  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.
