The Hertzian theory in AFM nanoindentation experiments regarding biological samples: Overcoming limitations in data processing

Mechanomemory of nucleoplasm and RNA polymerase II after chromatin stretching by a microinjected magnetic nanoparticle force

Increasing evidence suggests that the mechanics of chromatin and nucleoplasm regulate gene transcription and nuclear function. However, how the chromatin and nucleoplasm sense and respond to forces remains elusive. Here, we employed a strategy of applying forces directly to the chromatin of a cell via a microinjected 200-nm anti-H2B-antibody-coated ferromagnetic nanoparticle (FMNP) and an anti-immunoglobulin G (IgG)-antibody-coated or an uncoated FMNP. The chromatin behaved as a viscoelastic gel-like structure and the nucleoplasm was a softer viscoelastic structure at loading frequencies of 0.1-5 Hz. Protein diffusivity of the chromatin, nucleoplasm, and RNA polymerase II (RNA Pol II) and RNA Pol II activity were upregulated in a chromatin-stretching-dependent manner and stayed upregulated for tens of minutes after force cessation. Chromatin stiffness increased, but the mechanomemory duration of chromatin diffusivity decreased, with substrate stiffness. These findings may provide a mechanomemory mechanism of transcription upregulation and have implications on cell and nuclear functions.

Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young's modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young's modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

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.

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.

Thickness Gradient in Polymer Coating by Reactive Layer-by-Layer Assembly on Solid Substrate

The study describes a simple yet robust methodology for forming gradients in polymer coatings with nanometer-thickness precision. The thickness gradients of 0-20 nm in the coating are obtained by a reactive layer-by-layer assembly of polyester and polyethylenimine on gold substrates. Three parameters are important in forming thickness gradients: (i) the incubation time, (ii) the incubation concentration of the polymer solutions, and (iii) the tilt angle of the gold substrate during the dipping process. After examining these parameters, the characterization of the anisotropic surface obtained under the best conditions is presented in the manuscript. The thickness profile and nanomechanical characterization of the polymer gradients are characterized by atomic force microscopy. The roughness analysis has demonstrated that the coating exhibited decreasing roughness with increasing thickness. On the other hand, Young's moduli of the thin and thick coatings are 0.50 and 1.4 MPa, respectively, which assured an increase in mechanical stability with increasing coating thickness. Angle-dependent infrared spectroscopy reveals that the C-O-C ester groups of the polyesters exhibit a perpendicular orientation to the surface, while the C≡C groups are parallel to the surface. The surface properties of the polymer gradients are explored by fluorescence microscopy, proving that the dye's fluorescence intensity increases as the coating thickness increases. The significant benefit of the suggested methodology is that it promises thickness control of gradients in the coating as a consequence of the fast reaction kinetics between layers and the reaction time.

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.

Extracellular vesicle-matrix interactions

The extracellular matrix in microenvironments harbors a variety of signals to control cellular functions and the materiality of tissues. Most efforts to synthetically reconstitute the matrix by biomaterial design have focused on decoupling cell-secreted and polymer-based cues. Cells package molecules into nanoscale lipid membrane-bound extracellular vesicles and secrete them. Thus, extracellular vesicles inherently interact with the meshwork of the extracellular matrix. In this Review, we discuss various aspects of extracellular vesicle-matrix interactions. Cells receive feedback from the extracellular matrix and leverage intracellular processes to control the biogenesis of extracellular vesicles. Once secreted, various biomolecular and biophysical factors determine whether extracellular vesicles are locally incorporated into the matrix or transported out of the matrix to be taken up by other cells or deposited into tissues at a distal location. These insights can be utilized to develop engineered biomaterials where EV release and retention can be precisely controlled in host tissue to elicit various biological and therapeutic outcomes.

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.

Hyperelastic characterization reveals proteoglycans drive the nanoscale strain-stiffening response in hyaline cartilage

Degenerative diseases such as osteoarthritis (OA) result in deterioration of cartilage extracellular matrix (ECM) components, significantly compromising tissue function. For measurement of mechanical properties at micron resolution, atomic force microscopy (AFM) is a leading technique in biomaterials research, including in the study of OA. It is common practice to determine material properties by applying classical Hertzian contact theory to AFM data. However, errors are consequential because the application of a linear elastic contact model to tissue ignores the fact that soft materials exhibit nonlinear properties even at small strains, influencing the biological conclusions of clinically-relevant studies. Additionally, nonlinear material properties are not well characterized, limiting physiological relevance of Young's modulus. Here, we probe the ECM of hyaline cartilage with AFM and explore the application of Hertzian theory in comparison to five hyperelastic models: NeoHookean, Mooney-Rivlin, Arruda-Boyce, Fung, and Ogden. The Fung and Ogden models achieved the best fits of the data, but the Fung model demonstrated robust sensitivity during model validation, demonstrating its ideal application to cartilage ECM and potentially other connective tissues. To develop a biological understanding of the Fung nonlinear parameter, we selectively degraded ECM components to target collagens (purified collagenase), hyaluronan (bacterial hyaluronidase), and glycosaminoglycans (chondroitinase ABC). We found significant differences in both Fung parameters in response to enzymatic treatment, indicating that proteoglycans drive the nonlinear response of cartilage ECM, and validating biological relevance of these phenomenological parameters. Our findings add value to the biomechanics community of using two-parameter material models for microindentation of soft biomaterials.