyse the influence of transient force generation on cytoskeletal evolution. A 1D implementation of the model is shown to correctly predict complex patterns of active cell force generation under a range of dynamic loading conditions, as reported in previous experimental studies.

Thermodynamic Modeling of the Statistics of Cell Spreading on Ligand-Coated Elastic Substrates

Biological spread cells exist in a perpetually fluctuating state and therefore cannot be described in terms of a unique deterministic system. For modeling approaches to provide novel insight and uncover new mechanisms that drive cell behavior, a framework is required that progresses from traditional deterministic methods (whereby simulation of an experiment predicts a single outcome). In this study, we implement a new, to our knowledge, modeling approach for the analysis of cell spreading on ligand-coated substrates, extending the framework for nonequilibrium thermodynamics of cells developed by Shishvan et al. to include active focal adhesion assembly. We demonstrate that the model correctly predicts the coupled influence of surface collagen density and substrate stiffness on cell spreading, as reported experimentally by Engler et al. Low surface collagen densities are shown to result in a high probability that cells will be restricted to low spread areas. Furthermore, elastic free energy induced by substrate deformation lowers the probability of observing a highly spread cell, and, consequentially, lower cell tractions affect the assembly of focal adhesions. Experimentally measurable observables such as cell spread area and aspect ratio can be directly postprocessed from the computed homeostatic ensemble of (several million) spread states. This allows for the prediction of mean and SDs of such experimental observables. This class of cell mechanics modeling presents a significant advance on conventional deterministic approaches.

Advanced Microfluidic Device Designed for Cyclic Compression of Single Adherent Cells

Cells in our body experience different types of stress including compression, tension, and shear. It has been shown that some cells experience permanent plastic deformation after a mechanical tensile load was removed. However, it was unclear whether cells are plastically deformed after repetitive compressive loading and unloading. There have been few tools available to exert cyclic compression at the single cell level. To address technical challenges found in a previous microfluidic compression device, we developed a new single-cell microfluidic compression device that combines an elastomeric membrane block geometry to ensure a flat contact surface and microcontact printing to confine cell spreading within cell trapping chambers. The design of the block geometry inside the compression chamber was optimized by using computational simulations. Additionally, we have implemented step-wise pneumatically controlled cell trapping to allow more compression chambers to be incorporated while minimizing mechanical perturbation on trapped cells. Using breast epithelial MCF10A cells stably expressing a fluorescent actin marker, we successfully demonstrated the new device design by separately trapping single cells in different chambers, confining cell spreading on microcontact printed islands, and applying cyclic planar compression onto single cells. We found that there is no permanent deformation after a 0.5 Hz cyclic compressive load for 6 min was removed. Overall, the development of the single-cell compression microfluidic device opens up new opportunities in mechanobiology and cell mechanics studies.

The effect of equiaxial stretching on the osteogenic differentiation and mechanical properties of human adipose stem cells

Although mechanical cues are known to affect stem cell fate and mechanobiology, the significance of such stimuli on the osteogenic differentiation of human adipose stem cells (hASCs) remains unclear. In this study, we investigated the effect of long-term mechanical stimulation on the attachment, osteogenic differentiation and mechanical properties of hASCs. Tailor-made, pneumatic cell stretching devices were used to expose hASCs to cyclic equiaxial stretching in osteogenic medium. Cell attachment and focal adhesions were visualised using immunocytochemical vinculin staining on days 3 and 6, and the proliferation and alkaline phosphatase activity, as a sign of early osteogenic differentiation, were analysed on days 0, 6 and 10. Furthermore, the mechanical properties of hASCs, in terms of apparent Young's modulus and normalised contractility, were obtained using a combination of atomic force microscopy based indentation and computational approaches. Our results indicated that cyclic equiaxial stretching delayed proliferation and promoted osteogenic differentiation of hASCs. Stretching also reduced cell size and intensified focal adhesions and actin cytoskeleton. Moreover, cell stiffening was observed during osteogenic differentiation and especially under mechanical stimulation. These results suggest that cyclic equiaxial stretching modifies cell morphology, focal adhesion formation and mechanical properties of hASCs. This could be exploited to enhance osteogenic differentiation.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

On intrinsic stress fiber contractile forces in semilunar heart valve interstitial cells using a continuum mixture model

Heart valve interstitial cells (VICs) play a critical role in the maintenance and pathophysiology of heart valve tissues. Normally quiescent in the adult, VICs can become activated in periods of growth and disease. When activated, VICs exhibit increased levels of cytokines and extracellular matrix (ECM) synthesis, and upregulated expression and strong contraction of α-smooth muscle actin (α-SMA) fibers. However, it remains unknown how expression and contraction of the α-SMA fibers, which vary among different VIC types, contribute to the overall VIC mechanical responses, including the nucleus and cytoskeleton contributions. In the present study, we developed a novel solid-mixture model for VIC biomechanical behavior that incorporated 1) the underlying cytoskeletal network, 2) the oriented α-SMA stress fibers with passive elastic and active contractile responses, 3) a finite deformable elastic nucleus. We implemented the model in a full 3D finite element simulation of a VIC based on known geometry. Moreover, we examined the respective mechanical responses of aortic and pulmonary VICs (AVICs and PVICs, respectively), which are known to have different levels of α-SMA expression levels and contractile behaviors. To calibrate the model, we simulated the combined mechanical responses of VICs in both micropipette aspiration (MA) and atomic force microscopy (AFM) experiments. These two states were chosen as the VICs were under significantly different mechanical loading conditions and activation states, with the α-SMA fibers inactivated in the MA studies while fully activated in the AFM studies. We also used the AFM to study the mechanical property of the nucleus. Our model predicted that the substantial differences found in stiffening of the AVIC compared to the PVICs was due to a 9 to 16 times stronger intrinsic AVIC α-SMA stress fiber contractile force. Model validation was done by simulating a traction force microscopy experiment to estimate the forces the VICs exert on the underlying substrate, and found good agreement with reported traction force microscopy results. Further, estimated nuclear stiffness for both AVICs and PVICs were similar and comparable to the literature, and were both unaffected by VIC activation level. These results suggest substantial functional differences between AVICs and PVICs at the subcellular level. Moreover, this first VIC computational biomechanical model is but a first step in developing a comprehensive, integrated view of the VIC pathophysiology and interactions with the valve ECM micro-environment based on simulation technologies.

Single cell active force generation under dynamic loading - Part I: AFM experiments

A novel series of experiments are performed on single cells using a bespoke AFM system where the response of cells to dynamic loading at physiologically relevant frequencies is uncovered. Measured forces for the untreated cells are dramatically different to cytochalasin-D (cyto-D) treated cells, indicating that the contractile actin cytoskeleton plays a critical role in the response of cells to dynamic loading. Following a change in applied strain magnitude, while maintaining a constant applied strain rate, the compression force for contractile cells recovers to 88.9±7.8% of the steady state force. In contrast, cyto-D cell compression forces recover to only 38.0±6.7% of the steady state force. Additionally, untreated cells exhibit strongly negative (pulling) forces during unloading half-cycles when the probe is retracted. In comparison, negligible pulling forces are measured for cyto-D cells during probe retraction. The current study demonstrates that active contractile forces, generated by actin-myosin cross-bridge cycling, dominate the response of single cells to dynamic loading. Such active force generation is shown to be independent of applied strain magnitude. Passive forces generated by the applied deformation are shown to be of secondary importance, exhibiting a high dependence on applied strain magnitude, in contrast to the active forces in untreated cells.

STATEMENT OF SIGNIFICANCE

A novel series of experiments are performed on single cells using a bespoke AFM system where the response of cells to dynamic loading at physiologically relevant frequencies is uncovered. Contractile cells, which contain the active force generation machinery of the actin cytoskeleton, are shown to be insensitive to applied strain magnitude, exhibiting high resistance to dynamic compression and stretching. Such trends are not observed for cells in which the actin cytoskeleton has been chemically disrupted. These biomechanical insights have not been previously reported. This detailed characterisation of single cell active and passive stress during dynamic loading has important implications for tissue engineering strategies, where applied deformation has been reported to significantly affect cell mechanotransduction and matrix synthesis.

Single cell active force generation under dynamic loading - Part II: Active modelling insights

In Part I of this two-part study a novel single cell AFM experimental investigation reveals a complex force-strain response of cells to cyclic loading. The biomechanisms underlying such complex behaviour cannot be fully understood without a detailed mechanistic analysis incorporating the key features of active stress generation and remodelling of the actin cytoskeleton. In order to simulate untreated contractile cells an active bio-chemo-mechanical model is developed, incorporating the key features of stress fibre (SF) remodelling and active tension generation. It is demonstrated that a fading memory SF contractility model accurately captures the transient response of cells to dynamic loading. Simulations reveal that high stretching forces during unloading half-cycles (probe retraction) occur due to tension actively generated by axially oriented SFs. On the other hand, hoop oriented SFs generate tension during loading half-cycles, providing a coherent explanation for the elevated compression resistance of contractile cells. Finally, it is also demonstrated that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted. In summary, our active modelling framework provides a coherent understanding of the biomechanisms underlying the complex patterns of experimentally observed single cell force generation presented in the first part of this study.

STATEMENT OF SIGNIFICANCE

A novel computational investigation into the active and passive response of cells to dynamic loading is performed. An active formulation that considers key features of actin cytoskeleton active contractility and remodelling throughout the cytoplasm is implemented. Simulations provide new insights into the sub-cellular biomechanical response, providing a coherent explanation for the complex patterns of cell force uncovered experimentally in the first part of this study. Our computational models also reveal that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted.

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.

On the role of the actin cytoskeleton and nucleus in the biomechanical response of spread cells

Micropipette aspiration (MA) has been used extensively in biomechanical investigations of un-adhered cells suspended in media. In the current study, a custom MA system is developed to aspirate substrate adhered spread cells. Additionally, the system facilitates immuno-fluorescent staining of aspirated cells to investigate stress fibre redistribution and nucleus deformation during MA. In response to an applied pressure, significantly lower aspiration length is observed for untreated contractile cells compared to cells in which actin polymerisation is chemically inhibited, demonstrating the important contribution of stress fibres in the biomechanical behaviour of spread cells. Additional experiments are performed in which untreated contractile cells are subjected to a range of applied pressures. Computational finite element simulations reveal that a viscoelastic material model for the cell cytoplasm is incapable of accurately predicting the observed aspiration length over the range of applied pressures. It is demonstrated that an active computational framework that incorporates stress fibre remodelling and contractility must be used in order to accurately simulate MA of untreated spread cells. Additionally, the stress fibre distribution observed in immuno-fluorescent experimental images of aspirated cells is accurately predicted using the active stress fibre modelling framework. Finally, a detailed experimental-computational investigation of the nucleus mechanical behaviour demonstrates that the nucleus is highly deformable in cyto, reaching strain levels in excess of 100% during MA. The characterisation of stress fibres and nucleus biomechanics in spread cells presented in the current study can potentially be used to guide tissue engineering strategies to control cell behaviour and gene expression.

Influence of spreading and contractility on cell detachment

Cell adhesion is a key phenomenon that affects fundamental cellular processes such as morphology, migration, and differentiation. In the current study, an active modelling framework incorporating actin cytoskeleton remodelling and contractility, combined with a cohesive zone model to simulate debonding at the cell-substrate interface, is implemented to investigate the increased resistance to detachment of highly spread chondrocytes from a substrate, as observed experimentally by Huang et al. (J. Orthop. Res. 21: 88-95, 2003). 3D finite element meshes of the round and spread cell geometries with the same material properties are created. It is demonstrated that spread cells with a flattened morphology and a larger adhesion area have a more highly developed actin cytoskeleton than rounded cells. Rounded cells provide less support for tension generated by the actin cytoskeleton; hence, a high level of dissociation is predicted. It is revealed that the more highly developed active contractile actin cytoskeleton of the spread cell increases the resistance to shear deformation, and subsequently increases the shear detachment force. These findings provide new insight into the link between cell geometry, cell contractility, and cell-substrate detachment.

Structural finite element analysis to explain cell mechanics variability

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

The role of mechanics in actin stress fiber kinetics

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