Volume and surface methods for microparticle traction force microscopy: a computational and experimental comparison

It is an essential element of mechanobiology to measure the forces of biological cells. In microparticle traction force microscopy, they are inferred from the deformation of elastic microparticles. Two complementary variants have been introduced before: the volume method, which reconstructs surface stresses from the displacements of fiducial markers embedded inside the particles, and the surface method, which infers stresses directly from the deformation of the particle surface. However, a systematic comparison of the two methods has been lacking. Here, we quantitatively compare both approaches using simulated traction fields representing biologically relevant loading scenarios. We find that the surface method consistently reconstructs traction profiles with substantially lower errors than the volume method, which suffers from displacement tracking and stress calculation at the surface. At high noise levels, however, the performance gap becomes smaller. To compare the performance of the two methods in a realistic experimental setting, we developed DNA-based hydrogel microparticles equipped with both fluorescent surface labels and embedded fluorescent nanoparticles, enabling the direct comparison of the two methods within the same system. Compression experiments produced traction profiles consistent with Hertzian contact mechanics and confirmed the trends observed in the simulations. We also show that despite large experimental deformations and strains (both up to 20 percent), linear elasticity theory should still be valid. While our computational workflow establishes a framework to apply both methods, our experimental workflow establishes DNA microparticles as versatile and biocompatible probes for measuring cellular forces.