The Proton Radius Puzzle refers to the ~7{\sigma} discrepancy that exists
between the proton charge radius determined from muonic hydrogen and that
determined from electronic hydrogen spectroscopy and electron-proton
scattering. One possible partial resolution to the puzzle includes errors in
the extraction of the proton radius from ep elastic scattering data. This
possibility is made plausible by certain fits which extract a smaller proton
radius from the scattering data consistent with that determined from muonic
hydrogen. The reliability of some of these fits that yield a smaller proton
radius was studied. We found that fits of form factor data with a truncated
polynomial fit are unreliable and systematically give values for the proton
radius that are too small. Additionally, a polynomial fit with a
\chi^2_{reduced} ~ 1 is not a sufficient indication for a reliable result
Current methods to dynamically tune three-dimensional hydrogel mechanics require specific chemistries and substrates that make modest, slow, and often irreversible changes in their mechanical properties, exclude the use of protein-based scaffolds, or alter the hydrogel microstructure and pore size. Here, we rapidly and reversibly alter the mechanical properties of hydrogels consisting of extracellular matrix proteins and proteoglycans by adding carbonyl iron microparticles (MPs) and applying external magnetic fields. This approach drastically alters hydrogel mechanics: rheology reveals that application of a 4000 Oe magnetic field to a 5 mg/mL collagen hydrogel containing 10 wt % MPs increases the storage modulus from approximately 1.5 to 30 kPa. Cell morphology experiments show that cells embedded within these hydrogels rapidly sense the magnetically induced changes in ECM stiffness. Ca 2+ transients are altered within seconds of stiffening or subsequent softening, and slower but still dynamic changes occur in YAP nuclear translocation in response to time-dependent application of a magnetic field. The near instantaneous change in hydrogel mechanics provides new insight into the effect of changing extracellular stiffness on both acute and chronic changes in diverse cell types embedded in protein-based scaffolds. Due to its flexibility, this method is broadly applicable to future studies interrogating cell mechanotransduction in three-dimensional substrates.
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