Final answer:
Polyhistidine's solubility is due to histidine's amine group protonation at lower pH values. At pH 5.0, it is protonated and soluble, while at pH 7.8, it is uncharged and insoluble.
Step-by-step explanation:
Polyhistidine is insoluble in water at pH 7.8 but soluble at pH 5.0 because histidine contains an amine group that can gain a proton and become positively charged. At pH 5.0, the amine group's pKa of 6.04 allows it to be protonated, thus making the polyhistidine chain cationic and soluble due to the attraction to water molecules. At pH 7.8, the amine groups are not protonated, resulting in an uncharged, less hydrophilic polyhistidine chain that precipitates because it has insufficient interactions with water.