Many cargoes destined for nuclear import carry nuclear localization signals that 
are recognized by karyopherins (Kaps). We present methods to quantitate import 
rates and measure Kap and cargo concentrations in single yeast cells in vivo, 
providing new insights into import kinetics. By systematically manipulating the 
amounts, types, and affinities of Kaps and cargos, we show that import rates in 
vivo are simply governed by the concentrations of Kaps and their cargo and the 
affinity between them. These rates fit to a straightforward pump-leak model for 
the import process. Unexpectedly, we deduced that the main limiting factor for 
import is the poor ability of Kaps and cargos to find each other in the 
cytoplasm in a background of overwhelming nonspecific competition, rather than 
other more obvious candidates such as the nuclear pore complex and Ran. It is 
likely that most of every import round is taken up by Kaps and nuclear 
localization signals sampling other cytoplasmic proteins as they locate each 
other in the cytoplasm.