Application of the Johnson–Kendall–Roberts model in AFM-based mechanical measurements on cells and gel

Plant Cell Wall-Like Soft Materials: Micro- and Nanoengineering, Properties, and Applications

Plant cell wall (CW)-like soft materials, referred to as artificial CWs, are composites of assembled polymers containing micro-/nanoparticles or fibers/fibrils that are designed to mimic the composition, structure, and mechanics of plant CWs. CW-like materials have recently emerged to test hypotheses pertaining to the intricate structure-property relationships of native plant CWs or to fabricate functional materials. Here, research on plant CWs and CW-like materials is reviewed by distilling key studies on biomimetic composites primarily composed of plant polysaccharides, including cellulose, pectin, and hemicellulose, as well as organic polymers like lignin. Micro- and nanofabrication of plant CW-like composites, characterization techniques, and in silico studies are reviewed, with a brief overview of current and potential applications. Micro-/nanofabrication approaches include bacterial growth and impregnation, layer-by-layer assembly, film casting, 3-dimensional templating microcapsules, and particle coating. Various characterization techniques are necessary for the comprehensive mechanical, chemical, morphological, and structural analyses of plant CWs and CW-like materials. CW-like materials demonstrate versatility in real-life applications, including biomass conversion, pulp and paper, food science, construction, catalysis, and reaction engineering. This review seeks to facilitate the rational design and thorough characterization of plant CW-mimetic materials, with the goal of advancing the development of innovative soft materials and elucidating the complex structure-property relationships inherent in native CWs.

Multidepth quantitative analysis of liver cell viscoelastic properties: Fusion of nanoindentation and finite element modeling techniques

Liver cells are the basic functional unit of the liver. However, repeated or sustained injury leads to structural disorders of liver lobules, proliferation of fibrous tissue and changes in structure, thus increasing scar tissue. Cellular fibrosis affects tissue stiffness, shear force, and other cellular mechanical forces. Mechanical force characteristics can serve as important indicators of cell damage and cirrhosis. Atomic force microscopy (AFM) has been widely used to study cell surface mechanics. However, characterization of the deep mechanical properties inside liver cells remains an underdeveloped field. In this work, cell nanoindentation was combined with finite element analysis to simulate and analyze the mechanical responses of liver cells at different depths in vitro and their internal responses and stress diffusion distributions after being subjected to normal stress. The sensitivities of the visco-hyperelastic parameters of the finite element model to the effects of the peak force and equilibrium force were compared. The force curves of alcohol-damaged liver cells at different depths were measured and compared with those of undamaged liver cells. The inverse analysis method was used to simulate the finite element model in vitro. Changes in the parameters of the cell model after injury were explored and analyzed, and their potential for characterizing hepatocellular injury and related treatments was evaluated. RESEARCH HIGHLIGHTS: This study aims to establish an in vitro hyperelastic model of liver cells and analyze the mechanical changes of cells in vitro. An analysis method combining finite element analysis model and nanoindentation was used to obtain the key parameters of the model. The multi-depth mechanical differences and internal structural changes of injured liver cells were analyzed.

Mechanical characterization of Xenopus laevis oocytes using atomic force microscopy

Mechanical properties are essential for the biological activities of cells, and they have been shown to be affected by diseases. Therefore, accurate mechanical characterization is important for studying the cell lifecycle, cell-cell interactions, and disease diagnosis. While the cytoskeleton and actin cortex are typically the primary structural stiffness contributors in most live cells, oocytes possess an additional extracellular layer known as the vitelline membrane (VM), or envelope, which can significantly impact their overall mechanical properties. In this study, we utilized nanoindentation via an atomic force microscope to measure the Young's modulus of Xenopus laevis oocytes at different force setpoints and explored the influence of the VM by conducting measurements on oocytes with the membrane removed. The findings revealed that the removal of VM led to a significant decrease in the apparent Young's modulus of the oocytes, highlighting the pivotal role of the VM as the main structural component responsible for the oocyte's shape and stiffness. Furthermore, the mechanical behavior of VM was investigated through finite element (FE) simulations of the nanoindentation process. FE simulations with the VM Young's modulus in the range 20-60 MPa resulted in force-displacement curves that closely resemble experimental in terms of shape and maximum force for a given indentation depth.

Role of adhesion in the mechanics of pathogenic Listeria monocytogenes EGDe as a function of the pH of growth

Atomic force microscopy was utilized to estimate the adhesion strengths to silicon nitride as well as the cellular elasticities of pathogenic Listeria monocytogenes EGDe cells cultured in media adjusted to five different pH conditions of growth (5, 6, 7, 8, and 9) under water with 0.0027 fixed ionic strength. Particularly, the role of adhesion on the bacterial elastic properties was investigated. The nonadhesive Hertz model of contact mechanics was used to extract Young's moduli of elasticity of bacterial cells from the approach force-indentation data. Additionally, the adhesive models of contact mechanics: Johnson-Kendall-Roberts (JKR) and Derjaguin-Muller-Toporov (DMT) were used to estimate Young's moduli of elasticity of bacterial cells from the retraction force-indentation data. Our results indicated that adhesion to silicon nitride was the highest for cells cultured at a pH of 7. Similarly, bacterial cells cultured at pH 7 were characterized by the highest Young's moduli of elasticities compared to the lower or higher pH conditions of growth. Young's moduli of elasticities estimated from the Hertz model were stiffer than those estimated using JKR or DMT models. As the adhesion between bacterial cells and indenters increased, the difference between the Hertz model and JKR or DMT models estimates of Young's moduli of elasticity increased as well. Contradicting the current norm of using the Hertz model to quantify bacterial elasticity in the literature, our results highlight the extreme importance of utilizing contact mechanics models with adhesion components in them such as the JKR and DMT models to estimate bacterial elasticity.

Dynamics of underwater microparticle adhesion to soft hydrated surfaces: Modeling and analysis by time-dependent AFM force spectroscopy

HYPOTHESIS

Understanding the attachment and detachment of microparticles and living cells to surfaces is crucial for developing antifouling strategies. Hydrogel coatings have shown promise in reducing fouling and particle adhesion due to their softness and high water content, yet the mechanisms involved are dynamic and complex, and relevant parameters are not easily accessible. AFM-based force spectroscopy (FS) experiments with colloidal probe particles is a direct way of evaluating adhesive and mechanical relaxational dynamics, yet their interpretation and modeling has been challenging. The present study proposes and examines several dynamic models, suitable for quantitative analysis of FS results with model probe particle on hydrogels surfaces.

EXPERIMENTS

FS were performed using polyethylene glycol (PEG) hydrogels and polystyrene microspheres including particle attachement to the hydrogel surface (loading), holding the particle on the surface with a constant force for variable times (dwell) and pulling the particle away from the surface (unloading) FINDINGS: It was found that a viscoelastic extension of the classical JKR model with energy of adhesion unevenly distributed over the contact area and vanishing at its circumferences accurately described all FS experiments and yielded physically consistent viscoelastic and adhesive dynamic parameters, steadily changing with dwell time and applied force. The observed time evolution and force dependence were rationalized as combination of osmotic and osmo-mechnical relaxation in the contact region.

Time-dependent plastic behavior of bacteria leading to rupture

A study of the mechanical response of bacteria is essential in designing an antibacterial surface for implants and food packaging applications. This research evaluated the mechanical response of Escherichia coli under different loading conditions. Indentation and prolonged creep tests were performed to understand their viscoelastic-plastic response. The results indicate that varying loading rates from 1 μm/s to 5 μm/s show an increase in modulus of 182% and 90%, calculated in the loading and unloading cycles, respectively, and a decrease in adhesion force by 42%. However, on varying loads from 5 nN to 25 nN, nominal change is observed in both modulus and adhesion force. The rupture curve at 100 nN load shows elastic and a small plastic deformation accompanied by a sharp peak indicating the cell wall rupture. The rupture force at the peak was found to be 34.38 ± 5.15 nN, irrespective of the loading rate, making it a failure criterion for bacteria rupture. The creep response of bacteria increases (for 6 s) and then remains constant (for 15 s) with time, indicating that a standard linear solid (SLS) model applies to this behavior. This work attempts to evaluate the mechanical properties of E. coli bacteria focusing on its rupture by contact killing mechanism.

Analytical Models for Measuring the Mechanical Properties of Yeast

The mechanical properties of yeast play an important role in many biological processes, such as cell division and growth, maintenance of internal pressure, and biofilm formation. In addition, the mechanical properties of cells can indicate the degree of damage caused by antifungal drugs, as the mechanical parameters of healthy and damaged cells are different. Over the past decades, atomic force microscopy (AFM) and micromanipulation have become the most widely used methods for evaluating the mechanical characteristics of microorganisms. In this case, the reliability of such an estimate depends on the choice of mathematical model. This review presents various analytical models developed in recent years for studying the mechanical properties of both cells and their individual structures. The main provisions of the applied approaches are described along with their limitations and advantages. Attention is paid to the innovative method of low-invasive nanomechanical mapping with scanning ion-conductance microscopy (SICM), which is currently starting to be successfully used in the discovery of novel drugs acting on the yeast cell wall and plasma membrane.

Atomic Force Microscopy Methods to Measure Tumor Mechanical Properties

Atomic force microscopy (AFM) is a popular tool for evaluating the mechanical properties of biological materials (cells and tissues) at high resolution. This technique has become particularly attractive to cancer researchers seeking to bridge the gap between mechanobiology and cancer initiation, progression, and treatment resistance. The majority of AFM studies thus far have been extensively focused on the nanomechanical characterization of cells. However, these approaches fail to capture the complex and heterogeneous nature of a tumor and its host organ. Over the past decade, efforts have been made to characterize the mechanical properties of tumors and tumor-bearing tissues using AFM. This has led to novel insights regarding cancer mechanopathology at the tissue scale. In this Review, we first explain the principles of AFM nanoindentation for the general study of tissue mechanics. We next discuss key considerations when using this technique and preparing tissue samples for analysis. We then examine AFM application in characterizing the mechanical properties of cancer tissues. Finally, we provide an outlook on AFM in the field of cancer mechanobiology and its application in the clinic.

Regulatory architecture of housekeeping genes is driven by promoter assemblies

Genes that are key to cell identity are generally regulated by cell-type-specific enhancer elements bound by transcription factors, some of which facilitate looping to distant gene promoters. In contrast, genes that encode housekeeping functions, whose regulation is essential for normal cell metabolism and growth, generally lack interactions with distal enhancers. We find that Ronin (Thap11) assembles multiple promoters of housekeeping and metabolic genes to regulate gene expression. This behavior is analogous to how enhancers are brought together with promoters to regulate cell identity genes. Thus, Ronin-dependent promoter assemblies provide a mechanism to explain why housekeeping genes can forgo distal enhancer elements and why Ronin is important for cellular metabolism and growth control. We propose that clustering of regulatory elements is a mechanism common to cell identity and housekeeping genes but is accomplished by different factors binding distinct control elements to establish enhancer-promoter or promoter-promoter interactions, respectively.

Ultra-lightweight living structural material for enhanced stiffness and environmental sensing

Natural materials such as bone, wood, and bamboo can inspire the fabrication of stiff, lightweight structural materials. Biofilms are one of the most dominant forms of life in nature. However, little is known about their physical properties as a structural material. Here we report an Escherichia coli biofilm having a Young's modulus close to 10 ​GPa with ultra-low density, indicating a high-performance structural material. The mechanical and structural characterization of the biofilm and its components illuminates its adaptable bottom-up design, consisting of lightweight microscale cells covered by a dense network of amyloid nanofibrils on the surface. We engineered E. coli such that 1) carbon nanotubes assembled on the biofilm, enhancing its stiffness to over 30 ​GPa, or that 2) the biofilm sensitively detected heavy metal as an example of an environmental toxin. These demonstrations offer new opportunities for developing responsive living structural materials to serve many real-world applications.

Applicability of atomic force microscopy to determine cancer-related changes in cells

The determination of mechanical properties of living cells as an indicator of cancer progression has become possible with the development of local measurement techniques such as atomic force microscopy (AFM). Its most important advantage is a nanoscopic character, implying that very local alterations can be quantified. The results gathered from AFM measurements of various cancers show that, for most cancers, individual cells are characterized by the lower apparent Young's modulus, denoting higher cell deformability. The measured value depends on various factors, like the properties of substrates used for cell growth, force loading rate or indentation depth. Despite this, the results proved the AFM capability to recognize mechanically altered cells. This can significantly impact the development of methodological approaches toward the precise identification of pathological cells. This article is part of the theme issue 'Nanocracks in nature and industry'.

Revealing Capillarity in AFM Indentation of Cells by Nanodiamond-Based Nonlocal Deformation Sensing

Nanoindentation based on atomic force microscopy (AFM) can measure the elasticity of biomaterials and cells with high spatial resolution and sensitivity, but relating the data to quantitative mechanical properties depends on information on the local contact, which is unclear in most cases. Here, we demonstrate nonlocal deformation sensing on biorelevant soft matters upon AFM indentation by using nitrogen-vacancy centers in nanodiamonds, providing data for studying both the elasticity and capillarity without requiring detailed knowledge about the local contact. Using fixed HeLa cells for demonstration, we show that the apparent elastic moduli of the cells would have been overestimated if the capillarity was not considered. In addition, we observe that both the elastic moduli and the surface tensions are reduced after depolymerization of the actin cytoskeleton in cells. This work demonstrates that the nanodiamond sensing of nonlocal deformation with nanometer precision is particularly suitable for studying mechanics of soft biorelevant materials.

The effects of measurement parameters on the cancerous cell nucleus characterization by atomic force microscopy in vitro

Cancer is now responsible for the major leading cause of death worldwide. It is noteworthy that lung cancer has been recognised as the highest incidence (11.6%) and mortality (18.4%) for combined sexes among a variety of cancer diseases. Therefore, it is of great value to investigate the mechanical properties of lung cancerous cells for early diagnosis. This paper focus on the influence of measurement parameters on the measured central Young's moduli of single live A549 cell in vitro based on the force spectroscopy mode of atomic force microscopy (AFM). The effects of the measurement parameters on the measured central Young's moduli were analysed by fitting the force–depth curves utilising the Sneddon model. The results revealed that the Young's moduli of A549 cells increased with the larger indentation force, higher indentation speed, less retraction time, deeper Z length and lower purity percentage of serum. The Young's moduli of cells increased first and then decreased with the increasing dwell time. Hence, this research may have potential significance to provide reference for the standardised detection of a single cancerous cell in vitro using AFM methodologies.

Cancer is now responsible for the majority leading cause of death worldwide and it is noteworthy that lung cancer has been recognised as the highest incidence (11.6%) and mortality (18.4%) for combined sexes among a variety of cancer diseases. Therefore, it is of great value to investigate the mechanical properties of lung cancerous cells for early diagnosis. This paper primarily investigated the morphological properties and the influence of measurement parameters on the measured local elastic moduli of single live A549 cell in vitro using the AFM‐based force spectroscopy mode. In practice, there are many factors for incorrect or inaccurate experimental results using AFM to measure the characteristics of live cells, such as non‐homogeneous nature of cells, probe geometry and size, mechanical analysis model, substrate stiffness and different measurement parameters. The various measurement parameters have become the huge impact factor to influence the measurement result. Hence, this research may have potential significance to provide reference for the standardised detection of a single cancerous cell in vitro using AFM methodologies.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

Free-standing conductive hydrogel electrode for potentiometric glucose sensing

Flexible conductive polymer hydrogels are attracting attention as an electrode material. Electrochemical biosensors with conductive polymer hydrogels have been developed because they have some advantages such as biocompatibility, high conductivity, 3D nanostructure, solvated surface, and enlarged interface. Conductive polymer hydrogels bearing receptor molecules such as enzymes in its 3D nanostructure enable the detection of target analytes with high sensitivity. However, because such hydrogels are fragile, they cannot stand on their own and a supporting substrate is required to fabricate them. This means that the loss of mechanical toughness is detrimental for their application to flexible biosensors. In this study, we have proposed a free-standing conductive hydrogel electrode with no coating on a substrate, which is composed of polyaniline with phenyl boronic acid including polyvinyl alcohol, for potentiometric glucose sensing. In addition, its electrical responsivity to glucose has been confirmed by investigating its mechanical properties at various glucose concentrations, considering the hydrogel compositions.

A free-standing conductive hydrogel electrode with no coating on a substrate is proposed for potentiometric glucose sensing.

Na+ i/K+ i imbalance contributes to gene expression in endothelial cells exposed to elevated NaCl

High-salt consumption contributes to the development of hypertension and is considered an independent risk factor for vascular remodelling, cardiac hypertrophy and stroke incidence. Alterations in NO production, inflammation and endothelial cell stiffening are considered now as plausible mediators of cardiovascular dysfunction. We studied early responses of endothelial cells (HUVEC) caused by a moderate increase in extracellular sodium concentration. Exposure of HUVEC to elevated sodium within the physiological range up to 24 h is accompanied by changes in monovalent cations fluxes and Na,K-ATPase activation, and, in turn, results in a significant decrease in the content of PTGS2, IL6 and IL1LR1 mRNAs. The expression of NOS3 and FOS genes, as well as the abundance of cytosolic and nuclear NFAT5 protein, remained unchanged. We assessed the mechanical properties of endothelial cells by estimating Young's modulus and equivalent elastic constant using atomic force and interference microscopy, respectively. These parameters were unaffected by elevated-salt exposure for 24 h. The data obtained suggest that even small and short-term elevations of extracellular sodium concentration affect the expression of genes involved in the control of endothelial function through the Na⁺_i/K⁺_i-dependent mechanism(s).

Determination by Relaxation Tests of the Mechanical Properties of Soft Polyacrylamide Gels Made for Mechanobiology Studies

Following the general aim of recapitulating the native mechanical properties of tissues and organs in vitro, the field of materials science and engineering has benefited from recent progress in developing compliant substrates with physical and chemical properties similar to those of biological materials. In particular, in the field of mechanobiology, soft hydrogels can now reproduce the precise range of stiffnesses of healthy and pathological tissues to study the mechanisms behind cell responses to mechanics. However, it was shown that biological tissues are not only elastic but also relax at different timescales. Cells can, indeed, perceive this dissipation and actually need it because it is a critical signal integrated with other signals to define adhesion, spreading and even more complicated functions. The mechanical characterization of hydrogels used in mechanobiology is, however, commonly limited to the elastic stiffness (Young's modulus) and this value is known to depend greatly on the measurement conditions that are rarely reported in great detail. Here, we report that a simple relaxation test performed under well-defined conditions can provide all the necessary information for characterizing soft materials mechanically, by fitting the dissipation behavior with a generalized Maxwell model (GMM). The simple method was validated using soft polyacrylamide hydrogels and proved to be very useful to readily unveil precise mechanical properties of gels that cells can sense and offer a set of characteristic values that can be compared with what is typically reported from microindentation tests.

Increasing AFM colloidal probe accuracy by optical tweezers

A precise determination of the cantilever spring constant is the critical point of all colloidal probe experiments. Existing methods are based on approximations considering only cantilever geometry and do not take into account properties of any object or substance attached to the cantilever. Neglecting the influence of the colloidal sphere on the cantilever characteristics introduces significant uncertainty in a spring constant determination and affects all further considerations. In this work we propose a new method of spring constant calibration for 'colloidal probe' type cantilevers based on the direct measurement of force constant. The Optical Tweezers based calibration method will help to increase the accuracy and repeatability of the AFM colloidal probe experiments.

Measuring (biological) materials mechanics with atomic force microscopy. 2. Influence of the loading rate and applied force (colloidal particles)

Atomic force microscopy (AFM) is the most often used tool to study the mechanical properties of eukaryotic cells. Due to their complex assembly, cells show viscoelastic properties. When performing experiments, one has to consider the influence of both loading rate and maximum load on the measured mechanical properties. Here, we employed colloidal particles of various sizes (from 2 to 20 μm diameter) to perform force spectroscopy measurements on endothelial cells at loading rates varying from 0.1 to 50 μm/s, and maximum loads ranging from 1 to 25 nN. We were able to determine the non-linear dependence of cell viscoelastic properties on the loading rate which followed a weak power law. In addition, we show that previous loading at high forces leads to a stiffening of cells. Based on these results we discuss a road map for determining cell mechanical properties using AFM. Finally, this work provides an experimental framework for cell mechanical measurements using force-cycle experiments.

Cationic π-Conjugated Polyelectrolyte Shows Antimicrobial Activity by Causing Lipid Loss and Lowering Elastic Modulus of Bacteria

Cationic, π-conjugated oligo-/polyelectrolytes (CCOEs/CCPEs) have shown great potential as antimicrobial materials to fight against antibiotic resistance. In this work, we treated wild-type and ampicillin-resistant (amp-resistant) Escherichia coli (E. coli) with a promising cationic, π-conjugated polyelectrolyte (P1) with a phenylene-based backbone and investigated the resulting morphological, mechanical, and compositional changes of the outer membrane of bacteria in great detail. The cationic quaternary amine groups of P1 led to electrostatic interactions with negatively charged moieties within the outer membrane of bacteria. Using atomic force microscopy (AFM), high-resolution transmission electron microscopy (TEM), we showed that due to this treatment, the bacterial outer membrane became rougher, decreased in stiffness/elastic modulus (AFM nanoindentation), formed blebs, and released vesicles near the cells. These evidences, in addition to increased staining of the P1-treated cell membrane by lipophilic dye Nile Red (confocal laser scanning microscopy (CLSM)), suggested loosening/disruption of packing of the outer cell envelope and release and exposure of lipid-based components. Lipidomics and fatty acid analysis confirmed a significant loss of phosphate-based outer membrane lipids and fatty acids, some of which are critically needed to maintain cell wall integrity and mechanical strength. Lipidomics and UV-vis analysis also confirmed that the extracellular vesicles released upon treatment (AFM) are composed of lipids and cationic P1. Such surface alterations (vesicle/bleb formation) and release of lipids/fatty acids upon treatment were effective enough to inhibit further growth of E. coli cells without completely disintegrating the cells and have been known as a defense mechanism of the cells against cationic antimicrobial agents.

A MEMS nanoindenter with an integrated AFM cantilever gripper for nanomechanical characterization of compliant materials

This work presents the development of a MEMS nanoindenter that uses exchangeable AFM probes for quasi-static nanomechanical characterization of compliant and ultra-compliant materials. While the electrostatic micro-force transducer of the MEMS nanoindenter provides a maximum indentation depth up to 9.5 µm with a maximum output force of 600 µN, experimental investigations reveal that it can achieve a depth and force resolution better than 4 pm Hz^-1/2 and 0.3 nN Hz^-1/2, in air for f≥ 1 Hz. A passive AFM probe gripper is integrated into the MEMS nanoindenter, allowing the nanoindenter to utilize various AFM probes as an indenter for material testing. A proof-of-principle experimental setup has been built to investigate the performance of the MEMS nanoindenter prototype. In proof-of-principle experiments, the prototype with a clamped diamond AFM probe successfully identified an atomic step (∼0.31 nm) within a Si < 111 > ultraflat sample using the scanning probe microscopy mode. The nanomechanical measurement capability of the MEMS nanoindenter prototype has been verified by means of measurements of reference polymer samples using a silicon AFM probe and by means of measurements of the elastic properties of a PDMS sample using a spherical diamond-coated AFM probe. Owing to its compact and low-cost but high-resolution capacitive readout system, this MEMS nanoindenter head can be further applied for in-situ quantitative nanomechanical measurements in AFMs and SEMs.

Measuring viscoelasticity of soft biological samples using atomic force microscopy

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

The role of vimentin in directional migration of rat fibroblasts

Cell migration is one of the most important processes in which the cytoskeleton plays a main role. The cytoskeleton network is formed by tubulin microtubules, actin filaments, and intermediate filaments (IFs). While the structure and functions of the two aforementioned proteins have been extensively investigated during the last decades, vimentin IFs structure and their role in cell migration and adhesion remain unclear. Here, we investigated polarity determination in rat fibroblasts with either a knocked out vim gene or with a mutation that blocks filament formation on the stage of unit-length filaments (ULFs). Structured illumination microscopy has demonstrated the difference in the morphology of IFs in wild-type fibroblasts and of ULFs in mutant fibroblasts. We have developed an approach to measure cell stiffness separately on the trailing and leading edges using atomic force microscopy. Young's modulus values on the leading and trailing edge of migrating rat fibroblasts differ approximately by two times, being larger on the leading edge. The knockout of the vim gene leads to having comparable values of Young's moduli on both edges. Vimentin-null cells change the direction of migration more frequently than those expressing wild-type or mutated vimentin. Our results have shown the principle role of vimentin, not only in the form of IFs, but also as ULFs, in the determination of the polarity and the directionality of fibroblast migration.

Viscoelastic mapping of cells based on fast force volume and PeakForce Tapping

Development of fast force volume (FFV), PeakForce Tapping (PFT), and related AFM techniques allow fast acquisition and mapping of a sample's mechanical properties. The methods are well-suited for studying soft biological samples like living cells in a liquid environment. However, the question remains how the measured mechanical properties are related to those acquired with the classical force volume (FV) technique conducted at low indentation rates. The difference is coming mostly from the pronounced viscoelastic behavior of cells, making apparent elastic parameters depending on the probing rate. Here, the viscoelastic analysis was applied directly to the force curves acquired with force volume or PeakForce Tapping by their post-processing based on the Ting's model. Maps from classical force volume, FFV and PFT obtained using special PFT cantilevers and cantilevers modified with microspheres were compared here. With the correct viscoelastic model, which was found to be the power-law rheology model, all the techniques have provided self-consistent results. The techniques were further modified for the mapping of the viscoelastic model-independent complex Young's modulus.

Measuring biomaterials mechanics with atomic force microscopy. 1. Influence of the loading rate and applied force (pyramidal tips)

Atomic force microscopy (AFM) is today an established tool in imaging and determination of mechanical properties of biomaterials. Due to their complex organization, those materials show intricate properties such as viscoelasticity. Therefore, one has to consider that the loading rate at which the sample is probed will lead to different mechanical response (properties). In this work, we studied the dependence of the mechanical properties of endothelial cells on the loading rate using AFM in force spectroscopy mode. We employed a sharp, four‐sided pyramidal indenter and loading rates ranging from 0.5 to 20 μm/s. In addition, by variation of the load (applied forces from 100 to 10,000 pN), the dependence of the cell properties on indentation depth could be determined. We then showed that the mechanical response of endothelial cells depends nonlinearly on the loading rate and follows a weak power‐law. In addition, regions of different viscous response at varying indentation depth could be determined. Based on the results we obtained, a general route map for AFM users for design of cell mechanics experiments was described.

Mechanical Characterization by Mesoscale Indentation: Advantages and Pitfalls for Tissue and Scaffolds

Regenerative medicine and tissue engineering are hindered by the lack of consistent measurements and standards for the mechanical characterization of tissue and scaffolds. Indentation methods for soft matter are favored because of their compatibility with small, arbitrarily shaped samples, but contact mechanics models required to interpret data are often inappropriate for soft, viscous materials. In this study, we demonstrate indentation experiments on a variety of human biopsies, animal tissue, and engineered scaffolds, and we explore the complexities of fitting analytical models to these data. Although objections exist to using Hertz contact models for soft, viscoelastic biological materials since soft matter violates their original assumptions, we demonstrate the experimental conditions that enable consistency and comparability (regardless of arguable misappropriation). Appropriate experimental conditions involving sample hydration, the indentation depth, and the ratio of the probe size to sample thickness enable repeatable metrics that are valuable when comparing synthetic scaffolds and host tissue, and bounds on these parameters are carefully described and discussed. We have also identified a reliable quasistatic parameter that can be derived from indentation data to help researchers compare results across materials and experiments. Although Hertz contact mechanics and linear viscoelastic models may constitute oversimplification for biological materials, the reporting of such simple metrics alongside more complex models is expected to support researchers in tissue engineering and regenerative medicine by providing consistency across efforts to characterize soft matter. Impact Statement To engineer replacement tissue requires a deep understanding of its biomechanical properties. Mesoscale indentation (between micron and millimeter length scales) is well-suited to characterize tissue and engineered replacements as it accommodates small, oddly shaped samples. However, it is easy to run afoul of the assumptions for common contact models when working with biological materials. In this study, we describe experimental procedures and modeling approaches that allow researchers to take advantage of indentation for biomechanical characterization while minimizing its weaknesses.

Structure and Nanomechanics of Dry and Hydrated Intermediate Filament Films and Fibers Produced from Hagfish Slime Fibers

Intermediate filaments (IFs) are known for their extensibility, flexibility, toughness, and their ability to hydrate. Using keratin-like IFs obtained from slime fibers from the invertebrate Atlantic hagfish ( Myxine glutinosa), films were produced by drop-casting and coagulation on the surface of a MgCl₂ buffer. Drop-casting produced self-supporting, smooth, and dense films rich in β-sheets (61%), whereas coagulation formed thin, porous films with a nanorough surface and a lower β-sheet content (51%). The films hydrated and swelled immediately when immersed in water and did not dissolve. X-ray diffraction showed that the β-crystallites remained stable upon hydration, that swelling presumably happens in the amorphous C-terminal tail-domains of the IFs, and that high salt conditions caused a denser network mesh size, suggesting polyelectrolyte behavior. Hydration resulted in a roughly 1000-fold decrease in apparent Young's modulus from 10⁹ to 10⁶ Pa as revealed by atomic force microscopy nanoindentation. Nanoindentation-based power-law rheology and stress-relaxation measurements indicated viscoelasticity and a soft-solid hydrogel character for hydrated films, where roughly 80% of energy is elastically stored and 20% is dissipated. By pulling coagulation films from the buffer interface, macroscopic fibers with highly aligned IF β-crystals similar to natural hagfish fibers were produced. We propose that viscoelasticity and strong hydrogen bonding interactions with the buffer interface are crucial for the production of such long biomimetic fibers with aligned β-sheets. This study demonstrates that hagfish fiber IFs can be reconstituted into functional biomimetic materials that are stiff when dry and retain the ability to hydrate to become soft and viscoelastic when in water.

Probing the swelling-dependent mechanical and transport properties of polyacrylamide hydrogels through AFM-based dynamic nanoindentation

Hydrogels are composed of a crosslinked polymer network and water. The constitutive behaviors of hydrogels have been modeled based on Flory-Huggins theory. Within this model, the thermodynamic and kinetic parameters are assumed to be of constant values and are typically characterized through swelling tests. Since most hydrogels can absorb a large amount of solvent from the dry state to the swollen state, and the network size and solvent concentration of the hydrogels change significantly, the assumption of constant values of the thermodynamic and kinetic properties as the network swells is questionable. In this work, we have experimentally shown that even for the simple neutral polyacrylamide (PAAm) hydrogels, their mechanical responses cannot be fully described by the Flory-Huggins theory with constant thermodynamic parameters: N (number of chains per unit volume of dry polymers) and χ (polymer-solvent interaction parameter). For a more complete and precise characterization of the hydrogels, we measure the evolving properties of the gels as the network swells. Here, we use dynamic indentation to measure the poroelastic properties (shear modulus G, Poisson's ratio ν and diffusivity D) of the hydrogels under a wide range of swelling ratios. We also use linear perturbation to build the link between G, ν and N, χ, and plot the thermodynamic parameters in the Flory-Huggins theory as a function of the hydrogel swelling ratio. Consequently, the validity of the hydrogel models based on Flory-Huggins theory can be quantitatively examined.

Viscoelastic properties of human pancreatic tumors and in vitro constructs to mimic mechanical properties

Pancreatic ductal adenocarcinoma (PDAC) is almost universally fatal, in large part due to a protective fibrotic barrier generated by tumor-associated stromal (TAS) cells. This barrier is thought to promote cancer cell survival and confounds attempts to develop effective therapies. We present a 3D in vitro system that replicates the mechanical properties of the PDAC microenvironment, representing an invaluable tool for understanding the biology of the disease. Mesoscale indentation quantified viscoelastic metrics of resected malignant tumors, inflamed chronic pancreatitis regions, and histologically normal tissue. Both pancreatitis (2.15 ± 0.41 kPa, Mean ± SD) and tumors (5.46 ± 3.18 kPa) exhibit higher Steady-State Modulus (SSM) than normal tissue (1.06 ± 0.25 kPa; p < .005). The average viscosity of pancreatitis samples (63.2 ± 26.7 kPa·s) is significantly lower than that of both normal tissue (252 ± 134 kPa·s) and tumors (349 ± 222 kPa·s; p < .005). To mimic this remodeling behavior, PDAC and TAS cells were isolated from human PDAC tumors. Conditioned medium from PDAC cells was used to culture TAS-embedded collagen hydrogels. After 7 days, TAS-embedded gels in control medium reached SSM (1.45 ± 0.12 kPa) near normal pancreas, while gels maintained with conditioned medium achieved higher SSM (3.38 ± 0.146 kPa) consistent with tumors. Taken together, we have demonstrated an in vitro system that recapitulates in vivo stiffening of PDAC tumors. In addition, our quantification of viscoelastic properties suggests that elastography algorithms incorporating viscosity may be able to more accurately distinguish between pancreatic cancer and pancreatitis.

STATEMENT OF SIGNIFICANCE

Understanding tumor-stroma crosstalk in pancreatic ductal adenocarcinoma (PDAC) is challenged by a lack of stroma-mimicking model systems. To design appropriate models, pancreatic tissue must be characterized with a method capable of evaluating in vitro models as well. Our indentation-based characterization tool quantified the distinct viscoelastic signatures of inflamed resections from pancreatitis, tumors from PDAC, and otherwise normal tissue to inform development of mechanically appropriate engineered tissues and scaffolds. We also made progress toward a 3D in vitro system that recapitulates mechanical properties of tumors. Our in vitro model of stromal cells in collagen and complementary characterization system can be used to investigate mechanisms of cancer-stroma crosstalk in PDAC and to propose and test innovative therapies.

Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves

Force-displacement (F-Z) curves are the most commonly used Atomic Force Microscopy (AFM) mode to measure the local, nanoscale elastic properties of soft materials like living cells. Yet a theoretical framework has been lacking that allows the post-processing of F-Z data to extract their viscoelastic constitutive parameters. Here, we propose a new method to extract nanoscale viscoelastic properties of soft samples like living cells and hydrogels directly from conventional AFM F-Z experiments, thereby creating a common platform for the analysis of cell elastic and viscoelastic properties with arbitrary linear constitutive relations. The method based on the elastic-viscoelastic correspondence principle was validated using finite element (FE) simulations and by comparison with the existed AFM techniques on living cells and hydrogels. The method also allows a discrimination of which viscoelastic relaxation model, for example, standard linear solid (SLS) or power-law rheology (PLR), best suits the experimental data. The method was used to extract the viscoelastic properties of benign and cancerous cell lines (NIH 3T3 fibroblasts, NMuMG epithelial, MDA-MB-231 and MCF-7 breast cancer cells). Finally, we studied the changes in viscoelastic properties related to tumorigenesis including TGF-β induced epithelial-to-mesenchymal transition on NMuMG cells and Syk expression induced phenotype changes in MDA-MB-231 cells.

Characterization of biomechanical properties of cells through dielectrophoresis-based cell stretching and actin cytoskeleton modeling

Background

Cytoskeleton is a highly dynamic network that helps to maintain the rigidity of a cell, and the mechanical properties of a cell are closely related to many cellular functions. This paper presents a new method to probe and characterize cell mechanical properties through dielectrophoresis (DEP)-based cell stretching manipulation and actin cytoskeleton modeling.

Methods

Leukemia NB4 cells were used as cell line, and changes in their biological properties were examined after chemotherapy treatment with doxorubicin (DOX). DEP-integrated microfluidic chip was utilized as a low-cost and efficient tool to study the deformability of cells. DEP forces used in cell stretching were first evaluated through computer simulation, and the results were compared with modeling equations and with the results of optical stretching (OT) experiments. Structural parameters were then extracted by fitting the experimental data into the actin cytoskeleton model, and the underlying mechanical properties of the cells were subsequently characterized.

Results

The DEP forces generated under different voltage inputs were calculated and the results from different approaches demonstrate good approximations to the force estimation. Both DEP and OT stretching experiments confirmed that DOX-treated NB4 cells were stiffer than the untreated cells. The structural parameters extracted from the model and the confocal images indicated significant change in actin network after DOX treatment.

Conclusion

The proposed DEP method combined with actin cytoskeleton modeling is a simple engineering tool to characterize the mechanical properties of cells.

Note: Nanomechanical characterization of soft materials using a micro-machined nanoforce transducer with an FIB-made pyramidal tip

The quantitative nanomechanical characterization of soft materials using the nanoindentation tech-nique requires further improvements in the performances of instruments, including their force resolution in particular. A micro-machined silicon nanoforce transducer based upon electrostatic comb drives featuring the force and depth resolutions down to ∼1 nN and 0.2 nm, respectively, is described. At the end of the MEMS transducer's main shaft, a pyramidal tip is fabricated using a focused ion beam facility. A proof-of-principle setup with this MEMS nanoindenter has been established to measure the mechanical properties of soft polydimethylsiloxane. First measurement results demonstrate that the prototype measurement system is able to quantitatively characterize soft materials with elastic moduli down to a few MPa.

A beginner's guide to atomic force microscopy probing for cell mechanics

Atomic Force microscopy (AFM) is becoming a prevalent tool in cell biology and biomedical studies, especially those focusing on the mechanical properties of cells and tissues. The newest generation of bio-AFMs combine ease of use and seamless integration with live-cell epifluorescence or more advanced optical microscopies. As a unique feature with respect to other bionanotools, AFM provides nanometer-resolution maps for cell topography, stiffness, viscoelasticity, and adhesion, often overlaid with matching optical images of the probed cells. This review is intended for those about to embark in the use of bio-AFMs, and aims to assist them in designing an experiment to measure the mechanical properties of adherent cells. In addition to describing the main steps in a typical cell mechanics protocol and explaining how data is analysed, this review will also discuss some of the relevant contact mechanics models available and how they have been used to characterize specific features of cellular and biological samples. Microsc. Res. Tech. 80:75-84, 2017. © 2016 Wiley Periodicals, Inc.

Contact Mechanics of Nanoparticles: Pulling Rigid Nanoparticles from Soft, Polymeric Surfaces

Detachment of rigid nanoparticles from soft, gel-like polymeric surfaces is studied by using a combination of the molecular dynamics simulations and theoretical calculations. Simulations show that detachment of nanoparticles from soft surfaces proceeds through a neck formation. Analysis of the simulation results demonstrates that the magnitude of the detachment force f* depends on the nanoparticle radius R(p), shear modulus of substrate G(s), surface tension of substrate γ(s), and work of adhesion W. It is controlled by the balance of the elastic energy, surface energy of the neck, and nanoparticle adhesion energy to a substrate and depends on the dimensionless parameter δ ∝ γ(s)(G(s)R(p))(-1/3)W(-2/3). In the case of small values of the parameter δ ≪ 1, the critical detachment force approaches a critical detachment force calculated by Johnson, Kendall, and Roberts for adhesive contact, f* = 1.5πWR(p). However, in the opposite limit, corresponding to soft substrates, for which δ ≫ 1, the critical detachment force f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2). All simulation data can be described by a scaling function f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2)δ(-1.89).