  We model the kinetics of ligand-receptor systems, where multiple ligands may
bind and unbind to the receptor, either randomly or in a specific order.
Equilibrium occupation and first occurrence of complete filling of the receptor
are determined and compared. At equilibrium, receptors that bind ligands
sequentially are more likely to be saturated than those that bind in random
order. Surprisingly however, for low cooperativity, the random process first
reaches full occupancy faster than the sequential one. This is true {\it
except} near a critical binding energy where a 'kinetic trap' arises and the
random process dramatically slows down when the number of binding sites $N\geq
8$. These results demonstrate the subtle interplay between cooperativity and
sequentiality for a wide class of kinetic phenomena, including chemical
binding, nucleation, and assembly line strategies.

Statistical Mechanics;Soft Condensed Matter