Model ground state of polyampholytes

The ground state of randomly charged polyampholytes is conjectured to have a structure similar to a necklace, made of weakly charged parts of the chain, compacting into globules, connected by highly charged stretched “strings.” We suggest a specific structure, within the necklace model, where all the neutral parts of the chain compact into globules: The longest neutral segment compacts into a globule; in the remaining part of the chain, the longest neutral segment (the second longest neutral segment) compacts into a globule, then the third longest, and so on. We investigate the size distributions of the longest neutral segments in random charge sequences, using analytical and Monte Carlo methods. We show that the length of the $n$th longest neutral segment in a sequence of $N$ monomers is proportional to ${N/n}^2$, while the mean number of neutral segments increases as $\sqrt{N}$. The polyampholyte in the ground state within our model is found to have an average linear size proportional to $\sqrt{N}$, and an average surface area proportional to $N^{2/3}$.