Load Rate and Temperature Dependent Mechanical Properties of the Cortical Neuron and Its Pericellular Layer Measured by Atomic Force Microscopy

The mechanical effects of chemical stimuli on neurospheres

The formulation of more accurate models to describe tissue mechanics necessitates the availability of tools and instruments that can precisely measure the mechanical response of tissues to physical loads and other stimuli. In this regard, neuroscience has trailed other life sciences owing to the unavailability of representative live tissue models and deficiency of experimentation tools. We previously addressed both challenges by employing a novel instrument called the cantilevered-capillary force apparatus (CCFA) to elucidate the mechanical properties of mouse neurospheres under compressive forces. The neurospheres were derived from murine stem cells, and our study was the first of its kind to investigate the viscoelasticity of living neural tissues in vitro. In the current study, we demonstrate the utility of the CCFA as a broadly applicable tool to evaluate tissue mechanics by quantifying the effect that oxidative stress has on the mechanical properties of neurospheres. We treated mouse neurospheres with non-cytotoxic levels of hydrogen peroxide and subsequently evaluated the storage and loss moduli of the tissues under compression and tension. We observed that the neurospheres exhibit viscoelasticity consistent with neural tissue and show that elastic modulus decreases with increasing size of the neurosphere. Our study yields insights for establishing rheological measurements as biomarkers by laying the groundwork for measurement techniques and showing that the influence of a particular treatment may be misinterpreted if the size dependence is ignored.

Mechanical Way To Study Molecular Structure of Pericellular Layer

Atomic force microscopy (AFM) has been used to study the mechanical properties of cells, in particular, malignant cells. Softening of various cancer cells compared to their nonmalignant counterparts has been reported for various cell types. However, in most AFM studies, the pericellular layer was ignored. As was shown, it could substantially change the measured cell rigidity and miss important information on the physical properties of the pericellular layer. Here we take into account the pericellular layer by using the brush model to do the AFM indentation study of bladder epithelial bladder nonmalignant (HCV29) and cancerous (TCCSUP) cells. It allows us to measure not only the quasistatic Young's modulus of the cell body but also the physical properties of the pericellular layer (the equilibrium length and grafting density). We found that the inner pericellular brush was longer for cancer cells, but its grafting density was similar to that found for nonmalignant cells. The outer brush was much shorter and less dense for cancer cells. Furthermore, we demonstrate a method to convert the obtained physical properties of the pericellular layer into biochemical language better known to the cell biology community. It is done by using heparinase I and neuraminidase enzymatic treatments that remove specific molecular parts of the pericellular layer. The presented here approach can also be used to decipher the molecular composition of not only pericellular but also other molecular layers.

Atomic force microscopy-based indentation of cells: modelling the effect of a pericellular coat

A simple analytical model is built up to account for the interface deformation effect in a spherical atomic force microscopy (AFM)-based quasi-static indentation of a living cell covered with a pericellular brush. The compression behaviour of the pericellular coat is described using the Alexander–de Gennes model that allows for nonlinear deformation. An approximate second-order relation between contact force and indenter displacement is obtained in implicit form, using the Hertzian solution as a first-order approximation. A method of fitting the indentation brush/cell model to experimental data is suggested based on the non-dimensionalized version of the displacement–force relation in the parametric form and illustrated with a specific example of AFM raw data taken from the literature.

Cell mechanics can be robustly derived from AFM indentation data using the brush model: error analysis

The brush model was introduced to interpret AFM indentation data collected on biological cells in a more consistent way compared just to the traditional Hertz model. It takes into account the presence of non-Hertzian deformation of the pericellular brush-like layer surrounding cells (a mix of glycocalyx molecules and microvilli/microridges). The model allows finding the effective Young's modulus of the cell body in a less depth-dependent manner. In addition, it allows finding the force due to the pericellular brush layer. Compared to simple mechanical models used to interpret the indentation experiments, the brush model has additional complexity. It raises the concern about the possible unambiguity of separation of mechanical properties of the cell body and pericellular layer. Here we present the analysis of the robustness of the brush model and demonstrate a weak dependence of the obtained results on the uncertainties within the model and experimental data. We critically analyzed the use of the brush model on a variety of AFM force curves collected on rather distinct cell types: human cervical epithelial cells, rat neurons, and zebrafish melanocytes. We conclude that the brush model is robust; the errors in the definition of the effective Young's modulus due to possible uncertainties of the model and experimental data are within 4%, which is less than the error, for example, due to a typical uncertainty in the spring constant of the AFM cantilever. We also discuss the errors of parameterization of the force due to the pericellular brush layer.

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.

Cortical cell stiffness is independent of substrate mechanics

Cortical stiffness is an important cellular property that changes during migration, adhesion and growth. Previous atomic force microscopy (AFM) indentation measurements of cells cultured on deformable substrates have suggested that cells adapt their stiffness to that of their surroundings. Here we show that the force applied by AFM to a cell results in a significant deformation of the underlying substrate if this substrate is softer than the cell. This 'soft substrate effect' leads to an underestimation of a cell's elastic modulus when analysing data using a standard Hertz model, as confirmed by finite element modelling and AFM measurements of calibrated polyacrylamide beads, microglial cells and fibroblasts. To account for this substrate deformation, we developed a 'composite cell-substrate model'. Correcting for the substrate indentation revealed that cortical cell stiffness is largely independent of substrate mechanics, which has major implications for our interpretation of many physiological and pathological processes.

Difference in biophysical properties of cancer-initiating cells in melanoma mutated zebrafish

Despite sharing oncogenetic mutations, only a small number of cells within a given tissue will undergo malignant transformation. Biochemical and physical factors responsible for this cancer-initiation process are not well understood. Here we study biophysical differences of pre-melanoma and melanoma cells in a BRAF^V600E/P53 zebrafish model. The AFM indentation technique was used to study the cancer-initiating cells while the surrounding melanocytes were the control. We observed a statistically significant decrease in the modulus of elasticity (the effective Young's modulus) of cancer-initiating cells compared to the surrounding melanocytes. No significant differences in the pericellular coat surrounding cells were observed. These results contribute to a better understanding of the factors responsible for the initiation of cancer.

Endothelial Glycocalyx Layer Properties and Its Ability to Limit Leukocyte Adhesion

The endothelial glycocalyx layer (EGL), which consists of long proteoglycans protruding from the endothelium, acts as a regulator of inflammation by preventing leukocyte engagement with adhesion molecules on the endothelial surface. The amount of resistance to adhesive events the EGL provides is the result of two properties: EGL thickness and stiffness. To determine these, we used an atomic force microscope to indent the surfaces of cultured endothelial cells with a glass bead and evaluated two different approaches for interpreting the resulting force-indentation curves. In one, we treat the EGL as a molecular brush, and in the other, we treat it as a thin elastic layer on an elastic half-space. The latter approach proved more robust in our hands and yielded a thickness of 110 nm and a modulus of 0.025 kPa. Neither value showed significant dependence on indentation rate. The brush model indicated a larger layer thickness (∼350 nm) but tended to result in larger uncertainties in the fitted parameters. The modulus of the endothelial cell was determined to be 3.0-6.5 kPa (1.5-2.5 kPa for the brush model), with a significant increase in modulus with increasing indentation rates. For forces and leukocyte properties in the physiological range, a model of a leukocyte interacting with the endothelium predicts that the number of molecules within bonding range should decrease by an order of magnitude because of the presence of a 110-nm-thick layer and even further for a glycocalyx with larger thickness. Consistent with these predictions, neutrophil adhesion increased for endothelial cells with reduced EGL thickness because they were grown in the absence of fluid shear stress. These studies establish a framework for understanding how glycocalyx layers with different thickness and stiffness limit adhesive events under homeostatic conditions and how glycocalyx damage or removal will increase leukocyte adhesion potential during inflammation.

Variations of Elastic Modulus and Cell Volume with Temperature for Cortical Neurons

Neurons change their growth dynamics and mechanical properties in response to external stimuli such as stiffness of the local microenvironment, ambient temperature, and biochemical or geometrical guidance cues. Here we use combined atomic force microscopy (AFM) and fluorescence microscopy experiments to investigate the relationship between external temperature, soma volume, and elastic modulus for cortical neurons. We measure how changes in ambient temperature affect the volume and the mechanical properties of neuronal cells at both the bulk (elastic modulus) and local (elasticity maps) levels. The experimental data demonstrate that both the volume and the elastic modulus of the neuron soma vary with changes in temperature. Our results show a decrease by a factor of 2 in the soma elastic modulus as the ambient temperature increases from room (25 °C) to physiological (37 °C) temperature, while the volume of the soma increases by a factor of 1.3 during the same temperature sweep. Using high-resolution AFM force mapping, we measure the temperature-induced variations within different regions of the elasticity maps (low and high values of elastic modulus) and correlate these variations with the dynamics of cytoskeleton components and molecular motors. We quantify the change in soma volume with temperature and propose a simple theoretical model that relates this change with variations in soma elastic modulus. These results have significant implications for understanding neuronal development and functions, as ambient temperature, cytoskeletal dynamics, and cellular volume may change with variations in physiological conditions, for example, during tissue compression and infections in vivo as well as during cell manipulation and tissue regeneration ex vivo.

Tissue mechanics, an important regulator of development and disease

A growing body of work describes how physical forces in and around cells affect their growth, proliferation, migration, function and differentiation into specialized types. How cells receive and respond biochemically to mechanical signals is a process termed mechanotransduction. Disease may arise if a disruption occurs within this mechanism of sensing and interpreting mechanics. Cancer, cardiovascular diseases and developmental defects, such as during the process of neural tube formation, are linked to changes in cell and tissue mechanics. A breakdown in normal tissue and cellular forces activates mechanosignalling pathways that affect their function and can promote disease progression. The recent advent of high-resolution techniques enables quantitative measurements of mechanical properties of the cell and its extracellular matrix, providing insight into how mechanotransduction is regulated. In this review, we will address the standard methods and new technologies available to properly measure mechanical properties, highlighting the challenges and limitations of probing different length-scales. We will focus on the unique environment present throughout the development and maintenance of the central nervous system and discuss cases where disease, such as brain cancer, arises in response to changes in the mechanical properties of the microenvironment that disrupt homeostasis. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.

Application of a layered model for determination of the elasticity of biological systems

Elasticity of biological systems is considered to be an important property that might be related to functional or pathological changes. Therefore, careful study and detailed understanding of cell and tissue elasticity is crucial for correct description of their functioning. Atomic Force Microscopy (AFM) is a powerful technique, which allows for determination of the physical properties, such as elasticity, of soft-matter systems in nano-scale. An important step in AFM elasticity studies is a proper interpretation of experimental data. Two most frequently used theoretical schemes applied to determine elasticity are due to Hertz and Sneddon, which are effectively one-parameter models. In this work, we go beyond this approach. Firstly, as elasticity is a local property, we extract from the slope of experimental force-indentation curve an elasticity parameter, which varies with indentation depth. Then secondly, we find best approximation of this parameter by applying the two-layer model with four effective parameters, as proposed by Kovalev. This method is employed to the experimental data taken on murine liver sinusoidal endothelial cells in non-alcoholic fatty liver disease model. The obtained results show additional effects, not seen within the traditional, simplified scheme. Namely, the elasticity of the first layer does not change its value in the model of non-alcoholic fatty liver disease, but the increase of stiffness is noticed in second layer. The second goal of this article is to reveal and discuss the differences between traditional approaches and the one being presented. The deviations from the original assumptions are analysed and the corresponding restrictions on utility of theoretical models are presented.

Image-based multi-scale mechanical analysis of strain amplification in neurons embedded in collagen gel

A general multi-scale strategy is presented for modeling the mechanical environment of a group of neurons that were embedded within a collagenous matrix. The results of the multi-scale simulation are used to estimate the local strains that arise in neurons when the extracellular matrix is deformed. The distribution of local strains was found to depend strongly on the configuration of the embedded neurons relative to the loading direction, reflecting the anisotropic mechanical behavior of the neurons. More importantly, the applied strain on the surrounding extracellular matrix is amplified in the neurons for all loading configurations that are considered. In the most severe case, the applied strain is amplified by at least a factor of 2 in 10% of the neurons' volume. The approach presented in this paper provides an extension to the capability of past methods by enabling the realistic representation of complex cell geometry into a multi-scale framework. The simulation results for the embedded neurons provide local strain information that is not accessible by current experimental techniques.

A comparison of methods to assess cell mechanical properties

The mechanical properties of cells influence their cellular and subcellular functions, including cell adhesion, migration, polarization, and differentiation, as well as organelle organization and trafficking inside the cytoplasm. Yet reported values of cell stiffness and viscosity vary substantially, which suggests differences in how the results of different methods are obtained or analyzed by different groups. To address this issue and illustrate the complementarity of certain approaches, here we present, analyze, and critically compare measurements obtained by means of some of the most widely used methods for cell mechanics: atomic force microscopy, magnetic twisting cytometry, particle-tracking microrheology, parallel-plate rheometry, cell monolayer rheology, and optical stretching. These measurements highlight how elastic and viscous moduli of MCF-7 breast cancer cells can vary 1,000-fold and 100-fold, respectively. We discuss the sources of these variations, including the level of applied mechanical stress, the rate of deformation, the geometry of the probe, the location probed in the cell, and the extracellular microenvironment.

AFM Indentation Analysis of Cells to Study Cell Mechanics and Pericellular Coat

Atomic force microscopy (AFM) indentation analysis of cells is a unique method of measuring stiffness of the cell body and physical properties of its pericellular coat. These cell parameters correlate with cells of abnormality and diseases. Viable biological cells can be studied with this method directly in a culture dish with no special preparation. Here we describe a step-by-step method to analyze the AFM force-indentation curves to derive cell mechanics (the modulus of elasticity of the cell body) and the parameters of the pericellular coat (density and the thickness of the coat layer). Technical details, potential difficulties, and points of special attention are described.

Single-Molecule Imaging of Proteoglycans in the Pericellular Matrix

The pericellular matrix is a robust, hyaluronan-rich polymer brush-like structure that controls access to the cell surface, and plays an important role in cell adhesion, migration, and proliferation. We report the observation of single bottlebrush proteoglycan dynamics in the pericellular matrix of living chondrocytes. Our investigations show that the pericellular matrix undergoes gross extension on the addition of exogenous aggrecan, and that this extension is significantly in excess of that observed in traditional particle exclusion assays. The mean-square displacement of single, bound proteoglycans increases with distance to cell surface, indicating reduced confinement by neighboring hyaluronan-aggrecan complexes. This is consistent with published data from quantitative particle exclusion assays that show openings in the pericellular matrix microstructure ranging from ∼150 nm near the cell surface to ∼400 nm near the cell edge. In addition, the mobility of tethered aggrecan drops significantly when the cell coat is enriched with bottlebrush proteoglycans. Single-molecule imaging in this thick polysaccharide matrix on living cells has significant promise in the drive to elucidate the role of the pericellular coat in human health.

AFM-based detection of glycocalyx degradation and endothelial stiffening in the db/db mouse model of diabetes

Degradation of the glycocalyx and stiffening of endothelium are important pathophysiological components of endothelial dysfunction. However, to our knowledge, these events have not been investigated in tandem in experimental diabetes. Here, the mechanical properties of the glycocalyx and endothelium in ex vivo mouse aorta were determined simultaneously in indentation experiments with an atomic force microscope (AFM) for diabetic db/db and control db/+ mice at ages of 11–19 weeks. To analyze highly heterogeneous aorta samples, we developed a tailored classification procedure of indentation data based on a bi-layer brush model supplemented with Hertz model for quantification of nanomechanics of endothelial regions with and without the glycocalyx surface. In db/db mice, marked endothelial stiffening and reduced glycocalyx coverage were present already in 11-week-old mice and persisted in older animals. In contrast, reduction of the effective glycocalyx length was progressive and was most pronounced in 19-week-old db/db mice. The reduction of the glycocalyx length correlated with an increasing level of glycated haemoglobin and decreased endothelial NO production. In conclusion, AFM nanoindentation analysis revealed that stiffening of endothelial cells and diminished glycocalyx coverage occurred in early diabetes and were followed by the reduction of the glycocalyx length that correlated with diabetes progression.

Cell Surface Access Is Modulated by Tethered Bottlebrush Proteoglycans

The hyaluronan-rich pericellular matrix (PCM) plays physical and chemical roles in biological processes ranging from brain plasticity, to adhesion-dependent phenomena such as cell migration, to the onset of cancer. This study investigates how the spatial distribution of the large negatively charged bottlebrush proteoglycan, aggrecan, impacts PCM morphology and cell surface access. The highly localized pericellular milieu limits transport of nanoparticles in a size-dependent fashion and sequesters positively charged molecules on the highly sulfated side chains of aggrecan. Both rat chondrocyte and human mesenchymal stem cell PCMs possess many unused binding sites for aggrecan, showing a 2.5x increase in PCM thickness from ∼7 to ∼18 μm when provided exogenous aggrecan. Yet, full extension of the PCM occurs well below aggrecan saturation. Hence, cells equipped with hyaluronan-rich PCM can in principle manipulate surface accessibility or sequestration of molecules by tuning the bottlebrush proteoglycan content to alter PCM porosity and the number of electrostatic binding sites.

Pericellular Brush and Mechanics of Guinea Pig Fibroblast Cells Studied with AFM

The atomic force microscopy (AFM) indentation method combined with the brush model can be used to separate the mechanical response of the cell body from deformation of the pericellular layer surrounding biological cells. Although self-consistency of the brush model to derive the elastic modulus of the cell body has been demonstrated, the model ability to characterize the pericellular layer has not been explicitly verified. Here we demonstrate it by using enzymatic removal of hyaluronic content of the pericellular brush for guinea pig fibroblast cells. The effect of this removal is clearly seen in the AFM force-separation curves associated with the pericellular brush layer. We further extend the brush model for brushes larger than the height of the AFM probe, which seems to be the case for fibroblast cells. In addition, we demonstrate that an extension of the brush model (i.e., double-brush model) is capable of detecting the hierarchical structure of the pericellular brush, which, for example, may consist of the pericellular coat and the membrane corrugation (microridges and microvilli). It allows us to quantitatively segregate the large soft polysaccharide pericellular coat from a relatively rigid and dense membrane corrugation layer. This was verified by comparison of the parameters of the membrane corrugation layer derived from the force curves collected on untreated cells (when this corrugation membrane part is hidden inside the pericellular brush layer) and on treated cells after the enzymatic removal of the pericellular coat part (when the corrugations are exposed to the AFM probe). We conclude that the brush model is capable of not only measuring the mechanics of the cell body but also the parameters of the pericellular brush layer, including quantitative characterization of the pericellular layer structure.

AFM study shows prominent physical changes in elasticity and pericellular layer in human acute leukemic cells due to inadequate cell-cell communication

Biomechanical properties of single cells in vitro or ex vivo and their pericellular interfaces have recently attracted a lot of attention as a potential biophysical (and possibly prognostic) marker of various diseases and cell abnormalities. At the same time, the influence of the cell environment on the biomechanical properties of cells is not well studied. Here we use atomic force microscopy to demonstrate that cell-cell communication can have a profound effect on both cell elasticity and its pericellular coat. A human pre-B p190^BCR/ABL acute lymphoblastic leukemia cell line (ALL3) was used in this study. Assuming that cell-cell communication is inversely proportional to the distance between cells, we study ALL3 cells in vitro growing at different cell densities. ALL3 cells demonstrate a clear density dependent behavior. These cells grow very well if started at a relatively high cell density (HD, >2 × 10⁵ cells ml^-1) and are poised to grow at low cell density (LD, <1 × 10⁴ cells ml^-1). Here we observe ∼6× increase in the elastic (Young's) modulus of the cell body and ∼3.6× decrease in the pericellular brush length of LD cells compared to HD ALL3 cells. The difference observed in the elastic modulus is much larger than typically reported for pathologically transformed cells. Thus, cell-cell communication must be taken into account when studying biomechanics of cells, in particular, correlating cell phenotype and its biophysical properties.

Laser Refrigeration of Ytterbium-Doped Sodium-Yttrium-Fluoride Nanowires

Sodium yttrium fluoride (β-NaYF₄ ) nanowires (NWs) with a hexagonal crystal structure are synthesized using a low-cost hydrothermal process and are shown to undergo laser refrigeration based on an upconversion process leading to anti-Stokes (blueshifted) photoluminescence. Single-beam laser trapping combined with forward light scattering is used to investigate cryophotonic laser refrigeration of individual NWs through analysis of their local Brownian dynamics.

Biophysical differences between chronic myelogenous leukemic quiescent and proliferating stem/progenitor cells

The treatment of chronic myeloid leukemia (CML), a clonal myeloproliferative disorder has improved recently, but most patients have not yet been cured. Some patients develop resistance to the available tyrosine kinase treatments. Persistence of residual quiescent CML stem cells (LSCs) that later resume proliferation is another common cause of recurrence or relapse of CML. Eradication of quiescent LSCs is a promising approach to prevent recurrence of CML. Here we report on new biophysical differences between quiescent and proliferating CD34+ LSCs, and speculate how this information could be of use to eradicate quiescent LSCs. Using AFM measurements on cells collected from four untreated CML patients, substantial differences are observed between quiescent and proliferating cells in the elastic modulus, pericellular brush length and its grafting density at the single cell level. The higher pericellular brush densities of quiescent LSCs are common for all samples. The significance of these observations is discussed.