Fig. 2: Extracting viscoelastic properties by mechanical de-embedding framework.

a To extract the mechanical properties of the cell, the setup is characterized using three sets of laser positions MM, MS, and SS. Top left, differential interference contrast (DIC) image of a rounded HeLa cell confined between master (left) and slave (right) microcantilever. Scale bar, 10 µm. DIC images (false colored) show the actuating blue laser having a spot size of 6 µm and red readout laser having a spot size of 21 µm. b Diagram showing the position of blue actuating and red readout laser spots on the cantilever. c Numerically acquired amplitude responses of a triangular cantilever actuated and readout at the free end (\({z}_{{\rm{blue}}}={z}_{{\rm{red}}}=0.9L\), dashed line) and actuated at the base end and readout at the free end (\({z}_{{\rm{blue}}}=0.1L,{z}_{{\rm{red}}}=0.9L,\) black line). Together with the corresponding phase curves (Supplementary Fig. 5), a correction for the laser position was extracted (Methods, Supplementary Fig. 6). d Procedure to extract the mechanical properties of the cell. Top, experimental acquisition of amplitude (black) and phase (red) response curves of the microcantilever. Middle, mathematically shifting the position of the blue laser actuating the cantilever to coincide with the point of cantilever readout gives a corrected amplitude (black, dashed) and phase (red, dashed). Bottom, applying the transfer function \({g}_{{\rm{c}}}(f)\) to extract the storage (red, E′_cort) and loss (black, E″_cort) moduli. e Model used for FEM simulations. Microcantilever dimension, stiffness, damping, and cell size are taken from the experiment. Colors encode deflections along the microcantilever actuated at 19 kHz (Methods). The model generates amplitude and phase responses to test the mechanical de-embedding framework (Supplementary Fig. 7a, b). f Extracting \({g}_{{\rm{c}}}\) (black data points imaginary part, red data points real part) by applying the method summarized in d to amplitude and phase response curves (Supplementary Fig. 7a, b) generated in e. The results are compared to \({g}_{{\rm{c}}}(f)\) calculated from simulating of a deformed cell excluding both cantilevers (thin green and black lines). Only deviations <1% are found for this particular rheological (Maxwell) model (other rheological models shown in Supplementary Fig. 7c). g Simulation of a single cell being deformed by a force. The relationship between the time-dependent force and deformation allows to determine ɡ_c(f).