  DNA looping plays a fundamental role in a wide variety of biological
processes, providing the backbone for long range interactions on DNA. Here we
develop the first model for DNA looping by an arbitrarily large number of
proteins and solve it analytically in the case of identical binding. We uncover
a switch-like transition between looped and unlooped phases and identify the
key parameters that control this transition. Our results establish the basis
for the quantitative understanding of fundamental cellular processes like DNA
recombination, gene silencing, and telomere maintenance.
