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Hydrogels of semiflexible biopolymers such as collagen have been shown to contract axially under shear strain, in contrast to the axial dilation observed for most elastic materials. Recent work has shown that this behavior can be understood in terms of the porous, two-component nature and consequent time-dependent compressibility of hydrogels. The apparent normal stress measured by a torsional rheometer reflects only the tensile contribution of the axial component σ zz on long (compressible) timescales, crossing over to the first normal stress difference, N 1 = σ xx − σ zz at short (incompressible) times. While the behavior of N 1 is well understood for isotropic viscoelastic materials undergoing affine shear deformation, biopolymer networks are often anisotropic and deform nonaffinely. Here, we numerically study the normal stresses that arise under shear in subisostatic, athermal semiflexible polymer networks. We show that such systems exhibit strong deviations from affine behavior and that these anomalies are controlled by a rigidity transition as a function of strain. 

The Comment on our paper introducing “a symmetric method to obtain shear moduli from microrheology” proposes an interpolation method to generate oversampled data from an original time series that are then used to approximate shear moduli at frequencies “beyond the Nyquist frequency.” The author states that this can be done without the use of “preconceived fitting functions,” implying that the results are unique and reliable. We disagree with these assertions. While it is possible to generate reasonable looking transforms at frequencies above the Nyquist limit by interpolation, any results obtained above the Nyquist limit will be questionable at best. Moreover, while the cubic spline interpolation the author uses may be standard, it constitutes a particular “preconceived” fit and produces oversampled data that are not unique. 

Passive microrheology deduces shear elastic moduli from thermally fluctuating motion of probe particles. We introduce and test an analysis method for direct determination of these moduli from the mean-squared displacement of a probe.