3D Viscoelastic traction force microscopy

Abstract

Native cell-material interactions occur on materials differing in their structural composition, chemistry, and physical compliance. While the last two decades have shown the importance of traction forces during cell-material interactions, they have been almost exclusively presented on purely elastic in-vitro materials. Yet, most bodily tissue materials exhibit some level of viscoelasticity, which could play an important role in how cells sense and transduce tractions. To expand the realm of cell traction measurements and to encompass all materials from elastic to viscoelastic, this paper presents a general, and comprehensive approach for quantifying 3D cell tractions in viscoelastic materials.This methodology includes the experimental characterization of the time-dependent material properties for any viscoelastic material with the subsequent mathematical implementation of the determined material model into a 3D traction force microscopy (3D TFM) framework. Utilizing this new 3D viscoelastic TFM (3D VTFM) approach, we quantify the influence of viscosity on the overall material traction calculations and quantify the error associated with omitting timedependent material effects, as is the case for all other TFM formulations. We anticipate that the 3D VTFM technique will open up new avenues of cell-material investigations on even more physiologically relevant time-dependent materials including collagen and fibrin gels.

Mean deformation metrics for quantifying 3D cell–matrix interactions without requiring information about matrix material properties

“…In cases where the mechanical properties are known, the FIDVC-derived displacement data can either be quantified using the presented MDM approach or be directly converted to traction data using, for example, our 3D viscoelastic TFM algorithm (see the MDM-TFM comparison chart; Fig. S5) (24).…”

“…Most physiologically important matrices have complicated, hierarchical microstructures and tend to be spatially heterogeneous. In addition, many cells apply significant forces leading to large matrix deformations that require more complicated, nonlinear constitutive laws for accurate calculation (17,(24)(25)(26)(27)(28). Moreover, to generate a quantitative map of tractions exerted by a moving cell, the mechanical properties of the surrounding matrix must be resolved at the cellular level.…”

“…In TFM, measured cell-induced displacements are converted into tractions using various mathematical frameworks (14,15,17,18,21,22). Both twoand 3D TFM techniques have steadily increased in sophistication and now feature high-spatial displacement resolution and advanced computational formalisms to connect this displacement information to complex material constitutive laws (17,23,24).To successfully perform TFM, it is critical to know the stressstrain constitutive behavior of the matrix surrounding the cell. Although many TFM substrates feature relatively simple artificial gel constructs, such as polyacrylamide and polyethylene glycol, these constructs are impenetrable by cells and obviate measures obtained while cells are in a 3D setting (as would be the case within a bodily tissue).…”

“…In TFM, measured cell-induced displacements are converted into tractions using various mathematical frameworks (14,15,17,18,21,22). Both twoand 3D TFM techniques have steadily increased in sophistication and now feature high-spatial displacement resolution and advanced computational formalisms to connect this displacement information to complex material constitutive laws (17,23,24).…”

For whom the cells pull: Hydrogel and micropost devices for measuring traction forces

“…As it occurs in 2D TFM, successful assessment of substrate force fields with 3D TFM also requires knowledge of substrate mechanical properties. Other deformable substrate materials, such as collagen [26–28] and fibrin [29], are used to encapsulate cells in 3D environments and track the forces they generate during cell-substrate interactions [30]. These materials are mechanically more complex than polyacrylamide gels [31, 32].…”