  In living cells, proteins combine 3D bulk diffusion and 1D sliding along the
DNA to reach a target faster. This process is known as facilitated diffusion,
and we investigate its dynamics in the physiologically relevant case of
confined DNA. The confining geometry and DNA elasticity are key parameters: we
find that facilitated diffusion is most efficient inside an isotropic volume,
and on a flexible polymer. By considering the typical copy numbers of proteins
in vivo, we show that the speedup due to sliding becomes insensitive to fine
tuning of parameters, rendering facilitated diffusion a robust mechanism to
speed up intracellular diffusion-limited reactions. The parameter range we
focus on is relevant for in vitro systems and for facilitated diffusion on
yeast chromatin.
