Integration of magnetic tweezers and traction force microscopy for the exploration of matrix rheology and keratinocyte mechanobiology: Model force- and displacement-controlled experiments

In this work, we present a new experimental methodology that integrates magnetic tweezers (MT) with substrate deformation tracking microscopy (DTM) and traction force microscopy (TFM). Two types of MT-DTM/TFM experiments are described: force-control mode and displacement-control mode experiments. In model bead-on-gel experiments for each mode, an MT device is used to apply a controlled force or displacement waveform to a fibronectin-coated superparamagnetic bead attached to a fibrillar type I collagen gel containing a layer of covalently attached red-fluorescent microspheres. Serial fast time-lapse differential interference contrast and epifluorescence image acquisition steps are used to capture displacements of the bead and microspheres, respectively, in response to the applied force or displacement. Due to the large number of acquired images and the dynamic nature of the experiment, new quantitative approaches are implemented to adapt TFM for the analysis of the data, including (i) a temporospatial correction algorithm for improved tracking of microsphere displacements, (ii) a method for the objective determination of L2 regularization parameters for computing incremental traction stress solutions, and (iii) an empirical means for identifying time intervals within the data that can be approximated by elastostatic conditions. We also illustrate how force and energy balances in a force-control mode bead-on-gel experiment can be used to estimate the elastic modulus of a collagen substrate. Finally, in a proof-of-concept, bead-on-cell demonstration, measurements of incremental cell–matrix traction stresses are used to observe how a force applied to a focal contact on the apical surface of a keratinocyte is transmitted to the collagen substrate below the cell.