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 ({\delta \sigma{\sigma}} > 1). In the opposite limit, R_g increases monotonically with increasing \kappa. 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 185 , the size grows as R_g \sim N^{0.6}, which agrees with data from Small Angle X-ray Scattering (SAXS) experiments . The theory also describes quantitatively the R_g measured using SAXS experiments for the wild type Tau proteins and fragments derived from it. In this case we find that R_g \sim N^{0.5. The variations in the scaling between these two sets are a consequence of differing values of \sigma and \delta \sigma, as well as conformational heterogeneity in the IDPs} .
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 ({\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 . The variations in the scaling between these two sets are a consequence of differing values of \sigma and \delta \sigma, as well as conformational heterogeneity in the IDPs} .
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Polyampholytes
Random polyampholytes
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increases
decreases
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The
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
R
185
441
D
. The theory also describes quantitatively the R_g measured using SAXS experiments for the wild type Tau proteins and fragments derived from it. In this case we find that R_g \sim N^{0.5