Adherent cells exert traction forces on to their environment, which allows
them to migrate, to maintain tissue integrity, and to form complex
multicellular structures. This traction can be measured in a perturbation-free
manner with traction force microscopy (TFM). In TFM, traction is usually
calculated via the solution of a linear system, which is complicated by
undersampled input data, acquisition noise, and large condition numbers for
some methods. Therefore, standard TFM algorithms either employ data filtering
or regularization. However, these approaches require a manual selection of
filter- or regularization parameters and consequently exhibit a substantial
degree of subjectiveness. This shortcoming is particularly serious when cells
in different conditions are to be compared because optimal noise suppression
needs to be adapted for every situation, which invariably results in systematic
errors. Here, we systematically test the performance of new methods from
computer vision and Bayesian inference for solving the inverse problem in TFM.
We compare two classical schemes, L1- and L2-regularization, with three
previously untested schemes, namely Elastic Net regularization, Proximal
Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that
Elastic Net regularization, which combines L1 and L2 regularization,
outperforms all other methods with regard to accuracy of traction
reconstruction. Next, we develop two methods, Bayesian L2 regularization and
Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization.
Using artificial data and experimental data, we show that these methods enable
robust reconstruction of traction without requiring a difficult selection of
regularization parameters specifically for each data set. Thus, Bayesian
methods can mitigate the considerable uncertainty inherent in comparing
cellular traction forces
