Measuring viscoelasticity of soft biological samples using atomic force microscopy.

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

Nanomechanical mapping in air or vacuum using multi-harmonic signals in tapping mode atomic force microscopy.

We present a method by which multi-harmonic signals acquired during a normal tapping mode (amplitude modulated) AFM scan of a sample in air or vacuum with standard microcantilevers can be used to map quantitatively the local mechanical properties of the sample such as elastic modulus, adhesion, and indentation. The approach is based on the observation that during the tapping mode operation in air or vacuum, the 0th and 2nd harmonic signals of microcantilever vibration are encountered under most operating conditions and can be mapped with sufficient signal to noise ratio. By measuring the amplitude and phase of the driven harmonic as well as the 0th and 2nd harmonic observables, we find analytical/semi-analytical formulas that relate these multi-harmonic observables to local mechanical properties for several classical tip-sample interaction models. Least squares estimation of the local mechanical properties is performed pixel by pixel. The method is validated through computations as well as experimental data acquired on a polymer blend made of Polystyrene and Polyolefin elastomer.

Evaluation of the elastic Young's modulus and cytotoxicity variations in fibroblasts exposed to carbon-based nanomaterials.

BACKGROUND: The conventional approaches to assess the potential cytotoxic effects of nanomaterials (NMs) mainly rely on in vitro biochemical assays. These assays are strongly dependent on the properties of the nanomaterials, for example; specific surface area (SSA), size, surface defects, and surface charge, and the host response. The NMs properties can also interfere with the reagents of the biochemical and optical assays leading to skewed interpretations and ambiguous results related to the NMs toxicity. Here, we proposed a structured approach for cytotoxicity assessment complemented with cells' mechanical responses represented as the variations of elastic Young's modulus in conjunction with conventional biochemical tests. Monitoring the mechanical properties responses at various times allowed understanding the effects of NMs to the filamentous actin cytoskeleton. The elastic Young's modulus was estimated from the force volume maps using an atomic force microscope (AFM). RESULTS: Our results show a significant decrease on Young's modulus, ~ 20%, in cells exposed to low concentrations of graphene flakes (GF), ~ 10% decrease for cells exposed to low concentrations of multiwalled carbon nanotubes (MWCNTs) than the control cells. These considerable changes were directly correlated to the disruption of the cytoskeleton actin fibers. The length of the actin fibers in cells exposed to GF was 50% shorter than the fibers of the cells exposed to MWCNT. Applying both conventional biochemical approach and cells mechanics, we were able to detect differences in the actin networks induced by MWCNT inside the cells and GF outside the cell's membrane. These results contrast with the conventional live/dead assay where we obtained viabilities greater than 80% after 24 h; while the elasticity dramatically decreased suggesting a fast-metabolic stress generation. CONCLUSIONS: We confirmed the production of radical oxygen species (ROS) on cells exposed to CBNs, which is related to the disruption of the cytoskeleton. Altogether, the changes in mechanical properties and the length of F-actin fibers confirmed that disruption of the F-actin cytoskeleton is a major consequence of cellular toxicity. We evidenced the importance of not just nanomaterials properties but also the effect of the location to assess the cytotoxic effects of nanomaterials.

High resolution subsurface imaging using resonance-enhanced detection in 2nd-harmonic KPFM.

Second harmonic Kelvin probe force microscopy is a robust mechanism for subsurface imaging at the nanoscale. Here we exploit resonance-enhanced detection as a way to boost the subsurface contrast with higher force sensitivity using lower bias voltages, in comparison to the traditional off-resonance case. In this mode, the second harmonic signal of the electrostatic force is acquired at one of the eigenmode frequencies of the microcantilever. As a result, high resolution subsurface images are obtained in a variety of nanocomposites. To further understand the subsurface imaging detection upon electrostatic forces, we use a finite element model that approximates the geometry of the probe and sample. This allows the investigation of the contrast mechanism, the depth sensitivity and lateral resolution depending on tip-sample properties.

Enhancing the optical lever sensitivity of microcantilevers for dynamic atomic force microscopy via integrated low frequency paddles.

A method is presented to enhance the optical lever sensitivity in dynamic atomic force microscopy (AFM) by nearly an order of magnitude over a wide frequency bandwidth. This is achieved by fabricating or releasing a paddle with a soft hinge close to the free end of the AFM microcantilever such that the paddle resonance frequency is well below the fundamental resonance frequency of the microcantilever. We show a significant increase in signal to noise ratio when cantilever motion is observed at the paddle for AFM systems that are not limited by thermal noise. Also, any effects due to the excitation of the second eigenmode were decoupled by locating the paddle at the node of the second eigenmode. We use these probes for higher harmonic imaging in amplitude modulated AFM (AM-AFM) on a standard polymer blend made of polystyrene and low density polyethylene. We demonstrate significantly improved contrast in higher harmonic images when observing cantilever motion at the paddle. Thus this microcantilever design can improve significantly conventional cantilever performance for dynamic AFM and is compatible with low-cost, high yield microfabrication processes.

Substrate Deformation Predicts Neuronal Growth Cone Advance.

Although pulling forces have been observed in axonal growth for several decades, their underlying mechanisms, absolute magnitudes, and exact roles are not well understood. In this study, using two different experimental approaches, we quantified retrograde traction force in Aplysia californica neuronal growth cones as they develop over time in response to a new adhesion substrate. In the first approach, we developed a novel method, to our knowledge, for measuring traction forces using an atomic force microscope (AFM) with a cantilever that was modified with an Aplysia cell adhesion molecule (apCAM)-coated microbead. In the second approach, we used force-calibrated glass microneedles coated with apCAM ligands to guide growth cone advance. The traction force exerted by the growth cone was measured by monitoring the microneedle deflection using an optical microscope. Both approaches showed that Aplysia growth cones can develop traction forces in the 10(0)-10(2) nN range during adhesion-mediated advance. Moreover, our results suggest that the level of traction force is directly correlated to the stiffness of the microneedle, which is consistent with a reinforcement mechanism previously observed in other cell types. Interestingly, the absolute level of traction force did not correlate with growth cone advance toward the adhesion site, but the amount of microneedle deflection did. In cases of adhesion-mediated growth cone advance, the mean needle deflection was 1.05 ± 0.07 µm. By contrast, the mean deflection was significantly lower (0.48 ± 0.06 µm) when the growth cones did not advance. Our data support a hypothesis that adhesion complexes, which can undergo micron-scale elastic deformation, regulate the coupling between the retrogradely flowing actin cytoskeleton and apCAM substrates, stimulating growth cone advance if sufficiently abundant.

Nanomechanical property maps of breast cancer cells as determined by multiharmonic atomic force microscopy reveal Syk-dependent changes in microtubule stability mediated by MAP1B.

The Syk protein-tyrosine kinase, a well-characterized modulator of immune recognition receptor signaling, also plays important, but poorly characterized, roles in tumor progression, acting as an inhibitor of cellular motility and metastasis in highly invasive cancer cells. Multiharmonic atomic force microscopy (AFM) was used to map nanomechanical properties of live MDA-MB-231 breast cancer cells either lacking or expressing Syk. The expression of Syk dramatically altered the cellular topography, reduced cell height, increased elasticity, increased viscosity, and allowed visualization of a more substantial microtubule network. The microtubules of Syk-expressing cells were more stable to nocodazole-induced depolymerization and were more highly acetylated than those of Syk-deficient cells. Silencing of MAP1B, a major substrate for Syk in MDA-MB-231 cells, attenuated Syk-dependent microtubule stability and reversed much of the effect of Syk on cellular topography, stiffness, and viscosity. This study illustrates the use of multiharmonic AFM both to quantitatively map the local nanomechanical properties of living cells and to identify the underlying mechanisms by which these properties are modulated by signal transduction machinery.

Three-dimensional mapping of optical near field with scattering SNOM.

Scattering-type scanning near-field optical microscopy (s-SNOM) is applied to investigate three-dimensional optical near field distribution, including both amplitude and phase information. A method analogous to the force volume mode of the atomic force microscopy (AFM) technique is adapted for the measurement. The results show high lateral resolution of tens of nanometers, and even higher vertical resolution of only a few nanometers. The experiment results provide a straightforward illustration of the optical near fields in the space above the sample surface. Numerical computations support the experimental data. The ability to map the 3D optical near filed helps to reveal the factors that influence the performance of the designed near-field structures.

Vibrational shape tracking of atomic force microscopy cantilevers for improved sensitivity and accuracy of nanomechanical measurements.

Contact resonance atomic force microscopy (CR-AFM) methods currently utilize the eigenvalues, or resonant frequencies, of an AFM cantilever in contact with a surface to quantify local mechanical properties. However, the cantilever eigenmodes, or vibrational shapes, also depend strongly on tip-sample contact stiffness. In this paper, we evaluate the potential of eigenmode measurements for improved accuracy and sensitivity of CR-AFM. We apply a recently developed, in situ laser scanning method to experimentally measure changes in cantilever eigenmodes as a function of tip-sample stiffness. Regions of maximum sensitivity for eigenvalues and eigenmodes are compared and found to occur at different values of contact stiffness. The results allow the development of practical guidelines for CR-AFM experiments, such as optimum laser spot positioning for different experimental conditions. These experiments provide insight into the complex system dynamics that can affect CR-AFM and lay a foundation for enhanced nanomechanical measurements with CR-AFM.

Local viscoelastic properties of live cells investigated using dynamic and quasi-static atomic force microscopy methods.

The measurement of viscoelasticity of cells in physiological environments with high spatio-temporal resolution is a key goal in cell mechanobiology. Traditionally only the elastic properties have been measured from quasi-static force-distance curves using the atomic force microscope (AFM). Recently, dynamic AFM-based methods have been proposed to map the local in vitro viscoelastic properties of living cells with nanoscale resolution. However, the differences in viscoelastic properties estimated from such dynamic and traditional quasi-static techniques are poorly understood. In this work we quantitatively reconstruct the local force and dissipation gradients (viscoelasticity) on live fibroblast cells in buffer solutions using Lorentz force excited cantilevers and present a careful comparison between mechanical properties (local stiffness and damping) extracted using dynamic and quasi-static force spectroscopy methods. The results highlight the dependence of measured viscoelastic properties on both the frequency at which the chosen technique operates as well as the interactions with subcellular components beyond certain indentation depth, both of which are responsible for differences between the viscoelasticity property maps acquired using the dynamic AFM method against the quasi-static measurements.

A modified motor-clutch model reveals that neuronal growth cones respond faster to soft substrates.

Neuronal growth cones sense a variety of cues including chemical and mechanical ones to establish functional connections during nervous system development. Substrate-cytoskeletal coupling is an established model for adhesion-mediated growth cone advance; however, the detailed molecular and biophysical mechanisms underlying the mechanosensing and mechanotransduction process remain unclear. Here, we adapted a motor-clutch model to better understand the changes in clutch and cytoskeletal dynamics, traction forces, and substrate deformation when a growth cone interacts with adhesive substrates of different stiffnesses. Model parameters were optimized using experimental data from Aplysia growth cones probed with force-calibrated glass microneedles. We included a reinforcement mechanism at both motor and clutch level. Furthermore, we added a threshold for retrograde F-actin flow that indicates when the growth cone is strongly coupled to the substrate. Our modeling results are in strong agreement with experimental data with respect to the substrate deformation and the latency time after which substrate-cytoskeletal coupling is strong enough for the growth cone to advance. Our simulations show that it takes the shortest time to achieve strong coupling when substrate stiffness was low at 4 pN/nm. Taken together, these results suggest that Aplysia growth cones respond faster and more efficiently to soft than stiff substrates.

Sub-surface imaging of carbon nanotube-polymer composites using dynamic AFM methods.

High-resolution sub-surface imaging of carbon nanotube (CNT) networks within polymer nanocomposites is demonstrated through electrical characterization techniques based on dynamic atomic force microscopy (AFM). We compare three techniques implemented in the single-pass configuration: DC-biased amplitude modulated AFM (AM-AFM), electrostatic force microscopy (EFM) and Kelvin probe force microscopy (KPFM) in terms of the physics of sub-surface image formation and experimental robustness. The methods were applied to study the dispersion of sub-surface networks of single-walled nanotubes (SWNTs) in a polyimide (PI) matrix. We conclude that among these methods, the KPFM channel, which measures the capacitance gradient (∂C/∂d) at the second harmonic of electrical excitation, is the best channel to obtain high-contrast images of the CNT network embedded in the polymer matrix, without the influence of surface conditions. Additionally, we propose an analysis of the ∂C/∂d images as a tool to characterize the dispersion and connectivity of the CNTs. Through the analysis we demonstrate that these AFM-based sub-surface methods probe sufficiently deep within the SWNT composites, to resolve clustered networks that likely play a role in conductivity percolation. This opens up the possibility of dynamic AFM-based characterization of sub-surface dispersion and connectivity in nanostructured composites, two critical parameters for nanocomposite applications in sensors and energy storage devices.

Subsurface imaging of carbon nanotube networks in polymers with DC-biased multifrequency dynamic atomic force microscopy.

The characterization of dispersion and connectivity of carbon nanotube (CNT) networks inside polymers is of great interest in polymer nanocomposites in new material systems, organic photovoltaics, and in electrodes for batteries and supercapacitors. We focus on a technique using amplitude modulation atomic force microscopy (AM-AFM) in the attractive regime of operation, using both single and dual mode excitation, which upon the application of a DC tip bias voltage allows, via the phase channel, the in situ, nanoscale, subsurface imaging of CNT networks dispersed in a polymer matrix at depths of 10-100 nm. We present an in-depth study of the origins of phase contrast in this technique and demonstrate that an electrical energy dissipation mechanism in the Coulomb attractive regime is key to the formation of the phase contrast which maps the spatial variations in the local capacitance and resistance due to the CNT network. We also note that dual frequency excitation can, under some conditions, improve the contrast for such samples. These methods open up the possibility for DC-biased amplitude modulation AFM to be used for mapping the variations in local capacitance and resistance in nanocomposites with conducting networks.

Comparative Analysis of an Expandable Modular Plant and a Stick-Built TiO2 Plant.

Expandable modular plants (EMPs) can be the future of the chemical industry, especially in emerging markets. Using the relative position of points on alternative NPV-time curves from the period of 10-20 years, we compare the economics of an expandable modular TiO2 plant with that of a large-scale TiO2 plant constructed fully on site (stick-built) and present scenarios where the expandable modular approach is economically favorable over the stick-built approach. To simplify the assessment of economic viability between constructing an EMP and a stick-built plant, we introduce a measure known as the flexibility feasibility ratio-a certain ratio of unit installed capacity in an EMP to the nameplate capacity of a stick-built plant at which the NPVs are equal at all points on alternative NPV-time curves. We determine that a flexibility feasibility ratio of 0.25 is suitable to install an expandable modular TiO2 plant in Nigeria, relatively.

Origins of phase contrast in the atomic force microscope in liquids.

We study the physical origins of phase contrast in dynamic atomic force microscopy (dAFM) in liquids where low-stiffness microcantilever probes are often used for nanoscale imaging of soft biological samples with gentle forces. Under these conditions, we show that the phase contrast derives primarily from a unique energy flow channel that opens up in liquids due to the momentary excitation of higher eigenmodes. Contrary to the common assumption, phase-contrast images in liquids using soft microcantilevers are often maps of short-range conservative interactions, such as local elastic response, rather than tip-sample dissipation. The theory is used to demonstrate variations in local elasticity of purple membrane and bacteriophage 29 virions in buffer solutions using the phase-contrast images.

3D nanomechanical mapping of subcellular and sub-nuclear structures of living cells by multi-harmonic AFM with long-tip microcantilevers.

Recent developments such as multi-harmonic Atomic Force Microscopy (AFM) techniques have enabled fast, quantitative mapping of nanomechanical properties of living cells. Due to their high spatiotemporal resolution, these methods provide new insights into changes of mechanical properties of subcellular structures due to disease or drug response. Here, we propose three new improvements to significantly improve the resolution, identification, and mechanical property quantification of sub-cellular and sub-nuclear structures using multi-harmonic AFM on living cells. First, microcantilever tips are streamlined using long-carbon tips to minimize long-range hydrodynamic interactions with the cell surface, to enhance the spatial resolution of nanomechanical maps and minimize hydrodynamic artifacts. Second, simultaneous Spinning Disk Confocal Microscopy (SDC) with live-cell fluorescent markers enables the unambiguous correlation between observed heterogeneities in nanomechanical maps with subcellular structures. Third, computational approaches are then used to estimate the mechanical properties of sub-nuclear structures. Results are demonstrated on living NIH 3T3 fibroblasts and breast cancer MDA-MB-231 cells, where properties of nucleoli, a deep intracellular structure, were assessed. The integrated approach opens the door to study the mechanobiology of sub-cellular structures during disease or drug response.

Quantitative force and dissipation measurements in liquids using piezo-excited atomic force microscopy: a unifying theory.

The use of a piezoelectric element (acoustic excitation) to vibrate the base of microcantilevers is a popular method for dynamic atomic force microscopy. In air or vacuum, the base motion is so small (relative to tip motion) that it can be neglected. However, in liquid environments the base motion can be large and cannot be neglected. Yet it cannot be directly observed in most AFMs. Therefore, in liquids, quantitative force and energy dissipation spectroscopy with acoustic AFM relies on theoretical formulae and models to estimate the magnitude of the base motion. However, such formulae can be inaccurate due to several effects. For example, a significant component of the piezo excitation does not mechanically excite the cantilever but rather transmits acoustic waves through the surrounding liquid, which in turn indirectly excites the cantilever. Moreover, resonances of the piezo, chip and holder can obscure the true cantilever dynamics even in well-designed liquid cells. Although some groups have tried to overcome these limitations (either by theory modification or better design of piezos and liquid cells), it is generally accepted that acoustic excitation is unsuitable for quantitative force and dissipation spectroscopy in liquids. In this paper the authors present a careful study of the base motion and excitation forces and propose a method by which quantitative analysis is in fact possible, thus opening this popular method for quantitative force and dissipation spectroscopy using dynamic AFM in liquids. This method is validated by experiments in water on mica using a scanning laser Doppler vibrometer, which can measure the actual base motion. Finally, the method is demonstrated by using small-amplitude dynamic AFM to extract the force gradients and dissipation on solvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica.

Uncertainty quantification in nanomechanical measurements using the atomic force microscope.

Quantifying uncertainty in measured properties of nanomaterials is a prerequisite for the manufacture of reliable nanoengineered materials and products. Yet, rigorous uncertainty quantification (UQ) is rarely applied for material property measurements with the atomic force microscope (AFM), a widely used instrument that can measure properties at nanometer scale resolution of both inorganic and biological surfaces and nanomaterials. We present a framework to ascribe uncertainty to local nanomechanical properties of any nanoparticle or surface measured with the AFM by taking into account the main uncertainty sources inherent in such measurements. We demonstrate the framework by quantifying uncertainty in AFM-based measurements of the transverse elastic modulus of cellulose nanocrystals (CNCs), an abundant, plant-derived nanomaterial whose mechanical properties are comparable to Kevlar fibers. For a single, isolated CNC the transverse elastic modulus was found to have a mean of 8.1 GPa and a 95% confidence interval of 2.7-20 GPa. A key result is that multiple replicates of force-distance curves do not sample the important sources of uncertainty, which are systematic in nature. The dominant source of uncertainty is the nondimensional photodiode sensitivity calibration rather than the cantilever stiffness or Z-piezo calibrations. The results underscore the great need for, and open a path towards, quantifying and minimizing uncertainty in AFM-based material property measurements of nanoparticles, nanostructured surfaces, thin films, polymers and biomaterials.

Discrimination of adhesion and viscoelasticity from nanoscale maps of polymer surfaces using bimodal atomic force microscopy.

The simultaneous excitation and measurement of two eigenmodes in bimodal atomic force microscopy (AFM) during sub-micron scale surface imaging augments the number of observables at each pixel of the image compared to the normal tapping mode. However, a comprehensive connection between the bimodal AFM observables and the surface adhesive and viscoelastic properties of polymer samples remains elusive. To address this gap, we first propose an algorithm that systematically accommodates surface forces and linearly viscoelastic three-dimensional deformation computed via Attard's model into the bimodal AFM framework. The proposed algorithm simultaneously satisfies the amplitude reduction formulas for both resonant eigenmodes and enables the rigorous prediction and interpretation of bimodal AFM observables with a first-principles approach. We used the proposed algorithm to predict the dependence of bimodal AFM observables on local adhesion and standard linear solid (SLS) constitutive parameters as well as operating conditions. Secondly, we present an inverse method to quantitatively predict the local adhesion and SLS viscoelastic parameters from bimodal AFM data acquired on a heterogeneous sample. We demonstrate the method experimentally using bimodal AFM on polystyrene-low density polyethylene (PS-LDPE) polymer blend. This inverse method enables the quantitative discrimination of adhesion and viscoelastic properties from bimodal AFM maps of such samples and opens the door for advanced computational interaction models to be used to quantify local nanomechanical properties of adhesive, viscoelastic materials using bimodal AFM.

Cantilever signature of tip detachment during contact resonance AFM.

Contact resonance atomic force microscopy, piezoresponse force microscopy, and electrochemical strain microscopy are atomic force microscopy modes in which the cantilever is held in contact with the sample at a constant average force while monitoring the cantilever motion under the influence of a small, superimposed vibrational signal. Though these modes depend on permanent contact, there is a lack of detailed analysis on how the cantilever motion evolves when this essential condition is violated. This is not an uncommon occurrence since higher operating amplitudes tend to yield better signal-to-noise ratio, so users may inadvertently reduce their experimental accuracy by inducing tip-sample detachment in an effort to improve their measurements. We shed light on this issue by deliberately pushing both our experimental equipment and numerical simulations to the point of tip-sample detachment to explore cantilever dynamics during a useful and observable threshold feature in the measured response. Numerical simulations of the analytical model allow for extended insight into cantilever dynamics such as full-length deflection and slope behavior, which can be challenging or unobtainable in a standard equipment configuration. With such tools, we are able to determine the cantilever motion during detachment and connect the qualitative and quantitative behavior to experimental features.