  Many types of cells can sense external ligand concentrations with
cell-surface receptors at extremely high accuracy. Interestingly, ligand-bound
receptors are often internalized, a process also known as receptor-mediated
endocytosis. While internalization is involved in a vast number of important
functions for the life of a cell, it was recently also suggested to increase
the accuracy of sensing ligand as the overcounting of the same ligand molecules
is reduced. Here we show, by extending simple ligand-receptor models to
out-of-equilibrium thermodynamics, that internalization increases the accuracy
with which cells can measure ligand concentrations in the external environment.
Comparison with experimental rates of real receptors demonstrates that our
model has indeed biological significance.
