Nanorheology of living cells measured by AFM-based force-distance curves

Protocol for measuring the Young's modulus of organoids using atomic force microscopy

Atomic force microscopy (AFM) is extensively applied to measure cell and tissue mechanics but lacks a standardized organoid stiffness assessment. Here, we present a protocol for quantifying the Young's modulus of organoids via AFM, combining force-curve analysis with an optimized probe. We describe steps for preparing organoids, OCT embedding, slicing, AFM detection, and force-curve analysis. By mechanically addressing gaps in organoids, this protocol improves reproducibility and expands the capabilities of biomechanical research.

Adhesive Force Between Biconcave Red Blood Cell Membrane and Bulk Substrate

Adhesion between a red blood cell and substrates is essential to many biophysical processes and has significant implications for medical applications. This study derived a theoretical formula for the adhesive force between a red blood cell and a bulk substrate, incorporating the Hamaker constant to account for van der Waals interactions. The derivation is based on a biconcave shape of an RBC, described by the well-known Ouyang-Helfrich equation and its analytical solution developed by Ouyang. The theoretical predictions align with experimental observations and the empirical spherical model, revealing a F∝D-2.5 relationship for biconcave RBCs versus F∝D-2 for spheres. While the current study focuses on idealized geometries and static conditions, future work will extend these findings to more complex environmental conditions, such as dynamic flow and interactions with plasma proteins, thereby broadening the applicability of the model. This work bridges foundational research in cell membrane mechanics with practical applications in hemostatic materials, platelet adhesion, and biomaterials engineering. The findings provide insights for designing advanced biological sensors, surgical tools, and innovative medical materials with enhanced biocompatibility and performance.

Poroelastic and viscoelastic properties of soft materials determined from AFM force relaxation and force-distance curves

In the field of tissue engineering, determining the mechanical properties of hydrogels is a key prerequisite to develop biomaterials mimicking the properties of the extracellular matrix. In mechanobiology, understanding the relationships between the mechanical properties and physiological state of cells is also essential. Time-dependent mechanical characterization of these soft materials is commonly achieved by atomic force microscopy (AFM) experiments in liquid environment. However, the determination of an appropriate model to correctly interpret the experimental data is often missing, making it difficult to extract quantitative mechanical properties. Here, force relaxation and force-distance curves were combined to elucidate the origin of dissipative processes involved in hydrogels and cells, before applying the relevant poroelastic or viscoelastic theory to model the curves. By using spherical AFM tips, analytical equations were developed to transform these curves into mechanical parameters by describing the relationships between the exerted force and the elastic, poroelastic or viscoelastic responses of semi-infinite and finite-thickness materials. Poroelastic behavior was evidenced for a thermoresponsive hydrogel and a set of poroelastic parameters was extracted from the force relaxation curves. In contrast, cells exhibited viscoelastic properties characterized by a single power-law relaxation over three-decade time scales. In addition, compressive modulus and fluidity exponent of cells were obtained by fitting force relaxation curves and approach-retraction force-distance curves. This combined theoretical and experimental framework opens a rigorous way toward quantitative mechanical properties of soft materials by (1) systematically determining the origin of their relaxation mechanisms, (2) defining the theoretical models to correctly interpret the experimental data, (3) using analytically solved equations to extract the mechanical parameters.

Biomechanical Insights into the Proteomic Profiling of Cells in Response to Red Light Absorption

Photobiomodulation (PBM) is a promising non-invasive therapy for tissue repair, but its underlying cellular mechanisms are not fully understood. In this study, the biomechanical and proteomic responses of three cell types - keratinocytes (HACAT), fibroblasts (L929), and osteoblasts (OFCOLII) - exposed to red light (633 nm) are investigated using atomic force microscopy (AFM) and mass spectrometry-based proteomic analysis. Red light absorption resulted in cell-type-specific changes in viscoelastic properties, with fibroblasts exhibiting increased fluidity, reduced stiffness, and enhanced motility. Conversely, keratinocytes exhibited intensity-dependent responses, while osteoblasts appeared to be relatively insensitive to irradiation conditions. Proteomic profiling identified key signaling pathways involved in immune response, ATP production, and stress regulation. The immune and ATP pathways are strongly linked to the modulation of viscoelastic properties, particularly in fibroblasts, while weaker correlations were observed in keratinocytes. Cytoskeletal remodeling, primarily within the F-actin network, is identified as the main driver of mechanical alterations, with additional contributions from microtubules and intermediate filaments. These findings provide new insights into how red light absorption modulates cellular viscoelasticity through cytoskeletal remodeling, with potential applications in optimizing light-based therapies for tissue regeneration and disease treatment.

Local Stiffness Measurement of Hepatic Steatosis Model Liver Organoid by Fluorescence Imaging-Assisted Probe Indentation

Mechanical stiffness of liver organoid is a key indicator for the progress of hepatic steatosis. Probe indentation is a noninvasive methodology to measure Young's modulus (YM); however, the inhomogeneous nature of the liver organoid induces measurement uncertainty requiring a large number of indentations covering a wide scanning area. Here, we demonstrate that lipid-stained fluorescence imaging-assisted probe indentation significantly reduces the number of measurements by specifying the highly lipid-induced area. Lipid-stained hepatic steatosis model liver organoid shows broad fluorescence distributions that are spatially correlated with a decreased YM on a lipid-filled region with bright fluorescence compared with that measured on a blank region with dark fluorescence. The organoid viability remained robust even after exposure to an ambient condition up to 6 h, showing that probe indentations can be noninvasive methods for liver organoid stiffness measurements.

Soft glassy rheology of single cells with pathogenic protein aggregates

A correlation between the mechanical properties of cells and various diseases has been emerging in recent years. Atomic force microscopy (AFM) has been widely used to measure a single cell's apparent Young's modulus by treating it as a fully elastic object. More recently, quantitative characterization of the complete viscoelasticity of single cells has become possible. We performed AFM-based nano-indentation experiments on hemocytes isolated from third instar larvae to determine their viscoelasticity and found that live hemocytes, like many other cells, follow a scale-free power-law rheology (PLR) akin to soft glasses. Further, we examined the changes in the rheological response of hemocytes in the presence of pathogenic protein aggregates known to cause neurodegenerative diseases such as Huntington's disorder and amyotrophic lateral sclerosis. Our results show that cells lose their fluidity and appear more solid-like in the presence of certain aggregates, in a manner correlated to actin reorganization. More solid-like cells also display reduced intracellular transport through clathrin-mediated endocytosis (CME). However, the cell's rheology remains largely unaffected and is similar to that of wild-type (WT) hemocytes, if aggregates do not perturb the actin organization and CME. Moreover, the fluid-like nature was significantly recovered when actin organization was rescued by overexpressing specific actin interacting proteins or chaperones. Our study, for the first time, underscores a direct correlation between parameters governing glassy dynamics, actin organization and CME.

PyFMLab: Open-source software for atomic force microscopy microrheology data analysis

Background

Atomic force microscopy (AFM) is one of the main techniques used to characterize the mechanical properties of soft biological samples and biomaterials at the nanoscale. Despite efforts made by the AFM community to promote open-source data analysis tools, standardization continues to be a significant concern in a field that requires common analysis procedures. AFM-based mechanical measurements involve applying a controlled force to the sample and measure the resulting deformation in the so-called force-distance curves. These may include simple approach and retract or oscillatory cycles at various frequencies (microrheology). To extract quantitative parameters, such as the elastic modulus, from these measurements, AFM measurements are processed using data analysis software. Although open tools exist and allow obtaining the mechanical properties of the sample, most of them only include standard elastic models and do not allow the processing of microrheology data. In this work, we have developed an open-source software package (called PyFMLab, as of python force microscopy laboratory) capable of determining the viscoelastic properties of samples from both conventional force-distance curves and microrheology measurements.

Methods

PyFMLab has been written in Python, which provides an accessible syntax and sufficient computational efficiency. The software features were divided into separate, self-contained libraries to enhance code organization and modularity and to improve readability, maintainability, testability, and reusability. To validate PyFMLab, two AFM datasets, one composed of simple force curves and another including oscillatory measurements, were collected on HeLa cells.

Results

The viscoelastic parameters obtained on the two datasets analysed using PyFMLab were validated against data processing proprietary software and against validated MATLAB routines developed before obtaining equivalent results.

Conclusions

Its open-source nature and versatility makes PyFMLab an open-source solution that paves the way for standardized viscoelastic characterization of biological samples from both force-distance curves and microrheology measurements.

Unveiling the role of hydroxyapatite and hydroxyapatite/silver composite in osteoblast-like cell mineralization: An exploration through their viscoelastic properties

Mechanical properties are becoming fundamental for advancing the comprehension of cellular processes. This study addresses the relationship between viscoelastic properties and the cellular mineralization process. Osteoblast-like cells treated with an osteogenic medium were employed for this purpose. Additionally, the study explores the impact of hydroxyapatite (HA) and hydroxyapatite/silver (HA/Ag) composite on this process. AFM relaxation experiments were conducted to extract viscoelastic parameters using the Fractional Zener (FZ) and Fractional Kelvin (FK) models. Our findings revealed that the main phases of mineralization are associated with alterations in the viscoelastic properties of osteoblast-like cells. Furthermore, HA and HA/Ag treatments significantly influenced changes in the viscoelastic properties of these cells. In particular, the HA/Ag treatment demonstrated a marked enhancement in cell fluidity, suggesting a possible role of silver in accelerating the mineralization process. Moreover, the study underscores the independence observed between fluidity and stiffness, indicating that modifications in one parameter may not necessarily correspond to changes in the other. These findings shed light on the factors involved in the cellular mineralization process and emphasize the importance of using viscoelastic properties to discern the impact of treatments on cells.

Critical review of single-cell mechanotyping approaches for biomedical applications

Accurate mechanical measurements of cells has the potential to improve diagnostics, therapeutics and advance understanding of disease mechanisms, where high-resolution mechanical information can be measured by deforming individual cells. Here we evaluate recently developed techniques for measuring cell-scale stiffness properties; while many such techniques have been developed, much of the work examining single-cell stiffness is impacted by difficulties in standardization and comparability, giving rise to large variations in reported mechanical moduli. We highlight the role of underlying mechanical theories driving this variability, and note opportunities to develop novel mechanotyping devices and theoretical models that facilitate convenient and accurate mechanical characterisation. Moreover, many high-throughput approaches are confounded by factors including cell size, surface friction, natural population heterogeneity and convolution of elastic and viscous contributions to cell deformability. We nevertheless identify key approaches based on deformability cytometry as a promising direction for further development, where both high-throughput and accurate single-cell resolutions can be realized.

Measuring the viscoelastic relaxation function of cells with a time-dependent interpretation of the Hertz-Sneddon indentation model

The Hertz-Sneddon elastic indentation model is widely adopted in the biomechanical investigation of living cells and other soft materials using atomic force microscopy despite the explicit viscoelastic nature of these materials. In this work, we demonstrate that an exact analytical viscoelastic force model for power-law materials, can be interpreted as a time-dependent Hertz-Sneddon-like model. Characterizing fibroblasts (L929) and osteoblasts (OFCOLII) demonstrates the model's accuracy. Our results show that the difference between Young's modulus E Y obtained by fitting force curves with the Hertz-Sneddon model and the effective Young's modulus derived from the viscoelastic force model is less than 3%, even when cells are probed at large forces where nonlinear deformation effects become significant. We also propose a measurement protocol that involves probing samples at different indentation speeds and forces, enabling the construction of the average viscoelastic relaxation function of samples by conveniently fitting the force curves with the Hertz-Sneddon model.

Atomic Force Microscopy for the Study of Cell Mechanics in Pharmaceutics

Cell mechanics is gaining attraction in drug screening, but the applicable methods have not yet become part of the standardized norm. This review presents the current state of the art for atomic force microscopy, which is the most widely available method. The field is first motivated as a new way of tracking pharmaceutical effects, followed by a basic introduction targeted at pharmacists on how to measure cellular stiffness. The review then moves on to the current state of the knowledge in terms of experimental results and supplementary methods such as fluorescence microscopy that can give relevant additional information. Finally, rheological approaches as well as the theoretical interpretations are presented before ending on additional methods and outlooks.

An AFM-Based Model-Fitting-Free Viscoelasticity Characterization Method for Accurate Grading of Primary Prostate Tumor

Viscoelasticity is a crucial property of cells, which plays an important role in label-free cell characterization. This paper reports a model-fitting-free viscoelasticity calculation method, correcting the effects of frequency, surface adhesion and liquid resistance on AFM force-distance (FD) curves. As demonstrated by quantifying the viscosity and elastic modulus of PC-3 cells, this method shows high self-consistency and little dependence on experimental parameters such as loading frequency, and loading mode (Force-volume vs. PeakForce Tapping). The rapid calculating speed of less than 1ms per curve without the need for a model fitting process is another advantage. Furthermore, this method was utilized to characterize the viscoelastic properties of primary clinical prostate cells from 38 patients. The results demonstrate that the reported characterization method a comparable performance with the Gleason Score system in grading prostate cancer cells, This method achieves a high average accuracy of 97.6% in distinguishing low-risk prostate tumors (BPH and GS6) from higher-risk (GS7-GS10) prostate tumors and a high average accuracy of 93.3% in distinguishing BPH from prostate cancer.

Mechanical properties of human tumour tissues and their implications for cancer development

The mechanical properties of cells and tissues help determine their architecture, composition and function. Alterations to these properties are associated with many diseases, including cancer. Tensional, compressive, adhesive, elastic and viscous properties of individual cells and multicellular tissues are mostly regulated by reorganization of the actomyosin and microtubule cytoskeletons and extracellular glycocalyx, which in turn drive many pathophysiological processes, including cancer progression. This Review provides an in-depth collection of quantitative data on diverse mechanical properties of living human cancer cells and tissues. Additionally, the implications of mechanical property changes for cancer development are discussed. An increased knowledge of the mechanical properties of the tumour microenvironment, as collected using biomechanical approaches capable of multi-timescale and multiparametric analyses, will provide a better understanding of the complex mechanical determinants of cancer organization and progression. This information can lead to a further understanding of resistance mechanisms to chemotherapies and immunotherapies and the metastatic cascade.

Protocol for measuring mechanical properties of live cells using atomic force microscopy

Atomic force microscope (AFM) is a powerful and versatile tool to determine the physical properties of cells. The force-distance curves obtained from AFM experiments can be used to determine the stiffness and viscoelastic properties of cells. Here, we present a protocol for the determination of viscoelasticity from live cells such as Drosophila hemocytes or mouse embryonic stem cells using AFM. This protocol has potential application in determining the physical properties of cells in healthy and diseased conditions. For complete details on the use and execution of this protocol, please refer to Mote et al. (2020),1 and Singh et al. (2023).2.

Dynamically Mapping the Topography and Stiffness of the Leading Edge of Migrating Cells Using AFM in Fast-QI Mode

Cell migration profoundly influences cellular function, often resulting in adverse effects in various pathologies including cancer metastasis. Directly assessing and quantifying the nanoscale dynamics of living cell structure and mechanics has remained a challenge. At the forefront of cell movement, the flat actin modules─the lamellipodium and the lamellum─interact to propel cell migration. The lamellipodium extends from the lamellum and undergoes rapid changes within seconds, making measurement of its stiffness a persistent hurdle. In this study, we introduce the fast-quantitative imaging (fast-QI) mode, demonstrating its capability to simultaneously map both the lamellipodium and the lamellum with enhanced spatiotemporal resolution compared with the classic quantitative imaging (QI) mode. Specifically, our findings reveal nanoscale stiffness gradients in the lamellipodium at the leading edge, where it appears to be slightly thinner and significantly softer than the lamellum. Additionally, we illustrate the fast-QI mode's accuracy in generating maps of height and effective stiffness through a streamlined and efficient processing of force-distance curves. These results underscore the potential of the fast-QI mode for investigating the role of motile cell structures in mechanosensing.

Hybrid hydrogels support neural cell culture development under magnetic actuation at high frequency

The combination of hydrogels and magnetic nanoparticles, scarcely explored to date, offers a wide range of possibilities for innovative therapies. Herein, we have designed hybrid 3D matrices integrating natural polymers, such as collagen, chitosan (CHI) and hyaluronic acid (HA), to provide soft and flexible 3D networks mimicking the extracellular matrix of natural tissues, and iron oxide nanoparticles (IONPs) that deliver localized heat when exposed to an alternating magnetic field (AMF). First, colloidally stable nanoparticles with a hydrodynamic radius of ∼20 nm were synthesized and coated with either CHI (NPCHI) or HA (NPHA). Then, collagen hydrogels were homogeneously loaded with these coated-IONPs resulting in soft (E0 ∼ 2.6 kPa), biodegradable and magnetically responsive matrices. Polymer-coated IONPs in suspension preserved primary neural cell viability and neural differentiation even at the highest dose (0.1 mg Fe/mL), regardless of the coating, even boosting neuronal interconnectivity at lower doses. Magnetic hydrogels maintained high neural cell viability and sustained the formation of highly interconnected and differentiated neuronal networks. Interestingly, those hydrogels loaded with the highest dose of NPHA (0.25 mgFe/mg polymer) significantly impaired non-neuronal differentiation with respect to those with NPCHI. When evaluated under AMF, cell viability slightly diminished in comparison with control hydrogels magnetically stimulated, but not compared to their counterparts without stimulation. Neuronal differentiation under AMF was only affected on collagen hydrogels with the highest dose of NPHA, while non-neuronal differentiation regained control values. Taken together, NPCHI-loaded hydrogels displayed a superior performance, maybe benefited from their higher nanomechanical fluidity. STATEMENT OF SIGNIFICANCE: Hydrogels and magnetic nanoparticles are undoubtedly useful biomaterials for biomedical applications. Nonetheless, the combination of both has been scarcely explored to date. In this study, we have designed hybrid 3D matrices integrating both components as promising magnetically responsive platforms for neural therapeutics. The resulting collagen scaffolds were soft (E0 ∼ 2.6 kPa) and biodegradable hydrogels with capacity to respond to external magnetic stimuli. Primary neural cells proved to grow on these substrates, preserving high viability and neuronal differentiation percentages even under the application of a high-frequency alternating magnetic field. Importantly, those hydrogels loaded with chitosan-coated iron oxide nanoparticles displayed a superior performance, likely related to their higher nanomechanical fluidity.

Emergence of nanoscale viscoelasticity from single cancer cells to established tumors

Tumors are complex materials whose physical properties dictate growth and treatment outcomes. Recent evidence suggests time-dependent physical properties, such as viscoelasticity, are crucial, distinct mechanical regulators of cancer progression and malignancy, yet the genesis and consequences of tumor viscoelasticity are poorly understood. Here, using Wide-bandwidth AFM-based ViscoElastic Spectroscopy (WAVES) coupled with mathematical modeling, we probe the origins of tumor viscoelasticity. From single carcinoma cells to increasingly sized carcinoma spheroids to established tumors, we describe a stepwise evolution of dynamic mechanical properties that create a nanorheological signature of established tumors: increased stiffness, decreased rate-dependent stiffening, and reduced energy dissipation. We dissect this evolution of viscoelasticity by scale, and show established tumors use fluid-solid interactions as the dominant mechanism of mechanical energy dissipation as opposed to fluid-independent intrinsic viscoelasticity. Additionally, we demonstrate the energy dissipation mechanism in spheroids and established tumors is negatively correlated with the cellular density, and this relationship strongly depends on an intact actin cytoskeleton. These findings define an emergent and targetable signature of the physical tumor microenvironment, with potential for deeper understanding of tumor pathophysiology and treatment strategies.

Atomic Force Microscopy Applied to the Study of Tauopathies

Atomic force microscopy (AFM) is a scanning probe microscopy technique which has a physical principle, the measurement of interatomic forces between a very thin tip and the surface of a sample, allowing the obtaining of quantitative data at the nanoscale, contributing to the surface study and mechanical characterization. Due to its great versatility, AFM has been used to investigate the structural and nanomechanical properties of several inorganic and biological materials, including neurons affected by tauopathies. Tauopathies are neurodegenerative diseases featured by aggregation of phosphorylated tau protein inside neurons, leading to functional loss and progressive neurotoxicity. In the broad universe of neurodegenerative diseases, tauopathies comprise the most prevalent, with Alzheimer's disease as its main representative. This review highlights the use of AFM as a suitable research technique for the study of cellular damages in tauopathies, even in early stages, allowing elucidation of pathogenic mechanisms of these diseases.

Nanorheology and Nanoindentation Revealed a Softening and an Increased Viscous Fluidity of Adherent Mammalian Cells upon Increasing the Frequency

The nanomechanical response of a cell depends on the frequency at which the cell is probed. The components of the cell that contribute to this property and their interplay are not well understood. Here, two force microscopy methods are integrated to characterize the frequency and/or the velocity-dependent properties of living cells. It is shown on HeLa and fibroblasts, that cells soften and fluidize upon increasing the frequency or the velocity of the deformation. This property was independent of the type and values (25 or 1000 nm) of the deformation. At low frequencies (2-10 Hz) or velocities (1-10 µm s-1 ), the response is dominated by the mechanical properties of the cell surface. At higher frequencies (>10 Hz) or velocities (>10 µm s-1 ), the response is dominated by the hydrodynamic drag of the cytosol. Softening and fluidization does not seem to involve any structural remodeling. It reflects a redistribution of the applied stress between the solid and liquid-like elements of the cell as the frequency or the velocity is changed. The data indicates that the quasistatic mechanical properties of a cell featuring a cytoskeleton pathology might be mimicked by the response of a non-pathological cell which is probed at a high frequency.

Fluorescence lifetime Hong-Ou-Mandel sensing

Fluorescence Lifetime Imaging Microscopy in the time domain is typically performed by recording the arrival time of photons either by using electronic time tagging or a gated detector. As such the temporal resolution is limited by the performance of the electronics to 100's of picoseconds. Here, we demonstrate a fluorescence lifetime measurement technique based on photon-bunching statistics with a resolution that is only dependent on the duration of the reference photon or laser pulse, which can readily reach the 1-0.1 picosecond timescale. A range of fluorescent dyes having lifetimes spanning from 1.6 to 7 picoseconds have been here measured with only ~1 s measurement duration. We corroborate the effectiveness of the technique by measuring the Newtonian viscosity of glycerol/water mixtures by means of a molecular rotor having over an order of magnitude variability in lifetime, thus introducing a new method for contact-free nanorheology. Accessing fluorescence lifetime information at such high temporal resolution opens a doorway for a wide range of fluorescent markers to be adopted for studying yet unexplored fast biological processes, as well as fundamental interactions such as lifetime shortening in resonant plasmonic devices.

Atomic force microscopy-mediated mechanobiological profiling of complex human tissues

Tissue mechanobiology is an emerging field with the overarching goal of understanding the interplay between biophysical and biochemical responses affecting development, physiology, and disease. Changes in mechanical properties including stiffness and viscosity have been shown to describe how cells and tissues respond to mechanical cues and modify critical biological functions. To quantitatively characterize the mechanical properties of tissues at physiologically relevant conditions, atomic force microscopy (AFM) has emerged as a highly versatile biomechanical technology. In this review, we describe the fundamental principles of AFM, typical AFM modalities used for tissue mechanics, and commonly used elastic and viscoelastic contact mechanics models to characterize complex human tissues. Furthermore, we discuss the application of AFM-based mechanobiology to characterize the mechanical responses within complex human tissues to track their developmental, physiological/functional, and diseased states, including oral, hearing, and cancer-related tissues. Finally, we discuss the current outlook and challenges to further advance the field of tissue mechanobiology. Altogether, AFM-based tissue mechanobiology provides a mechanistic understanding of biological processes governing the unique functions of tissues.

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.

Insights in Cell Biomechanics through Atomic Force Microscopy

We review the advances obtained by using Atomic Force Microscopy (AFM)-based approaches in the field of cell/tissue mechanics and adhesion, comparing the solutions proposed and critically discussing them. AFM offers a wide range of detectable forces with a high force sensitivity, thus allowing a broad class of biological issues to be addressed. Furthermore, it allows for the accurate control of the probe position during the experiments, providing spatially resolved mechanical maps of the biological samples with subcellular resolution. Nowadays, mechanobiology is recognized as a subject of great relevance in biotechnological and biomedical fields. Focusing on the past decade, we discuss the intriguing issues of cellular mechanosensing, i.e., how cells sense and adapt to their mechanical environment. Next, we examine the relationship between cell mechanical properties and pathological states, focusing on cancer and neurodegenerative diseases. We show how AFM has contributed to the characterization of pathological mechanisms and discuss its role in the development of a new class of diagnostic tools that consider cell mechanics as new tumor biomarkers. Finally, we describe the unique ability of AFM to study cell adhesion, working quantitatively and at the single-cell level. Again, we relate cell adhesion experiments to the study of mechanisms directly or secondarily involved in pathologies.

Characterizing viscoelastic properties of human melanoma tissue using Prony series

Melanoma is the most invasive and deadly skin cancer, which causes most of the deaths from skin cancer. It has been demonstrated that the mechanical properties of tumor tissue are significantly altered. However, data about characterizing the mechanical properties of in vivo melanoma tissue are extremely scarce. In addition, the viscoelastic or viscous properties of melanoma tissue are rarely reported. In this study, we measured and quantitated the viscoelastic properties of human melanoma tissues based on the stress relaxation test, using the indentation-based mechanical analyzer that we developed previously. The melanoma tissues from eight patients of different ages (57–95), genders (male and female patients), races (White and Asian), and sites (nose, arm, shoulder, and chest) were excised and tested. The results showed that the elastic property (i.e., shear modulus) of melanoma tissue was elevated compared to normal tissue, while the viscous property (i.e., relaxation time) was reduced. Moreover, the tissue thickness had a significant impact on the viscoelastic properties, probably due to the amount of the adipose layer. Our findings provide new insights into the role of the viscous and elastic properties of melanoma cell mechanics, which may be implicated in the disease state and progression.

Methodologies and models for measuring viscoelastic properties of cancer cells: Towards a universal classification

Different methods and several physical models exist to study cell viscoelasticity with the atomic force microscope (AFM). In search of a robust mechanical classification of cells through AFM, in this work, viscoelastic parameters of the cancer cell lines MDA-MB-231, DU-145, and MG-63 are obtained using two methodologies; through force-distance and force-relaxation curves. Four mechanical models were applied to fit the curves. The results show that both methodologies agree qualitatively on the parameters that quantify elasticity but disagree on the parameters that account for energy dissipation. The Fractional Zener (FZ) model represents well the information given by the Solid Linear Standard and Generalized Maxwell models. The Fractional Kelvin (FK) model concentrates the viscoelastic information mainly in two parameters, which could be an advantage over the other models. Therefore, the FZ and FK models are proposed as the basis for the classification of cancer cells. However, more research using these models is needed to obtain a broader view of the meaning of each parameter and to be able to establish a relationship between the parameters and the cellular components.

Multi-Step Extracellular Matrix Remodelling and Stiffening in the Development of Idiopathic Pulmonary Fibrosis

The extracellular matrix (ECM) of the lung is a filamentous network composed mainly of collagens, elastin, and proteoglycans that provides structural and physical support to its populating cells. Proliferation, migration and overall behaviour of those cells is greatly determined by micromechanical queues provided by the ECM. Lung fibrosis displays an aberrant increased deposition of ECM which likely changes filament organization and stiffens the ECM, thus upregulating the profibrotic profile of pulmonary cells. We have previously used AFM to assess changes in the Young's Modulus (E) of the ECM in the lung. Here, we perform further ECM topographical, mechanical and viscoelastic analysis at the micro- and nano-scale throughout fibrosis development. Furthermore, we provide nanoscale correlations between topographical and elastic properties of the ECM fibres. Firstly, we identify a softening of the ECM after rats are instilled with media associated with recovery of mechanical homeostasis, which is hindered in bleomycin-instilled lungs. Moreover, we find opposite correlations between fibre stiffness and roughness in PBS- vs bleomycin-treated lung. Our findings suggest that changes in ECM nanoscale organization take place at different stages of fibrosis, with the potential to help identify pharmacological targets to hinder its progression.

Surface characterization of an ultra-soft contact lens material using an atomic force microscopy nanoindentation method

As new ultra-soft materials are being developed for medical devices and biomedical applications, the comprehensive characterization of their physical and mechanical properties is both critical and challenging. To characterize the very low surface modulus of the novel biomimetic lehfilcon A silicone hydrogel contact lens coated with a layer of a branched polymer brush structure, an improved atomic force microscopy (AFM) nanoindentation method has been applied. This technique allows for precise contact-point determination without the effects of viscous squeeze-out upon approaching the branched polymer. Additionally, it allows individual brush elements to be mechanically characterized in the absence of poroelastic effects. This was accomplished by selecting an AFM probe with a design (tip size, geometry, and spring constant) that was especially suited to measuring the properties of soft materials and biological samples. The enhanced sensitivity and accuracy of this method allows for the precise measurement of the very soft lehfilcon A material, which has an extremely low elastic modulus in the surface region (as low as 2 kPa) and extremely high elasticity (nearly 100%) in an aqueous environment. The surface-characterization results not only reveal the ultra-soft nature of the lehfilcon A lens surface but also demonstrate that the elastic modulus exhibits a 30 kPa/200 nm gradient with depth due to the disparity between the modulus of the branched polymer brushes and the SiHy substrate. This surface-characterization methodology may be applied to other ultra-soft materials and medical devices.

Studies of probe tip materials by atomic force microscopy: a review

As a tool that can test insulators' surface morphology and properties, the performance index of atomic force microscope (AFM) probes is the most critical factor in determining the resolution of microscopy, and the performance of probes varies in various modes and application requirements. This paper reviews the latest research results in metal, carbon nanotube, and colloidal probes and reviews their related methods and techniques, analyses the advantages and disadvantages of the improved probes compared with ordinary probes by comparing the differences in spatial resolution, sensitivity, imaging, and other performance aspects, and finally provides an outlook on the future development of AFM probes. This paper promotes the development of AFM probes in the direction of new probes and further promotes the broader and deeper application of scanning probe microscope (SPM).

Measuring biological materials mechanics with atomic force microscopy - Determination of viscoelastic cell properties from stress relaxation experiments

Cells are complex, viscoelastic bodies. Their mechanical properties are defined by the arrangement of semiflexible cytoskeletal fibers, their crosslinking, and the active remodeling of the cytoskeletal network. Atomic force microscopy (AFM) is an often-used technique for the study of cell mechanics, enabling time- and frequency-dependent measurements with nanometer resolution. Cells exhibit time-dependent deformation when stress is applied. In this work, we have investigated the stress relaxation of HeLa cells when subjected to a constant strain. We have varied the applied force (1, 2, 4, and 8 nN) and pause time (1, 10, and 60 s) to check for common assumptions for the use of models of linear viscoelasticity. Then, we have applied three models (standard linear solid, five element Maxwell, power law rheology) to study their suitability to fit the datasets. We show that the five element Maxwell model captures the stress relaxation response the best while still retaining a low number of free variables. This work serves as an introduction and guide when performing stress relaxation experiments on soft matter using AFM. RESEARCH HIGHLIGHTS: Cells exhibit linear viscoelastic properties when subjected to stress relaxation measurements at the studied different forces and times. The stress relaxation is best described by a five element Maxwell model. All three used models capture a softening and fluidization of cells when disrupting actin filaments.

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy

Dynamic atomic force microscopy (AFM) is a key platform that enables topological and nanomechanical characterization of novel materials. This is achieved by linking the nanoscale forces that exist between the AFM tip and the sample to specific mathematical functions through modeling. However, the main challenge in dynamic AFM is to quantify these nanoscale forces without the use of complex models that are routinely used to explain the physics of tip-sample interaction. Here, we make use of machine learning and data science to characterize tip-sample forces purely from experimental data with sub-microsecond resolution. Our machine learning approach is first trained on standard AFM models and then showcased experimentally on a polymer blend of polystyrene (PS) and low density polyethylene (LDPE) sample. Using this algorithm we probe the complex physics of tip-sample contact in polymers, estimate elasticity, and provide insight into energy dissipation during contact. Our study opens a new route in dynamic AFM characterization where machine learning can be combined with experimental methodologies to probe transient processes involved in phase transformation as well as complex chemical and biological phenomena in real-time.

Field-induced rheological characterization of nano/micro-scaled suspensions based on a multi-peak fitting method

Nano/micro-scaled suspensions used in damping systems, bulletproof materials and flexible machining regions are developing towards external energy field control and multi-type and multi-scale dispersed phase particles. However, the above-mentioned changes make the rheological properties of the fluid more complex, which cannot be characterized efficiently with high quality by traditional constitutive equations. In order to solve the above-mentioned problems, based on the multi-peak fitting characterization method of the Gaussian function, the field-induced rheological constitutive equation of a multi-scale particle suspension turbidity system (MRSTPF as an example) was established. Under the condition of shear distribution and external magnetic field affection, the rheological characteristic curves of the dispersion system were measured using an Antompa MCR301 rheometer. The Origin software was used to fit and characterize the above-mentioned rheological data. The results indicate that the method can effectively establish field-induced constitutive equations of different dispersed systems, and the fitting goodness evaluation parameters are above 95% (R-square) and 90% (adjusted R-square) respectively.

An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

Atomic force microscopy (AFM) is widely used for quantifying the mechanical properties of soft materials such as cells. AFM force-indentation curves are conventionally fitted with a Hertzian model to extract elastic properties. These properties solely are, however, insufficient to describe the mechanical properties of cells. Here, we expand the analysis capabilities to describe the viscoelastic behavior while using the same force-indentation curves. Our model gives an explicit relation of force and indentation and extracts physically meaningful mechanical parameters. We first validated the model on simulated force-indentation curves. Then, we applied the fitting model to the force-indentation curves of two hydrogels with different crosslinking mechanisms. Finally, we characterized HeLa cells in two cell cycle phases, interphase and mitosis, and showed that mitotic cells have a higher apparent elasticity and a lower apparent viscosity. Our study provides a simple method, which can be directly integrated into the standard AFM framework for extracting the viscoelastic properties of materials.

•

Simple mechanical model to describe viscoelastic properties of soft matter

•

A model fitted directly to force-indentation curves

•

Capturing the distinct nature of hydrogels crosslinked in different mechanisms

•

Comparing viscoelastic properties of cells in interphase and mitotic states

Atomic Force Microscopy for Tumor Research at Cell and Molecule Levels

Tumors have posed a serious threat to human life and health. Researchers can determine whether or not cells are cancerous, whether the cancer cells are invasive or metastatic, and what the effects of drugs are on cancer cells by the physical properties such as hardness, adhesion, and Young's modulus. The atomic force microscope (AFM) has emerged as a key important tool for biomechanics research on tumor cells due to its ability to image and collect force spectroscopy information of biological samples with nano-level spatial resolution and under near-physiological conditions. This article reviews the existing results of the study of cancer cells with AFM. The main foci are the operating principle of AFM and research advances in mechanical property measurement, ultra-microtopography, and molecular recognition of tumor cells, which allows us to outline what we do know it in a systematic way and to summarize and to discuss future directions.

Epithelial cells fluidize upon adhesion but display mechanical homeostasis in the adherent state

Atomic force microscopy is used to study the viscoelastic properties of epithelial cells in three different states. Force relaxation data are acquired from cells in suspension, adhered but single cells, and polarized cells in a confluent monolayer using different indenter geometries comprising flat bars, pyramidal cones, and spheres. We found that the fluidity of cells increased substantially from the suspended to the adherent state. Along this line, the prestress of suspended cells generated by cortical contractility is also greater than that of cells adhering to a surface. Polarized cells that are part of a confluent monolayer form an apical cap that is soft and fluid enough to respond rapidly to mechanical challenges from wounding, changes in the extracellular matrix, osmotic stress, and external deformation. In contrast to adherent cells, cells in the suspended state show a pronounced dependence of fluidity on the external areal strain. With increasing areal strain, the suspended cells become softer and more fluid. We interpret the results in terms of cytoskeletal remodeling that softens cells in the adherent state to facilitate adhesion and spreading by relieving internal active stress. However, once the cells spread on the surface they maintain their mechanical phenotype displaying viscoelastic homeostasis.

Biophysical Approaches for Applying and Measuring Biological Forces

Over the past decades, increasing evidence has indicated that mechanical loads can regulate the morphogenesis, proliferation, migration, and apoptosis of living cells. Investigations of how cells sense mechanical stimuli or the mechanotransduction mechanism is an active field of biomaterials and biophysics. Gaining a further understanding of mechanical regulation and depicting the mechanotransduction network inside cells require advanced experimental techniques and new theories. In this review, the fundamental principles of various experimental approaches that have been developed to characterize various types and magnitudes of forces experienced at the cellular and subcellular levels are summarized. The broad applications of these techniques are introduced with an emphasis on the difficulties in implementing these techniques in special biological systems. The advantages and disadvantages of each technique are discussed, which can guide readers to choose the most suitable technique for their questions. A perspective on future directions in this field is also provided. It is anticipated that technical advancement can be a driving force for the development of mechanobiology.

Viscoelastic parameterization of human skin cells characterize material behavior at multiple timescales

Countless biophysical studies have sought distinct markers in the cellular mechanical response that could be linked to morphogenesis, homeostasis, and disease. Here, an iterative-fitting methodology visualizes the time-dependent viscoelastic behavior of human skin cells under physiologically relevant conditions. Past investigations often involved parameterizing elastic relationships and assuming purely Hertzian contact mechanics, which fails to properly account for the rich temporal information available. We demonstrate the performance superiority of the proposed iterative viscoelastic characterization method over standard open-search approaches. Our viscoelastic measurements revealed that 2D adherent metastatic melanoma cells exhibit reduced elasticity compared to their normal counterparts—melanocytes and fibroblasts, and are significantly less viscous than fibroblasts over timescales spanning three orders of magnitude. The measured loss angle indicates clear differential viscoelastic responses across multiple timescales between the measured cells. This method provides insight into the complex viscoelastic behavior of metastatic melanoma cells relevant to better understanding cancer metastasis and aggression.

Parvini, Cartagena and Solares introduce an iterative viscoelastic approach based on the generalized Maxwell and Kelvin-Voigt models. The results showed that metastatic melanoma cells had lower elasticity than normal fibroblasts and melanoma cells were less viscous than the fibroblasts over a large frequency range, enhancing the understanding of cellular responses at different frequencies.

A Continuum-Tensegrity Computational Model for Chondrocyte Biomechanics in AFM Indentation and Micropipette Aspiration

Mechanical stimuli are fundamental in the development of organs and tissues, their growth, regeneration or disease. They influence the biochemical signals produced by the cells, and, consequently, the development and spreading of a disease. Moreover, tumour cells are usually characterized by a decrease in the cell mechanical properties that may be directly linked to their metastatic potential. Thus, recently, the experimental and computational study of cell biomechanics is facing a growing interest. Various experimental approaches have been implemented to describe the passive response of cells; however, cell variability and complex experimental procedures may affect the obtained mechanical properties. For this reason, in-silico computational models have been developed through the years, to overcome such limitations, while proposing valuable tools to understand cell mechanical behaviour. This being the case, we propose a combined continuous-tensegrity finite element (FE) model to analyse the mechanical response of a cell and its subcomponents, observing how every part contributes to the overall mechanical behaviour. We modelled both Atomic Force Microscopy (AFM) indentation and micropipette aspiration techniques, as common mechanical tests for cells and elucidated also the role of cell cytoplasm and cytoskeleton in the global cell mechanical response.

Viscoelastic properties of epithelial cells

Epithelial cells form tight barriers that line both the outer and inner surfaces of organs and cavities and therefore face diverse environmental challenges. The response to these challenges relies on the cells' dynamic viscoelastic properties, playing a pivotal role in many biological processes such as adhesion, growth, differentiation, and motility. Therefore, the cells usually adapt their viscoelastic properties to mirror the environment that determines their fate and vitality. Albeit not a high-throughput method, atomic force microscopy is still among the dominating methods to study the mechanical properties of adherent cells since it offers a broad range of forces from Piconewtons to Micronewtons at biologically significant time scales. Here, some recent work of deformation studies on epithelial cells is reviewed with a focus on viscoelastic models suitable to describe force cycle measurements congruent with the architecture of the actin cytoskeleton. The prominent role of the cortex in the cell's response to external forces is discussed also in the context of isolated cortex extracts on porous surfaces.

Viscoelasticity of basal plasma membranes and cortices derived from MDCK II cells

The mechanical properties of cells are largely determined by the architecture and dynamics of their viscoelastic cortex, which consists of a contractile, cross-linked actin mesh attached to the plasma membrane via linker proteins. Measuring the mechanical properties of adherent, polarized epithelial cells is usually limited to the upper, i.e., apical side, of the cells because of their accessibility on culture dishes. Therefore, less is known about the viscoelastic properties of basal membranes. Here, I investigate the viscoelastic properties of basolateral membranes derived from polarized MDCK II epithelia in response to external deformation and compare them to living cells probed at the apical side. MDCK II cells were grown on porous surfaces to confluence, and the upper cell body was removed via a squirting-lysis protocol. The free-standing, defoliated basal membranes were subject to force indentation and relaxation experiments permitting a precise assessment of cortical viscoelasticity. A new theoretical framework to describe the force cycles is developed and applied to obtain the time-dependent area compressibility modulus of cell cortices from adherent cells. Compared with the viscoelastic response of living cells, the basolateral membranes are substantially less fluid and stiffer but obey to the same universal scaling law if excess area is taken correctly into account.

The viscoelasticity of adherent cells follows a single power-law with distinct local variations within a single cell and across cell lines

AFM-based force-distance curves are commonly used to characterize the nanomechanical properties of live cells. The transformation of these curves into nanomechanical properties requires the development of contact mechanics models. Spatially-resolved force-distance curves involving 1 to 2 μm deformations were obtained on HeLa and NIH 3T3 (fibroblast) cells. An elastic and two viscoelastic models were used to describe the experimental force-distance curves. The best agreement was obtained by applying a contact mechanics model that accounts for the geometry of the contact and the finite-thickness of the cell and assumes a single power-law dependence with time. Our findings show the shortcomings of elastic and semi-infinite viscoelastic models to characterize the mechanical response of a mammalian cell under micrometer-scale deformations. The parameters of the 3D power-law viscoelastic model, compressive modulus and fluidity exponent showed local variations within a single cell and across the two cell lines. The corresponding nanomechanical maps revealed structures that were not visible in the AFM topographic maps.

Viscoelasticity and Noise Properties Reveal the Formation of Biomemory in Cells

Living cells are neither perfectly elastic nor liquid and return a viscoelastic response to external stimuli. Nanoindentation provides force–distance curves, allowing the investigation of cell mechanical properties, and yet, these curves can differ from point to point on the cell surface, revealing its inhomogeneous character. In the present work, we propose a mathematical method to estimate both viscoelastic and noise properties of cells as these are depicted on the values of the scaling exponents of relaxation function and power spectral density, respectively. The method uses as input the time derivative of the response force in a nanoindentation experiment. Generalized moments method and/or rescaled range analysis is used to study the resulting time series depending on their nonstationary or stationary nature. We conducted experiments in living Ulocladium chartarum spores. We found that spores in the approaching phase present a viscoelastic behavior with the corresponding scaling exponent in the range 0.25–0.52 and in the retracting phase present a liquid-like behavior with exponents in the range 0.67–0.85. This substantial difference of the scaling exponents in the two phases suggests the formation of biomemory as a response of the spores to the indenting AFM mechanical stimulus. The retracting phase may be described as a process driven by bluish noises, while the approaching one is driven by persistent noise.

A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques

Viscoelastic characterization of materials at the micro- and the nanoscale is commonly performed with the aid of force-distance relationships acquired using atomic force microscopy (AFM). The general strategy for existing methods is to fit the observed material behavior to specific viscoelastic models, such as generalized viscoelastic models or power-law rheology models, among others. Here we propose a new method to invert and obtain the viscoelastic properties of a material through the use of the Z-transform, without using a model. We present the rheological viscoelastic relations in their classical derivation and their z-domain correspondence. We illustrate the proposed technique on a model experiment involving a traditional ramp-shaped force-distance AFM curve, demonstrating good agreement between the viscoelastic characteristics extracted from the simulated experiment and the theoretical expectations. We also provide a path for calculating standard viscoelastic responses from the extracted material characteristics. The new technique based on the Z-transform is complementary to previous model-based viscoelastic analyses and can be advantageous with respect to Fourier techniques due to its generality. Additionally, it can handle the unbounded inputs traditionally used to acquire force-distance relationships in AFM, such as ramp functions, in which the cantilever position is displaced linearly with time for a finite period of time.

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.

Effect of trypsin concentration on living SMCC-7721 cells studied by atomic force microscopy

Trypsin is playing an important role in the processes of cancer proliferation, invasion and metastasis which require the precise information of morphology and mechanical properties on the nano-scale for the related research. In this work, living human hepatoma (SMCC-7721) cells were treated with different concentrations of trypsin solution. The morphology and mechanical properties of the cells were measured via atomic force microscope (AFM). Statistical analyses of measurement data indicated that with the increase of trypsin concentration, the average cell height and the surface roughness were both increased, but the cell viability, the cell surface adhesion and the elasticity modulus were decreased significantly. The force required to puncture the cells was also gradually reduced. It indicates that trypsin not only hydrolyses the proteins between the cell and the substrate but also the membrane proteins. The results offer valuable clues for the cancerous process study, pathological analysis and trypsin inhibitor drug development. And this work provides an effective way for overcoming the cell membrane in drug injection for cell-targeted therapy.

Quantitative Nanomechanical Mapping of Polyolefin Elastomer at Nanoscale with Atomic Force Microscopy

Elastomeric nanostructures are normally expected to fulfill an explicit mechanical role and therefore their mechanical properties are pivotal to affect material performance. Their versatile applications demand a thorough understanding of the mechanical properties. In particular, the time dependent mechanical response of low-density polyolefin (LDPE) has not been fully elucidated. Here, utilizing state-of-the-art PeakForce quantitative nanomechanical mapping jointly with force volume and fast force volume, the elastic moduli of LDPE samples were assessed in a time-dependent fashion. Specifically, the acquisition frequency was discretely changed four orders of magnitude from 0.1 up to 2 k Hz. Force data were fitted with a linearized DMT contact mechanics model considering surface adhesion force. Increased Young's modulus was discovered with increasing acquisition frequency. It was measured 11.7 ± 5.2 MPa at 0.1 Hz and increased to 89.6 ± 17.3 MPa at 2 kHz. Moreover, creep compliance experiment showed that instantaneous elastic modulus E₁, delayed elastic modulus E₂, viscosity η, retardation time τ were 22.3 ± 3.5 MPa, 43.3 ± 4.8 MPa, 38.7 ± 5.6 MPa s and 0.89 ± 0.22 s, respectively. The multiparametric, multifunctional local probing of mechanical measurement along with exceptional high spatial resolution imaging open new opportunities for quantitative nanomechanical mapping of soft polymers, and can potentially be extended to biological systems.

Measuring the elastic modulus of soft culture surfaces and three-dimensional hydrogels using atomic force microscopy

Growing interest in exploring mechanically mediated biological phenomena has resulted in cell culture substrates and 3D matrices with variable stiffnesses becoming standard tools in biology labs. However, correlating stiffness with biological outcomes and comparing results between research groups is hampered by variability in the methods used to determine Young's (elastic) modulus, E, and by the inaccessibility of relevant mechanical engineering protocols to most biology labs. Here, we describe a protocol for measuring E of soft 2D surfaces and 3D hydrogels using atomic force microscopy (AFM) force spectroscopy. We provide instructions for preparing hydrogels with and without encapsulated live cells, and provide a method for mounting samples within the AFM. We also provide details on how to calibrate the instrument, and give step-by-step instructions for collecting force-displacement curves in both manual and automatic modes (stiffness mapping). We then provide details on how to apply either the Hertz or the Oliver-Pharr model to calculate E, and give additional instructions to aid the user in plotting data distributions and carrying out statistical analyses. We also provide instructions for inferring differential matrix remodeling activity in hydrogels containing encapsulated single cells or organoids. Our protocol is suitable for probing a range of synthetic and naturally derived polymeric hydrogels such as polyethylene glycol, polyacrylamide, hyaluronic acid, collagen, or Matrigel. Although sample preparation timings will vary, a user with introductory training to AFM will be able to use this protocol to characterize the mechanical properties of two to six soft surfaces or 3D hydrogels in a single day.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

Clustering of Major Histocompatibility Complex-Class I Molecules in Healthy and Cancer Colon Cells Revealed from Their Nanomechanical Properties

The activation of the T cell mediated immune response relies on the fine interaction between the T cell receptor on the immune cell and the antigen-presenting major histocompatibility complex (MHC) molecules on the membrane surface of antigen-presenting cells. Both the distribution and quantity of MHC/peptide complexes and their adequate morphological presentation affect the activation of the immune cells. In several types of cancer the immune response is down-regulated due to the low expression of MHC-class I (MHC-I) molecules on the cell's surface, and in addition, the mechanical properties of the membrane seem to play a role. Herein, we investigate the distribution of MHC-I molecules and the related nanoscale mechanical environment on the cell surface of two cell lines derived from colon adenocarcinoma and a healthy epithelial colon reference cell line. Atomic force microscopy (AFM) force spectroscopy analysis using an antibody-tagged pyramidal probe specific for MHC-I molecules and a formula that relates the elasticity of the cell to the energy of adhesion revealed the different population distributions of MHC-I molecules in healthy cells compared to cancer cells. We found that MHC-I molecules are significantly less expressed in cancer cells. Moreover, the local elastic modulus is significantly reduced in cancer cells. We speculate that these results might be related to the proven ability of cancer cells to evade the immune system, not only by reducing MHC-I cell surface expression but also by modifying the local mechanical properties affecting the overall morphology of MHC-I synapse presentation to immune cells.