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. 2025 Aug 4;19(32):29109–29121. doi: 10.1021/acsnano.5c01873

Multiplexed Nanoscale Viscoelastic Mapping at Multiple Time Scales of Melanoma Cells as a Label-Free Cancer Biomarker

Cameron Parvini 1, Andrew Massey 1, Mazen Mezher 1, Alexander X Cartagena-Rivera 1,*
PMCID: PMC12369005  PMID: 40758976

Abstract

Evaluating nanoscale cellular mechanics for disease biomarkers has been challenging due to the significant heterogeneity between cells and other biological structures, which reflects the variability in gene expression. Atomic force microscopy-based methods can visualize these heterogeneities with high spatiotemporal resolution; however, processing large time-dependent viscoelastic data sets is computationally expensive. Here, we introduce a novel viscoelastic method based on a modified Fourier transform, enabling multitime-scale viscoelastic analysis at drastically improved rates (over 37,386-fold) compared to traditional approaches. We used this method to quantify multitime-scale viscoelastic properties of living melanoma cells with varying degrees of malignancy. More malignant cells are softer and more fluid near the nucleus, while the leading edge is stiffer and more viscous, suggesting that regional mechanical effects are critical for enhanced migration. Cellular population heterogeneity analyses revealed that metastatic cells exhibit fluid-like viscoelastic behavior, while benign cells exhibit more solid-like behavior. This new method provides novel label-free biophysical indicators to aid in diagnostic and therapeutic approaches.

Keywords: atomic force microscopy, mechanobiology, viscoelasticity, melanoma, cancer, biomarker

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Multiplexed imaging approaches can detect multiple biomarkers simultaneously. Standard multiplexed techniques (such as fluorescence microscopy, magnetic resonance imaging, CT scan, among several others) use externally applied agents to label specific structures, and thus are limited in the number of labels that can be used simultaneously. Mechanical properties have often been assessed as biomarkers of multiple diseases, especially cancer. Growing scientific evidence suggests that several mechanical properties emerge as potential biomarkers of cancer. − Mechanical properties such as stiffness, viscosity, tension, pressure, and adhesion have been shown to significantly change in response to cancer development, progression, and metastasis. ,− Given the wide array of potentially important mechanical properties, there is a need to develop novel multiplex imaging approaches capable of simultaneously detecting several relevant new biomarkers. These biomarkers can be correlated with those from standard imaging technologies for studying disease progression and treatment response and for monitoring potential disease recurrence.

The study of cellular and tissue nanomechanics is not new, ,, but progress in developing robust correlations for medical applications has been limited due to the nature of the methods used, which are often fundamentally inapplicable to the problem at hand. Most nanomechanical characterization approaches rely on either qualitative and/or indirect measures or approximate empirical quantities. , For example, the most popular mechanical quantity that is not rigorous for characterizing soft biological complex systems is the apparent Young’s modulus, which is based on fitting AFM force–indentation curves using Hertzian (elastic) contact mechanics models. This methodology has been extensively applied to both tissues and single cells in various contexts, including cancer. − However, this approach is physically inappropriate because the Young’s modulus strictly applies to linear-elastic materials, and thus is not well suited to characterize viscoelastic materials. , Viscoelasticity is a mechanical behavior that describes a material that simultaneously exhibits viscous and elastic behaviors. Cellular functions are directly influenced by viscoelastic properties, as cells undergo deformation and relaxation in response to both internal and external mechanical forces. To quantitatively characterize material behavior at multiple time scales, we recently developed an iterative, parametrized viscoelastic method to determine the time-dependent viscoelastic properties of living human skin cells under physiologically relevant conditions. However, this approach requires nonlinear optimization of traditional rheological models for each AFM force curve, making the method computationally expensive and extremely slow, requiring ∼18 min to process one force curve. This made our previous method impractical for running viscoelastic analyses of large data sets. To overcome this challenge, we have developed a method that leverages recent advancements in viscoelastic analysis via the discrete modified Fourier transform (Z-transform). The method uses model-free viscoelastic quantities such as material retardance and relaxance and avoids the need to optimize potentially inappropriate material models for raw data. Instead, the Z-transform approach allows for direct viscoelastic inversion of high-resolution spatiotemporal data at rates that are orders of magnitude faster (more than 37,386 times) than optimizing a traditional rheological model for every AFM force curve.

Cutaneous metastatic melanoma is a highly aggressive disease that is responsible for most melanoma-related deaths. It is characterized by a high mutational burden, resistance to traditional chemotherapies, and rapid metastasis. Melanoma arises from transformed melanocytes, which are pigment-producing cells that reside in the skin. The developmental history of melanocytes is an important factor underlying melanoma aggressiveness. Unlike other cell types in the epidermis, melanocytes constitutively express antiapoptotic BCL2 proteins, which makes them resistant to apoptosis and allows them to survive for decades in the skin, where they can acquire numerous mutations. A recent study has shown that a mutated BRAF gene (V600E) in human metastatic melanoma cells drives abnormalities in actomyosin cytoskeletal dynamics related to the activation of myosins, which can lead to high myosin contractility in cancer cells. Previously, we have shown that human BRAF V600E mutant melanoma A375-MA2 cells display a significant increase in myosin contractility and cortical tension, leading to a switch in cell migration from mesenchymal to an upregulated highly motile migration modality called fast-ameboid leader-bleb migration. − These observations suggest that while cutaneous metastatic melanoma has a high degree of heterogeneity, there is a more simplistic biomechanical phenotype responsible for subcellular modifications that could be elucidated to better understand malignancy progression and develop novel personalized medicine strategies.

Here, we investigated whether a multiplexed, high spatiotemporal resolution, AFM-based nanomechanical mapping method combined with our Z-transform viscoelastic characterization strategy could be used to acquire quantitative measurements of viscoelastic properties from living human BRAF V600E mutant melanoma cells at multiple time scales. The Z-transform approach has been successful for single-point measurements of viscoelastic behavior at multiple time scales for stiffer and viscous synthetic polymers. However, the capability of generating nanoscale viscoelastic property maps of softer and more fluid living cells has not yet been shown. First, we modified the Z-transform viscoelastic approach for high spatiotemporal mapping applications, demonstrating that it indeed visualizes detailed nanoscale heterogeneity across single cells present in viscoelastic maps at multiple time scales (μs to ms). This capability was verified through the measurement of cells that exhibit viscoelastic behavior in important cellular structures, such as the plasma membrane and filamentous actin cytoskeleton. Second, we characterized the viscoelastic behavior of human BRAF V600E mutant melanoma A375 cells with increasing malignancy (primary tumor to highly metastatic) and compared them with the viscoelastic behavior of benign melanocytes. We found that melanoma cells are softer and more fluid than melanocytes and cells tend to be softer and more fluid with increasing malignancy. Overall, this new method enables the efficient viscoelastic inversion of many experiments, creating a large data set that could be easily passed to machine learning methods and thus dramatically improve the type and quantity of biomarkers available for designing next-generation precision therapeutics.

Results and Discussion

Z-Transform-Based High Spatiotemporal Resolution Viscoelastic Mapping Approach

Traditional viscoelastic approaches often involve parametrizing a viscoelastic rheological model via nonlinear optimization methods, such that the model mimics a recorded force curve. ,, This approach is stochastic in nature because of the random starting guess for each parameter; it is very sensitive to how close the starting guesses are to the “true” material values and leaves room for error in the approximation. In addition, these approaches are slow, and for large data sets acquired using AFM nanomechanical mapping methods (including Quantitative Imaging mode (QI), Force Volume, or PeakForce Tapping), there is simply too much data to apply these methods to every pixel. To overcome this key challenge, we modified a Z-transform-based viscoelastic approach to analyze the viscoelastic properties of living cells at higher spatiotemporal resolution. The Z-transform approach achieves this by leveraging discrete-time data to conduct viscoelastic analysis; when this approach is applied to each pixel of a QI map, viscoelastic information can be extracted in a fraction of the time versus traditional nonlinear parametrization approaches. Here, a raw 128 × 128 pixel map (containing 16,384 pixels) can be analyzed for viscoelastic properties using the Z-transform method after 1 h and 25 min, whereas only 195 force curves can be analyzed after 7–10 days via the iterative-fitting viscoelastic parametrization methodology.

The noteworthy benefits of using the Z-transform-based viscoelastic approach include (a) avoiding a predefined mechanical model designation and (b) allowing the quantification of viscoelastic properties at multiple time scales. First, by avoiding a model designation, the approach requires fewer potentially problematic mechanical assumptions about the cell surface and composition, providing a more straightforward quantification of viscoelasticity by directly computing the stress and strain components. The improvement is analogous to taking a picture of an object versus looking at the shape of its shadow: direct inversion allows for less ambiguity, and if the user requires a mechanical model for their study, this enables better parametrization of such viscoelastic models in the frequency domain (thus avoiding computationally costly convolution integrals in the time domain). Second, since the method works in the frequency domain, it allows preservation of material behavior at all time points measured instead of utilizing one specific time point and discarding the rest. Overall, both the improvements in speed and the avoidance of difficult mechanical assumptions represent significant improvements over the state-of-the-art methods in nanoscale viscoelastic material analysis for cells and soft biological surfaces.

We began by applying the Z-transform mathematical framework to analyze, at high spatiotemporal resolution, the viscoelastic properties of living cells. Using the fundamental definition of the modified Fourier Transform, a set of equations is derived that allows the Z-transformation of discrete-time data into the frequency domain (Supporting Information, Section 1). Through a process similar to the derivation of Laplace Transform viscoelasticity relationships, we obtained a stress–strain relationship in the Z-domain (eqs S13 and S14). These equations form the fundamental basis of the relationship between force and indentation (which are observed in AFM experiments) and allow the direct calculation of viscoelastic properties. To be appropriate for AFM nanoindentation, we finally introduced a geometrical correction to better describe the indentation profile using a paraboloidal indenter (eqs S19a and S19b). To this point, the analysis follows what was outlined in the original methodology, with the significant improvement that the Z-transform quantities can be calculated using the data contained within each pixel of a QI map instead of just a single force curve.

Next, we benchmarked the performance of our Z-transform AFM nanomechanical mapping approach by determining the nanoscale viscoelastic properties of soft polyacrylamide (PAA) hydrogels and previously characterized adherent human fibroblast cells. Figure shows a detailed workflow of the Z-transform AFM nanomechanical mapping method. First, we performed high spatial resolution AFM QI to record force vs indentation and force vs time responses for each pixel (Figure a). Then, we used our new Z-transform approach to determine the viscoelastic properties of each specimen, including the storage modulus (E S), loss modulus (E L), and loss angle (θ) at multiple time scales for each individual pixel and then combined all the pixels to generate high spatiotemporal resolution files (Figure a,b). To validate our approach using a standard specimen mimicking the soft material behaviors of living cells, we extracted the viscoelastic properties (E S, E L, and θ) of soft PAA hydrogels (Young’s modulus of 2 and 8 kPa measured by quasi-static AFM). We observed that the viscoelastic response obtained by our Z-transform AFM nanomechanical mapping approach is similar to values measured using shear rheology (Figure a,b and Movies S1 and S2). In addition, the extracted average storage modulus values from maps (soft gel 1.66 ± 0.36 kPa and stiff gel 3.84 ± 0.66 kPa) correlate well with the Young’s modulus values obtained by colloidal AFM. Lastly, to validate our approach using a highly characterized living cell, we extracted the viscoelastic properties of 2D adherent human fibroblast (HFF) cells. We observed that the extracted viscoelastic properties (E S, E L, and θ) of adherent HFF cells are similar to previously reported values (Figure c and Movie S3).

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High spatiotemporal Z-transform AFM-based viscoelastic mapping approach. (a) Schematics of the Z-transform AFM-based nanomechanical method showing an adherent cell being indented in several locations by an AFM probe. Each pixel records the force vs indentation and force vs time curves that will be transformed to the Z-domain to determine the viscoelastic properties at multiple time scales. (b) Workflow chart summarizing a step-by-step computational strategy indicating how our Z-visco data processing script works: (a) handle and precondition the data, (b) determine the viscoelastic properties (E S, E L, and θ) per pixel, (c) generate nanoscale maps for each individual viscoelastic property at each recorded time point, and (d) generate compiled animations showing all the viscoelastic property maps across all the measured time points. As an additional optional step, the script can perform clustering analysis of multiple cells to classify data and identify emergent mechanical features.

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Benchmarking the performance of our Z-transform AFM nanomechanical mapping approach on soft PAA hydrogels and 2D adherent human fibroblasts. (a) Nanoscale viscoelastic mapping (E S, E L, and θ) of two soft PAA hydrogels (soft gel 2 kPa and stiff gel 8 kPa) mimicking living cell Young’s modulus at one recorded time point (2 kHz). Data represented in box plots are mean ± SD (N = 10 soft and N = 10 stiff PAA gels) from 2 independent experiments. Statistical analysis was performed using the Kolmogorov–Smirnov test (significance level of 0.05). P values are indicated in each graph. The complete nanomechanical multitime scales data sets (Movies S1 and S2) contain recorded high spatiotemporal resolution viscoelastic characterization (from 500 Hz to 60 kHz) of the 2 and 8 kPa PAA hydrogels. (b) Shear moduli (shear storage modulus G′ and shear loss modulus G″) of two soft PAA hydrogels (soft gel 2 kPa and stiff gel 8 kPa) obtained from shear rheology were used to estimate the effective Young’s modulus. Data represented are mean ± SD (N = 3 soft and N = 3 stiff PAA gels) from 3 independent experiments. (c) Nanoscale viscoelastic mapping (E S, E L, and θ) of an adherent human fibroblast cell at one recorded time point (2 kHz). The complete nanomechanical multitime scales data set (Movie S3) contains recorded high spatiotemporal resolution viscoelastic characterization (from 500 Hz to 60 kHz) of the fibroblast cell.

Enhanced Spatiotemporal Resolution Viscoelastic Mapping of Living Cells

To demonstrate the enhancement in spatiotemporal resolution viscoelastic mapping of living cells by the Z-transform approach, we used physiologically relevant human cutaneous metastatic BRAF V600E mutant melanoma model cell lines (A375-P, A375-MA1, and A375-MA2) and compared them against benign counterparts, primary human melanocytes (HeMA), and HFF cells. Here, we performed high spatial resolution AFM-QI mapping and used our Z-transform approach to determine the nanoscale viscoelastic behavior at multiple time scales (Figure a–d and Movies S4–S8). The viscoelastic maps obtained from adherent HFFs, A375-P, A375-MA1, and A375-MA2 cells clearly display nonuniform and heterogeneous contrasts in viscoelastic properties across the cells (lamellipodium, nucleus, and trailing edge regions), with subcellular cytoskeletal structures clearly visible (Figure and Movies S4 and S6–S8). However, viscoelastic maps of adherent HeMA cells clearly displayed more homogeneously distributed viscoelastic properties across the cell (Figure b–d and Movie S5). These differences in viscoelastic behavior correlate with filamentous actin and microtubular cytoskeletal organization (Figure ). 2D adherent HFF and HeMA cells have more thicker actin stress fibers and more abundant microtubules compared to melanoma cells; thus, an increase in actin and microtubule skeletal structure abundance correlates with increased viscoelastic properties, whereas reduced cytoskeletal structures correlate with decreased viscoelastic properties (Figure ). In addition, observed differences in viscoelastic behavior correspond well with the biological functions of the cell types; for example, HFFs and melanoma cells are more polarized and migratory, whereas HeMA cells are less migratory.

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High spatiotemporal resolution and quantitative viscoelastic mapping of several different living adherent cell types. (a) Topography image of the different cell types probed (HFF, HeMA, A375-P, A327-MA1, and A375-MA2). A375 melanoma cells are a well-established metastatic model. (b–d) Resulting high spatiotemporal resolution and quantitative storage modulus (b), loss modulus (c), and loss angle (d) maps for all the adherent cell types tested at three different widely spaced frequencies (2, 20, and 40 kHz). The presented data are a subset extracted from the complete resulting data sets (Movies S4–S8). We performed 3 independent experiments for all the different cell types, with a total number of individual cells probed and analyzed (N = 16 HFF, N = 17 HeMA, N = 17 A375-P, N = 18 A375-MA1, and N = 18 A375-MA2). Representative data from a single experiment per cell type are shown.

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Altered organization of filamentous actin and microtubule cytoskeletons in melanoma cancer cells. Maximum intensity Z-projections (XY) demonstrating alterations in filamentous actin (magenta) and microtubule cytoskeletons (green). Immunofluorescence images of cells were captured using a Zeiss LSM 900 Airyscan 2. Compared with benign counterpart fibroblasts and melanocytes, highly malignant melanoma cells exhibit significant decreases in F-actin and microtubule network density.

The viscoelastic response of the measured living cells varies not only spatially across the cells but also with time and frequency. To visualize the frequency dependence of these properties, three different frequencies were selected: 2, 20, and 40 kHz (Figure b–d). Both E S (indicates elastic action, elasticity) and E L (indicates viscous action, viscosity) change with increasing frequency; however, E L was observed to change more profoundly. Interestingly, large changes in E L occurred in regions with increased cytoskeletal density and structures, demonstrating the dominant contribution of cytoskeletal mechanical properties (Figures c and ). In all of the measured cells, E L seems to increase from low frequencies (2 kHz) to a maximum value at moderate frequencies (∼20 kHz) and then decrease at higher frequencies (∼40 kHz); however, E L is still greater at high frequencies than at lower frequencies. This could suggest that in crowded environments, such as inside living cells, denser and stiffer cytoskeletal elements and structures increase viscosity, potentially by increasing friction with the cytoplasm. Interestingly, θ (loss angle, which describes the ratio of E L/E S) indicates more ambiguous behavior in metastatic melanoma cells, where θ at higher frequencies is much lower in value compared to lower frequencies (Figure d). This finding indicates an apparent shift in viscoelastic behavior from frequency-dependent stiffening of benign cells and parental melanoma A375-P cells to frequency-dependent softening exhibited by metastatic melanoma cells A375-MA1 and A375-MA2.

It is noteworthy that the proposed viscoelastic inversion method is indifferent to the range of frequencies in the data set. The limiting factor in the temporal bandwidth is the time scales at which the experimental data are collected. Faster experimental AFM sampling (high data collection rates) would give additional high-frequency information, whereas longer overall tip–sample interactions (slower data collection) would give more low-frequency information. In this way, the method can be tailored to provide viscoelastic insight for any time scale of interest (based on hardware and sample limitations) without the need to capture unnecessary data points in less desirable temporal ranges.

Increased Melanoma Malignancy Correlates with Localized Nanoscale Fluidization

The enhanced spatiotemporal resolution of viscoelastic properties resulting from the Z-transform approach allowed us to investigate the localized nanoscale fluidization of cells during melanoma development and metastasis. To better quantify and compare the temporal changes in viscoelastic properties for all of the cells, we performed kymograph analyses. We traced lines from the leading to trailing edges of cells to extract the viscoelastic properties along the lines at every frequency measured and then plotted them in a kymograph (Figure ). As expected, we observed a significant decrease in elasticity (E S) and viscosity (E L) between melanoma cells and HeMA. Interestingly, when we compared melanoma cells with graded metastasis progression, we observed a significant increase in stiffness and viscosity in the nuclear region in metastatic A375-MA1 cells compared to primary tumor A375-P cells and highly metastatic A375-MA2 cells. Another surprising observation was the profound increase in the stiffness and viscosity at the leading edge of the lamellipodium in highly metastatic A375-MA2 cells, which could be explained by the increased aggressiveness and motility of these cells. Visualizing these localized nanoscale changes in viscoelastic properties at multiple time scales in living adherent cells would not have been possible before due to the absence of a nanomechanical method capable of such analysis.

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Increased melanoma malignancy and metastasis correlate with localized differential softening and fluidization. (a–e) Kymograph analyses from time-lapse movies (Movies S4–S8) of nanoscale viscoelastic properties (E S, E L, and θ). Kymographs were generated by scanning mean intensities within a 2 μm-wide line (red line) along the polarization axis from the lamellipodium’s leading edge (a) to the trailing edge (b). We performed 3 independent experiments for all the different cell types, with a total number of individual cells probed and analyzed (N = 16 HFF, N = 17 HeMA, N = 17 A375-P, N = 18 A375-MA1, and N = 18 A375-MA2). Experiments were repeated three times for all the different cell types, with a total of individual cells probed (N = 16 HFF, 17 HeMA, 17 A375-P, 18 A375-MA1, and 18 A375-MA2). Representative data from a single experiment per cell type are shown.

A noteworthy viscoelastic behavior to highlight that emerges from this method is the apparent temporal changes in E L and θ that the measured cells exhibit at the frequencies tested. Interestingly, E L strongly depends on the frequency at the nanoscale, while E S seems to be almost insensitive to the frequency (Figure ). Since θ directly depends on E L, it also exhibits the same frequency dependency.

Cellular Population-Based Viscoelastic Spatial Pattern Analysis at Multiple Time Scales

Viscoelastic materials are typically categorized as materials with either predominantly solid-like or fluid-like viscoelastic behaviors. A solid-like viscoelastic behavior usually results in a high storage modulus and low loss modulus, whereas a fluid-like viscoelastic behavior typically results in a high loss modulus and low storage modulus. The density scatter plots of calculated viscoelastic properties at 3 time points (2, 20, and 40 kHz) containing all the mechanical measurements from every pixel recorded in all the cells measured are presented in Figure (see Figure S1 for nonprocessed scatter plots). A clear feature observed in the density scatter plots is that, compared with malignant melanoma cells, benign melanocytes possess a well-defined second data cluster at higher time points with markedly greater storage and loss moduli (Figure , white circles). Another interesting observation extracted from the density scatter plots is the spatiotemporal patterns of viscoelastic behavior with an increasing frequency. For all the measured cells except for metastatic A375-MA1 cells, we observed a significant increase in viscoelasticity, defined as an increase in both the storage and loss moduli, as shown by the region of peak data point density. This frequency-dependent viscoelastic behavior has been previously observed and reported in living cells, including neurons, fibroblasts, and breast cancer cells. − However, it is surprising to observe that metastatic melanoma cells may not follow a similar increase in viscoelastic properties at higher frequencies but exhibit an apparent decrease in viscoelastic properties, which suggests that viscoelastic property measurements at multiple time scales could be used as another cancer biomarker.

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Density scatter plots comparing the elastic storage modulus and viscous loss modulus of living benign and melanoma cells at different frequencies. Red color indicates a greater density of points, while blue color indicates a lower density. We performed 3 independent experiments for all the different cell types, with a total number of individual cells probed and analyzed (N = 16 HFF, N = 17 HeMA, N = 17 A375-P, N = 18 A375-MA1, and N = 18 A375-MA2). The plots contained many points collected on many different cells: HFF 16 cells with 102,045 points, HeMA 17 cells with 107,873 points, A375-P 18 cells with 88,899 points, A375-MA1 18 cells with 73,864 points, and A375-MA2 18 cells with 95,283 points.

Conclusions

We have described a new method capable of acquiring AFM-based viscoelastic maps with high spatiotemporal resolution at multiple time scales. Our new method leverages recent advancements in viscoelastic analyses via the discrete modified Fourier transform (Z-transform), allowing efficient viscoelastic inversion of AFM force spectroscopy data. The method directly observes model-assumption-free viscoelastic behavior and thus uses generalized viscoelastic quantities (material retardance and relaxance). By combining the Z-transform approach with model-assumption-free generalized viscoelastic quantities, our approach allows for viscoelastic inversion of high spatiotemporal resolution of physiologically relevant viscoelastic property maps (E S, E L, and θ) at computational rates that are several orders of magnitude faster (over 37,386 times faster) than existing viscoelastic methods, thus allowing faster postprocessing of data and making significant progress toward live viscoelastic analysis while AFM data are being recorded.

Compared with standard viscoelastic approaches, our current method provides superior spatiotemporal performance. Single-point force spectroscopy methods capable of determining the nanoscale viscoelastic properties of cells have been developed. ,,, However, these methods both have low spatial resolution and require a traditional iterative approach to determine viscoelastic properties (which are slow and computationally expensive), thus rendering them inadequate for high spatiotemporal resolution mapping. More sophisticated and faster dynamic AFM methodologies have been developed, aiming to measure the viscoelasticity of living cells at the micro- and nanoscale. ,− For example, a multifrequency methodology called multiharmonic AFM has even been used in other biological systems, such as on intact bacterial and viral particles. , However, multiharmonic AFM treats biomaterials as simple Kelvin–Voight solids and does not reproduce the major viscoelastic behaviors expected in complex biomaterials, including creep, fluidity (the ability of the material to experience steady state flow), or multiple retardation times. , A comparison of the spatial resolution and viscoelastic processing speed of the proposed method with those of existing quasi-static and multiharmonic AFM methods is shown in Table . The table clearly shows that the viscoelastic processing throughput of our proposed method in mapping nanoscale viscoelastic properties at multiple time scales of live cells represents an improvement of more than 37,386-fold in viscoelastic processing compared to the existing iterative-fitting viscoelastic AFM approach.

1. Comparison of the Spatial and Temporal Resolutions of the Proposed Z-Transform Viscoelastic AFM Papping Method with Existing Methods .

methodology cell types data set size (curves per cell or pixels) spatial resolution imaging time (per data set) viscoelastic processing time (per data set) time points measured (frames) viscoelastic mapping throughput
this work HFF, HeMA, A375-P, A375-MA1, A375-MA2 65,536 120 nm 26 min 174 min 238 89,726 pixels/min
iterative-fitting viscoelastic AFM HFF, HeMA, A375-P 5 10 μm 10 min 207 min 99 2.4 pixels/min
multiharmonic AFM rat fibroblasts, human red blood cells 65,536 150 nm 15 min 30 min 1 2185 pixels/min
force-volume AFM rat fibroblasts 4096 781 nm 20 min not capable not capable not capable
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a

The presented method can reach sub-50 nm spatial resolution in less than 10–30 min per 256 × 256 pixels maps, depending on the type of live cells and structures being scanned. In contrast with existing methods, this Z-transform viscoelastic method is the only method capable of mapping viscoelastic properties at multiple time scales with nanoscale resolution. Combining the metrics of spatial resolution (pixels) and viscoelastic processing time (minutes), our proposed method generates high-resolution maps of nanoscale viscoelastic properties at multiple time scales from live cells while delivering an enormous 37,386-fold improvement in viscoelastic processing compared to the existing iterative-fitting viscoelastic AFM approach.

Similar to any viscoelastic characterization method, the Z-transform performance may degrade if presented with data containing excessive electronic or thermal noise (Supporting Information, Section 5). Additionally, if there are a large enough number of samples in the data set to reduce the computational precision (which is 10–16 for modern equipment) to below the scale appropriate for the AFM quantities measured, this can introduce large numerical errors during transformation; observing the discrete definition of the Z-transform (eq S11), one can see that for a large N the complex variable z will converge toward zero and effectively drop its values below the machine precision threshold. Provided that users select an appropriate number of samples, this issue can be avoided entirely. Nevertheless, compared with existing viscoelastic mapping approaches, our current method offers improved quantitative, multiparametric, multifrequency, and spatiotemporal resolution performance in all areas.

We envision several potential extensions of our current work. Since we have demonstrated that we can successfully use high spatial resolution AFM mapping data to determine the viscoelastic properties of living adherent cells at multiple time scales, the next logical application of this method is investigating the viscoelastic behavior of complex tissues, including 2D monolayers, 3D spheroids/organoids, and harvested functional tissues. − Another potential improvement could be to perform simultaneous optical fluorescent structural information with AFM-based nanoscale viscoelastic properties for enhanced mechanobiological interpretation of data on living cells. It would also be interesting to explore whether emerging artificial intelligence platforms could be used to (a) further improve the spatiotemporal resolution of obtained viscoelastic maps by denoising and deblurring, (b) implement automated assessment of data quality at the single cell and population levels, and (c) perform automated nanomechanical image feature recognition and classification. −

Methods

Cell Culture and Preparation

Human foreskin fibroblast cells were obtained from the American Type Culture Collection (ATCC, Cat. # SCRC-1041, Manassas, VA) and cultured in Dulbecco’s Modified Eagle’s Medium (DMEM, Life Technologies, Carlsbad, CA) supplemented with 10% fetal bovine serum (FBS, Life Technologies), 1 mM sodium pyruvate (Life Technologies), 1× GlutaMAX (Life Technologies), and 1% Penicillin-Streptomycin (Life Technologies).

Human primary epidermal melanocyte cells were obtained from ATCC (Cat. # PCS-200-013) and cultured in Dermal Cell Basal Medium (ATCC, Cat. # PCS-200-030) supplemented with Phenol Red (ATCC) and Adult Melanocyte Growth Kit (ATCC, Cat. # PCS-200-042).

Human melanoma A375-P cells (Cat. #: CRL-1619), A375-MA1 cells (Cat. # CRL-3222), and A375-MA2 cells (Cat. # CRL-3223) were obtained from ATCC. All three melanoma cell lines were cultured in DMEM supplemented with 10% FBS (Life Technologies), 1× GlutaMAX (Life Technologies), 1% Penicillin-Streptomycin (Life Technologies), and 20 mM HEPES pH 7.4.

All measured cell lines were seeded on 35 mm glass bottom dishes (FluoroDish FD35-100, World Precision Instruments) to <50% confluence. Cells were left to adhere to the glass bottom dishes overnight and maintained at 37 °C and 5% CO2. On the following day, the cells were rinsed with PBS, and fresh media were added. The cells were then transported to the AFM system and placed on the AFM X–Y stage for AFM-based force spectroscopy measurements.

Confocal Immunofluorescence Microscopy

Cells were plated on 35 mm glass bottom dishes (FluoroDish) for 24 h. Once the desired confluency was reached (≤50%), the cells were fixed for 15 min at room temperature with 4% paraformaldehyde (PFA; Life Technologies). After rinsing with 1× PBS three times, the cells were permeabilized with 0.5% Triton X-100 in 1× PBS at room temperature for 10 min. For filamentous actin labeling, the cells were rinsed with PBS 1× three times before they were incubated with Alexa Fluor-647-labeled Phalloidin (cat. # A12379; Life Technologies) diluted 1:400 in PBS for 40 min. For microtubule labeling, after the cells were permeabilized as described above, the cells were first blocked for 1 h at room temperature with blocking solution (BSA + 5% goat serum). Then, the cells were promptly incubated with a mouse monoclonal β-tubulin primary antibody (Cat. # MA5-16308; Life Technologies) diluted 2.5 μg/mL in blocking solution for 2 h at room temperature, followed by three rinses with 1× PBS, and then incubated with an Alexa Fluor-488-conjugated secondary antibody (Cat. # A-11001; Life Technologies) diluted 1:500 in blocking solution for 1 h. Finally, the cells were rinsed with 1× PBS three times. Hoechst 33342 (Cat. # 62249; Life Technologies) was added, the cells were incubated for 10 min, and then rinsed 3 more times. The cells were then transported to a microscope for imaging.

Immunofluorescence imaging of adherent cells to visualize cytoskeletal networks was performed on a Zeiss Axio Observer.7 optical microscope (Zeiss) equipped with a Confocal Laser Scanning Microscope LSM 900 with Airyscan 2 and Multiplex Module (LSM 900, Zeiss) and a 63x oil immersion objective (1.45 NA, Plan-Apochromat, Zeiss). The laser power and photomultiplier (gains) settings were maintained at similar values for all conditions to allow a direct comparison. Z stack volumetric images were acquired through the whole-cell volume with a fixed pinhole of 0.7 μm (all channels) and a step size of 0.5 μm. All Z stack files were deconvoluted using the Airyscan image processing software (Zeiss). The processed files were subsequently analyzed using the open-access image analysis software ImageJ (National Institutes of Health) to generate maximum intensity Z projections.

Shear Rheology

To prepare soft polyacrylamide (PAA) hydrogels were used to collect rheometric data, a polycarbonate hydrophobic sheet was used as a support base at the bottom, and then a custom-made acrylic ring (outer diameter: 2 in., inner diameter: 1.5 in., thickness: 0.06 in.) was placed on top of the polycarbonate sheet to hold the PAA hydrogel solution within the circular ring. Soft PAA hydrogels were prepared according to the protocol mentioned by Tse and Engler by mixing acrylamide and bis­(acrylamide) (BioRad) in a mix ratio of 4%:0.15% for 2 kPa and 5%:0.3% for 8 kPa, followed by adding 4 μL of TEMED for cross-linking and 10 μL of APS, to a total volume of 1 mL gel solution. Each PAA hydrogel solution (∼900 μL) was pipetted onto the polycarbonate sheet within the acrylic circular ring, and then another polycarbonate sheet was placed on top of the ring with a glass slide to fully seal any gap between the two polycarbonate sheets. Then, a heavy-weight block (similar in size to the glass slide) was placed on top of the glass slide to guarantee the perfect sealing of the PAA hydrogel between the two polycarbonate sheets. A small amount (∼100 μL) of the PAA hydrogel was left in the 1 mL tube to be used as an indicator of gelation. The PAA hydrogels were kept polymerizing for 3 h, then the heavy block and the glass slide were carefully removed, the top polycarbonate sheet was flipped upside-down, and the fully polymerized PAA hydrogel was now facing upward. Last, the PAA hydrogels were kept inside the biosafety cabinet for 1.5 h to dry the excess liquid from their outer surface.

After drying, the polymerized PAA hydrogel on the polycarbonate sheet was placed facing down on the rheometer plate, and the top polycarbonate sheet was gently removed. Resulting soft PAA hydrogels had a diameter of roughly 25 mm and a thickness of ∼1 mm. Shear rheology of soft PAA hydrogels was performed by using a Kinexus Prime pro+ rotational rheometer (Netzsch) with a 25 mm diameter plate–plate geometry. The shear viscoelastic properties of PAA hydrogels were measured using a frequency sweep test with 2% constant strain and a sweeping frequency range of 1–10 Hz. The estimated Young’s modulus from the rheometer data was calculated from the shear modulus (G) using the formulas E = 2­(1 + v)G, where v is Poisson’s ratio and was assumed to be 0.5 for incompressible materials.

Atomic Force Microscopy

Quantitative Imaging (QI) mode high spatiotemporal resolution AFM mapping of either soft PAA hydrogels or living 2D adherent cells was performed using a Bruker JPK NanoWizard 4XP BioScience AFM system (Bruker) mounted on an inverted Zeiss Axio Observer.7 optical microscope (Zeiss) equipped with a Confocal Laser Scanning Microscope LSM 900 with Airyscan 2 and Multiplex Module (LSM 900, Zeiss) and with a 40× objective (0.95 NA, Plan-Apochromat, Zeiss). During the QI-AFM experiments, living cells were maintained at 37 °C using a Bruker Petri dish heating stage. The soft PAA hydrogels and living cells were scanned using a probe appropriate for live cell imaging with a tip height of 17 μm, a controlled tip radius of 65 nm, and an opening angle of 15° (PFQNM-LC, Bruker). The cantilever probes used had calibrated spring constant values ranging between 0.048 and 0.083 N/m, as determined using the thermal tuning method. After calibration, the probes were left at 37 °C to equilibrate for 30 min before any scans were conducted to prevent excess thermal drift. Probes were replaced for each new experiment or replaced more frequently as needed. The applied force was set between 500 and 800 pN, yielding indentations between 200 and 500 nm. The probe was indented at a constant speed of 125 μm/s with a ramp size ranging between 1.25 and 1.5 μm. Images were collected at a scan resolution of either 256 × 256 pixels, 128 × 128 pixels, or 32 × 32 pixels in 50 × 50 μm2 or 5 × 5 μm2 scan areas. With these scanning parameters, each cell scan took ∼2 min for 32 × 32 pixels, ∼8 min for 128 × 128 pixels, and ∼32 min for 256 × 256 pixels to finish capturing.

Z-Transform Viscoelastic Inversion

Given both the extreme complexity and ambiguity of specifying an appropriate viscoelastic material model for biological samples, the data sets presented have been processed using a modern model-free approach based upon the Discrete Fourier Transform. This approach allows the transformation of discrete-time series data into the complex-valued frequency-domain representation and represents a marked improvement over traditional Laplace transform methods in both speed and flexibility.

For a deeper discussion on the topic of how and why the Z-Transform Inversion approach is appropriate, readers are directed to the Supporting Information chapter titled “Extracting Viscoelastic Information from AFM Data using a Discrete Integral Transform”, which further explains how the method and transformation parameters are derived. The function that controls the transformation is called “zTransformCurve” and takes a variety of arguments, which are more comprehensively described in the Supporting Information.

The key equations are eqs S17–S19, which allow calculation of the Z-Domain relaxance and retardance – the mechanical properties that describe how a sample will respond to force or displacement inputs. To use these equations, the force and indentation data must already be transformed into the Z-Domain. This is achieved by performing an FFT-based convolution (line 86 of the zTransformCurve function) which follows exactly the form of eq S11, where the complex variable z has been replaced by the first exponential form described in eq S12. The decay exponent α and complex frequency iω thus fully describe that exponential form e α e iω, and the frequency domain force F(z) and indentation h(z) are calculated directly by the multiplication and summation of their respective time series data according to eq S11.

The Z-Domain transformation decay exponent (α) given by eq S21 is calculated via the method recommended by Uluutku et al. and is the ratio of the last and first data values (x[N] and x[1], respectively) normalized by the number of data points in the set. The decay constant was therefore calculated for each pixel independently, according to the frequency information contained therein. At this stage, the Z-Transform Inversion of experimental data was complete, which presented a unique advantage over inversion approaches that would have required nonlinear optimization to reach a similar point in the analysis.

Data Analysis

Data Management and Correction

For the data analysis of all cell types, the MATLAB script was modified to function on a High-Performance Computing (HPC) cluster at the National Institutes of Health’s Biowulf Linux cluster (http://biowulf.nih.gov; modified to meet specific HPC requirements for job scheduling). The 28-core “norm” queue for Biowulf (Dual 28-core × 2.4 GHz Intel E5-2680v4 processor, 256 GB of RAM, and a 56 Gb/s FDR Infiniband controller) was used for fitting, which allowed a maximum of 28 parallel workers. Due to the large number of cells analyzed, all five cell lines (a total of 100 cells) required up to 72 h of total runtime on Biowulf. The commanding data handling and analysis script, which is run for every map, is named “analyze_map_zTransform”. This function contains all of the important settings for the data analysis, including whether the raw map data will be corrected for substrate tilt and whether the substrate is skipped during the data handling. An overview of how to use the functionality provided in the QIVisco GitHub repository is provided in the Supporting Information Chapter titled “Using the ‘QIVisco’ GitHub Repository”.

Initial handling and analysis required the following steps in order for every pixel: data intake (from the AFM); basic correction of the AFM data to acquire time-series force and indentation; special adjustment of the AFM data for the specific case of thin cells on a glass substrate; Z-transform Viscoelastic Inversion of the time-series data with the zTransformCurve function; calculation of the relaxance and retardance via eqs S17a, S17b, S18a, S18b, S19a, and S19b (for spherical, conical, and paraboloidal tip geometries); extraction of the material storage modulus, loss modulus, and loss angle from the calculated relaxance; and ultimately data storage. Further discussion of the data handling for pixels is provided in the Supporting Information section titled “Data Conditioning for Individual Pixels During Loading”.

The loading and handling of the force, indentation, time, and other positional information for each pixel were performed by the “open_JPK” function contained within the “lib” directory of this article’s GitHub repository. The data loading is involved and requires parsing encoded binary data provided by the Bruker AFM to extract force, indentation, tip height, velocity, and other important AFM quantities. Once the raw data were loaded, the “LoadAFMData” function was used to clean and crop the data prior to the data being stored in a data structure that would be accessible and accessed moving forward.

The substrate tilt was corrected by fitting a plane to the height data for the map edges and normalizing each pixel’s height data to account for substrate curvature. The substrates were not ignored as the analysis was exceptionally fast, and those pixels were skipped during the clustering process later. A discussion on the adjustment of the substrate tilt is provided in the Supporting Information section titled “Adjusting to Substrate Tilt Ahead of Finite Thickness Correction”.

The data was smoothed in the time domain during analysis to avoid undesirable noise levels in the frequency domain data sets. This involved using a simple moving average with a 5% window width (based on the number of samples in each data set) to smooth the time domain force and indentation before Z-Transformation. This approach was chosen because the authors felt that smoothing should occur reasonably close to the point of data collection, as opposed to at an arbitrary point later in the processing. Further discussion on this topic can be found in the Supporting Information section titled “The Effects of Smoothing on Data Quality”.

The AFM retraction curve information was not used or stored during analysis to save space and processing time, since it is not required at any point in the approach presented in this article. In most rheological stress–strain relationships, the sample Poisson’s ratio needs to be provided from previous testing or public data. Given how heterogeneous the cells are, we assumed that the cells were incompressible (thus, ν = 0.5), as is commonly done in AFM experimentation.

Given that the experiments were performed on adherent cells with thin protrusions on a rigid glass substrate, additional pressure effects were generated during the indentation, which were not initially accounted for in the standard AFM data corrections. As such, a generalized AFM-specific bottom effect correction for live cells on glass substrates was implemented in the code to adjust the observed force data set directly before Z-transformation. The setting that controls whether this bottom effect correction is used is labeled “thinSample” and was activated for the analysis of the data sets presented in this article. The bottom effect correction occurs in the zTransformCurve function.

Generating Animations

To create animations of the viscoelastic observables, the “makeZAnimation” function was created. A variety of arguments change the framerate and plot appearance and use them to generate an animation frame-by-frame. In this case, each frame represents a unique frequency sample of the viscoelastic properties extracted from the Z-Transform method. The makeZAnimation function loads a data set-generated “analyze_map_zTransform”, and then, based on the user’s input, plots a 2D heatmap of a specific observable for the frequencies or times specified. In situations in which there is no information at that frequency or time, a NaN value is inserted and appears as an empty pixel (light gray color). The result can be an animated.gif,.avi, or.mp4 video file. It is important to note that the results file absolutely must contain the strings “Results”, “zTransform”, and “.mat” to meet the internal criteria for animating.

Kymograph Analysis

For spatiotemporal representation of the viscoelastic response, we used ImageJ (NIH) to generate representative kymographs as extracted from the. avi output files from the viscoelastic analysis discussed in this paper. Using the Reslice function, a single line was chosen (running from the leading edge through the perinuclear region to the trailing edge for each cell chosen). Pixel interpolation was avoided, yielding a 1-pixel spacing of the raw data. The generated kymographs have time as the vertical axis (going from approximately 60 kHz at the top down to 0 Hz at the bottom), with the horizontal axis running from the leading to the trailing edge left to right. This same line was used to generate kymographs visualizing the storage modulus, loss modulus, and loss angle for each cell chosen.

Supplementary Material

nn5c01873_si_001.pdf (243.1KB, pdf)
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Acknowledgments

The authors wish to acknowledge the help of Alan Hoofring (Medical Arts Design Section, NIH) with the preparation of the illustrations in Figure . The authors thank Dr. Hari Shroff (HHMI Janelia), Dr. Emilios Dimitriadis (NIBIB), and all of the lab members from the Section on Mechanobiology for critical reading and thoughtful comments. The authors thank Dr. Nicole Morgan and Paniz Rezvan Sangsari (NIBIB/BEPS) for assistance with the shear rheometer measurements. The authors acknowledge the use of the high-performance computational capabilities of the Biowulf Linux cluster at the NIH (http://biowulf.nih.gov). We thank Kun Do (NIBIB) for providing assistance with the computational data analysis. The authors acknowledge support from the intramural funding of the Division of Intramural Research Program at the National Institute of Biomedical Imaging and Bioengineering with grant ZIA-EB000094 and the NIH central funds for the NIH Distinguished Scholars Program award.

The data sets for each cell type (fibroblasts, melanocytes, and melanomas A375-P/A375-MA1/A375-MA2) measured in this study are available in Figshare – https://figshare.com/account/items/26207204. Due to size limitations, the output “.mat” files have been excluded from the repository; these files can be made available upon reasonable request by contacting the corresponding author. The MATLAB codes used in this article to (a) extract the viscoelastic properties at multiple time scales, (b) generate spatiotemporal movies, and (c) perform density scatter plots are openly accessible in a GitHub repository, https://github.com/NIBIBmechanobiologylab/AFM-CellsTissues-Viscoelastic-ZTransform-HPC.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.5c01873.

  • Extracting Viscoelastic Information from AFM Data using a Discrete Integral Transform. Using the “QIVisco” Github Repository. Data Conditioning for Individual Pixels During Loading. Adjusting to Substrate Tilt Ahead of Finite Thickness Correction. The Effects of Smoothing on Data Quality (PDF)

  • Movie S1: Nanoscale topographic and viscoelastic mapping of a soft polyacrylamide hydrogel at multiple timescales (AVI)

  • Movie S2: Nanoscale topographic and viscoelastic mapping of a stiffer polyacrylamide hydrogel at multiple timescales (AVI)

  • Movie S3: Nanoscale topographic and viscoelastic mapping of an adherent human fibroblast cell at multiple timescales (AVI)

  • Movie S4: Nanoscale topographic and viscoelastic mapping of an adherent human fibroblast cell at multiple timescales (AVI)

  • Movie S5: Nanoscale topographic and viscoelastic mapping of an adherent human primary melanocyte cell at multiple timescales (AVI)

  • Movie S6: Nanoscale topographic and viscoelastic mapping of an adherent human parental melanoma (A-375P) cell at multiple timescales (AVI)

  • Movie S7: Nanoscale topographic and viscoelastic mapping of an adherent human metastatic melanoma (A-375M1) cell at multiple timescales (AVI)

  • Movie S8: Nanoscale topographic and viscoelastic mapping of an adherent human highly metastatic melanoma (A-375M2) cell at multiple timescales (AVI)

†.

C.P. and A.M. are co-first authors. C.P., A.M., and A.X.C.-R. designed the research. C.P. implemented the Z-transform viscoelastic approach to analyze high spatiotemporal resolution AFM maps. C.P., A.M., and M.M. performed atomic force microscopy experiments. A.M. performed confocal microscopy experiments. M.M. performed shear rheology experiments. C.P., A.M., and A.X.C.-R. analyzed the data. C.P., A.M., and A.X.C.-R. cowrote the paper. A.X.C.-R. supervised the research work.

The authors declare no competing financial interest.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

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Data Availability Statement

The data sets for each cell type (fibroblasts, melanocytes, and melanomas A375-P/A375-MA1/A375-MA2) measured in this study are available in Figshare – https://figshare.com/account/items/26207204. Due to size limitations, the output “.mat” files have been excluded from the repository; these files can be made available upon reasonable request by contacting the corresponding author. The MATLAB codes used in this article to (a) extract the viscoelastic properties at multiple time scales, (b) generate spatiotemporal movies, and (c) perform density scatter plots are openly accessible in a GitHub repository, https://github.com/NIBIBmechanobiologylab/AFM-CellsTissues-Viscoelastic-ZTransform-HPC.

Articles from ACS Nano are provided here courtesy of American Chemical Society

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