  Colloids coated with single-stranded DNA (ssDNA) can bind selectively to
other colloids coated with complementary ssDNA. The fact that DNA-coated
colloids (DNACCs) can bind to specific partners opens the prospect of making
colloidal `molecules'. However, in order to design DNACC-based molecules, we
must be able to control the valency of the colloids, i.e. the number of
partners to which a given DNACC can bind. One obvious, but not very simple
approach is to decorate the colloidal surface with patches of single-stranded
DNA that selectively bind those on other colloids. Here we propose a design
principle that exploits many-body effects to control the valency of otherwise
isotropic colloids. Using a combination of theory and simulation, we show that
we can tune the valency of colloids coated with mobile ssDNA, simply by tuning
the non-specific repulsion between the particles. Our simulations show that the
resulting effective interactions lead to low-valency colloids self-assembling
in peculiar open structures, very different from those observed in DNACCs with
immobile DNA linkers.

Soft Condensed Matter