  Recent studies point out that there exists some rough scaling relations for
dark matter and some tight connections between dark matter and baryons.
However, most of the relations and tight connections can only be found in
galaxies, but not in galaxy clusters. In this article, we consider a new
expression that can characterize the properties of dark matter-baryon interplay
for both galactic and galaxy cluster scales. By using the archival
observational data of galaxies and galaxy clusters, we show that the value
$K=\bar{n}_D \bar{n}_Br_oV/v^4$ is almost a constant and scale independent
within the optical radius $r_o$, where $\bar{n}_D$ is the average dark matter
number density, $\bar{n}_B$ is the average baryon number density, $v$ is the
characteristic velocity and $V$ is the interacting volume. This would be the
first universal relation between dark matter and baryons on both galactic and
galaxy cluster scales. We anticipate this result to be a starting point to
explain the small-scale problem and the scaling relations for dark matter in
galaxies. The constant $K$ discovered may reveal some underlying global
interaction between dark matter and baryons.
