Fig. 3: Experiment rendering and representative example datasets used for viscoelastic parameterization.

This figure showcases the model performance vs. action integral data for the 2D adherent human skin cell lines under study. The experiment configuration is rendered in (a). Note that h(t_i) is the final indentation depth and l(t_i) the final contact radius. The force curves reconstructed using the optimal parameter sets for each adherent cell type are provided in (b), where the thick colored lines represent the observed data and the thinner, marked lines represent the optimal model estimations. For subfigure b the melanocyte model was fit using two viscoelastic elements, the melanoma model using three elements, and the fibroblast model also used two elements. The experimental data collected through the AFM force curves has also been visualized in terms of an action integral in log-spaced form as scattered markers (“Data”), and the corresponding colored lines show the action integral predicted by the model’s approximation of that dataset for a varying number of terms for melanocytes (c), melanoma (d), and fibroblasts (e), respectively. These subfigures are the basis upon which the “optimal” parameter sets are determined; the lowest number of terms that most accurately represent the input data has been selected in each case. In some cases, the first order of magnitude was difficult to approximate (as is evident in (c−e), especially for melanoma), due in part to data acquisition frequency limitations and the cost of performing numerical convolutions. Gray shaded regions represent the same temporal regions in (b−e) and have been included to showcase why subtle changes at longer timescales in (c−e) are critical to the quality of fit in the timescales visible in (b) and are given additional preference over high-quality fits at shorter times. This figure showcases results for the Generalized Maxwell Model in the Lee and Radok framework. Panels b−e show the results for a single representative force curve taken at the nuclear region of the cell; this process was repeated for between 70 and 193 AFM force curves from each cell type. Note that the sparse markers for the model estimations included in the force plot (b) are deliberately periodically spaced for representation purposes to differentiate the model estimation from the dataset without completely obscuring the latter—there are an equivalent number of model and AFM observable datapoints. The standard error for each model configuration in (c−e) is provided in Supplementary Table 2. In addition, the fit quality c−e has been visualized using the Generalized Maxwell viscoelastic model convolution integral of the fit (\({\int }_{0}^{t}Q\left(t-\zeta \right)* {\left\{h\left(\zeta \right)\right\}}^{\frac{3}{2}}{{{{{\rm{d}}}}}}\zeta\)) against the normalized dataset (\(\frac{3\left(1-\nu \right)}{8\sqrt{R}}F\left(t\right)\)).