The protocol presents a complete workflow for soft material nanoindentation experiments, including hydrogels and cells. First, the experimental steps to acquire force spectroscopy data are detailed; then, the analysis of such data is detailed through a newly developed open-source Python software, which is free to download from GitHub.
Nanoindentation refers to a class of experimental techniques where a micrometric force probe is used to quantify the local mechanical properties of soft biomaterials and cells. This approach has gained a central role in the fields of mechanobiology, biomaterials design and tissue engineering, to obtain a proper mechanical characterization of soft materials with a resolution comparable to the size of single cells (μm). The most popular strategy to acquire such experimental data is to employ an atomic force microscope (AFM); while this instrument offers an unprecedented resolution in force (down to pN) and space (sub-nm), its usability is often limited by its complexity that prevents routine measurements of integral indicators of mechanical properties, such as Young's Modulus (E). A new generation of nanoindenters, such as those based on optical fiber sensing technology, has recently gained popularity for its ease of integration while allowing to apply sub-nN forces with µm spatial resolution, therefore being suitable to probe local mechanical properties of hydrogels and cells.
In this protocol, a step-by-step guide detailing the experimental procedure to acquire nanoindentation data on hydrogels and cells using a commercially available ferrule-top optical fiber sensing nanoindenter is presented. Whereas some steps are specific to the instrument used herein, the proposed protocol can be taken as a guide for other nanoindentation devices, granted some steps are adapted according to the manufacturer's guidelines. Further, a new open-source Python software equipped with a user-friendly graphical user interface for the analysis of nanoindentation data is presented, which allows for screening of incorrectly acquired curves, data filtering, computation of the contact point through different numerical procedures, the conventional computation of E, as well as a more advanced analysis particularly suited for single-cell nanoindentation data.
The fundamental role of mechanics in biology is nowadays established1,2. From whole tissues to single cells, mechanical properties can inform about the pathophysiological state of the biomaterial under investigation3,4. For example, breast tissue affected by cancer is stiffer than healthy tissue, a concept that is the basis of the popular palpation test5. Notably, it has been recently shown that the coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is underlined by changes in the mechanical properties of blood cells, including decreased erythrocyte deformability and decreased lymphocyte and neutrophil stiffness as compared to blood cells from SARS-CoV-2-naïve individuals6.
In general, the mechanics of cells and tissues are inherently intertwined: each tissue has specific mechanical properties that simultaneously influence and depend on those of the constituent cells and extracellular matrix (ECM)5. Because of this, strategies to study mechanics in biology often involve engineering substrates with physiologically relevant mechanical stimuli to elucidate cell behavior in response to those stimuli. For example, the seminal work by Engler and colleagues demonstrated that mesenchymal stem cell linage commitment is controlled by matrix elasticity, as studied on soft and stiff two-dimensional polyacrylamide (PAAm) hydrogels7.
Many strategies to mechanically characterize the biomaterial under investigation exist, varying in spatial scale (i.e., local to bulk) and in the mode of deformation (e.g., axial vs shear), consequently yielding different information, which needs careful interpretation3,8,9,10. The mechanics of soft biomaterials is commonly expressed in terms of stiffness. However, stiffness depends on both material properties and geometry, whereas elastic moduli are fundamental properties of a material and are independent of the material's geometry11. As such, different elastic moduli are related to the stiffness of a given sample, and each elastic modulus encompasses the material's resistance to a specific mode of deformation (e.g., axial vs shear) under different boundary conditions (e.g., free expansion vs confinement)11,12. Nanoindentation experiments allow the quantification of mechanical properties through the E which is associated with uniaxial deformation (indentation) when the biomaterial is not laterally confined10,11,12.
The most popular method to quantify E of biological systems at the microscale is AFM13,14,15,16. AFM is an extremely powerful tool with force resolution down to the pN level and spatial resolution down to the sub-nm scale. Further, AFM offers extreme flexibility in terms of coupling with complementary optical and mechanical tools, extending its capabilities to extract a wealth of information from the biomaterial under investigation13. Those attractive features, however, come with a barrier-to-entry represented by the complexity of the experimental set-up. AFM requires extensive training before users can acquire robust data, and its use for everyday mechanical characterization of biological materials is often unjustified, especially when its unique force and spatial resolutions are not required.
Because of this, a new class of nanoindenters has recently gained popularity due to their ease of use, while still offering AFM-comparable data with sub-nN force resolution and µm spatial resolution, reflecting forces exerted and perceived by cells over relevant length scales2. Particularly, ferrule-top nanoindentation devices based on optical fiber sensing technology17,18 have gained popularity among researchers active in the field of mechanobiology and beyond; and a wealth of works reporting the mechanical properties of biomaterials using these devices, including cells19,20, hydrogels8,21, and tissues22,23 have been published. Despite the capabilities of these systems to probe local dynamic mechanical properties (i.e., storage and loss modulus), quasi-static experiments yielding E remain the most popular choice8,19,20,21. In brief, quasi-static nanoindentation experiments consists of indenting the sample with a constant speed up to a set-point defined either by a maximum displacement, force, or indentation depth, and recording both the force and the vertical position of the cantilever in so-called force-distance (F-z) curves. F-z curves are then converted into force-indentation (F-δ) curves through the identification of the contact point (CP), and fitted with an appropriate contact mechanics model (usually the Hertz model13) to compute E.
While the operation of ferrule-top nanoindenters resembles AFM measurements, there are specificities worth considering. In this work, a step-by-step guide to robustly acquire F-z curves from cells and tissue-mimicking hydrogels using a commercially available ferrule-top nanoindenter is provided, in order to encourage standardization of experimental procedures between research groups using this and other similar devices. In addition, advice on how to best prepare hydrogel samples and cells to perform nanoindentation experiments is given, together with troubleshooting tips along the experimental pathway.
Furthermore, much of the variability in nanoindentation results (i.e., E and its distribution) depends on the specific procedure used to analyze data, which is non-trivial. To address this issue, instructions for the use of a newly developed open-source software programmed in Python and equipped with a user-friendly graphical user interface (GUI) for batch analysis of F-z curves are provided. The software allows for fast data screening, filtering of data, computation of the CP through different numerical procedures, the conventional computation of E, as well a more advanced analysis named the elasticity spectra24, allowing to estimate the cell's bulk Young's modulus, actin cortex's Young's modulus, and actin cortex's thickness. The software can be freely downloaded from GitHub and can be easily adapted to analyze data originating from other systems by adding an appropriate data parser. It is emphasized that this protocol can be used for other ferrule-top nanoindentation devices, and other nanoindentation devices in general, granted some steps are adapted according to the specific instrument's guidelines. The protocol is schematically summarized in Figure 1.
1. Preparation of substrates/cells for nanoindentation measurements
2. Starting up the device, probe choice, and probe calibration
3. Probe calibration
NOTE: The following steps are specific to ferrule-top nanoindentation devices based on optical fiber sensing technology, and they are detailed for software version 3.4.1. For other nanoindentation devices, follow the steps recommended by the device manufacturer.
4. Measuring the Young's Modulus of soft materials
5. Data analysis
6. Formal data analysis
Following the protocol, a set of F-z curves is obtained. The dataset will most likely contain good curves, and curves to be discarded before continuing with the analysis. In general, curves should be discarded if their shape is different from the one shown in Figure 4A. Figure 5AI shows a dataset of ~100 curves obtained on a soft PAAm hydrogel of expected E 0.8 KPa35 uploaded in the NanoPrepare GUI. Most curves present a clear, flat baseline, a transition region, and a sloped region that is proportional to the apparent stiffness of the material13. However, a minority of curves show alterations from the shape shown in Figure 4A, such as the absence of a baseline, missed contact, or a sloped baseline. These curves can be easily removed from the dataset using NanoPrepare (Figure 5AII, red curves), and a clean dataset saved in the standard JSON format (Figure 5AIII). The clean dataset is uploaded in NanoAnalysis (Figure 5BIV), which has been designed so that it batch processes all curves. This means each step of the workflow is applied to the whole dataset. After being uploaded, curves can be filtered to remove random noise using one or more filters described in the Discussion, critical steps in the protocol (Figure 5BV). The CP is then located using one of the algorithms implemented in the software and detailed in the Discussion, critical steps in the protocol (Figure 5BVI). Once the CP has been identified, F-z data is converted into F-δ data. Because the software has been designed to primarily analyze data from ferrule-top nanoindentation devices based on optical fiber sensing, which use probes having a spherical tip, the Hertz analysis is based on the Hertz model approximating the contact between a sphere of radius R and an infinitely extended linear elastic homogeneous isotropic (LEHI) half space13:
where F is the force, δ is the indentation, E is Young's Modulus, and ν is the Poisson's ratio, taken as 0.5 assuming incompressibility. By fitting F-δ curves with equation (1), E can be therefore estimated (see Discussion-critical steps in the protocol-for assumptions of the Hertz model) (Figure 5BVII).
In addition to the Hertz analysis, the software can perform a more advanced analysis, namely, the elasticity spectra, which is particularly useful for cell nanoindentation data; and can also be used as a tool to estimate the influence of the underlying substrate on the mechanical properties obtained via the Hertz model. Below, the approach is briefly summarized. Full details can be found in the original publication24.
Starting from the Oliver-Pharr model36, which describes the indentation of an axisymmetric punch of arbitrary geometry and an elastic half space, one can derive E(δ) for the specific case of a spherical indenter. Taking ν as 0.5, E(δ) has the form24:
Computing E(δ) for each F-δ curve using equation (2) yields a set of curves, namely, the elasticity spectra (ES). By taking the average of all curves in the data set, the average ES is obtained (Figure 5BVIII, red solid line). The average ES is a useful tool because it provides information on how E varies with δ in the dataset. In the specific case of cell nanoindentation experiments, the thickness of the cell is not known a priori, which means that choosing an appropriate fitting range for the Hertz analysis is somewhat arbitrary. By using the average ES, substrate effects on the apparent E(δ) become evident, which means the tool can be used to select an appropriate fitting range, corresponding to the point where E(δ) starts increasing after its decay. Further, it has been previously demonstrated and computationally and experimentally validated that a simple bilayer model is effective in the estimation of the actin cortex's thickness (d0), the actin cortex's Young's modulus (E0), and the cell's bulk Young's modulus (Eb)24. The model describes the cell as a bilayer, with an outermost layer of thickness d0 and modulus E0, and an inner layer of infinite thickness with elastic modulus Eb<E0:
where R is the tip's radius and Λ is a phenomenological parameter, which was determined to be 1.74 from finite element analysis simulations24. This procedure has been implemented in the NanoAnalysis software, which allows to fit the average ES with equation (3) to obtain an estimate of E0, Eb, and d0 (Figure 5BVIII, black dashed line). For full methodological details, refer to the original publication24.
To demonstrate the viability of the protocol, the elasticity of PAAm hydrogels of known E (measured by AFM)35 were prepared and tested using the procedure suggested in Part 1 of the protocol. For each gel, two stiffness maps in two different areas of the sample were acquired using a commercial ferrule-top nanoindenter equipped with a tip having R = 52 µm and k = 0.46 N/m. Each map consisted of 50 indentations performed in displacement control, and the step size in x and y was set to 20 µm to avoid oversampling. Figure 6A shows the average F-δ curve together with the average Hertz model for a soft PAAm hydrogel (expected E 0.8 kPa) and a stiff PAAm hydrogel (expected E 8 kPa)35. By performing the Hertz analysis through the NanoAnalysis software and plotting individual values of E, the expected E was retrieved for both hydrogels (Figure 6B).
Further, nanoindentation experiments on HEK293T cells were performed. Six individual cells were indented by performing a matrix scan with x and y step size set to 0.5 µm on each cell and acquiring a minimum of 25 curves on each cell. This resulted in the analyzed dataset containing ~200 curves. The selected probe had R = 3.5 µm and k =0.02 N/m.
Figure 7A shows the average Hertz curve and the corresponding average Hertz model, plotted using the mean E obtained from fitting equation (1) to each individual curve in NanoAnalysis up to an indentation of 200 nm. E was found to be 915 ± 633 Pa (mean ± SD), which is in accordance with values reported in the literature24. Despite its wide use, the Hertz model does not fully capture the evolution of the force with increasing indentation depth for cell nanoindentation experiments (Figure 7A). Because of this, the ES is a particularly suitable tool to study the mechanical properties of single cells.
Figure 7B shows the average ES, together with equation (3) fitted up to an indentation of 200 nm. The average ES starts increasing at an indentation depth of ~200 nm, which indicates the contribution of the substrate to the probed apparent E (Figure S4). Because of this, 200 nm was chosen as the fitting range for both the Hertz model (Figure 7A) and the bilayer model (Figure 7B). Fitting equation (3) to the average ES allowed to extract important information, which would otherwise remain inaccessible from simple nanoindentation experiments analyzed using the Hertz model. Specifically, the actin cortex's modulus E0 was estimated to be 5.794 ± 0.095 kPa, the actin cortex's thickness d0 was found to be 311 ± 3 nm and the bulk modulus Eb was found to be 0.539 ± 0.002 kPa (mean ± SD). All values are in accordance with previous experiments performed using AFM on the same cell type24, and with values that have been reported in the literature37,38. Specifically, the actin cortex is expected to be between 300-400 nm for adherent cells37, and up to 10 times stiffer than the bulk of the cell38.
Regardless of the bilayer model, a direct comparison between results obtained with the standard Hertz model and the ES approach is given in Figure 7C, which reveals overlapping distributions with comparable means.
Figure 1: Protocol overview. The protocol consists of the following parts: (A) Part 1: Preparing the sample (either hydrogels or cells) for nanoindentation experiments. (B) Part 2: Choosing the right probe and calibrating the probe. (C) Part 3: Performing nanoindentation experiments by acquiring stiffness maps on the sample. (D) Part 4: Analyzing the data, which consists of i) cleaning the acquired dataset through the first GUI (NanoPrepare) and saving the cleaned dataset and associated metadata as a standard JSON file; and ii) analyzing the cleaned dataset in the second GUI (NanoAnalysis), which consists of data filtering, CP identification, and model fitting to estimate Young's modulus E of the sample. Results are saved for further plotting and statistical analysis, which can be performed in any software of choice. Created with Biorender.com. Please click here to view a larger version of this figure.
Figure 2: Sample preparation. (A) Steps suggested to prepare flat PAAm hydrogels for nanoindentation experiments. These are: I) pouring the hydrogel solution onto a hydrophobic glass slide and covering it with a silanized coverslip; II) waiting for 20 min for polymerization to occur and peeling off the coverslip-gel composite from the glass slide; and III) attaching the coverslip-gel composite to a Petri dish and adding appropriate solution (purified water in the context of this protocol) for nanoindentation experiments. The same rationale can be adapted and applied to any other type of hydrogel. (B) Steps suggested to prepare cells for nanoindentation experiments. These are: I) seeding cells and waiting for cell adhesion; II) serum starving the cells to synch the cell population in terms of the cell cycle (optional); and III) waiting for cells to be in an adhered state at desired confluency before starting nanoindentation experiments. Created with Biorender.com. Please click here to view a larger version of this figure.
Figure 3: Nanoindentation probe overview and selection. (A) Schematic of ferrule-top probe (left) and picture of a ferrule-top probe with the spherical tip of radius 250 µm (right). All components are labeled in the photo. (B) Enlarged schematic of the cantilever and the spherical tip. The cantilever is treated as a Hookean spring of elastic constant k (shown at an angle for representation purposes). The tip is defined by its radius, R. When the sample is indented, the probe is displaced by an amount z from its reference position z0, which results in the cantilever bending d from its reference bending d0. A force of F = k (d – d0) is applied to the sample, which results in an indentation δ = (z – z0) – (d – d0). (C) Cantilever's stiffness k should be chosen according to the expected elasticity of the substrate. The plot was obtained considering Hertzian contact with an indentation of 1 µm, assuming that the energy is equally shared between the cantilever's bending and the substrate's indentation (i.e., d =δ). The larger the tip radius, the stiffer the cantilever should be to reach the same indentation for a substrate with a given E. Please click here to view a larger version of this figure.
Figure 4: Morphological characteristics of F-z curves. (A) A successful experiment results in the approach segment of an F-z curve having a clear baseline (tip approaching the sample but not in contact); a transition region where the tip first contacts the sample; and a region where the force increases with the displacement, where the tip is progressively indenting the sample. The slope of this region is proportional to the apparent stiffness of the material13, meaning that curves belonging to stiff biomaterials (e.g., highly crosslinked gels) will be steeper than those belonging to softer biomaterials (e.g., weakly crosslinked gels and cells). (B) An approach curve where the tip never entered contact with the sample. See troubleshooting of the method in the Discussion for resolution. (C) An approach curve where the tip started in contact with the sample. See troubleshooting of the method in the Discussion for resolution. The data shown is from an experiment performed on a soft PAAm hydrogel of expected E 0.8 kPa35. Please click here to view a larger version of this figure.
Figure 5: Data analysis workflow using the Python GUIs. (A) An example dataset of F-z curves acquired using a commercially available ferrule-top nanoindenter on a soft PAAm hydrogel (expected E 0.8 kPa35) was uploaded in NanoPrepare. Curves that do not follow the shape described in Figure 4A are excluded from the dataset, and the clean dataset and associated metadata are saved as a standard JSON file. (B) The clean dataset is uploaded in the second GUI (NanoAnalysis) where curves can be filtered by applying one or more filters to remove noise (see Discussion, critical steps in the protocol). Further, a CP algorithm is selected to automatically locate the CP for all curves (see Discussion, critical steps in the protocol). The Hertz analysis is then performed, yielding a F-δ curve for each indentation, which is fitted with the Hertz model to yield a scatter plot of E. The obtained results can be saved for further plotting. For cells, an additional analysis called the elasticity spectra24 can be performed. All graphs shown were directly exported from both NanoPrepare and NanoAnalysis GUIs. Details for each step of the workflow are given in the main text. Please click here to view a larger version of this figure.
Figure 6: Elasticity of PAAm hydrogels. (A) Average F-δ curve from a set of ~100 curves acquired on a soft PAAm hydrogel (expected E 0.8 kPa35) and a stiff PAAm hydrogel (expected E 8 kPa35). Solid lines show the mean and shaded band shows one SD. The dashed line shows the Hertz model plotted using the average E from the NanoAnalysis software, obtained by fitting the Hertz model to each curve up to a maximum indentation of 2,000 nm (~4% of R, R = 52 µm, k = 0.46 N/m). Curves were smoothed using the prominecy filter with default parameters, and the CP was identified using the RoV algorithm32. (B) Individual values of E obtained from the analysis performed in NanoAnalysis plotted for statistical comparison. The raincloud plot was obtained using the Python module described in reference39. **** p < 0.0001, two-tailed unpaired t-test, α=0.05. Please click here to view a larger version of this figure.
Figure 7: Elasticity of HEK293T cells. (A) Average F-δ curve from a set of ~200 curves acquired on six individual HEK293T cells. The solid blue line shows the mean and the shaded band shows one SD. The dashed line shows the Hertz model plotted using the average E computed using the NanoAnalysis software, obtained by fitting the Hertz model to each curve up to a maximum indentation of 200 nm (~6% of R, R = 3.5 µm, k = 0.02 N/m). Curves were smoothed using the prominecy filter with default parameters and a SAVGOL filter34 with order 3 and window length 80 nm, and the CP was identified using the Threshold algorithm33. Using the Hertz model, the cell is treated as a homogeneous sphere with Young's Modulus E, as schematically shown in the inset (the nucleus is depicted for pictorial purposes). (B) Average elasticity spectra computed on the same data set described in (A). The solid red line shows the mean and the shaded band shows one SD. By fitting a bilayer model to the average elasticity spectra, estimations of E0, Eb, and d0 are computed. For the dataset shown: E0 = 5.79 ± 0.09 kPa, Eb = 0.539 ± 0.002 kPa and d0 = 311 ± 3 nm (mean ± SD). (C) Comparison between the Hertz model and the elasticity spectra approach in terms of E distribution. For the elasticity spectra, the distribution represents the values of E from the average elasticity spectra, regardless of indentation depth (up to a maximum indentation of 200 nm). The continuous lines superimposed on the histograms are Gaussian kernel density estimates of the underlying distributions. E = 915 ± 633 Pa (Hertz) and E = 890 ± 297 Pa (elasticity spectra) (mean ± SD). Please click here to view a larger version of this figure.
Figure S1: Calibration Procedure. (A) Successful wavelength scan. The cantilever's deflection and piezo's displacement signals during the wavelength scan (left). The sinusoidal wave on the interferometer's screen at the end of the wavelength scan (right). (B) Find surface procedure. cantilever's deflection and piezo's displacement signals as the probe is lowered in 1 μm steps after contact with a stiff substrate. (C) Geometrical factor calibration. During indentation of a stiff substrate, the cantilever's deflection follows the cantilever's displacement (green and blue lines, respectively). The indentation should be approximately zero (red line). If the deflection lags the displacement in time (green dashed line), the probe is not fully in contact with the stiff substrate. (D) Demodulation signal. The demodulation signal on the interferometer's screen at the end of the calibration procedure (left) and when tapping on the nanoindenter (right). Please click here to download this File.
Figure S2: NanoPrepare GUI. Screenshots of the NanoPrepare GUI. Details on the functionality of each widget are given in the main Protocol and the Discussion. Please click here to download this File.
Figure S3: NanoAnalysis GUI. Screenshots of the NanoAnalysis GUI. Details on the functionality of each widget are given in the main Protocol and the Discussion. Please click here to download this File.
Supplementary Note 1: Adding custom filters and CP algorithms to the NanoAnalysis software. Please click here to download this File.
Supplementary Protocol. Please click here to download this File.
Figure S4: Depth dependency of average elasticity spectra. The plot shows the average elasticity spectra <E (δ)> (solid red line) together with one SD (σ(E(δ)). After an initial decay, the average elasticity spectra start increasing, which is mainly associated with the effects of the stiff underlying substrate on the probed apparent elastic modulus. The maximum indentation depth used to fit the Hertz model to F–δ curves, and the decay model to the average elasticity spectra should be chosen so that the underlying substrate does not affect the results (Fit range). Please click here to download this File.
This protocol shows how to robustly acquire force spectroscopy nanoindentation data using a commercially available ferrule-top nanoindenter on both hydrogels and single cells. In addition, instructions for the use of an open-source software programmed in Python comprising a precise workflow for the analysis of nanoindentation data are provided.
Critical steps in the protocol
The following steps have been identified to be of particular importance when following this protocol.
Sample preparation
It is crucial that before initiating measurements, the sample is prepared with the restraints of the measurement in mind. That is, the sample must be adhered to a surface and be as flat as possible. This is especially important when preparing samples that do not naturally adhere to surfaces as cells do, such as hydrogels. Firstly, the sample must not float in solution as this will interfere with measurements and potentially damage the probe. For this, chemical functionalization of a coverslip is recommended, so that the hydrogel can be polymerized adhered to a surface, which can later be glued to a Petri dish while submerged. Moreover, the sample's surface must be as flat as possible to ensure coherent surface detection by the probe and avoid damaging the probe while moving in x and y during a matrix scan. The hydrogel solution can be polymerized on a hydrophobic glass slide, which makes the resulting hydrogel flat without adhering to it. If these considerations are not followed, it will be difficult to obtain clean F-z data.
In the case of cell preparation, it is best to indent cells with similar morphology to improve data homogeneity. In the event that cells grow in a heterogeneous population, a serum starvation step can be introduced pre-measurement, to aid cell cycle synchronization and, therefore, remove potential experimental confounders40,41. In the case of non-adherent cells or organoid cultures, one must perform extra steps to ensure stability and adherence of the biological sample while measurements are being performed. Extra steps might include chemically binding cells to culture plates or using tissue adhesives that are now widely commercially available.
Nanoindentation experiments
It is important that a cantilever with the right k is chosen depending on the sample's expected E15. This is because if the cantilever is too stiff, the sample will be indented but no significant cantilever bending will occur. Conversely, if the cantilever is too soft with respect to the sample, the cantilever will excessively bend with minimal indentation. Both instances will result in the miscalculation of E in the subsequent analysis.
For probe calibration, the probe must be wet prior to insertion into the calibration dish to minimize surface tension when encountering the liquid of the calibration dish. Not doing so may cause the trapping of air bubbles or push the cantilever against the optical fiber. This can also result in the probe being damaged.
The use of a thick glass Petri dish is recommended for calibration. Glass is infinitely stiff compared to the cantilever, which allows accurate calibration of the cantilever's k while indenting the glass. Further, the weight of the glass ensures a stable substrate that is more robust against noise (e.g., airflow and acoustic vibrations) compared to a lighter plastic Petri dish. The calibration performs a linearization procedure of the interferometric signal measured at the detector (V/t), which means the signal will be converted into linear cantilever bending (µm/t) using the unit circle (demodulation circle) as a linearization tool18. The deflection sensitivity (µm/V) is set by default in the interferometer and used to convert V to µm. During this procedure, the calibration factor is also determined, which originates from the mismatch in position between the spherical tip and the fiber position where the signal read-out occurs (Figure 3A). By indenting on a stiff substrate-like glass, the deflection measured by the fiber is approximately the same as the distance displaced by the piezo, which means the indentation depth is approximately zero. Taking their ratio yields the calibration factor. It is important that the calibration of the instrument is performed correctly, and that all checks are satisfied before continuing to acquire F-z data.
When configuring an indentation profile, it is useful to keep in mind the assumptions of the Hertz model, which will be used later to analyze the data. The Hertz model is derived assuming that the sample is a LEHI infinitely extended half-space, which results in the following practical consequences: i) applied strains should not exceed 20% (as a rule of thumb, δ should not exceed 10% of the tip's R) and ii) δ should be less than 10% of the sample thickness, and small compared to the other sample's dimensions13.
The maximum displacement (or indentation depth/force depending on the operation mode) can be adjusted depending on the resulting δ, and whether surface or bulk mechanical properties are desired. If the sample has been indented to a slightly larger δ, the Hertz model can still be fitted up to a maximum δ which lies within its assumptions in the NanoAnalysis software, and the average ES used to estimate this range (see Representative Results).
For cell nanoindentation experiments, it is challenging to perform multiple matrix scans on the same cell. However, if the cell is large enough, it may be possible to find another suitable region and repeat the procedure on the same cell, for example, an experiment where the user wants to detect differences in the mechanical properties of a certain region of the cell compared to another. Usually, a map per cell is performed, and a minimum of five cells are indented per biological condition. It is advisable to repeat the experiment at least three times so that sufficient data is acquired on each sample (i.e., three replicates for each biological condition).
Critically, acquired curves should present a flat baseline, a transition region, and a sloped region. Curves that do not present a baseline cannot be later analyzed due to uncertainty on the location of the CP. If curves deviate from the shape shown in Figure 4A, the contact threshold should be optimized before continuing with the experiment (see troubleshooting of the method below).
Sufficient data should be acquired to ensure statistically robust results, given the nature of the technique, which probes mechanical properties locally.
Data analysis
The software described in this protocol is routinely adopted to analyze nanoindentation data and it has been used to obtain results published in several peer-reviewed journals (e.g., nanoindentation of hydrogels8,21, nanoindentation of cells24,42). Analysis of nanoindentation data is non-trivial. It is suggested to pay particular attention to the following parts:
Screening of the dataset: The dataset should be thoroughly screened in the NanoPrepare software, and all unsuccessful curves should be removed before saving the cleaned dataset as a JSON file. Curves can still be excluded from the analysis in the NanoAnalysis software, but the JSON file cannot be changed. As such, to ensure consistency between the cleaned and analyzed dataset, it is suggested to carefully perform the screening process in the NanoPrepare software.
Filtering data: Using filters is useful when the data is noisy and recommended when performing the ES analysis. Three major filters are used as described below.
Prominency: This filter removes prominent peaks in the Fourier space, to eliminate instrumental oscillations typical of commercially available ferrule-top nanoindenters. The filter is based on three parameters: Prominency (a.u.): the peak prominency in the Fourier space; Minimum frequency (channels): the minimum frequency to be filtered; Band (% of peak position): the width around the filtered frequency in percentage of the peak position. Activate this filter for data originating from commercially available ferrule-top nanoindenters by clicking on the checkbox and leaving default parameters.
Savitzky Golay (SAVGOL), algorithm from the SciPy library34 (scipy.signal.savgol_filter): This filter smooths the data based on a local least-squares polynomial approximation. Activate this filter if the data is particularly noisy. Change the order of the polynomial and the filter window length in the GUI depending on how noisy the data is. For more details, see references30,31. Activate this filter for the ES analysis.
Median filter, algorithm from the SciPy library34 (scipy.signal.medfilt): This filter smooths the data based on replacing each point with the median calculated around that point in a given window. Change the window length in the GUI depending on how noisy the data is. This filter is used as an alternative to the SAVGOL filter.
Activating the prominency filter helps remove instrumental noise (low-frequency oscillations) typical of commercial ferrule-top nanoindenters. In general, activating other filters such as the SAVGOL34 when performing the simple Hertz analysis is not necessary. When computing the ES, it is recommended to activate both the prominency filter and the SAVGOL filter34, with a smoothing window depending on the level of noise present in the data. This is because the ES contains a derivative term (equation 2), which is very sensitive to noise. For example, results in Figure 7 were obtained using the prominency filter together with a SAVGOL filter34 with window 80 nm and polynomial order 3. However, it is important not to over smooth the data, because this may hide any differences that are present between datasets.
CP identification: The most important part of the analysis is the identification of the CP, which strongly influences both the absolute value of E and its distribution32,33. Four algorithms based on automatic search procedures that locate the CP in order to remove human bias have been implemented in the NanoAnalysis software. All algorithms have been documented in the literature32,33. In general, every point in a region of interest is tested as a trial CP while an algorithm-specific parameter is being computed. The point that returns the optimized parameter, which can be its maximum or minimum value depending on the algorithm, is taken as the CP32. Those procedures have been implemented to remove human bias and take a statistical approach to the problem. Because each algorithm computes the CP based on the optimization of a given parameter, the identified CP will be slightly different for each algorithm. As such, it is paramount to maintain the same CP algorithm and specific parameters (e.g., window length for the RoV algorithm) between datasets that one wants to compare, as relative differences in E will be preserved. The different CP algorithms and their parameters are summarized below.
Goodness of Fit (GoF): An approach based on fitting a contact mechanics model (Hertz) from each (z, F) pair in a region of interest and selecting the fit having the highest R2 value. It works well where the transition between non-contact and contact is evident, which happens with stiff materials such as highly crosslinked hydrogels. The algorithm is computationally expensive, and generally the slowest. Here, it has been implemented so that the Hertz model is only fitted up to a maximum δ of about 10% of R, as this has been shown to yield more accurate results32.
Ratio of Variances (RoV): An approach based on computing the ratio of the variance of the deflection (force) signal in the non-contact and contact region32.
Second derivative: An approach based on the second derivative of the deflection (force) signal33. It works well when the signal is clean. If the signal is too noisy, this approach is not recommended.
Threshold: An approach based on the average deflection (force) in the noncontact region33. In short, starting from a force value selected by the user near the contact region, the algorithm iterates through each point towards the baseline, until it finds the first point whose force value is larger than the average of the baseline. This point is selected as the CP. This algorithm is very robust and is the recommended one to use.
Details on how to use each algorithm are given below. The CP algorithms involve numerical constants that need to be changed in the GUI to suit the specific dataset. Specifically, the following parameters are common to the GoF, the RoV, and the Second Derivative method, allowing to select a sub-region of the curves (region of interest or ROI) where the CP will be searched for:
Safe threshold (nN): It defines the maximum force in nN (and the corresponding z point) from which the CP will be searched. This is the right boundary of the ROI, whose default value is 10 nN. All curves whose maximum force is below this threshold will be automatically moved to the failed set. Change this value to a force value slightly above the transition from non-contact to contact.
X range (nm): It defines the range in nm from the z point corresponding to the safe threshold. This is the left boundary of the ROI. The default of 1,000 nm is a good starting point, but if the CP is found too late in the curve (i.e., in the sloped region), increase this value. Conversely, if the CP is found too early (i.e., in the baseline), decrease this value.
Parameters specific to each algorithm are summarized here. For the GoF, the Window Fit (nm) represents the window in nm from the trial CP up to which the Hertz model is fitted. This is capped at a value of 10% of R. For the RoV, the Window RoV (nm) represents the window in nm to the left and right of the trial CP over which the variance of the deflection (force) signal is computed. For the second derivative, the Window P (nm) represents the window passed to the SAVGOL filter34 used to compute the second derivative of the deflection (force) signal. Default values have been set from testing the different algorithms and it is generally not required to change them.
For the threshold algorithm, the following parameters can be changed:
Align threshold (nN): The force (F0) from which the CP will be looked for starting from this point and moving toward the baseline. All curves whose maximum force is below this threshold will automatically be moved to the failed set. Its default value is 10 nN; however, change this value to a force value slightly above the transition from non-contact to contact. The corresponding z point (z0) is stored for later use in the algorithm (see below).
Align left step (nm): This parameter defines the shift to add to the left of z0 (default value 2,000 nm), which results in the calculation of a point defined by (z0 - align left step). This point is the point around which the average of the baseline will be computed (see below).
Average area (nm): This parameter defines the average area to the left and right of (z0 - align left step), over which the average of the baseline will be computed. Its default value is 100 nm, and it is not required to change it.
Iterating down from F0, the CP is taken as the first point whose value is above the force defined by the average of the baseline.
Note on the ES and noise: The average ES may appear noisy at first with prominent sinusoidal oscillations, and as a result equation (3) may not fit correctly. If this is the case, increasing the window of the smoothing SAVGOL filter34 usually solves this issue.
Modifications and troubleshooting of the method
Troubleshooting of the method
Wavelength scan troubleshooting
If an error message appears on the interferometer's display after performing the wavelength scan, the following problems may be the cause: i) The environment may be contaminated by noise. Get rid of any noise sources, including airflow, loud noises, and mechanical vibrations; ii) The probe may not be properly connected. Unplug and re-plug the green optical fiber connector; iii) The cantilever may be dirty. Clean it by submerging the probe in a Petri dish containing isopropanol for a few minutes, and then water; iv) An air bubble may be present on the cantilever. Submerge the probe in a Petri dish containing isopropanol and create some flow by pipetting the liquid up and down; v) The cantilever may be bent/stuck to the fiber, which can be seen under the microscope. Release it by gently touching the cantilever with a tissue wipe. Take extra care when touching the cantilever as the application of excessive force can break it; vi) The cantilever is missing from the probe, which can be seen under the microscope. The only solution is using a new probe. Try the wavelength scan again, which should now be successful.
Calibration troubleshooting
If calibration fails and the new factor is either NaN or is not in the expected range, the following problems may be the cause: i) The tip is not fully in contact with the substrate. Make sure the tip is in contact with the substrate by following the steps given in the Protocol; ii) Attractive forces between the tip and the glass surface (snap-on behavior) result in the calibration of the over-bended cantilever. Clean the probe by suberging it in isopropanol for 5 min, and then water. Clean the dish with isopropanol; iii) The tip/dish may be contaminated: Clean the probe by suberging it in isopropanol for 5 min, and then water. Clean the dish with isopropanol; iv) The cantilever may be bent/stuck to the fiber. Release it by gently touching it with a tissue wipe. Repeat both wavelength scan and calibration after troubleshooting.
Contact troubleshooting
If curves deviate from the shape shown in Figure 4A, experimental parameters need to be adjusted before continuing with the experiment. Two of the most common problems are:
An approach curve where the tip never enters contact with the sample (Figure 4B). This occurs when the contact threshold is set to a value that is too low, and noise causes the cantilever to bend by an amount corresponding to the given threshold. To solve this issue, navigate to the Options menu and slowly increase the threshold at steps of 0.01 and perform an indentation until the curve resembles the one shown in Figure 4A. Decreasing the speed in the same menu can also help solve this issue.
An approach curve where the tip started in contact with the sample (Figure 4C). This happens when the contact threshold is set to a value that is too high, and the cantilever does not bend by the amount corresponding to the given threshold when first touching the sample. To solve this issue, slowly decrease the threshold in the Options menu at steps of 0.01 and perform an indentation until the curve resembles the one shown in Figure 4A. This issue is particularly problematic because the absence of a baseline prevents the correct computation of the CP, eventually leading to a miscalculation of E.
Modifications of the method
The protocol can be extended to quantify the E of different types of hydrogels. PAAm hydrogels were chosen for this protocol as they are the most common hydrogels used within the field of mechanobiology. However, the protocol is equally applicable to any type of elastic hydrogel25, both synthetic, for example, polyethylene-glycol (PEG)43 and gelatin methacryloyl (GelMA)44,45; and natural, such as collagen46. Moreover, there are no constraints on the dimensions of the sample to test, within reasonable limits. For example, this protocol has been used to quantify the E of synthetic PEG hydrogels that were later tested using a bulk rheometer and required to be ~15 mm in diameter and ~2 mm in thickness8. The protocol has also been implemented to characterize the E of PDMS membranes that were polymerized in a Petri dish (results not published).
Besides standard indentation of single cells performed using a conventional inverted phase-contrast microscope, ferrule-top nanoindenters are compatible with complex imaging systems and have been used to probe the local elasticity subcellular structures, such as the cell's nucleus and cytoplasm47. Whereas steps will need to be adjusted depending on the specific optical system, this protocol is of general applicability with respect to performing nanoindentation experiments and analyzing the resulting data.
Further, the protocol is not limited to measuring the mechanical properties of cells and hydrogels and can be adapted to measure the local elastic properties of more complex systems, including organoids48, spheroids49, and whole tissues such as kidneys, liver, spleen, and uterus23. The reader is directed to references23,48,49 for specificities on performing nanoindentation experiments on such samples. One aspect to consider is that displacement control works in open-loop mode and does not receive feedback from the sample. As such, constant stress/strain and speed are not ensured, and softer parts of the sample will be indented more and faster as compared to stiffer regions. This is relevant for mechanically heterogeneous samples such as tissues, where it is more appropriate to choose either indentation control (I mode) or load control (P mode), ensuring a consistent stress/strain and speed across mechanically heterogeneous regions of the sample.
Limitations of the method
There is a growing body of evidence that viscoelasticity, in addition to elasticity, plays an important role in regulating physiologically and pathologically relevant processes. This is because cells, the ECM, and tissues are viscoelastic, and elasticity represents only one component of their mechanical behavior50,51,52,53. Whereas ferrule-top nanoindenters provide functionality for characterizing viscoelasticity, including stress relaxation, creep compliance, and dynamic mechanical analysis to extract both the storage and loss modulus over different frequency (time) regimes, this protocol only focuses on elasticity, which remains the most studied mechanical variable in the context of mechanobiology and tissue engineering (for example, see reference3).
The underlying assumption with consequences on both experiments and data analysis is that the indented substrate behaves as a LEHI solid. This means that the stress-strain response is linear, there are no time-dependent behaviors, and the sample is mechanically homogeneous and isotropic. Based on these assumptions, the mechanical properties of the substrate are quantified through Young's modulus following a specific contact mechanics model, in this case, the Hertz model (equation 1). For small quasi-static forces/deformations, chemically crosslinked hydrogels such as PAAm gels used in this protocol35 behave nearly as elastic solids and viscoelastic effects are minimal and negligible53. On the other hand, cells are not LEHI solids and show complex mechanical behavior9. The Young's modulus of cells is highly dependent on the strain rate (i.e., speed) of the indentation procedure, however, no clear trend is established and additional variables such as tip size and maximum indentation depth influence this relationship9. Nonetheless, for quasi-static deformations, such as those used in this protocol (v = 5 μm/s), cells show a marked elastic response and dissipative effects are minimal9. Strain rate dependency can be captured by more complex models taking into account time-dependent variables, to which the reader is referred to54.
Further, following the same underlying assumption, the Poisson's ratio (ν) is taken as 0.5 both in the Hertz and ES analysis. When comparing between samples, this only impacts results as a coefficient; however ν has been shown to be a frequency-dependent quantity for cells55 and to deviate from 0.5 for hydrogels56.
Another limitation of the protocol lies in the fact that the software does not provide quantification of E through more sophisticated contact mechanics models. The Hertz model is the most used contact mechanics model in AFM experiments and it is extremely effective13,15; however, it does not take into account more complex events such as short- or long-range attractive forces between the tip and the sample. More complex models such as the Johnson-Kendall-Roberts model can capture these behaviors13, but are not implemented in the software. For an overview of different contact mechanics models ranging in complexity, the reader is directed to reference13.
Significance of the method with respect to existing/alternative methods
The most common approach to quantify the local elastic properties of biomaterials and single cells at the microscale is AFM13,14,15,16. Despite being a powerful and versatile instrument, the AFM requires extensive training due to its complex setup before users can robustly perform experiments. Ferrule-top nanoindenters offer a plug-and-play solution while still allowing to apply nN forces with µm resolution to probe the local mechanical properties of biomaterials (e.g., references8,19,20,21). Whereas standardized protocols exist for the use of the AFM in the context of mechanobiology16 and tissue engineering14, there are no protocols detailing the operation of ferrule-top nanoindenter devices. This protocol allows an inexperienced user to perform nanoindentation experiments on both hydrogels and cells, by following guidelines that are intended to standardize the experimental workflow within the community. Further, data analysis of nanoindentation experiments is non-trivial and would remain largely inaccessible for users without experience in programming. Instructions are provided for the use of intuitive software that allows to clean and save the acquired dataset in light and standard format and perform both the standard Hertz analysis as well as the ES analysis24 with a few clicks and in a reproducible way.
By following this protocol, results comparable with those obtained using the AFM are obtained, both for hydrogels' E (results in Figure 6 compared to those in reference35) and cells' mechanical properties (results in Figure 7 compared to those in reference24) at a fraction of the complexity. The method is of general applicability and can be adapted to different types of nanoindenters granted some steps are modified based on the specific device.
Importance and potential applications of the method in specific research areas
Characterizing the elastic properties of cells, hydrogels, and tissues is standard practice in many research labs focusing on mechanobiology, tissue engineering/regenerative medicine, and beyond3. This protocol can be used to quantify the elastic properties of single cells, hydrogels, and adapted for tissues and more complex biomaterials in the context of physiologically relevant processes marked by a change in mechanical properties. For example, to mimic the dynamics of the native ECM, it has been shown that degradable 3D PEG-laminin hydrogels allow cells to remodel their surrounding environment, leading to a decrease in the gels' E of ~50% over a period of 9 days as compared to the same gels without cells21. The protocol is of general applicability and is not restricted to the samples and optical setup described herein. It is envisaged that this protocol will facilitate the use of nanoindenters in research labs focusing on the study of mechanical properties in physiology and disease.
The authors have nothing to disclose.
GC and MAGO acknowledge all members of the CeMi. MSS acknowledges support via an EPSRC Programme Grant (EP/P001114/1).
GC: software (contribution to software development and algorithms), formal analysis (analysis of nanoindentation data), validation, Investigation (nanoindentation experiments on polyacrylamide gels), data curation, writing (original draft, review and editing), visualization (figures and graphs). MAGO: investigation (preparation of gels and cells samples, nanoindentation experiments on cells), writing (original draft, review and editing), visualization (figures and graphs). NA: validation, writing (review and editing). IL: software (contribution to software development and algorithms), validation, writing (review and editing); MV: conceptualization, software (design and development of original software and algorithms), validation, resources, writing (original draft, review and editing), supervision, project administration, funding acquisition MSS: resources, writing (review and editing), supervision, project administration, funding acquisition. All authors read and approved the final manuscript.
12 mm coverslips | VWR | 631-1577P | |
35 mm cell treated culture dishes | Greiner CELLSTAR | 627160 | |
Acrylamide | Sigma-Aldrich | A4058 | |
Acrylsilane | Alfa Aesar | L16400 | |
Ammonium Persulfate | Merk | 7727-54-0 | |
Bisacrylamide | Merk | 110-26-9 | |
Chiaro nanoindenter | Optics 11 Life | no catologue number | |
Ethanol | general | ||
Fetal bovine serum | Gibco | 16140071 | |
High glucose DMEM | Gibco | 11995065 | |
Isopropanol | general | ||
Kimwipe | Kimberly Clark | 21905-026 | |
Microscope glass slides | VWR | 631-1550P | |
MilliQ system | Merk Millipore | ZR0Q008WW | |
OP1550 Interferometer | Optics11 Life | no catalogue number | |
Optics 11 Life probe (k = 0.02-0.005 N/m, R = 3-3.5 um) | Optics 11 Life | no catologue number | |
Optics 11 Life probe (k = 0.46-0.5 N/m, R = 50-55 um) | Optics 11 Life | no catologue number | |
Penicillin/Streptomycin | Gibco | 15140122 | |
RainX rain repellent | RainX | 26012 | |
Standard petri dishes (90 mm) | Thermo Scientific | 101RTIRR | |
Tetramethylethylenediamine | Sigma-Aldrich | 110-18-9 | |
Vaccum dessicator | Thermo Scientific | 531-0250 | |
Software | |||
Data acquisition software (v 3.4.1) | Optics 11 Life | ||
GitHub Desktop (Optional) | Microsoft | ||
Python 3 | Python Software Foundation | ||
Visual Studio Code (Optional) | Microsoft |