Nonlinear elastic properties of polyacrylamide gels: Implications for quantification of cellular forces

Because of their tunable mechanical properties, polyacrylamide gels (PAG) are frequently used for studying cell adhesion and migratory responses to extracellular substrate stiffness. Since these responses are known to heavily depend on the tensional balance between cell contractility and substrate mechanical resistance, a precise knowledge of PAG's mechanical properties becomes quite crucial. Using the micropipette aspiration technique, we first exhibited the nonlinear elastic behavior of PAG and then successfully modeled it by an original strain-energy function. This function depends on the Poisson's ratio and on two material parameters, which have been explicitly related to acrylamide and bis-acrylamide concentrations. Implications of these results have been highlighted with regard to traction force microscopy experiments where cellular force quantification is derived from displacements of beads embedded in PAG. We found that considering PAG as a linear elastic medium tends to significantly underestimate traction forces for substrate displacements larger than 2 μm. Interestingly, we also showed that in the range of cellular force amplitude and PAG stiffness currently used in cell traction force experiments, finite size effects become critical for PAG substrate thickness below 60 μm. Thus, our improved characterization of PAG nonlinear mechanical properties through a new constitutive law could have significant impact onto biological experimentations where such extracellular substrates experience large strains.