Interplay of hierarchical dynamics and their microscopic structures of polyampholyte gels and proteins

Polyampholyte gel is a perfect physics model to mimic condensed state of proteins. We have studied the hierarchical dynamics of polyampholyte gels by dynamic light scattering. In addition to the normal gel mode, which indicates the gel elasticity, we also discovered a new mode with a stretched exponential decay with the stretched exponent β = 1/3, and a diffusive exponential decay, which indicates the coupled motion between counterion and the polyampholyte backbone. After dialysis to low salt concentration, the coupled motion of the counterion will go away, so that there are only two modes. Combined with a newly developed theory, we attribute this stretched exponential mode to hierarchical dynamics of the segments between two crosslinking junctions, whose segmental distribution obeys Poisson distribution. As salt concentration inside the gel increases, β decreases from 0.38 to 0.33, which is consistent with theoretical results. The gel with the molar charge ratio R=1, which is at the charge balance point, has the highest value β = 0.38. As long as R deviates further away from the charge balance point from either side, the β values decrease. When the gel is 100% positive charged, their dynamic light scattering results will go back to that of the normal polyelectrolyte gels.