The Temkin isotherm describes heterogeneous protein adsorption.

Here we examine how heterogeneous protein adsorption arises from multivalent interactions with a seemingly homogeneous functional surface. During adsorption, some arrangement of functional groups on the protein (e.g., charged or hydrophobic amino-acid residues or specific ligand binding sites) interacts with complementary sites distributed on the adsorbent surface. The protein will show the highest affinity for the surface arrangements which best match its own distribution of functional sites, resulting in a distribution of binding energies. To support this interpretation, we show that changing the density of affinity ligands on a surface (immobilized metal ions) is equivalent to changing the number of target groups on a protein (surface histidines). We also report that reversible protein adsorption obeys the Temkin isotherm and propose that model as a practical framework for describing the behavior of proteins adsorbing via multivalent interactions onto surfaces densely derivatized with a random distribution of binding functionalities. This result has important implications for the design of separations materials and the interpretation of biological recognition phenomena.