Abstract
Essential cellular processes such as cell adhesion, migration and division strongly depend on mechanical forces. The standard method to measure cell forces is traction force microscopy (TFM) on soft elastic substrates with embedded marker beads. While in 2D TFM one only reconstructs tangential forces, in 2.5D TFM one also considers normal forces. Here we present a systematic comparison between two fundamentally different approaches to 2.5D TFM, which in particular require different methods to deal with noise in the displacement data. In the direct method, one calculates strain and stress tensors directly from the displacement data, which in principle requires a divergence correction. In the inverse method, one minimizes the difference between estimated and measured displacements, which requires some kind of regularization. By calculating the required Green’s functions in Fourier space from Boussinesq-Cerruti potential functions, we first derive a new variant of 2.5D Fourier Transform Traction Cytometry (FTTC). To simulate realistic traction patterns, we make use of an analytical solution for Hertz-like adhesion patches. We find that FTTC works best if only tangential forces are reconstructed, that 2.5D FTTC is more precise for small noise, but that the performance of the direct method approaches the one of 2.5D FTTC for larger noise, before both fail for very large noise. Moreover we find that a divergence correction is not really needed for the direct method and that it profits more from increased resolution than the inverse method.
Highlights
Mechanical forces are important for a wide range of essential cellular processes such as cell adhesion, migration and division [1]
Our results show that 2.5D Fourier Transform Traction Cytometry (FTTC) usually performs better than the 2.5D direct (or forward) method (DM), but that the performance of the DM approaches the one of FTTC for larger noise, before both fail at very large noise
Motivated by the observation that different traction force microscopy (TFM)-methods are often advanced in specific contexts, but rarely compared to each other, here we have conducted an in-depth comparison of inverse and direct methods in the framework of 2.5D TFM
Summary
Mechanical forces are important for a wide range of essential cellular processes such as cell adhesion, migration and division [1]. Regularization can be formulated in Fourier space and many schemes can be applied to deal with the noise issue [23, 29, 30] Together, these advances make the inverse method very attractive for measuring cell traction on soft elastic substrates. Such systems might by approached best with FEM-approaches, but in some cases (like elastic beads) GF-based inverse methods are possible [12, 36] We use this recent development as a motivation to compare direct and inverse methods in the traditional setup of 2.5D TFM for planar substrates. The direct method (bottom) cannot be used in a purely 2D setup, but requires 3D image data In this method, traction is calculated directly from the displacement field by differentiation and (linear) transformation between strain and stress. For relatively stiff homogeneous and isotropic materials, a linear approximation can be used that is given by
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
