  We investigate the measurement of DNA supercoiling density ($\sigma$) along
chromosomes using interaction frequencies between DNA and DNA-anchored clusters
of proteins. Specifically, we show how the physics of DNA supercoiling leads,
in bacteria, to the quantitative modeling of binding properties of ParB
proteins around their centromere-like site, {\it parS}. Using this framework,
we provide an upper bound for $\sigma$ in the {\it Escherichia coli}
chromosome, consistent with plasmid values, and offer a proof of concept for a
high accuracy measurement. To reach these conclusions, we revisit the problem
of the formation of ParB clusters. We predict, in particular, that they result
from a non-equilibrium, stationary balance between an influx of produced
proteins and an outflux of excess proteins, i.e., they behave like liquid-like
protein condensates with unconventional ``leaky'' boundaries.

Biological Physics;Biomolecules