A Model Ground State of Polyampholytes

TL;DR

This paper proposes a specific necklace-like ground state structure for polyampholytes, analyzing the size distribution of neutral segments and predicting the overall size and surface area scaling with chain length.

Contribution

It introduces a detailed model of polyampholyte ground states based on neutral segment arrangements and provides analytical and Monte Carlo analysis of segment size distributions.

Findings

Longest neutral segment length scales as N/n^2

Number of neutral segments scales as sqrt(N)

Ground state size scales as sqrt(N)

Abstract

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 2nd longest neutral segment) compacts into a globule, then the 3rd, 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).