A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis

Benefits and challenges of reconstituting the actin cortex

The cell's ability to change shape is a central feature in many cellular processes, including cytokinesis, motility, migration, and tissue formation. The cell constructs a network of contractile proteins underneath the cell membrane to form the cortex, and the reorganization of these components directly contributes to cellular shape changes. The desire to mimic these cell shape changes to aid in the creation of a synthetic cell has been increasing. Therefore, membrane-based reconstitution experiments have flourished, furthering our understanding of the minimal components the cell uses throughout these processes. Although biochemical approaches increased our understanding of actin, myosin II, and actin-associated proteins, using membrane-based reconstituted systems has further expanded our understanding of actin structures and functions because membrane-cortex interactions can be analyzed. In this review, we highlight the recent developments in membrane-based reconstitution techniques. We examine the current findings on the minimal components needed to recapitulate distinct actin structures and functions and how they relate to the cortex's impact on cellular mechanical properties. We also explore how co-processing of computational models with wet-lab experiments enhances our understanding of these properties. Finally, we emphasize the benefits and challenges inherent to membrane-based, reconstitution assays, ranging from the advantage of precise control over the system to the difficulty of integrating these findings into the complex cellular environment.

Nonlinear Poisson effect in affine semiflexible polymer networks

Stretching an elastic material along one axis typically induces contraction along the transverse axes, a phenomenon known as the Poisson effect. From these strains, one can compute the specific volume, which generally either increases or, in the incompressible limit, remains constant as the material is stretched. However, in networks of semiflexible or stiff polymers, which are typically highly compressible yet stiffen significantly when stretched, one instead sees a significant reduction in specific volume under finite strains. This volume reduction is accompanied by increasing alignment of filaments along the strain axis and a nonlinear elastic response, with stiffening of the apparent Young's modulus. For semiflexible networks, in which entropic bending elasticity governs the linear elastic regime, the nonlinear Poisson effect is caused by the nonlinear force-extension relationship of the constituent filaments, which produces a highly asymmetric response of the constituent polymers to stretching and compression. The details of this relationship depend on the geometric and elastic properties of the underlying filaments, which can vary greatly in experimental systems. Here, we provide a comprehensive characterization of the nonlinear Poisson effect in an affine network model and explore the influence of filament properties on essential features of both microscopic and macroscopic response, including strain-driven alignment and volume reduction.

Synthetic strain-stiffening hydrogels towards mechanical adaptability

Living organisms are made of wet, soft tissues. However, there is only one candidate to simultaneously replicate the mechanical and composition features of load-bearing tissues, that is, strain-stiffening hydrogels. The conventional mechanical match design principle is mostly limited to stiffness matching. However, this strategy cannot sufficiently and necessarily lead to mechanical matching over the whole physiologic deformation period for tissues and damages the tissues over time. In this review, we aim to provide a comprehensive summary of the reported synthetic strain-stiffening hydrogels and particularly focus on the relationship between their structure and performance. Initially, we present a brief introduction on the significance of strain-stiffening hydrogels in mimicking the mechanics of tissues, and then we discuss the qualitative evaluation of the strain-stiffening behaviors to guide the design of materials towards mimicking soft tissue. After distinguishing the mechanical testing methods, we focus on the methods for the preparation of typical strain-stiffening hydrogels based on categories, such as network without strand entanglement, semiflexible network, and anisotropic networks. Subsequently, we discuss the structural evolution of strain-stiffening hydrogels. We hope that this review will serve as an updated introduction and reference for researchers who are interested in exploring strain-stiffening hydrogels as tissue-mimics for addressing the societal needs at various frontiers.

Hyperelastic continuum models for isotropic athermal fibrous networks

Many biological materials contain fibrous protein networks as their main structural components. Understanding the mechanical properties of such networks is important for creating biomimicking materials for cell and tissue engineering, and for developing novel tools for detecting and diagnosing disease. In this work, we develop continuum models for isotropic, athermal fibrous networks by combining a single-fibre model that describes the axial response of individual fibres, with network models that assemble individual fibre properties into overall network behaviour. In particular, we consider four different network models, including the affine, three-chain, eight-chain, and micro-sphere models, which employ different assumptions about network structure and kinematics. We systematically investigate the ability of these models to describe the mechanical response of athermal collagen and fibrin networks by comparing model predictions with experimental data. We test how each model captures network behaviour under three different loading conditions: uniaxial tension, simple shear, and combined tension and shear. We find that the affine and three-chain models can accurately describe both the axial and shear behaviour, whereas the eight-chain and micro-sphere models fail to capture the shear response, leading to unphysical zero shear moduli at infinitesimal strains. Our study is the first to systematically investigate the applicability of popular network models for describing the macroscopic behaviour of athermal fibrous networks, offering insights for selecting efficient models that can be used for large-scale, finite-element simulations of athermal networks.

Effect of Therapeutic Ultrasound on the Mechanical and Biological Properties of Fibroblasts

Purpose

This paper explores the effect of therapeutic ultrasound on the mechanical and biological properties of ligament fibroblasts.

Methods and Results

We assessed pulsed ultrasound doses of 1.0 and 2.0 W/cm2 at 1 MHz frequency for five days on ligament fibroblasts using a multidisciplinary approach. Atomic force microscopy showed a decrease in cell elastic modulus for both doses, but the treated cells were still viable based on flow cytometry. Finite element method analysis exhibited visible cytoskeleton displacements and decreased harmonics in treated cells. Colorimetric assay revealed increased cell proliferation, while scratch assay showed increased migration at a low dose. Enzyme-linked immunoassay detected increased collagen and fibronectin at a high dose, and immunofluorescence imaging technique visualized β-actin expression for both treatments.

Conclusion

Both doses of ultrasound altered the fibroblast mechanical properties due to cytoskeletal reorganization and enhanced the regenerative and remodeling stages of cell repair.

Lay Summary

Knee ligament injuries are a lesion of the musculoskeletal system frequently diagnosed in active and sedentary lifestyles in young and older populations. Therapeutic ultrasound is a rehabilitation strategy that may lead to the regenerative and remodeling of ligament wound healing. This research demonstrated that pulsed therapeutic ultrasound applied for 5 days reorganized the ligament fibroblasts structure to increase the cell proliferation and migration at a low dose and to increase the releasing proteins that give the stiffness of the healed ligament at a high dose.

Future Works

Future research should further develop and confirm that therapeutic ultrasound may improve the regenerative and remodeling stages of the ligament healing process applied in clinical trials in active and sedentary lifestyles in young and older populations.

Graphical abstract

Continuum soft tissue models from upscaling of arrays of hyperelastic cells

Constitutive models for soft tissue mechanics are typically constructed by fitting phenomenological models to experimental measurements. However, a significant challenge is to rationally construct soft tissue models that encode the properties of the constituent cells and their extracellular matrix. This work presents a framework to derive multiscale soft tissue models that incorporate properties of individual cells without assuming homogeneity or periodicity at the cell level. We consider a viscoelastic model for each cell (which can deform, grow and divide), that we couple to form a network description of a one-dimensional line of cells. We use a discrete-to-continuum approach to form (nonlinear) continuum partial differential equation models for the tissue. These models elucidate the contrasting role of the two forms of dissipation: substrate dissipation localizes the deformation to the neighbourhood of the free boundary and inhibits morphoelastic growth, whereas internal cell dissipation promotes spatial uniformity and does not influence the elongation length. Furthermore, cell division is shown to increase the rate of elongation of the array compared with growth alone, provided the substrate dissipation is proportional to the cell surface area.

Cross-linked actin networks (CLANs) affect stiffness and/or actin dynamics in transgenic transformed and primary human trabecular meshwork cells

Cross-linked actin networks (CLANs) in trabecular meshwork (TM) cells may contribute to increased IOP by altering TM cell function and stiffness. However, there is a lack of direct evidence. Here, we developed transformed TM cells that form spontaneous fluorescently labelled CLANs. The stable cells were constructed by transducing transformed glaucomatous TM (GTM3) cells with the pLenti-LifeAct-EGFP-BlastR lentiviral vector and selection with blasticidin. The stiffness of the GTM3-LifeAct-GFP cells were studied using atomic force microscopy. Elastic moduli of CLANs in primary human TM cells treated with/without dexamethasone/TGFβ2 were also measured to validate findings in GTM3-LifeAct-GFP cells. Live-cell imaging was performed on GTM3-LifeAct-GFP cells treated with 1 μM latrunculin B or pHrodo bioparticles to determine actin stability and phagocytosis, respectively. The GTM3-LifeAct-GFP cells formed spontaneous CLANs without the induction of TGFβ2 or dexamethasone. The CLAN containing cells showed elevated cell stiffness, resistance to latrunculin B-induced actin depolymerization, as well as compromised phagocytosis, compared to the cells without CLANs. Primary human TM cells with dexamethasone or TGFβ2-induced CLANs were also stiffer and less phagocytic. The GTM3-LifeAct-GFP cells are a novel tool for studying the mechanobiology and pathology of CLANs in the TM. Initial characterization of these cells showed that CLANs contribute to at least some glaucomatous phenotypes of TM cells.

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.

Numerical analysis of the impact of cytoskeletal actin filament density alterations onto the diffusive vesicle-mediated cell transport

The interior of a eukaryotic cell is a highly complex composite material which consists of water, structural scaffoldings, organelles, and various biomolecular solutes. All these components serve as obstacles that impede the motion of vesicles. Hence, it is hypothesized that any alteration of the cytoskeletal network may directly impact or even disrupt the vesicle transport. A disruption of the vesicle-mediated cell transport is thought to contribute to several severe diseases and disorders, such as diabetes, Parkinson’s and Alzheimer’s disease, emphasizing the clinical relevance. To address the outlined objective, a multiscale finite element model of the diffusive vesicle transport is proposed on the basis of the concept of homogenization, owed to the complexity of the cytoskeletal network. In order to study the microscopic effects of specific nanoscopic actin filament network alterations onto the vesicle transport, a parametrized three-dimensional geometrical model of the actin filament network was generated on the basis of experimentally observed filament densities and network geometries in an adenocarcinomic human alveolar basal epithelial cell. Numerical analyzes of the obtained effective diffusion properties within two-dimensional sampling domains of the whole cell model revealed that the computed homogenized diffusion coefficients can be predicted statistically accurate by a simple two-parameter power law as soon as the inaccessible area fraction, due to the obstacle geometries and the finite size of the vesicles, is known. This relationship, in turn, leads to a massive reduction in computation time and allows to study the impact of a variety of different cytoskeletal alterations onto the vesicle transport. Hence, the numerical simulations predicted a 35% increase in transport time due to a uniformly distributed four-fold increase of the total filament amount. On the other hand, a hypothetically reduced expression of filament cross-linking proteins led to sparser filament networks and, thus, a speed up of the vesicle transport.

Many vital processes in our eukaryotic cells and organs require an astonishingly precise routing of intermediate products to various intra- and extracellular destinations using vesicles as transporters. This can be illustrated by numerous examples, such as the production and destruction of proteins, the export of neurotransmitters or insulin to the extracellular domain, etc. However, the inside of a cell is tightly packed with numerous structural scaffoldings (filaments), which serve as obstacles and impede the vesicle motion. It is thought that any disturbances of the vesicle-mediated cell transport contribute to numerous degenerative diseases and disorders, which highlights the clinical relevance for investigating this intracellular transport mechanism by developing computational models and performing experimental studies. In this study, we numerically quantified how different specific alterations of the filament density inside a human lung cell—due to changed mechanical loadings or genetic disorders of proteins being responsible for filament branching—affect the diffusion of vesicles inside the intracellular fluid. Therefore, based on the concept of homogenization, a computationally efficient numerical method was developed and utilized to simulate the diffusion of vesicles inside the whole cell, considering the detailed structural information of the filament network.

Continuum elastic models for force transmission in biopolymer gels

We review continuum elastic models for the transmission of both external forces and internal active cellular forces in biopolymer gels, and relate them to recent experiments. Rather than being exhaustive, we focus on continuum elastic models for small affine deformations and intend to provide a systematic continuum method and some analytical perspectives on the study of force transmission in biopolymer gels. We start from a very brief review of the nonlinear mechanics of individual biopolymers and a summary of constitutive models for the nonlinear elasticity of biopolymer gels. We next show that the simple 3-chain model can give predictions that fit well the shear experiments of some biopolymer gels, including the effects of strain-stiffening and negative normal stress. We then review continuum models for the transmission of internal active forces that are induced by a spherically contracting cell embedded in a three-dimensional biopolymer gel. Various scaling regimes for the decay of cell-induced displacements are identified for linear isotropic and anisotropic materials, and for biopolymer gels with nonlinear compressive-softening and strain-stiffening elasticity, respectively. After that, we present (using an energetic approach) the generic and unified continuum theory proposed in [D. Ben-Yaakov et al., Soft Matter, 2015, 11, 1412] about how the transmission of forces in the biogel matrix can mediate long-range interactions between cells with mechanical homeostasis. We show the predictions of the theory in a special hexagonal multicellular array, and relate them to recent experiments. Finally, we conclude this paper with comments on the limitations and outlook of continuum modeling, and highlight the need for complementary theoretical approaches, such as discrete network simulations, to force transmission in biopolymer gels and phenomenological active gel theories for multicellular systems.

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

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

Altered mechanics of vaginal smooth muscle cells due to the lysyl oxidase-like1 knockout

The remodeling mechanisms that cause connective tissue of the vaginal wall, consisting mostly of smooth muscle, to weaken after vaginal delivery are not fully understood. Abnormal remodeling after delivery can contribute to development of pelvic organ prolapse and other pelvic floor disorders. The present study used vaginal smooth muscle cells (vSMCs) isolated from knockout mice lacking the expression of the lysyl oxidase-like1 (LOXL1) enzyme, a well-characterized animal model for pelvic organ prolapse. We tested if vaginal smooth muscle cells from LOXL1 knockout mice have altered mechanics including stiffness and surface adhesion. Using atomic force microscopy, we performed nanoindentations on both isolated and confluent cells to evaluate the effect of LOXL1 knockout on in vitro cultures of vSMCs cells from nulliparous mice. The results show that LOXL1 knockout vSMCs have increased stiffness in pre-confluent but decreased stiffness in confluent cultures (p* < 0.05) and significant decreased surface adhesion in pre-confluent cultures (p* < 0.05). This study provides evidence that the weakening of vaginal connective tissue in the absense of LOXL1 changes the mechanical properties of the vSMCs. STATEMENT OF SIGNIFICANCE: Pelvic organ prolapse is a common condition affecting millions of women worldwide, which significantly impacts their quality of life. Alterations in vaginal and pelvic floor mechanical properties can change their ability to support the pelvic organs. This study provides evidence of altered stiffness of vaginal smooth muscle cells from mice resembling pelvic organ prolapse. The results from this study set a foundation to develop pathophysiology-driven therapies focused on the interplay between smooth muscle mechanics and extracellular matrix remodeling.

On the mechanical response of the actomyosin cortex during cell indentations

A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation

The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.

Polydispersity controls the strength of semi-flexible polymer networks

The classical theory of polymer elasticity is built upon the assumption of network monodispersity-the premise that polymer networks are comprised of sub-chains of equal length. The crosslinking of biopolymers, however, is a random process and the resultant networks are likely to be polydisperse. The effect of structural polydispersity on the mechanical behavior of biopolymer networks is not well understood. The purpose of this contribution is to show how network polydispersity controls mechanical behavior and the ultimate properties of crosslinked semi-flexible filaments at finite deformations. The proposed micromechanical continuum model is based on the force-elongation relation of individual chains of different lengths. It is shown that the mechanical strength of the network is controlled by the finite-extensibility of filaments and the degradation of shorter filaments at relatively small stretches. The progressive failure of filaments continues and eventually determines the ultimate strength of the network. The predicted stress-stretch behaviors are in reasonable agreement with the experimental data for connective tissues.

Investigation of fullerenol-induced changes in poroelasticity of human hepatocellular carcinoma by AFM-based creep tests

In this study, atomic force microscopy (AFM) is used to investigate the alterations of the poroelastic properties of hepatocellular carcinoma (SMMC-7721) cells treated with fullerenol. The SMMC-7721 cells were subject to AFM-based creep tests, and a corresponding poroelastic indentation model was used to determine the poroelastic parameters by curve fitting. Comparative analyses indicated that the both permeability and diffusion of fullerenol-treated cells increased significantly while their elastic modulus decreased by a small amount. From the change in the trend of the determined parameter, we verified the corresponding alternations of cytoskeleton (mainly filaments actin), which was reported by the previous study using confocal imaging method. Our investigation on SMMC-7721 cell reveals that the poroelastic properties could provide a better understanding how the cancer cells are affected by fullerenol or potentially other drugs which could find possible applications in drug efficacy test, cancer diagnosis and secure therapies.

Theory of Semiflexible Filaments and Networks

We briefly review the recent developments in the theory of individual semiflexible filaments, and of a crosslinked network of such filaments, both permanent and transient. Starting from the free energy of an individual semiflexible chain, models on its force-extension relation and other mechanical properties such as Euler buckling are discussed. For a permanently crosslinked network of filaments, theories on how the network responds to deformation are provided, with a focus on continuum approaches. Characteristic features of filament networks, such as nonlinear stress-strain relation, negative normal stress, tensegrity, and marginal stability are discussed. In the new area of transient filament network, where the crosslinks can be dynamically broken and re-formed, we show some recent attempts for understanding the dynamics of the crosslinks, and the related rheological properties, such as stress relaxation, yield stress and plasticity.

Nonlinear elasticity of semiflexible filament networks

We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model of network elasticity over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding stress-strain relationship. The theory fits well to a wide range of experimental data on simple shear in different filament networks, quantitatively matching the differential shear modulus variation with stress, with only two adjustable parameters (which represent the filament stiffness and the pre-tension in the network, respectively). The general theory accurately describes the crossover between the positive and negative Poynting effect (normal stress on imposed shear) on increasing the stiffness of filaments forming the network. We discuss the network stability (the point of marginal rigidity) and the phenomenon of tensegrity, showing that filament pre-tension on crosslinking into the network determines the magnitude of linear modulus G0.

Computation of the effective mechanical response of biological networks accounting for large configuration changes

The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with FE simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes.

Single-cell mechanics--An experimental-computational method for quantifying the membrane-cytoskeleton elasticity of cells

The membrane-cytoskeleton system plays a major role in cell adhesion, growth, migration, and differentiation. F-actin filaments, cross-linkers, binding proteins that bundle F-actin filaments to form the actin cytoskeleton, and integrins that connect the actin cytoskeleton network to the cell plasma membrane and extracellular matrix are major cytoskeleton constituents. Thus, the cell cytoskeleton is a complex composite that can assume different shapes. Atomic force microscopy (AFM)-based techniques have been used to measure cytoskeleton material properties without much attention to cell shape. A recently developed surface chemical patterning method for long-term single-cell culture was used to seed individual cells on circular patterns. A continuum-based cell model, which uses as input the force-displacement response obtained with a modified AFM setup and relates the membrane-cytoskeleton elastic behavior to the cell geometry, while treating all other subcellular components suspended in the cytoplasmic liquid (gel) as an incompressible fluid, is presented and validated by experimental results. The developed analytical-experimental methodology establishes a framework for quantifying the membrane-cytoskeleton elasticity of live cells. This capability may have immense implications in cell biology, particularly in studies seeking to establish correlations between membrane-cytoskeleton elasticity and cell disease, mortality, differentiation, and migration, and provide insight into cell infiltration through nonwoven fibrous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscoelasticity, examine the role of other subcellular components (e.g., nucleus envelope) in cell elasticity, and elucidate the effects of mechanical stimuli on cell differentiation and motility.

STATEMENT OF SIGNIFICANCE

This is the first study to decouple the membrane-cytoskeleton elasticity from cell stiffness and introduce an effective approach for measuring the elastic modulus. The novelty of this study is the development of new technology for quantifying the elastic stiffness of the membrane-cytoskeleton system of cells. This capability could have immense implications in cell biology, particularly in establishing correlations between various cell diseases, mortality, and differentiation with membrane-cytoskeleton elasticity, examining through-tissue cell migration, and understanding cell infiltration in porous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscous behavior, identify the contribution of other subcellular components (e.g., nucleus envelope) to load sharing, and elucidate mechanotransduction effects due to repetitive compressive loading and unloading on cell differentiation and motility.

Computational analysis of morphologies and phase transitions of cross-linked, semi-flexible polymer networks

The eukaryotic cytoskeleton is a protein fibre network mainly consisting of the semi-flexible biopolymer F-actin, microtubules and intermediate filaments. It is well known to exhibit a pronounced structural polymorphism, which enables intracellular processes such as cell adhesion, cell motility and cell division. We present a computational study on cross-linked networks of semi-flexible polymers, which offers a detailed analysis of the network structure and phase transitions from one morphology to another. We elaborate the morphological differences, their mechanical implications and the order of the observed phase transitions. Finally, we present a perspective on how the information gained in our simulations can be exploited in order to build both flexible and accurate, microstructurally informed, homogenized constitutive models of the cytoskeleton.

Building an artificial actin cortex on microscopic pillar arrays

Eukaryotic cells obtain their morphology and mechanical strength from the cytoskeleton and in particular from the cross-linked actin network that branches throughout the whole cell. This actin cortex lies like a quasi-two-dimensional (2D) biopolymer network just below the cell membrane, to which it is attached. In the quest for building an artificial cell, one needs to make a biomimetic model of the actin cortex and combine this in a bottom-up approach with other "synthetic" components. Here, we describe a reconstitution method for such an artificial actin cortex, which is freely suspended on top of a regular array of pillars. By this immobilization method, the actin network is only attached to a surface at discrete points and can fluctuate freely in between. By discussing the method to make the micropillars and the way to reconstitute a quasi-2D actin network on top, we show how one can study an isolated, reconstituted part of a cell. This allows the study of fundamental interaction mechanisms of actin networks, providing handles to design a functional actin cortex in an artificial cell.

Multiscale impact of nucleotides and cations on the conformational equilibrium, elasticity and rheology of actin filaments and crosslinked networks

Cells are able to respond to mechanical forces and deformations. The actin cytoskeleton, a highly dynamic scaffolding structure, plays an important role in cell mechano-sensing. Thus, understanding rheological behaviors of the actin cytoskeleton is critical for delineating mechanical behaviors of cells. The actin cytoskeleton consists of interconnected actin filaments (F-actin) that form via self-assembly of actin monomers. It has been shown that molecular changes of the monomer subunits impact the rigidity of F-actin. However, it remains inconclusive whether or not the molecular changes can propagate to the network level and thus alter the rheological properties of actin networks. Here, we focus on how cation binding and nucleotide state tune the molecular conformation and rigidity of F-actin and a representative rheological behavior of actin networks, strain-stiffening. We employ a multiscale approach by combining established computational techniques: molecular dynamics, normal mode analysis and Brownian dynamics. Our findings indicate that different combinations of nucleotide (ATP, ADP or ADP-Pi) and cation [Formula: see text] or [Formula: see text] at one or multiple sites) binding change the molecular conformation of F-actin by varying inter- and intra-strand interactions which bridge adjacent subunits between and within F-actin helical strands. This is reflected in the rigidity of actin filaments against bending and stretching. We found that differences in extension and bending rigidity of F-actin induced by cation binding to the low-, intermediate- and high-affinity sites vary the strain-stiffening response of actin networks crosslinked by rigid crosslinkers, such as scruin, whereas they minimally impact the strain-stiffening response when compliant crosslinkers, such as filamin A or [Formula: see text]-actinin, are used.

Direct visualization of flow-induced conformational transitions of single actin filaments in entangled solutions

While semi-flexible polymers and fibres are an important class of material due to their rich mechanical properties, it remains unclear how these properties relate to the microscopic conformation of the polymers. Actin filaments constitute an ideal model polymer system due to their micron-sized length and relatively high stiffness that allow imaging at the single filament level. Here we study the effect of entanglements on the conformational dynamics of actin filaments in shear flow. We directly measure the full three-dimensional conformation of single actin filaments, using confocal microscopy in combination with a counter-rotating cone-plate shear cell. We show that initially entangled filaments form disentangled orientationally ordered hairpins, confined in the flow-vorticity plane. In addition, shear flow causes stretching and shear alignment of the hairpin tails, while the filament length distribution remains unchanged. These observations explain the strain-softening and shear-thinning behaviour of entangled F-actin solutions, which aids the understanding of the flow behaviour of complex fluids containing semi-flexible polymers.

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach.

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.

The obligatory role of the actin cytoskeleton on inward remodeling induced by dithiothreitol activation of endogenous transglutaminase in isolated arterioles

Inward remodeling is the most prevalent structural change found in the resistance arteries and arterioles of hypertensive individuals. Separate studies have shown that the inward remodeling process requires transglutaminase activation and the polymerization of actin. Therefore, we hypothesize that inward remodeling induced via endogenous transglutaminase activation requires and depends on actin cytoskeletal structures. To test this hypothesis, isolated and cannulated rat cremaster arterioles were exposed to dithiothreitol (DTT) to activate endogenous transglutaminases. DTT induced concentration-dependent vasoconstriction that was suppressed by coincubation with cystamine or cytochalasin-D to inhibit tranglutaminase activity or actin polymerization, respectively. Prolonged (4 h) exposure to DTT caused arteriolar inward remodeling that was also blocked by the presence of cystamine or cytochalasin-D. DTT inwardly remodeled arterioles had reduced passive diameters, augmented wall thickness-to-lumen ratios and altered elastic characteristics that were reverted upon disruption of the actin cytoskeleton with mycalolide-B. In freshly isolated arterioles, exposure to mycalolide-B caused no changes in their passive diameters or their elastic characteristics. These results suggest that, in arterioles, the early stages of the inward remodeling process induced by prolonged endogenous transglutaminase activation require actin dynamics and depend on changes in actin cytoskeletal structures.