Effects of excluded surface area and adsorbate clustering on surface adsorption of proteins I. Equilibrium models

Statistical-thermodynamic models for the equilibrium adsorption of proteins onto homogeneous, locally planar surfaces are presented. An extension of earlier work [R.C. Chatelier, A.P. Minton, Biophys. J. 71 (1996) 2367], the models presented here allow for the formation of a broadly heterogeneous population of adsorbate clusters in addition to excluded volume interactions between all adsorbate species. Calculations are carried out for three simple models for the structure of adsorbate, illustrating similarities and differences in the equilibrium properties of maximally compact clusters, minimally compact clusters and isomerizing clusters. Depending upon the strength of attractive interactions between adsorbate molecules, the resulting equilibrium isotherms may exhibit negative cooperativity, positive cooperativity, essentially no apparent cooperativity, or a mixture of positive cooperativity at low surface density and negative cooperativity at high surface density of adsorbate. The condition of apparent lack of cooperativity, which might naively be interpreted as evidence of a lack of interaction between adsorbate molecules, actually conceals a balance between attractive and repulsive interactions and extensive clustering of adsorbate.