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Adherent cells exert traction forces on to their environment, which allowsthem to migrate, to maintain tissue integrity, and to form complexmulticellular structures. This traction can be measured in a perturbation-freemanner with traction force microscopy (TFM). In TFM, traction is usuallycalculated via the solution of a linear system, which is complicated byundersampled input data, acquisition noise, and large condition numbers forsome methods. Therefore, standard TFM algorithms either employ data filteringor regularization. However, these approaches require a manual selection offilter- or regularization parameters and consequently exhibit a substantialdegree of subjectiveness. This shortcoming is particularly serious when cellsin different conditions are to be compared because optimal noise suppressionneeds to be adapted for every situation, which invariably results in systematicerrors. Here, we systematically test the performance of new methods fromcomputer vision and Bayesian inference for solving the inverse problem in TFM.We compare two classical schemes, L1- and L2-regularization, with threepreviously untested schemes, namely Elastic Net regularization, ProximalGradient Lasso, and Proximal Gradient Elastic Net. Overall, we find thatElastic Net regularization, which combines L1 and L2 regularization,outperforms all other methods with regard to accuracy of tractionreconstruction. Next, we develop two methods, Bayesian L2 regularization andAdvanced Bayesian L2 regularization, for automatic, optimal L2 regularization.Using artificial data and experimental data, we show that these methods enablerobust reconstruction of traction without requiring a difficult selection ofregularization parameters specifically for each data set. Thus, Bayesianmethods can mitigate the considerable uncertainty inherent in comparingcellular traction forces.

Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells