Measurement and characterization of whole-cell mechanical behavior

10 μm thick ultrathin glass sheet to realize a highly sensitive cantilever for precise cell stiffness measurement

The micro-cantilever-based sensor platform has become a promising technique in the sensing area for physical, chemical and biological detection due to its portability, small size, label-free characteristics and good compatibility with "lab-on-a-chip" devices. However, traditional micro-cantilever methods are limited by their complicated fabrication, manipulation and detection, and low sensitivity. In this research, we proposed a 10 μm thick ultrathin, highly sensitive, and flexible glass cantilever integrated with a strain gauge sensor and presented its application for the measurement of single-cell mechanical properties. Compared to conventional methods, the proposed ultrathin glass sheet (UTGS)-based cantilever is easier to fabricate, has better physical and chemical properties, and shows a high linear relationship between resistance change and applied small force or displacement. The sensitivity of the cantilever is 15 μN μm-1 and the minimum detectable displacement at the current development stage is 500 nm, which is sufficient for cell stiffness measurement. The cantilever also possesses excellent optical transparency that supports real-time observation during measurement. We first calibrated the cantilever by measuring the Young's modulus of PDMS with known specific stiffness, and then we demonstrated the measurement of Xenopus oocytes and fertilized eggs in different statuses. By further optimizing the UTGS-based cantilever, we can extend its applicability to various measurements of different cells.

Mechanical characterization of vesicles and cells: A review

Vesicles perform many essential functions in all living organisms. They respond like a transducer to mechanical stress in converting the applied force into mechanical and biological responses. At the same time, both biochemical and biophysical signals influence the vesicular response in bearing mechanical loads. In recent years, liposomes, artificial lipid vesicles, have gained substantial attention from the pharmaceutical industry as a prospective drug carrier which can also serve as an artificial cell-mimetic system. The ability of these vesicles to enter through pores of even smaller size makes them ideal candidates for therapeutic agents to reach the infected sites effectively. Engineering of vesicles with desired mechanical properties that can encapsulate drugs and release as required is the prime challenge in this field. This requirement has led to the modifications of the composition of the bilayer membrane by adding cholesterol, sphingomyelin, etc. In this article, we review the manufacturing and characterization techniques of various artificial/synthetic vesicles. We particularly focus on the electric field-driven characterization techniques to determine different properties of vesicle and its membranes, such as bending rigidity, viscosity, capacitance, conductance, etc., which are indicators of their content and mobility. Similarities and differences between artificial vesicles, natural vesicles, and cells are highlighted throughout the manuscript since most of these artificial vesicles are intended for cell mimetic functions.

Fast automated processing of AFM PeakForce curves to evaluate spatially resolved Young modulus and stiffness of turgescent cells

Atomic Force Microscopy (AFM) is a powerful technique for the measurement of mechanical properties of individual cells in two (x × y) or three (x × y × time) dimensions. The instrumental progress makes it currently possible to generate a large amount of data in a relatively short time, which is particularly true for AFM operating in so-called PeakForce tapping mode (Bruker corporation). The latter corresponds to an AFM probe that periodically hits the sample surface while the pico-newton level interaction force is recorded from cantilever deflection. The method provides unprecedented high-resolution (a few tens of nm) imaging of the mechanical features of soft biological samples (e.g. bacteria, yeasts) and of hard abiotic surfaces (e.g. minerals). The rapid conversion of up to several tens of thousands spatially resolved force curves typically collected in AFM PeakForce tapping mode over a given cell surface area into comprehensive nanomechanical information requires the development of robust data analysis methodologies and dedicated numerical tools. In this work, we report an automated algorithm for (i) a rapid and unambiguous detection of the indentation regimes corresponding to non-linear and linear deformations of bacterial surfaces upon compression by the AFM probe, (ii) the subsequent evaluation of the Young modulus and cell surface stiffness, and (iii) the generation of spatial mappings of relevant nanomechanical properties at the single cell level. The procedure involves consistent evaluation of the contact point between the AFM probe and sample biosurface and that of the threshold indentation value marking the transition between non-linear and linear deformation regimes. For comparison purposes, the former regime is here analyzed on the basis of Hertz and Sneddon models corrected or not for effects of finite sample thickness. Analysis of AFM measurements performed on a selected Escherichia coli strain is detailed to demonstrate the feasibility, rapidity and robustness of the here-proposed PeakForce data treatment process. The flexibility of the algorithm allows consideration of force curve parameterizations other than that detailed here, which may be desired for investigation of e.g. eukaryotes nanomechanics. The performance of the adopted Hertz-based and Sneddon-based contact mechanics formalisms in recovering experimental data and in identifying nanomechanical heterogeneities at the bacterium scale is further thoroughly discussed.

A numerical method is proposed for the modeling of AFM PeakForce curves and the automated extraction of relevant spatially-resolved nanomechanical properties of turgescent cells.

Nanoindentation of Soft Biological Materials

Nanoindentation techniques, with high spatial resolution and force sensitivity, have recently been moved into the center of the spotlight for measuring the mechanical properties of biomaterials, especially bridging the scales from the molecular via the cellular and tissue all the way to the organ level, whereas characterizing soft biomaterials, especially down to biomolecules, is fraught with more pitfalls compared with the hard biomaterials. In this review we detail the constitutive behavior of soft biomaterials under nanoindentation (including AFM) and present the characteristics of experimental aspects in detail, such as the adaption of instrumentation and indentation response of soft biomaterials. We further show some applications, and discuss the challenges and perspectives related to nanoindentation of soft biomaterials, a technique that can pinpoint the mechanical properties of soft biomaterials for the scale-span is far-reaching for understanding biomechanics and mechanobiology.

Effects of blocking integrin β1 and N-cadherin cellular interactions on mechanical properties of vascular smooth muscle cells

Experimental measurements of cellular mechanical properties have shown large variability in whole-cell mechanical properties between cells from a single population. This heterogeneity has been observed in many cell populations and with several measurement techniques but the sources are not yet fully understood. Cell mechanical properties are directly related to the composition and organization of the cytoskeleton, which is physically coupled to neighboring cells through adherens junctions and to underlying matrix through focal adhesion complexes. This high level of heterogeneity may be attributed to varying cellular interactions throughout the sample. We tested the effect of cell-cell and cell-matrix interactions on the mechanical properties of vascular smooth muscle cells (VSMCs) in culture by using antibodies to block N-cadherin and integrin β1 interactions. VSMCs were cultured on substrates of varying stiffness with and without tension. Under each of these conditions, cellular mechanical properties were characterized by performing atomic force microscopy (AFM) and cellular structure was analyzed through immunofluorescence imaging. As expected, VSMC mechanical properties were greatly affected by the underlying culture substrate and applied tension. Interestingly, the cell-to-cell variation in mechanical properties within each sample decreased significantly in the antibody conditions. Thus, the cells grown with blocking antibodies were more homogeneous in their mechanical properties on both glass and soft substrates. This suggests that diversified adhesion binding between cells and the ECM is responsible for a significant amount of mechanical heterogeneity that is observed in 2D cell culture studies.

Endogenously generated amyloid-β increases stiffness in human neuroblastoma cells

Amyloid-β (Aβ) is widely recognized as toxic to neuronal cells. Its deposition on plasma and intracellular membranes and aggregation into amyloid plaques can disturb the composition and physiological function of neurons. Whether a physical property of cells, such as stiffness, is altered by endogenously overexpressed Aβ has not yet been investigated. In this study, we used human neuroblastoma cells stably overexpressing amyloid precursor protein (APP) and its Swedish mutant form (APPswe) to measure the changes in cell stiffness. Our results showed that the stiffness of cells overexpressing APP or APPswe was higher than that of control SH-SY5Y cells. Either reducing levels of Aβ with the γ secretase inhibitor DAPT or blocking the membrane calcium channel formed by Aβ with tromethamine decreased cell stiffness to a level close to the control SH-SY5Y cells. Our results suggested that Aβ, not APP, contributed to increased cell stiffness and that closure of calcium channels formed by Aβ can alleviate the effects of Aβ on membrane stiffness.

An inverted dielectrophoretic device for analysis of attached single cell mechanics

Dielectrophoresis (DEP), the force induced on a polarizable body by a non-uniform electric field, has been widely used to manipulate single cells in suspension and analyze their stiffness. However, most cell types do not naturally exist in suspension but instead require attachment to the tissue extracellular matrix in vivo. Cells alter their cytoskeletal structure when they attach to a substrate, which impacts cell stiffness. It is therefore critical to be able to measure mechanical properties of cells attached to a substrate. We present a novel inverted quadrupole dielectrophoretic device capable of measuring changes in the mechanics of single cells attached to a micropatterned polyacrylamide gel. The device is positioned over a cell of defined size, a directed DEP pushing force is applied, and cell centroid displacement is dynamically measured by optical microscopy. Using this device, single endothelial cells showed greater centroid displacement in response to applied DEP pushing force following actin cytoskeleton disruption by cytochalasin D. In addition, transformed mammary epithelial cell (MCF10A-NeuT) showed greater centroid displacement in response to applied DEP pushing force compared to untransformed cells (MCF10A). DEP device measurements were confirmed by showing that the cells with greater centroid displacement also had a lower elastic modulus by atomic force microscopy. The current study demonstrates that an inverted DEP device can determine changes in single attached cell mechanics on varied substrates.

Nanomechanics of Cells and Biomaterials Studied by Atomic Force Microscopy

The behavior and mechanical properties of cells are strongly dependent on the biochemical and biomechanical properties of their microenvironment. Thus, understanding the mechanical properties of cells, extracellular matrices, and biomaterials is key to understanding cell function and to develop new materials with tailored mechanical properties for tissue engineering and regenerative medicine applications. Atomic force microscopy (AFM) has emerged as an indispensable technique for measuring the mechanical properties of biomaterials and cells with high spatial resolution and force sensitivity within physiologically relevant environments and timescales in the kPa to GPa elastic modulus range. The growing interest in this field of bionanomechanics has been accompanied by an expanding array of models to describe the complexity of indentation of hierarchical biological samples. Furthermore, the integration of AFM with optical microscopy techniques has further opened the door to a wide range of mechanotransduction studies. In recent years, new multidimensional and multiharmonic AFM approaches for mapping mechanical properties have been developed, which allow the rapid determination of, for example, cell elasticity. This Progress Report provides an introduction and practical guide to making AFM-based nanomechanical measurements of cells and surfaces for tissue engineering applications.

High-Throughput Assessment of Cellular Mechanical Properties

Traditionally, cell analysis has focused on using molecular biomarkers for basic research, cell preparation, and clinical diagnostics; however, new microtechnologies are enabling evaluation of the mechanical properties of cells at throughputs that make them amenable to widespread use. We review the current understanding of how the mechanical characteristics of cells relate to underlying molecular and architectural changes, describe how these changes evolve with cell-state and disease processes, and propose promising biomedical applications that will be facilitated by the increased throughput of mechanical testing: from diagnosing cancer and monitoring immune states to preparing cells for regenerative medicine. We provide background about techniques that laid the groundwork for the quantitative understanding of cell mechanics and discuss current efforts to develop robust techniques for rapid analysis that aim to implement mechanophenotyping as a routine tool in biomedicine. Looking forward, we describe additional milestones that will facilitate broad adoption, as well as new directions not only in mechanically assessing cells but also in perturbing them to passively engineer cell state.

Physicochemical and nanomechanical investigation of electrodeposited chitosan:PEO blends

Cathodic electrodeposition is a bottom up process that is emerging as a simple yet efficient strategy to engineer thin polymeric films with well-defined physicochemical properties.

Probabilistic estimation of mechanical properties of biomaterials using atomic force microscopy

Nanoindentation using contact-mode atomic force microscopy (AFM) has emerged as a powerful tool for effective material characterization of a wide variety of biomaterials across multiple length scales. However, the interpretation of force-indentation experimental data from AFM is subject to some debate. Uncertainties in AFM data analysis stems from two primary sources: The exact point of contact between the AFM probe and the biological specimen and the variability in the spring constant of the AFM probe. While a lot of attention has been directed toward addressing the contact-point uncertainty, the effect of variability in the probe spring constant has not received sufficient attention. In this paper, we report on an error-in-variables-based Bayesian change-point approach to quantify the elastic modulus of human breast tissue samples after accounting for variability in both contact point and the probe spring constant. We also discuss the efficacy of our approach to a wide range of hyperparameter values using a sensitivity analysis.

Automated AFM force curve analysis for determining elastic modulus of biomaterials and biological samples

The analysis of atomic force microscopy (AFM) force data requires the selection of a contact point (CP) and is often time consuming and subjective due to influence from intermolecular forces and low signal-to-noise ratios (SNR). In this report, we present an automated algorithm for the selection of CPs in AFM force data and the evaluation of elastic moduli. We propose that CP may be algorithmically easier to detect by identifying a linear elastic indentation region of data (high SNR) rather than the contact point itself (low SNR). Utilizing Hertzian mechanics, the data are fitted for the CP. We first detail the algorithm and then evaluate it on sample polymeric and biological materials. As a demonstration of automation, 64 × 64 force maps were analyzed to yield spatially varying topographical and mechanical information of cells. Finally, we compared manually selected CPs to automatically identified CPs and demonstrated that our automated approach is both accurate (< 10nm difference between manual and automatic) and precise for non-interacting polymeric materials. Our data show that the algorithm is useful for analysis of both biomaterials and biological samples.

Nanobiomechanics of living cells: a review

Nanobiomechanics of living cells is very important to understand cell-materials interactions. This would potentially help to optimize the surface design of the implanted materials and scaffold materials for tissue engineering. The nanoindentation techniques enable quantifying nanobiomechanics of living cells, with flexibility of using indenters of different geometries. However, the data interpretation for nanoindentation of living cells is often difficult. Despite abundant experimental data reported on nanobiomechanics of living cells, there is a lack of comprehensive discussion on testing with different tip geometries, and the associated mechanical models that enable extracting the mechanical properties of living cells. Therefore, this paper discusses the strategy of selecting the right type of indenter tips and the corresponding mechanical models at given test conditions.

Estradiol influences the mechanical properties of human fetal osteoblasts through cytoskeletal changes

Estrogen is known to have a direct effect on bone forming osteoblasts and bone resorbing osteoclasts. The cellular and molecular effects of estrogen on osteoblasts and osteoblasts-like cells have been extensively studied. However, the effect of estrogen on the mechanical property of osteoblasts has not been studied yet. It is important since mechanical property of the mechanosensory osteoblasts could be pivotal to its functionality in bone remodeling. This is the first study aimed to assess the direct effect of estradiol on the apparent elastic modulus (E∗) and corresponding cytoskeletal changes of human fetal osteoblasts (hFOB 1.19). The cells were cultured in either medium alone or medium supplemented with β-estradiol and then subjected to Atomic Force Microscopy indentation (AFM) to determine E∗. The underlying changes in cytoskeleton were studied by staining the cells with TRITC-Phalloidin. Following estradiol treatment, the cells were also tested for proliferation, alkaline phosphatase activity and mineralization. With estradiol treatment, E∗ of osteoblasts significantly decreased by 43-46%. The confocal images showed that the changes in f-actin network observed in estradiol treated cells can give rise to the changes in the stiffness of the cells. Estradiol also increases the inherent alkaline phosphatase activity of the cells. Estradiol induced stiffness changes of osteoblasts were not associated with changes in the synthesized mineralized matrix of the cells. Thus, a decrease in osteoblast stiffness with estrogen treatment was demonstrated in this study, with positive links to cytoskeletal changes. The estradiol associated changes in osteoblast mechanical properties could bear implications for bone remodeling and its mechanical integrity.

Bone cell elasticity and morphology changes during the cell cycle

The mechanical properties of cells are reported to be regulated by a range of factors including interactions with the extracellular environment and other cells, differentiation status, the onset of pathological states, as well as the intracellular factors, for example, the cytoskeleton. The cell cycle is considered to be a well-ordered sequence of biochemical events. A number of processes reported to occur during its progression are inherently mechanical and, as such, require mechanical regulation. In spite of this, few attempts have been made to investigate the putative regulatory role of the cell cycle in mechanobiology. In the present study, Atomic Force Microscopy (AFM) was employed to investigate the elastic modulus of synchronised osteoblasts. The data obtained confirm that osteoblast elasticity is regulated by cell cycle phase; specifically, cells in S phase were found to have a modulus approximately 1.7 times that of G1 phase cells. Confocal microscopy studies revealed that aspects of osteoblast morphology, namely F-actin expression, were also modulated by the cell cycle, and tended to increase with phase progression from G0 onwards. The data obtained in this study are likely to have implications for the fields of tissue- and bio-engineering, where prior knowledge of cell mechanobiology is essential for the effective replacement and repair of tissue. Furthermore, studies focused on biomechanics and the biophysical properties of cells are important in the understanding of the onset and progression of disease states, for example cancer at the cellular level. Our study demonstrates the importance of the combined use of traditional and relatively novel microscopy techniques in understanding mechanical regulation by crucial cellular processes, such as the cell cycle.

Atomic force microscopy comes of age

AFM (atomic force microscopy) analysis, both of fixed cells, and live cells in physiological environments, is set to offer a step change in the research of cellular function. With the ability to map cell topography and morphology, provide structural details of surface proteins and their expression patterns and to detect pico-Newton force interactions, AFM represents an exciting addition to the arsenal of the cell biologist. With the explosion of new applications, and the advent of combined instrumentation such as AFM-confocal systems, the biological application of AFM has come of age. The use of AFM in the area of biomedical research has been proposed for some time, and is one where a significant impact could be made. Fixed cell analysis provides qualitative and quantitative subcellular and surface data capable of revealing new biomarkers in medical pathologies. Image height and contrast, surface roughness, fractal, volume and force analysis provide a platform for the multiparameter analysis of cell and protein functions. Here, we review the current status of AFM in the field and discuss the important contribution AFM is poised to make in the understanding of biological systems.

Over-expression of alpha-actinin with a GFP fusion protein is sufficient to increase whole-cell stiffness in human osteoblasts

Osteoblasts respond to shear stress by simultaneously increasing their whole-cell stiffness and up-regulating the cytoskeletal crosslinking protein alpha-actinin. The stiffness of reconstituted cytoskeletal networks increases following the addition of alpha-actinin, but the effect of alpha-actinin on whole-cell mechanical behavior has not been investigated. The hypothesis of this study was that increasing alpha-actinin in the cytoskeleton would be sufficient to increase whole-cell stiffness. hFOB osteoblasts were transfected with a plasmid for GFP-tagged alpha-actinin, resulting in a 150% increase in the amount of alpha-actinin. The GFP-alpha-actinin fusion protein co-fractionated with the cytoskeleton and co-localized to the same regions of the cytoskeleton as endogenous alpha-actinin. Whole-cell mechanical behavior was measured by atomic force microscopy using a 25 mum diameter microsphere as an indenter. The whole-cell stiffness of cells over-expressing GFP-alpha-actinin was 60% higher than cells expressing only endogenous alpha-actinin (p < 0.002), which was within the range of mechanical behavior observed in osteoblastic cells exposed to 1 and 2 Pa of fluid shear. These results indicate that the up-regulation of alpha-actinin synthesis in osteoblasts is sufficient to alter the whole-cell mechanical behavior and highlights the potential role of alpha-actinin to reinforce cells against mechanical loads.

Effects of serum deprivation on the mechanical properties of adherent vascular smooth muscle cells

Vascular smooth muscle cell (VSMC) function plays a key role in regulating the development and progression of vascular lesions. Among the more significant phenomena that occur during the development of these lesions is the phenotypic switching of VSMCs from a contractile to a synthetic state. A better understanding of the concurrent changes to VSMC mechanical properties that occur with phenotypic shifts can help to elucidate the role of VSMC mechanics in the development of vascular diseases. In the current study, the mechanical properties of adherent cultured rat aortic VSMCs were assessed by atomic force microscopy. Serum starvation was used to induce a phenotypic shift in vitro. It was concluded that serum starvation led to a statistically significant increase in apparent elastic modulus after 5 days, as well as a statistically significant decrease in hysteresis after culture for 3 days. If this trend of VSMC mechanical properties changing concurrently with phenotypic shifts were to hold true in vivo, such changes could affect the processes of mechanotransduction and/or arterial mechanical properties, thereby contributing to the progression of vascular disease.

Nanomechanics of polymer gels and biological tissues: A critical review of analytical approaches in the Hertzian regime and beyond

We survey recent progress in the application of nanoindentation to characterize the local mechanical properties of polymer gels and biological tissues. We review the theories, analytical models based thereon, and data processing techniques commonly used to determine elastic properties of these classes of materials by instrumented nanoindentation. Examples from the testing of synthetic and biological gels are used to illustrate the limitations of existing theories and approaches. Emphasis is placed on the need for contact mechanics models that more accurately represent the large-strain behaviour of soft matter.

Robust Strategies for Automated AFM Force Curve Analysis—I. Non-adhesive Indentation of Soft, Inhomogeneous Materials

The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young’s modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young’s modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young’s modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.

Adaptation of cellular mechanical behavior to mechanical loading for osteoblastic cells

Numerous cellular biochemical responses to mechanical loading are transient, indicating a cell's ability to adapt its behavior to a new mechanical environment. Since load-induced cellular deformation can initiate these biochemical responses, the overall goal of this study was to investigate the adaptation of global, or whole-cell, mechanical behavior, i.e., cellular deformability, in response to mechanical loading for osteoblastic cells. Confluent cell cultures were subjected to 1 or 2 Pa flow-induced shear stress for 2 h. Whole-cell mechanical behavior was then measured for individual cells using an atomic force microscope. Compared to cells maintained under static conditions, whole-cell stiffness was 1.36-fold (p=0.006) and 1.70-fold (p<0.001) greater for cells exposed to 1 and 2 Pa shear loading, respectively. The increase in shear stress magnitude from 1 to 2 Pa also caused a statistically significant, 1.25-fold increase in cell stiffness (p=0.02). Increases in cell stiffness were not altered in either flow group for 70 min after flow was terminated (p=0.15). Flow-induced rearrangement of the actin cytoskeleton was also maintained for at least 90 min after flow was terminated. Taken together, these findings support the hypothesis that cells become mechanically adapted to their mechanical environment via cytoskeletal modifications. Accordingly, cellular mechanical adaptation may play a key role in regulation of cellular mechanosensitivity and the related effects on tissue structure and function.

The effects of morphology, confluency, and phenotype on whole-cell mechanical behavior

Emerging evidence indicates that cellular mechanical behavior can be altered by disease, drug treatment, and mechanical loading. To effectively investigate how disease and mechanical or biochemical treatments influence cellular mechanical behavior, it is imperative to determine the source of large inter-cell differences in whole-cell mechanical behavior within a single cell line. In this study, we used the atomic force microscope to investigate the effects of cell morphological parameters and confluency on whole-cell mechanical behavior for osteoblastic and fibroblastic cells. For nonconfluent cells, projected nucleus area, cell area, and cell aspect ratio were not correlated with mechanical behavior (p>or=0.46), as characterized by a parallel-spring recruitment model. However, measured force-deformation responses were statistically different between osteoblastic and fibroblastic cells (p<0.001) and between confluent and nonconfluent cells (p<0.001). Osteoblastic cells were 2.3-2.8 times stiffer than fibroblastic cells, and confluent cells were 1.5-1.8 times stiffer than nonconfluent cells. The results indicate that structural differences related to phenotype and confluency affect whole-cell mechanical behavior, while structural differences related to global morphology do not. This suggests that cytoskeleton structural parameters, such as filament density, filament crosslinking, and cell-cell and cell-matrix attachments, dominate inter-cell variability in whole-cell mechanical behavior.