  The Landau-de Gennes free energy is used to study theoretically the effective
interaction of a spherical "key" and an anisotropic "lock" colloidal particles.
We assume identical anchoring properties of the surfaces of the key and of the
lock particles, and consider planar degenerate and perpendicular anchoring
conditions separately. {The lock particle is modeled} as a spherical particle
with a spherical dimple. When such a particle is introduced into a nematic
liquid crystal, it orients its dimple at an oblique angle $\theta_{eq}$ with
respect to the far field director ${\bf n}_{\infty}$. This angle depends on the
depth of the dimple. Minimization results show that the free energy of a pair
of key and lock particles exhibits a global minimum for the configuration when
the key particle is facing the dimple of the lock colloidal particle. The
preferred orientation $\phi_{eq}$ of the key-lock composite doublet relative to
${\bf n}_{\infty}$ is robust against thermal fluctuations. The preferred
orientation $\theta_{eq}^{(2)}$ of the dimple particle in the doublet is
different from the isolated situation. {This is related to the "direct"
interaction of defects accompanying the key particle with the edge of the
dimple}. We propose that this nematic-amplified key-lock interaction can play
an important role in self-organization and clustering of mixtures of colloidal
particles with dimple colloids present.
