Charge fluctuation effects on the shape of flexible polyampholytes with applications to Intrinsically disordered proteins

TL;DR

This paper investigates how charge fluctuations influence the size and shape of polyampholytes, including intrinsically disordered proteins, revealing non-monotonic behavior and sequence heterogeneity effects through theory and simulations.

Contribution

It introduces a theoretical framework combining electrostatic and charge fluctuation effects to explain polyampholyte conformations, supported by simulations and experimental data on IDPs.

Findings

Non-monotonic dependence of $R_g$ on $rac{1}{ ext{Debye length}}$ when charge fluctuations dominate.

Simulations show conformational heterogeneity among sequences with identical parameters.

Theoretical predictions match SAXS data for IDPs with $N$ between 24 and 441.

Abstract

Random polyampholytes (PAs) contain positively and negatively charged monomers that are distributed randomly along the polymer chain. The interaction between charges is assumed to be given by the Debye-Huckel potential. We show that the size of the PA is determined by an interplay between electrostatic interactions, giving rise to the polyelectrolyte (PE) effect due to net charge per monomer ($\sigma$), and an effective attractive PA interaction due to charge fluctuations, $\delta \sigma$. The interplay between these terms gives rise to non-monotonic dependence of the radius of gyration, $R_g$ on the inverse Debye length, $\kappa$ when PA effects are important (${\frac{\delta \sigma}{\sigma}} > 1$). In the opposite limit, $R_g$ decreases monotonically with increasing $\kappa$. Simulations of PA chains, using a charged bead-spring model, further corroborates our theoretical predictions. The simulations unambiguously show that conformational heterogeneity manifests itself among sequences that have identical PA parameters. A clear implication is that the phases of PA sequences, and by inference IDPs, cannot be determined using only the bare PA parameters ($\sigma$ and $\delta \sigma$). The theory is used to calculate the changes in $R_g$ on $N$, the number of residues for a set of Intrinsically Disordered Proteins (IDPs). For a certain class of IDPs, with $N$ between 24 to 441, the size grows as $R_g \sim N^{0.6}$, which agrees with data from Small Angle X-ray Scattering (SAXS) experiments.