Prediction of traction forces of motile cells

Abstract

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

A note on how to develop interdisciplinary collaborations between experimentalists and theoreticians

“…In many of these papers, experts in theory and experimentation teamed up to work on a problem of significant importance during the programme thereby exemplifying the fruits of interdisciplinary research (articles that form this special issue; [1][2][3][4][5][6][7][8][9][10][11] …”

From Energy to Cellular Force in the Cellular Potts Model

“…Such inverse 111 methods quantify and reveal very detailed force fields. Traction forces roughly point 112 towards the cell's centroid, are highest in protruding regions and decline towards the 113cell's centroid [8,[13][14][15][16]. Via cell-cell adhesions, cells also apply forces on neighbouring 114 cells and these forces can propagate through tissues [17].…”

“…We asked how the predictions of the CPM-based force fields compare with data for 116 actual traction forces observed in real cell experiments. Consequently, we utilized data 117 kindly provided by the authors of [8] for two cancer cell lines. Several steps were needed 118 to arrive at a shared grid, to select CPM parameters, and to compare magnitudes on a 119 similar range, and adjust smoothing.…”

“…Verdier for two cancer cell lines (T24 and RT112) as described by [8]. The authors 349 plated cells on polyacrylamide gels containing fluorescent beads, and computed traction 350 forces from bead displacements and known gel rheology [9].…”

“…• Supplementary Fig. 17 Triangular mesh on which cell traction data from [8] 463 was supplied, and the corresponding CPM cell (spin value = 1).…”