Forward and Inverse Approaches to Characterizing Cellular Traction Forces

Abstract

Adherent cells exert tractional stresses on substrates through transmission of intracellular contractile forces. Traction forces influence processes including cell migration, crucial in cancer metastasis and wound healing. Quantification of these forces is hence essential to our understanding of cell-ECM interactions in normal and pathological conditions. In this study, we adapted the finite element (FE) method to quantify cellular tractions and used strain energy, stress and reaction forces as measures to characterize cell-substrate interactions using fibroblasts transfected with GFP-paxillin cultured on polyacrylamide substrates. FE analysis showed rapid convergence in strain energy and net reaction force with mesh refinement; stresses however converged slowly. We compared these results with Fourier Transform Traction Cytometry (FTTC) and regularised FTTC (Reg-FTTC) method which overcomes problems in inversion occurring due to noise. Mesh convergence for high stress nodes in FE was comparable to Reg-FTTC; FTTC stresses had poor convergence in comparison. Strain energy from FE method was lower than that obtained from both Fourier methods. Further, maximum stress was highest for FTTC, followed by FE and Reg-FTTC methods. Overall, the FE method performed significantly better than FTTC based on these metrics. The Reg-FTTC provides an improvement over slow stress convergence in FE but depends crucially on choice of regularization parameter which necessitates optimization for individual cell types. We used reaction force output, unique to FE, to quantify localized adhesion forces acting on discrete regions of cell periphery that may provide insights into spatial organization of cell-ECM interactions. Together, we hope these studies will help in creation of robust tools to characterize the mechanical interplay between cell and microenvironment which will further our understanding of disease progression and cell behaviour.