Are elastic moduli of biological cells depth dependent or not? Another explanation using a contact mechanics model with surface tension

Accurate Modelling of AFM Force-Indentation Curves with Blunted Indenters at Small Indentation Depths

When testing biological samples with atomic force microscopy (AFM) nanoindentation using pyramidal indenters, Sneddon's equation is commonly used for data processing, approximating the indenter as a perfect cone. While more accurate models treat the AFM tip as a blunted cone or pyramid, these are complex and lack a direct relationship between applied force and indentation depth, complicating data analysis. This paper proposes a new equation derived from simple mathematical processes and physics-based criteria. It is accurate for small indentation depths and serves as a viable alternative to complex classical approaches. The proposed equation has been validated for ℎ < 3R (where h is the indentation depth and R is the tip radius) and confirmed through simulations with blunted conical and pyramidal indenters, as well as experiments on prostate cancer cells. It is a reliable method for experiments where the tip radius cannot be ignored, such as in shallow indentations on thin samples to avoid substrate effects.

High-throughput mechanical phenotyping and transcriptomics of single cells

The molecular system regulating cellular mechanical properties remains unexplored at single-cell resolution mainly due to a limited ability to combine mechanophenotyping with unbiased transcriptional screening. Here, we describe an electroporation-based lipid-bilayer assay for cell surface tension and transcriptomics (ELASTomics), a method in which oligonucleotide-labelled macromolecules are imported into cells via nanopore electroporation to assess the mechanical state of the cell surface and are enumerated by sequencing. ELASTomics can be readily integrated with existing single-cell sequencing approaches and enables the joint study of cell surface mechanics and underlying transcriptional regulation at an unprecedented resolution. We validate ELASTomics via analysis of cancer cell lines from various malignancies and show that the method can accurately identify cell types and assess cell surface tension. ELASTomics enables exploration of the relationships between cell surface tension, surface proteins, and transcripts along cell lineages differentiating from the haematopoietic progenitor cells of mice. We study the surface mechanics of cellular senescence and demonstrate that RRAD regulates cell surface tension in senescent TIG-1 cells. ELASTomics provides a unique opportunity to profile the mechanical and molecular phenotypes of single cells and can dissect the interplay among these in a range of biological contexts.

Quantifying both viscoelasticity and surface tension: Why sharp tips overestimate cell stiffness

Quantifying the mechanical properties of cells is important to better understand how mechanics constrain cellular processes. Furthermore, because pathologies are usually paralleled by altered cell mechanical properties, mechanical parameters can be used as a novel way to characterize the pathological state of cells. Key features used in models are cell tension, cell viscoelasticity (representing the average of the cell bulk), or a combination of both. It is unclear which of these features is the most relevant or whether both should be included. To clarify this, we performed microindentation experiments on cells with microindenters of various tip radii, including micrometer-sized microneedles. We obtained different cell-indenter contact radii and measured the corresponding contact stiffness. We derived a model predicting that this contact stiffness should be an affine function of the contact radius and that, at vanishing contact radius, the cell stiffness should be equal to the cell tension multiplied by a constant. When microindenting leukocytes and both adherent and trypsinized adherent cells, the contact stiffness was indeed an affine function of the contact radius. For leukocytes, the deduced surface tension was consistent with that measured using micropipette aspiration. For detached endothelial cells, agreement between microindentation and micropipette aspiration was better when considering these as only viscoelastic when analyzing micropipette aspiration experiments. This work suggests that indenting cells with sharp tips but neglecting the presence of surface tension leads to an effective elastic modulus whose origin is in fact surface tension. Accordingly, using sharp tips when microindenting a cell is a good way to directly measure its surface tension without the need to let the viscoelastic modulus relax.

Electroconductive Collagen-Carbon Nanodots Nanocomposite Elicits Neurite Outgrowth, Supports Neurogenic Differentiation and Accelerates Electrophysiological Maturation of Neural Progenitor Spheroids

Neuronal disorders are characterized by the loss of functional neurons and disrupted neuroanatomical connectivity, severely impacting the quality of life of patients. This study investigates a novel electroconductive nanocomposite consisting of glycine-derived carbon nanodots (GlyCNDs) incorporated into a collagen matrix and validates its beneficial physicochemical and electro-active cueing to relevant cells. To this end, this work employs mouse induced pluripotent stem cell (iPSC)-derived neural progenitor (NP) spheroids. The findings reveal that the nanocomposite markedly augmented neuronal differentiation in NP spheroids and stimulate neuritogenesis. In addition, this work demonstrates that the biomaterial-driven enhancements of the cellular response ultimately contribute to the development of highly integrated and functional neural networks. Lastly, acute dizocilpine (MK-801) treatment provides new evidence for a direct interaction between collagen-bound GlyCNDs and postsynaptic N-methyl-D-aspartate (NMDA) receptors, thereby suggesting a potential mechanism underlying the observed cellular events. In summary, the findings establish a foundation for the development of a new nanocomposite resulting from the integration of carbon nanomaterials within a clinically approved hydrogel, toward an effective biomaterial-based strategy for addressing neuronal disorders by restoring damaged/lost neurons and supporting the reestablishment of neuroanatomical connectivity.

Universal contact stiffness of elastic solids covered with tensed membranes and its application in indentation tests of biological materials

The inherent membrane tension of biological materials could vitally affect their responses to contact loading but is generally ignored in existing indentation analysis. In this paper, the authors theoretically investigate the contact stiffness of axisymmetric indentations of elastic solids covered with thin tensed membranes. When the indentation size decreases to the same order as the ratio of membrane tension to elastic modulus, the contact stiffness accounting for the effect of membrane tension becomes much higher than the prediction of conventional contact theory. An explicit expression is derived for the contact stiffness, which is universal for axisymmetric indentations using indenters of arbitrary convex profiles. On this basis, a simple method of analysis is proposed to estimate the membrane tension and elastic modulus of biological materials from the indentation load-depth data, which is successfully applied to analyze the indentation experiments of cells and lungs. This study might be helpful for the comprehensive assessment of the mechanical properties of soft biological systems. STATEMENT OF SIGNIFICANCE: This paper highlights the crucial effect of the inherent membrane tension on the indentation response of soft biomaterials, which has been generally ignored in existing analysis of experiments. For typical indentation tests on cells and organs, the contact stiffness can be twice or higher than the prediction of conventional contact model. A universal expression of the contact stiffness accounting for the membrane tension effect is derived. On this basis, a simple method of analysis is proposed to abstract the membrane tension of biomaterials from the experimentally recorded indentation load-depth data. With this method, the elasticity of soft biomaterials can be characterized more comprehensively.

AFM-Based Poroelastic@Membrane Analysis of Cells and its Opportunities for Translational Medicine

Cell mechanics is an emerging field of research for translational medicine. Here, the cell is modeled as poroelastic cytoplasm wrapped by tensile membrane (poroelastic@membrane model) and is characterized by the atomic force microscopy (AFM). The parameters of cytoskeleton network modulus EC , cytoplasmic apparent viscosity ηC , and cytoplasmic diffusion coefficient DC are used to describe the mechanical behavior of cytoplasm, and membrane tension γ is used to evaluate the cell membrane. Poroelastic@membrane analysis of breast cells and urothelial cells show that non-cancer cells and cancer cells have different distribution regions and distribution trends in the four-dimensional space composed of EC , ηC . From non-cancer to cancer cells, there is often a trend of γ, EC , ηC decreases and DC increases. Patients with urothelial carcinoma at different malignant stages can be distinguished at high sensitivity and specificity by analyzing the urothelial cells from tissue or urine. However, sampling directly from tumor tissues is an invasive method, may lead to undesirable consequences. Thus, AFM-based poroelastic@membrane analysis of urothelial cells from urine may provide a non-invasive and no-bio-label method to detecting urothelial carcinoma.

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.

3D AFM Nanomechanical Characterization of Biological Materials

Atomic Force Microscopy (AFM) is a powerful tool enabling the mechanical characterization of biological materials at the nanoscale. Since biological materials are highly heterogeneous, their mechanical characterization is still considered to be a challenging procedure. In this paper, a new approach that leads to a 3-dimensional (3D) nanomechanical characterization is presented based on the average Young's modulus and the AFM indentation method. The proposed method can contribute to the clarification of the variability of the mechanical properties of biological samples in the 3-dimensional space (variability at the x-y plane and depth-dependent behavior). The method was applied to agarose gels, fibroblasts, and breast cancer cells. Moreover, new mathematical methods towards a quantitative mechanical characterization are also proposed. The presented approach is a step forward to a more accurate and complete characterization of biological materials and could contribute to an accurate user-independent diagnosis of various diseases such as cancer in the future.

Determining Spatial Variability of Elastic Properties for Biological Samples Using AFM

Measuring the mechanical properties (i.e., elasticity in terms of Young's modulus) of biological samples using Atomic Force Microscopy (AFM) indentation at the nanoscale has opened new horizons in studying and detecting various pathological conditions at early stages, including cancer and osteoarthritis. It is expected that AFM techniques will play a key role in the future in disease diagnosis and modeling using rigorous mathematical criteria (i.e., automated user-independent diagnosis). In this review, AFM techniques and mathematical models for determining the spatial variability of elastic properties of biological materials at the nanoscale are presented and discussed. Significant issues concerning the rationality of the elastic half-space assumption, the possibility of monitoring the depth-dependent mechanical properties, and the construction of 3D Young's modulus maps are also presented.

Cell-Specific Response of NSIP- and IPF-Derived Fibroblasts to the Modification of the Elasticity, Biological Properties, and 3D Architecture of the Substrate

The fibrotic fibroblasts derived from idiopathic pulmonary fibrosis (IPF) and nonspecific interstitial pneumonia (NSIP) are surrounded by specific environments, characterized by increased stiffness, aberrant extracellular matrix (ECM) composition, and altered lung architecture. The presented research was aimed at investigating the effect of biological, physical, and topographical modification of the substrate on the properties of IPF- and NSIP-derived fibroblasts, and searching for the parameters enabling their identification. Soft and stiff polydimethylsiloxane (PDMS) was chosen for the basic substrates, the properties of which were subsequently tuned. To obtain the biological modification of the substrates, they were covered with ECM proteins, laminin, fibronectin, and collagen. The substrates that mimicked the 3D structure of the lungs were prepared using two approaches, resulting in porous structures that resemble natural lung architecture and honeycomb patterns, typical of IPF tissue. The growth of cells on soft and stiff PDMS covered with proteins, traced using fluorescence microscopy, confirmed an altered behavior of healthy and IPF- and NSIP-derived fibroblasts in response to the modified substrate properties, enabling their identification. In turn, differences in the mechanical properties of healthy and fibrotic fibroblasts, determined using atomic force microscopy working in force spectroscopy mode, as well as their growth on 3D-patterned substrates were not sufficient to discriminate between cell lines.

Building a tissue: mesenchymal and epithelial cell spheroids' mechanical properties at micro- and nanoscale

Cell transitions between the epithelial and mesenchymal phenotypes provide the regulated morphogenesis and regeneration throughout the ontogenesis. The tissue mechanics and mechanotransduction play an essential role in these processes. Cell spheroids reproduce the cell density of native tissues and represent simple building blocks for the tissue engineering purposes. The mechanical properties of mesenchymal and epithelial cells have been extensively studied in 2D monolayer cultures, but have not been sufficiently compared in spheroids. Here, we have simultaneously applied several techniques to assess the mechanical parameters of such spheroids. The local surface mechanical properties were measured by AFM, and the bulk properties were analyzed with parallel-plate compression, as well as by observing cut opening after microdissection. The comparison of the collected data allowed us to apply the model of a solid body with surface tension, and estimate the parameters of this model. We found an expectedly higher surface tension in mesenchymal spheroids, as well as a higher bulk modulus and relaxation time. The two latter parameters agree with the bulk poroelastic behavior of spheroids, and with the higher cell density and extracellular matrix content in mesenchymal spheroids. The higher tension of the surface layer cells in mesenchymal cell spheroids was also confirmed by the viscoelastic AFM characterization. The cell phenotype affected the self-organization during the spheroid formation, as well as the structure, biomechanical properties, and spreading of spheroids. The obtained results will contribute to a more detailed description of spheroid and tissue biomechanics, and will help in controlling the tissue regeneration and morphogenesis. STATEMENT OF SIGNIFICANCE: Spheroids are widely used as building blocks for scaffold-based and scaffold-free strategies in tissue engineering. In the majority of the past studies, either the concept of a solid body or a liquid with surface tension was used to describe the biomechanical behavior of spheroids. Here, we have used a model which combines both aspects, a solid body with surface tension. The "solid" aspect was described as a visco-poroelastic material, affected by the liquid redistribution through the cells and ECM at the scale of the whole spheroid. A higher surface tension was found for mesenchymal spheroids than that for epithelial spheroids, observed as a higher stiffness of the spheroid surface, as well as a larger spontaneous opening of the cut edges after microdissection.

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.

Elastic moduli of normal and cancer cell membranes revealed by molecular dynamics simulations

Recent studies indicate that there are mechanical differences between normal cells and cancer cells. Because the cell membrane takes part in a variety of vital processes, we test the hypothesis of whether or not two fundamental alterations in the cell membrane, i.e., the overexpression of phosphatidylserine lipids in the outer leaflet and a reduction in cholesterol concentration, could cause the softening in cancer cells. Adopting ten models of normal and cancer cell membranes, we carry out 1 μs all-atom molecular dynamics simulations to compare the structural properties and elasticity properties of two membrane types. We find that the overexpression of the phosphatidylserine lipids in the outer leaflet does not significantly alter the area per lipid, the membrane thickness, the lipid order parameters and the elasticity moduli of the cancer membranes. However, a reduction in the cholesterol concentration leads to clear changes in those quantities, especially decreases in the bending, tilt and twist moduli. This implies that the reduction of cholesterol concentration in the cancer membranes could contribute to the softening of cancer cells.

Is It Possible to Directly Determine the Radius of a Spherical Indenter Using Force Indentation Data on Soft Samples?

An important factor affecting the accuracy of Young's modulus calculation in Atomic Force Microscopy (AFM) indentation experiments is the determination of the dimensions of the indenter. This procedure is usually performed using AFM calibration gratings or Scanning Electron Microscopy (SEM) imaging. However, the aforementioned procedure is frequently omitted because it requires additional equipment. In this paper, a new approach is presented that focused on the calibration of spherical indenters without the need of special equipment but instead using force indentation data on soft samples. Firstly, the question whether it is mathematically possible to simultaneously calculate the indenter's radius and the Young's modulus of the tested sample (under the restriction that the sample presents a linear elastic response) using the same force indentation data is discussed. Using a simple mathematical approach, it was proved that the aforementioned procedure is theoretically valid. In addition, to test this method in real indentation experiments agarose gels were used. Multiple measurements on different agarose gels showed that the calibration of a spherical indenter is possible and can be accurately performed. Thus, the indenter's radius and the soft sample's Young's modulus can be determined using the same force indentation data. It is also important to note that the provided accuracy is similar to the accuracy obtained when using AFM calibration gratings. The major advantage of this paper is that it provides a method for the simultaneous determination of the indenter's radius and the sample's Young's modulus without requiring any additional equipment.

Discrimination between NSIP- and IPF-Derived Fibroblasts Based on Multi-Parameter Characterization of Their Growth, Morphology and Physic-Chemical Properties

Background: The aim of the research presented here was to find a set of parameters enabling discrimination between three types of fibroblasts, i.e., healthy ones and those derived from two disorders mimicking each other: idiopathic pulmonary fibrosis (IPF), and nonspecific interstitial pneumonia (NSIP). Methods: The morphology and growth of cells were traced using fluorescence microscopy and analyzed quantitatively using cell proliferation and substrate cytotoxicity indices. The viability of cells was recorded using MTS assays, and their stiffness was examined using atomic force microscopy (AFM) working in force spectroscopy (FS) mode. To enhance any possible difference in the examined parameters, experiments were performed with cells cultured on substrates of different elasticities. Moreover, the chemical composition of cells was determined using time-of-flight secondary ion mass spectrometry (ToF-SIMS), combined with sophisticated analytical tools, i.e., Multivariate Curve Resolution (MCR) and Principal Component Analysis (PCA). Results: The obtained results demonstrate that discrimination between cell lines derived from healthy and diseased patients is possible based on the analysis of the growth of cells, as well as their physical and chemical properties. In turn, the comparative analysis of the cellular response to altered stiffness of the substrates enables the identification of each cell line, including distinguishing between IPF- and NSIP-derived fibroblasts.

Endothelial glycocalyx detection and characterization by means of atomic force spectroscopy: Comparison of various data analysis approaches

In recent years, atomic force spectroscopy (AFS) has been used to detect and characterize the endothelial glycocalyx (eGlx) in in vitro and ex vivo experiments. Several analysis methods were proposed, which differ not only in the numerical implementations, but also in physical models of glycocalyx description. Therefore, it is difficult to directly relate the experiments performed by different groups. In this work, we compared different models used for quantitative analysis of atomic force spectroscopy datasets recorded for eGlx. To capture glycocalyx at various structural conditions, we used basic enzymatic protocols for glycocalyx removal and restoration in human aortal endothelial cells (HAEC). Nanoindentation experiments for this model system were performed for (i) untreated cells, (ii) for cells after heparinase incubation, which enzymatically removes glycocalyx, (iii) for cells with successive heparin treatment, which partially restores the glycocalyx layer. Analysis of nanoindentation data was performed using different models: (a) a single-layer contact mechanics, (b) a double-layer model contact mechanics, (c) a polymer "brush" two-layer model based on the Alexander - de Gennes theory and (d) a simple single-layer "mechanical spring" model. Although different physical parameters are evaluated in methods (a-d), we show that all approaches revealed similar qualitative changes of the glycocalyx layer, which reflected the processes of glycocalyx degradation and its partial restoration. This paper may facilitate a direct comparison of past and future glycocalyx oriented AFS experiments that are analysed with different approaches.

Auxeticity in biosystems: an exemplification of its effects on the mechanobiology of heterogeneous living cells

Auxeticity (negative Poisson's ratio) is the unique mechanical property found in an extensive variety of materials, such as metals, graphene, composites, polymers, foams, fibers, ceramics, zeolites, silicates and biological tissues. The enhanced mechanical features of the auxetic materials have motivated scientists to design, engineer and manufacture man-made auxetic materials to fully leverage their capabilities in different fields of research applications, including aeronautics, medical, protective equipments, smart sensors, filter cleaning, and so on. Atomic force microscopy (AFM) indentation is one of the most widely used methods for characterizing the mechanical properties and response of the living cells. In this contribution, we highlight main consequences of auxeticity for biosystems and provide a representative example to quantify the effect of nucleus auxeticity on the force response of the embryonic stem cells. A parametric study has been conducted on a heterogeneous stem cell to evaluate the effect of nucleus diameter, nucleus elasticity, indenter's shape and location on the force-indentation curve. The developed model has also been validated with the recently reported experimental studies available in the literature. Our results suggest that the nucleus auxeticity plays a profound role in cell mechanics especially for large size nucleus. We also report the mechanical stresses induced within the hyperelastic cell model under different loading conditions that would be quite useful in decoding the interrelations between mechanical stimuli and cellular behavior of auxetic biosystems. Finally, current and potential areas of applications of our findings for regenerative therapies, tissue engineering, 3 D/4D bioprinting, and the development of meta-biomaterials are discussed.

AFM Force Relaxation Curve Reveals That the Decrease of Membrane Tension Is the Essential Reason for the Softening of Cancer Cells

Differences in stiffness constitute an extremely important aspect of the mechanical differences between cancer cells and normal cells, and atomic force microscopy (AFM) is the most commonly used tool to characterize the difference in stiffness. However, the process of mechanical characterization using AFM has been controversial and the influence of the membrane tension on AFM measurement results was often ignored. Here, a physical model involving a simultaneous consideration of the effects of the cell membrane, cytoskeleton network and cytosol was proposed. We carried out a theoretical analysis of AFM force relaxation curves, and as a result solved many of the remaining controversial issues regarding AFM-based mechanical characterization of cells, and provided a quantitative solution for the membrane tension measured using AFM indentation experiments for the first time. From the results of experiments on cells with different adherent shapes and different pairs of normal cells and cancer cells, we found additional force provided by membrane tension to be the main component of the force applied to the AFM probe, with decreased cell membrane tension being the essential reason for the greater softness of cancer cells than of normal cells. Hence, regulating membrane tension may become an important method for regulating the behavior of cancer cells.

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.

In-Situ Investigation on Nanoscopic Biomechanics of Streptococcus mutans at Low pH Citric Acid Environments Using an AFM Fluid Cell

Streptococcus mutans (S. mutans) is widely regarded as the main cause of human dental caries via three main virulence factors: adhesion, acidogenicity, and aciduricity. Citric acid is one of the antibiotic agents that can inhibit the virulence capabilities of S. mutans. A full understanding of the acidic resistance mechanisms (ARMs) causing bacteria to thrive in citrate transport is still elusive. We propose atomic force microscopy (AFM) equipped with a fluid cell to study the S. mutans ARMs via surface nanomechanical properties at citric acid pH 3.3, 2.3, and 1.8. Among these treatments, at pH 1.8, the effect of the citric acid shock in cells is demonstrated through a significantly low number of high adhesion zones, and a noticeable reduction in adhesion forces. Consequently, this study paves the way to understand that S. mutans ARMs are associated with the variation of the number of adhesion zones on the cell surface, which is influenced by citrate and proton transport. The results are expected to be useful in developing antibiotics or drugs involving citric acid for dental plaque treatment.

A New Approach for the AFM-Based Mechanical Characterization of Biological Samples

The AFM nanoindentation technique is a powerful tool for the mechanical characterization of biological samples at the nanoscale. The data analysis of the experimentally obtained results is usually performed using the Hertzian contact mechanics. However, the aforementioned theory can be applied only in cases that the sample is homogeneous and isotropic and presents a linear elastic response. However, biological samples often present depth-dependent mechanical properties, and the Hertzian analysis cannot be used. Thus, in this paper, a different approach is presented, based on a new physical quantity used for the determination of the mechanical properties at the nanoscale. The aforementioned physical quantity is the work done by the indenter per unit volume. The advantages of the presented analysis are significant since the abovementioned magnitude can be used to examine if a sample can be approximated to an elastic half-space. If this approximation is valid, then the new proposed method enables the accurate calculation of Young's modulus. Additionally, it can be used to explore the mechanical properties of samples that are characterized by a depth-dependent mechanical behavior. In conclusion, the proposed analysis presents an accurate yet simple technique for the determination of the mechanical properties of biological samples at the nanoscale that can be also used beyond the Hertzian limit.

Cell spheroid fusion: beyond liquid drops model

Biological self-assembly is crucial in the processes of development, tissue regeneration, and maturation of bioprinted tissue-engineered constructions. The cell aggregates-spheroids-have become widely used model objects in the study of this phenomenon. Existing approaches describe the fusion of cell aggregates by analogy with the coalescence of liquid droplets and ignore the complex structural properties of spheroids. Here, we analyzed the fusion process in connection with structure and mechanical properties of the spheroids from human somatic cells of different phenotypes: mesenchymal stem cells from the limbal eye stroma and epithelial cells from retinal pigment epithelium. A nanoindentation protocol was applied for the mechanical measurements. We found a discrepancy with the liquid drop fusion model: the fusion was faster for spheroids from epithelial cells with lower apparent surface tension than for mesenchymal spheroids with higher surface tension. This discrepancy might be caused by biophysical processes such as extracellular matrix remodeling in the case of mesenchymal spheroids and different modes of cell migration. The obtained results will contribute to the development of more realistic models for spheroid fusion that would further provide a helpful tool for constructing cell aggregates with required properties both for fundamental studies and tissue reparation.

Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications

Fast, high-resolution, non-destructive and quantitative characterization methods are needed to develop materials with tailored properties at the nanoscale or to understand the relationship between mechanical properties and cell physiology. This review introduces the state-of-the-art force microscope-based methods to map at high-spatial resolution the elastic and viscoelastic properties of soft materials. The experimental methods are explained in terms of the theories that enable the transformation of observables into material properties. Several applications in materials science, molecular biology and mechanobiology illustrate the scope, impact and potential of nanomechanical mapping methods.

An AFM-Based Nanomechanical Study of Ovarian Tissues with Pathological Conditions

BACKGROUND

Different diseases affect both mechanical and chemical features of the involved tissue, enhancing the symptoms.

METHODS

In this study, using atomic force microscopy, we mechanically characterized human ovarian tissues with four distinct pathological conditions: mucinous, serous, and mature teratoma tumors, and non-tumorous endometriosis. Mechanical elasticity profiles were quantified and the resultant data were categorized using K-means clustering method, as well as fuzzy C-means, to evaluate elastic moduli of cellular and non-cellular parts of diseased tissues and compare them among four disease conditions. Samples were stained by hematoxylin-eosin staining to further study the content of different locations of tissues.

RESULTS

Pathological state vastly influenced the mechanical properties of the ovarian tissues. Significant alterations among elastic moduli of both cellular and non-cellular parts were observed. Mature teratoma tumors commonly composed of multiple cell types and heterogeneous ECM structure showed the widest range of elasticity profile and the stiffest average elastic modulus of 14 kPa. Samples of serous tumors were the softest tissues with elastic modulus of only 400 Pa for the cellular part and 5 kPa for the ECM. Tissues of other two diseases were closer in mechanical properties as mucinous tumors were insignificantly stiffer than endometriosis in cellular part, 1300 Pa compared to 1000 Pa, with the ECM average elastic modulus of 8 kPa for both.

CONCLUSION

The higher incidence of carcinoma out of teratoma and serous tumors may be related to the intense alteration of mechanical features of the cellular and the ECM, serving as a potential risk factor which necessitates further investigation.

Finite Element Analysis of the Nanomechanics of Hard Coatings on a Soft Polymer Substrate by a Spherical Indenter

Composite has been widely used in various fields due to its advanced performance. To reveal the relation between the mechanical properties of the composite and that of each individual component, finite element analysis (FEA) has usually been adopted. In this study, in order to predict the mechanical properties of hard coating on a soft polymer, the response of this coating system during nanoindentation was modelled. Various models, such as a viscoelastic model and fitting model, were adopted to analyse the indentation response of this coating system. By varying the substrate properties (i.e., Young’s modulus, viscoelasticity, and Poisson’s ratio), Young’s modulus, energy loss, and the viscoelastic model of the coating system were analysed, and how the mechanical properties of the substrate will affect the indentation response of the coating system was discussed.

A platform for light-controlled formation of free-stranding lipid membranes

The engineering of artificial cells is one of the most significant scientific challenges. Thus, controlled fabrication and in situ monitoring of biomimetic nanoscale objects are among the central issues in current science and technology. Studies of transmembrane channels and cell mechanics often require the formation of lipid bilayers (LBs), their modification and their transfer to a particular place. We present here a novel approach for remotely controlled manipulation of LBs. Layer-by-layer deposition of polyethyleneimine and poly(sodium 4-styrenesulfonate) on a nanostructured TiO 2 photoanode was performed to obtain a surface with the desired net charge and to enhance photocatalytic performance. The LB was deposited on top of a multi-layer positive polymer cushion by the dispersion of negative vesicles. The separation distance between the electrostatically linked polyelectrolyte cushion and the LB can be adjusted by changing the environmental pH, as zwitter-ionic lipid molecules undergo pH-triggered charge-shifting. Protons were generated remotely by photoanodic water decomposition on the TiO 2 surface under 365 nm illumination. The resulting pH gradient was characterized by scanning vibrating electrode and scanning ion-selective electrode techniques. The light-induced reversible detachment of the LB from the polymer-cushioned photoactive substrate was found to correlate with suggested impedance models.

Discovery and design of soft polymeric bio-inspired materials with multiscale simulations and artificial intelligence

Establishing the “Materials 4.0” paradigm requires intimate knowledge of the virtual space in materials design.

Quantitative mechanical analysis of indentations on layered, soft elastic materials

Atomic force microscopy (AFM) is becoming an increasingly popular method for studying cell mechanics, however the existing analysis tools for determining the elastic modulus from indentation experiments are unable to quantitatively account for mechanical heterogeneity commonly found in biological samples. In this work, we numerically calculated force-indentation curves onto two-layered elastic materials using an analytic model. We found that the effect of the underlying substrate can be quantitatively predicted by the mismatch in elastic moduli and the homogeneous-case contact radius relative to the layer height for all tested probe geometries. The effect is analogous to one-dimensional Hookean springs in series and was phenomenologically modeled to obtain an approximate closed-form equation for the indentation force onto a two-layered elastic material which is accurate for up to two orders of magnitude mismatch in Young's modulus when the contact radius is less than the layer height. We performed finite element analysis simulations to verify the model and AFM microindentation experiments and macroindentation experiments to demonstrate its ability to deconvolute the Young's modulus of each layer. The model can be broadly used to quantify and serve as a guideline for designing and interpreting indentation experiments into mechanically heterogeneous samples.

Electrochemical triggering of lipid bilayer lift-off oscillation at the electrode interface

In situ studies of transmembrane channels often require a model bioinspired artificial lipid bilayer (LB) decoupled from its underlaying support. Obtaining free-standing lipid membranes is still a challenge. In this study, we suggest an electrochemical approach for LB separation from its solid support via hydroquinone oxidation. Layer-by-layer deposition of polyethylenimine (PEI) and polystyrene sulfonate (PSS) on the gold electrode was performed to obtain a polymeric nanocushion of [PEI/PSS]3/PEI. The LB was deposited on top of an underlaying polymer support from the dispersion of small unilamellar vesicles due to their electrostatic attraction to the polymer support. Since lipid zwitterions demonstrate pH-dependent charge shifting, the separation distance between the polyelectrolyte support and LB can be adjusted by changing the environmental pH, leading to lipid molecules recharge. The proton generation associated with hydroquinone oxidation was studied using scanning vibrating electrode and scanning ion-selective electrode techniques. Electrochemical impedance spectroscopy is suggested to be a powerful instrument for the in situ observation of processes associated with the LB-solid support interface. Electrochemical spectroscopy highlighted the reversible disappearance of the LB impact on impedance in acidic conditions set by dilute acid addition as well as by electrochemical proton release on the gold electrode due to hydroquinone oxidation.

Modeling the mechanosensitivity of fast-crawling cells on cyclically stretched substrates

The mechanosensitivity of cells, which determines how they are able to respond to mechanical signals, is crucial for the functioning of biological systems. Experimentally, this is investigated by studying the reorientation of cells on cyclically stretched substrates. The reorientation depends on the type of cell and on the stretching protocol, but the mechanisms responsible for the response are still not completely understood. Here, we introduce a computational model for fast crawling cells on cyclically stretched substrates that accounts for the sub-cellular elements responsible for cell shape and motility. This includes the dynamics of the cell membrane, the actin cytoskeleton, and the focal adhesions with the stretching substrate. These processes evolve over characteristic time scales that can vary by orders of magnitude and naturally give rise to the frequency dependent reorientation observed experimentally. Depending on which processes are being probed by the stretching and on the type of coupling with the substrate, our simulations predict either no reorientation, a bi-stability in the parallel and perpendicular directions, or a complete reorientation in either the parallel or perpendicular direction. In particular, we show that an asymmetry in the adhesion dynamics during the loading and unloading phases of the stretching, whether it comes from the response of the cell itself or from the precise stretching protocol, can be used to selectively align the cells. Our results provide further evidence for the importance of focal adhesion dynamics in determining the mechanosensitive response of cells, as well as a way to interpret recent experiments.