title: Measuring cellular traction forces on non-planar substrates.
abstract: Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have already been established mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a workflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromoulded from polydimethylsiloxane and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector-based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite-element method. Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with an L1-norm for the residue and an L2-norm for a zeroth-order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.
authors.affiliation: Institute for Theoretical Physics, Heidelberg University, Heidelberg, Germany; BioQuant, Heidelberg University, Heidelberg, Germany.
authors.forename: Jérôme R D
authors.initials: JR
authors.lastname: Soiné
authors.affiliation: Institute of Complex Systems 7: Biomechanics , Forschungszentrum Jülich GmbH, 52425 Jülich , Germany.
authors.forename: Nils
authors.initials: N
authors.lastname: Hersch
authors.affiliation: Institute of Complex Systems 7: Biomechanics , Forschungszentrum Jülich GmbH, 52425 Jülich , Germany.
authors.forename: Georg
authors.initials: G
authors.lastname: Dreissen
authors.affiliation: Institute of Complex Systems 7: Biomechanics , Forschungszentrum Jülich GmbH, 52425 Jülich , Germany.
authors.forename: Nico
authors.initials: N
authors.lastname: Hampe
authors.affiliation: Institute of Complex Systems 7: Biomechanics , Forschungszentrum Jülich GmbH, 52425 Jülich , Germany.
authors.forename: Bernd
authors.initials: B
authors.lastname: Hoffmann
authors.affiliation: Institute of Complex Systems 7: Biomechanics , Forschungszentrum Jülich GmbH, 52425 Jülich , Germany.
authors.forename: Rudolf
authors.initials: R
authors.lastname: Merkel
authors.affiliation: Institute for Theoretical Physics, Heidelberg University, Heidelberg, Germany; BioQuant, Heidelberg University, Heidelberg, Germany.
authors.forename: Ulrich S
authors.identifier: 0000-0003-1483-640X
authors.initials: US
authors.lastname: Schwarz
keywords: cell adhesion; cell mechanics; elastic substrates; elasticity theory; finite-element method; traction force microscopy