  We present a statistical mechanical model of aggregation in colloidal systems
with DNA mediated interactions. We obtain a general result for the two-particle
binding energy in terms of the hybridization free energy $\Delta G$ of DNA and
two model dependent properties: the average number of available DNA bridges
$\left< N\right>$ and the effective DNA conccentration $c_{eff}$. We calculate
these parameters for a particular DNA bridging scheme. The fraction of all the
$n$-mers, including the infinite aggregate, are shown to be universal functions
of a single parameter directly related to the two-particle binding energy. We
explicitly take into account the partial ergodicity of the problem resulting
from the slow DNA binding-unbinding dynamics, and introduce the concept of
angular localization of DNA linkers. In this way, we obtain a direct link
between DNA thermodynamics and the global aggregation and melting properties in
DNA-colloidal systems. The results of the theory are shown to be in
quantitative agreement with two recent experiments with particles of micron and
nanometer size.
  PACS numbers: 81.16.Dn, 82.20.Db, 68.65.-k, 87.14.Gg
