Utilizing collagen-coated hydrogels with defined stiffness as calibration standards for AFM experiments on soft biological materials: the case of lung cells and tissue

2.1 Collagen hydrogels

For this study, commercially available collagen-coated hydrogels with predefined stiffness were utilized. Specifically, we used collagen-coated hydrogels with stiffness values of 0.5 kPa and 1.0 kPa, bound to 35 mm Petri dishes (Petrisoft™ 35 mm Dish Collagen, Cell Guidance Systems). More specifically, the hydrogels used in this study were commercially available polyacrylamide-based gels crosslinked with bisacrylamide and coated with type I collagen from bovine skin. These collagen-coated hydrogels were approximately 500 μm thick, bound to 35 mm polystyrene dishes. The collagen was applied at a surface density of 0.02 mg/ml across different stiffness values, as confirmed by chemiluminescence-based detection. This uniform surface collagen density enables cell attachment and growth, providing a more physiologically relevant environment for cellular mechanics studies. Importantly, the stiffness of the hydrogels can be tuned to reflect different biological environments, while the collagen coating offers an ECM-like surface for cells. Hence, the term “collagen-coated hydrogels” is used in the manuscript to accurately describe the experimental setup.

2.2 Cell culturing

Commercially available lung native human fibroblasts (FBs), specifically LL 24 (normal FBs), were cultured in F − 12 K Medium in an incubator set to 37 °C with 5 % CO₂. For AFM experiment, the lung cells were cultured on 35 mm Petri dishes, which could be directly mounted onto the AFM system for nanoindentation measurements.

2.3 Human lung specimens

Patients were recruited at the Nicosia Lung Center by Dr. Zachariades. Those who consented provided tissue samples for research. The Cyprus National Bioethics Committee (licenses EEBK/EΠ/2022/04) approved all procedures and experimental protocols. Human tissue samples were obtained via routine bronchoscopy conducted for diagnostic or therapeutic reasons in newly diagnosed pulmonary fibrosis patients. Following the biopsy, a portion of the collected tissue was allocated to our research, while the rest was processed by the clinical pulmonologist and histopathologist for histopathological analysis.

2.4 Atomic Force Microscopy

Atomic Force Microscopy (AFM) experiments were carried out using a commercial AFM (5,500 Keysight Technologies, Santa Rosa, CA, USA) equipped with V-shaped soft silicon nitride probes (MLCT-Bio, cantilever C for cells and D for tissue, Bruker) and colloidal AFM probe, AFM cantilever with round AFM tip like a ball (CP-PNPL-BSA-A, SQube, acquired through NanoAndMore). Given the high-water content of the sample, a Poisson’s ratio of ν = 0.5 was assumed. The spring constant was calibrated using the thermal noise method, while the sensitivity calibration (measured as nanometers of cantilever deflection per volt signal from the laser detection system) was performed by obtaining force-versus-distance curves on a Petri dish, which provided a pristine, rigid surface [16], [17]. For the AFM nanoindentation technique a set point of 1 nN normal force for the cells and 1.8 nN for the tissue [18]. The Young’s modulus was assessed by acquiring 8 × 8 points of force curves in an area of 1 × 1 µm. For the cells’ this area was selected to be near the centre of the cells. For each specimen at least 3 different regions of interest (ROI) were selected, while for the cells ∼10 cells per condition were studied [19], [20]. MLCT tips were approximated as conical, and the data was fitted to Sneddon’s equation:

For experiments using spherical indenters, the data were processed using the Hertz equation below:

In equations (1) and (2) E is the Young’s modulus, θ is the cone’s half-opening angle and R is the indenter’s radius.

The force-distance curves were processed using the AtomicJ software [21], which was also used to identify the contact point for each curve. The procedure is as follows: each point on the curve is treated as a potential contact point. A polynomial is fitted to the pre-contact region, and the corresponding contact model is applied to the force-indentation data. The associated sums of squares are recorded, and the point that results in the lowest total sum of squares is selected as the contact point.

2.5 Proposed methodology

The primary objective of this study is to propose a novel methodology using collagen-coated hydrogels with predefined stiffness as calibration standards for AFM experiments on soft biological materials, such as cells and tissues. This approach aims to: (i) Facilitate the selection of appropriate cantilevers for AFM experiments, (ii) Assess potential systematic errors in measuring mechanical properties in terms of Young’s modulus and (iii) Evaluate errors caused by AFM-induced damage.

The proposed methodology is very simple and is based on the use of collagen-coated hydrogels with pre-defined stiffness. Such hydrogels are commercially available, like the ones presented previously in Section 2.1. However, similar hydrogels (polyacrylamide gels coated with collagen) or pure collagen gels with different concentration (and consequently different stiffness) can be easily formed at a lab using commercially available collagen. Relevant protocols can be found in previous publications [16], [22].

3.1 Selection of hydrogel standards and cantilevers with appropriate spring constant

The first step of our study was to investigate whether collagen-coated hydrogels with predetermined stiffness can be utilized for selecting appropriate cantilevers for a specific material. This approach aims to enhance the accuracy of Atomic Force Microscopy (AFM)-based nanomechanical measurements by ensuring that the cantilever’s spring constant is suitably matched to the stiffness of the sample material.

To achieve this, we employed MLCT-BIO cantilevers (Bruker), which are frequently used in AFM-based nanomechanical experiments, particularly for force spectroscopy on soft biological samples, such as cells and tissues [18], [23], [24]. The MLCT-BIO chip is equipped with six cantilevers of varying spring constants and geometries, providing a versatile tool for a range of stiffness measurements.

For our specific application, we selected two triangular cantilevers from the MLCT-Bio chip, each featuring a nominal tip radius of 20 nm. The cantilevers chosen were the MLCT-BIO-C and MLCT-BIO-D, which have spring constants of 0.01 N/m and 0.03 N/m, respectively. These cantilevers were chosen based on our extensive prior experience with their use in nanomechanical characterization of biological samples [18], [23], [24]. The MLCT-BIO-C cantilever has been previously utilized for measuring the mechanical properties of cells, while the MLCT-BIO-D cantilever has been employed in studies involving tissue samples.

In our current study, we used these cantilevers to measure the stiffness of collagen-coated hydrogels, provided with known Young’s modulus values of 0.5 kPa and 1.0 kPa by the manufacturer. By measuring these hydrogels, we aimed to validate the use of MLCT-Bio cantilevers in obtaining accurate nanomechanical characterizations. Specifically, the MLCT-BIO-C cantilever was used to measure the softer 0.5 kPa hydrogel, and the MLCT-BIO-D cantilever was used for the 1.0 kPa hydrogel. These measurements served to confirm that the cantilevers with different spring constants can effectively capture the stiffness variations in collagen-coated hydrogels, thereby assisting in the selection of appropriate cantilevers for materials with specific mechanical properties.

As expected, the selection of the cantilever’s spring constant is critical to accurately measure the properties of the studied material. Figure 1 illustrates the importance of this selection. When we used the MLCT-BIO-C cantilever to measure the 0.5 kPa collagen hydrogel, the measurements were quite accurate, yielding a Young’s modulus of 0.46 ± 0.02 kPa. However, when this same cantilever was used to measure the 1.0 kPa collagen hydrogel, the results were less accurate, with a measured Young’s modulus of 0.37 ± 0.02 kPa.

Figure 1:

Young’s modulus measurements of collagen-coated hydrogels with predetermined stiffness using different AFM cantilevers and tips. The first column shows measurements with the MLCT-BIO-C cantilever (spring constant 0.01 N/m), which were accurate for the 0.5 kPa hydrogel (0.46 ± 0.02 kPa) but underestimated the stiffness of the 1.0 kPa hydrogel (0.37 ± 0.02 kPa). The second column presents measurements with the MLCT-BIO-D cantilever (spring constant 0.03 N/m), which overestimated the stiffness for both the 0.5 kPa hydrogel (1.14 ± 0.03 kPa) and the 1.0 kPa hydrogel (1.2 ± 0.04 kPa). The third column shows results using spherical tips with a 5 μm diameter (force constant 0.08 N/m), providing more accurate measurements for both the 0.5 kPa (0.58 ± 0.05 kPa) and the 1.0 kPa (0.98 ± 0.04 kPa) collagen-coated hydrogels.

Conversely, when using the MLCT-BIO-D cantilever, which has a higher spring constant, the results were more accurate for the stiffer 1.0 kPa hydrogel, yielding a measured Young’s modulus of 1.2 ± 0.04 kPa. However, the same cantilever overestimated the stiffness of the 0.5 kPa hydrogel, measuring it at 1.14 ± 0.03 kPa. This indicates that the MLCT-BIO-D cantilever is not suitable for softer hydrogels like the 0.5 kPa sample, and even the 1.0 kPa hydrogel might require a stiffer cantilever for accurate measurement.

To further investigate and improve our measurements, we utilized spherical tips with a 5 μm diameter (CP-PNPL-BSA-A, force constant 0.08 N/m). The results from these spherical tips are also shown in Figure 1, in the third column of each panel. The spherical tips provided more accurate measurements for both hydrogels: 0.58 ± 0.05 kPa for the 0.5 kPa hydrogel and 0.98 ± 0.04 kPa for the 1.0 kPa hydrogel. These results suggest that spherical tips might be more suitable for measuring the Young’s modulus of collagen-coated hydrogels, particularly at the micrometer scale, as the sphere’s size facilitates more accurate indentation over a larger contact area. In Figure S1, representative examples of force-displacement and force-indentation curves used in this paper are presented.

Our findings highlight the necessity of carefully selecting the cantilever’s spring constant to match the mechanical properties of the material being studied. The MLCT-BIO-C cantilever is appropriate for softer hydrogels, such as the 0.5 kPa collagen hydrogel, while the MLCT-BIO-D cantilever is better suited for stiffer hydrogels, though possibly requiring even stiffer samples for optimal performance. Additionally, spherical tips with a larger radius demonstrate potential for more accurate measurements across a range of stiffnesses, emphasizing their utility for micrometer-scale characterization.

3.2 Normalization factor

The next step in our investigation was to calculate the Normalization Factor (NF) based on Equation (3) for the measurements presented in the previous section. The NF serves as a crucial parameter for normalizing measurements across different cantilevers and materials, thereby enhancing the reliability and comparability of nanomechanical characterizations. Using Equation (3), we calculate the NF for each set of measurements discussed earlier. These calculations are summarized in Table 1.

From Table 1, it is evident that the Normalization Factor is close to 1 for the more accurate measurements. For example, the MLCT-BIO-C cantilever, which provided an accurate measurement of the 0.5 kPa hydrogel (0.46 ± 0.02 kPa), has an NF of 1.09. Similarly, the spherical tip measurements yielded NFs near 1, indicating high accuracy.

These NFs can be utilized for normalized measurements on unknown specimens, such as cells and tissues. By applying the NF, we can adjust for the discrepancies between measured and known values, thus ensuring that our nanomechanical characterizations are both precise and reliable across different experimental setups.

3.3 Error assessment

Using the provided technique, researchers can not only determine a Normalization Factor (NF) but also assess the percentage error in their measurements. This process involves measuring the stiffness of a selected collagen hydrogel with a known stiffness using AFM before conducting experiments on the actual biological material. The measured stiffness can then be compared to the known value to calculate the measurement error.

The measurement error can be calculated using the Equation (4).

This equation allows for a straightforward calculation of the percentage error, providing an indication of the accuracy of the AFM measurements.

To illustrate this, consider the measurements presented in the previous sections. For the MLCT-BIO-C cantilever measuring the 0.5 kPa collagen hydrogel, the known Young’s modulus is 0.5 kPa, and the measured Young’s modulus is 0.46 kPa. Using the equation, the error is calculated 8 %. Similarly, for the MLCT-BIO-D cantilever measuring the 1.0 kPa collagen hydrogel, where E_known = 1.0 kPa and E_measured = 1.2 kPa, the error is: −20 %. A negative error indicates an overestimation in the measured value compared to the known value.

From Table 1 (last column), it is apparent that the measurement errors vary significantly depending on the cantilever and the stiffness of the hydrogel being measured. For instance, the MLCT-BIO-C cantilever has a low error (8 %) for the 0.5 kPa hydrogel but a much higher error (63 %) for the 1.0 kPa hydrogel. The MLCT-BIO-D cantilever shows large negative errors, indicating an overestimation of stiffness. The spherical tips demonstrate relatively lower errors, highlighting their potential for more accurate measurements.

Assessing the percentage error in this manner allows researchers to identify and account for potential inaccuracies in their AFM measurements. By doing so, they can ensure greater precision and reliability in their nanomechanical characterizations of biological materials.

All the tested measurements have an indentation depth of approximately 1 μm (Figure S1). For conical indentations, we ensured that the maximum indentation depth is significantly larger than the tip apex radius (approximately 20 nm) to guarantee the applicability of Sneddon’s equation (Equation (1)). For spherical indentations, Hertz equation (equation (2)) is valid for h_max ≪ R [25]. However, a very small indentation depth can result in significant errors in contact point determination [26]. Indentation depths greater than 400 nm are required to avoid errors due to uncertain determination of the contact point [26]. In the case of the measurements presented in this paper, h_max/R ≈ 0.4 (since h_max ≈ 1 μm and R = 2.5 μm). According to previous studies [25], this ratio yields an approximately 4 % error in the calculation of Young’s modulus, which is considered small compared to other experimental uncertainties. It should also be noted that accurate expressions for deep spherical indentations are presented in [25].

3.4 Error measurement due to tip damage

A crucial parameter in AFM measurements is the AFM tip, and potential damage to the tip during use can significantly alter the measurements. As described in the Methodology section, collagen-coated hydrogels can be employed not only as calibration standards but also to assess errors that might arise from tip damage during repeated measurements. This assessment involves several steps, Initial Stiffness Measurement, Experimental Measurements, Post-Experiment Stiffness Measurement and Error Estimation as presented in the methodology section.

Using the MLCT-BIO-C cantilever on a 0.5 kPa collagen hydrogel and the MLCT-BIO-D cantilever on a 1.0 kPa collagen hydrogel, we conducted initial measurements as presented in Section 3.1. We then conducted experiments on lung cells (∼20 cells) with the MLCT-BIO-C cantilever and a human lung specimen (∼15 maps) with the MLCT-BIO-D cantilever. Subsequently, the same tips/cantilevers were used to measure the same hydrogels again.

The results presented in Figure 2 show a significant alteration in the Young’s modulus measurements, indicating potential tip damage. Table 2 summarizes the calculated errors based on Equation (5). By using the Normalization Factor (NF) to normalize the measurements (third column in the panels of Figure 2), we recalculated the error, demonstrating that the NF minimizes the error and enhances measurement accuracy.

Figure 2:

Young’s modulus measurements before and after biological material experiments, demonstrating the effect of cantilever damage.

The first column shows initial measurements of collagen-coated hydrogels (0.5 kPa and 1.0 kPa) using MLCT-BIO-C and MLCT-BIO-D cantilevers, respectively. The second column shows post-experiment measurements of the same hydrogels, indicating changes in measured Young’s modulus due to potential cantilever damage. The third column presents normalized measurements using the Normalization Factor (NF), highlighting improved accuracy.

By applying the NF, we can significantly reduce the measurement error attributed to cantilever damage, ensuring the integrity and reliability of AFM measurements in subsequent experiments. This approach enables more precise nanomechanical characterizations of biological materials, accounting for potential deviations due to repeated tip use.

3.5 Physical considerations and reasons behind the errors

In previous sections, it was demonstrated that the cantilever’s spring constant, the geometry of the AFM tip, and the excessive use of a tip significantly influence Young’s modulus calculations. The reasons behind these effects are presented in this section. More specifically, a major question that arises from the analysis presented above is why the choice of the spring constant so significantly affects the measurements of Young’s modulus. To accurately assess the mechanical properties of a biological system, it is essential to select cantilevers with spring constants that closely match the stiffness of the system [13]. If the cantilever is significantly stiffer than the sample, the resulting deflection will be minimal, rendering the measurement insensitive. In this case there is not ‘abrupt’ increase of force when the indenter comes into contact with the sample. Therefore, there is a major uncertainty regarding the contact point determination as presented in Figure 3. To provide a brief explanation, consider an experiment using a pyramidal tip, which can be approximated as a cone with the same projected contact area as the actual tip at the same indentation depth. For example, according to the manufacturer, the front, back, and side angles of the MLCT tips used in this paper are 35 ± 2°. To simplify the analysis, we can consider an equivalent cone with a half-angle of θ ≈ 29° according to the mathematical procedure described in [27], and use Sneddon’s equation (equation (1)) for conical indenters. The indentation depth is defined as h = z − δ, where z is the sample’s displacement towards the AFM tip (also known as “piezo-displacement” due to the piezoelectric material below the tested sample), and δ is the cantilever’s deflection (which equals the “piezo-displacement” when testing a hard material that is not deformed by the indenter, such as mica). If the contact point is at “point A,” then the maximum indentation depth would be h_max(A). If the contact point is at “point B,” the maximum indentation depth would be h_max(B), where h_max(A) > h_max(B).

Figure 3:

When using cantilevers with large spring constants on soft samples, there is no abrupt increase in the applied force on the sample, making the determination of the contact point very difficult. The contact point in the F–z curve could be either ‘point A’ or ‘point B’ or any point in between.

The work done by the indenter (which is equal to the area under the force (F)-indentation (h) curve) can be easily calculated as follows:

Therefore, the Young’s modulus equals to:

Choosing “point A” or “point B” as the contact point in the Figure 3 will have minimal influence on the work done by the indenter due to the very small forces present at the initial stage of the experiment (as previously mentioned, the cantilever is only slightly deflected, which makes determining the contact point difficult). However, the maximum indentation depth is significantly affected. Thus, if h_max(A) > h_max(B) and W_A ≈ W_B, then calculating Young’s modulus using point B as the contact point will result in a significantly higher value according to Equation (7). This explains the substantial overestimation of Young’s modulus when using the MLCT-BIO D tip (k = 0.03 N/m) on the sample with E = 0.5 kPa.

It is also important to note that a stiff cantilever may result in large indentation depths, leading to a substrate effect. In this case, Young’s modulus will be significantly overestimated (the maximum indentation depth should not exceed 10 % of the sample’s thickness) [13].

In addition, the average stiffness of the system when using a conical indenter can be calculated as follows:

while for a spherical indenter,

Equations (8) and (9) offer a straightforward explanation for why the micro-spherical tip with k = 0.08 N/m was more suitable for both samples (with E = 0.5 kPa and 1 kPa). The average stiffness when using a conical indenter is proportional to the indentation depth (equation (8)), so it can vary widely. In other words, depending on the indentation depth (or the maximum applied force on the sample), the average stiffness can be similar to or significantly different from the cantilever’s spring constant (an experiment with a maximum indentation depth of 1,000 nm results in an average stiffness that is an order of magnitude larger compared to an experiment with a maximum indentation depth of 100 nm). On the other hand, when using a spherical tip, the average stiffness is proportional to the square root of the maximum indentation depth, resulting in a much smaller variation in average stiffness when the indentation depth is changed. Therefore, a micrometer-sized spherical indenter with an appropriate spring constant can be effectively used across a wide range of materials with Young’s moduli of the same order of magnitude. Another reason for the suitability of spherical tips is related to the linear elastic behavior of the sample. In particular, the applied strains should not exceed 20 % [13]. The deformation of the sample when using a conical can be approximated to [18]:

Therefore, a conical indenter with θ ≈ 29° can cause significant deformation, making it difficult to describe the behavior using equations derived from linear elastic models. On the other hand, when using a spherical indenter [28],

Thus, using spherical tips with micrometer-sized diameters will result in low strain, ensuring that linear elastic models remain valid.

In addition, significant errors in determining Young’s modulus can arise from extensive use of the AFM tip. As shown in Table 2, tip damage can lead to either overestimation or underestimation of the calculated Young’s modulus. The overestimation can be easily explained by modelling the tip as a truncated cone (a simplified geometric representation of a blunt tip [29]. The results for this case can also be extended to more complex models, such as the sphero-conical model of the tip). As previously shown in [29] when using a truncated cone, the applied force on the sample equals to:

The first term on the right side of Equation (12) is Sneddon’s classic equation, while the second term is a correction factor accounting for tip damage. The magnitude h_tip represents the difference in indentation depth between using a perfect conical indenter and a truncated cone [29]. By comparing Equations (1) and (12) and considering that E is the actual Young’s modulus while E _c is the Young’s modulus obtained using Equation (1) instead of Equation (12) for data processing, it is easy to derive the following equation [29]:

Depending on the extent of tip damage (i.e., the value of h_tip), the Young’s modulus can be significantly overestimated – by as much as 150 %, as shown in [29]. The possibility of underestimating Young’s modulus is also significant. Consider a scenario where contamination of the AFM tip substantially affects the attractive surface forces (such as adhesion) between the tip and the sample. In this case,

In Equation (14), F_Sn/Hetrz represents the classic Sneddon/Hertz equations (i.e., Equations (1) and (2)), while F_attr⋅ denotes the attractive forces from the surface. As shown, using Equation (12), which adds a term to the classic Sneddon equation, can lead to a significant overestimation of Young’s modulus if Equation (1) is used for data processing instead of Equation (12). Therefore, by subtracting the term F_attr⋅, we can conclude that there may be a significant underestimation of Young’s modulus when using Equation (1) if attractive forces have increased due to contamination (the case of the MLCT-BIO C tips in Table 2).

3.6 Proof of concept: human lung specimens

As a proof of concept for the proposed methodology, we used human lung fibroblasts (FBs) and human lung specimens from a patient with pulmonary fibrosis. To carry out the measurements, we employed the MLCT-C and MLCT-D cantilevers, respectively. In cases where there is a non-negligible influence from the substrate effect, equations (1) and (2) can be corrected by adding a correction function f(h, H), where h is the indentation depth and H is the sample’s thickness, as discussed in [26], [30], [31]. The only difference is that the force-indentation data should be fitted to these extended equations instead of fitting them to (1) and (2) [26], [30], [31], [32], [33]. At this point, it is important to note that the bottom effect correction for conical indenters was first studied by Gavara and Chadwick [26]. However, when applying this model, the force exerted by a conical tip on the sample does not converge as more terms are included in the force calculation. This issue was identified by Garcia and Garcia, who corrected the equation for conical indenters [32]. In Garcia and Garcia’s expression, the forces for the third and fourth orders are almost identical [32]. Finite element simulations have demonstrated the accuracy of the corrected equation [32].

3.6.1 Lung cells

For the cellular measurements, we employed the softer cantilever, MLCT-BIO-C, which has a lower spring constant suited for measuring softer biological materials. The initial measurements, without applying the Normalization Factor (NF), yielded an average Young’s modulus of 0.666 kPa (Figure 4A). Upon applying the normalization methodology, the average Young’s modulus was adjusted to 0.724 kPa. The percentage error associated with these measurements was calculated to be 8 %. This adjustment demonstrates the importance of normalization in correcting for systematic overestimation and ensuring the accuracy of AFM measurements.

Figure 4:

Proof-of-concept application of the proposed methodology. (A) Human lung cells elasticity with and without normalization. For the cells we used the MLCT-BIO-C cantilever. (B) Elasticity spectrum of human lung specimens with pulmonary fibrosis. The solid line represents the average Young’s modulus (∼0.48 kPa) obtained from direct measurements using the MLCT-BIO-D cantilever. The dotted line represents the normalized average Young’s modulus (∼0.4 kPa) after applying the proposed normalization methodology. The normalization corrects for the systematic overestimation of stiffness, shifting the spectrum to lower values.