A Quasi-Equilibrium Theory of Protein Adsorption

Abstract

A model is developed to describe the adsorption and desorption of proteins to and from a surface film under quasi-equilibrium conditions. Starting from Fick's first law of diffusion, an equation for the flux of molecules to a surface is derived assuming a gradient in the chemical potential from the bulk to the surface and a potential barrier due to an existing surface film. Protein molecules are modeled as components with varying surface areas to depict the different orientations of molecules with respect to the film. For concentrated solutions, formation of multilayer protein films is described by allowing components with small minimum surface areas. The thermodynamic analysis is based on Butler's equation for the chemical potentials of the components of a Gibbs surface layer and a first-order model for the nonideality of the surface layer enthalpy and entropy. The model assumes reversible adsorption, consistent with globular proteins that show little denaturation or flexible-chain proteins that reversibly denature at the interface. The model predicts the behavior of five different experiments measuring film properties of the serum protein albumin in quasi-equilibrium and equilibrium conditions at over 2 orders of magnitude in concentration using a single set of parameters. This provides a new framework for analyzing interactions and adsorption of protein films. The key new features of this model are an extension of the classical Smoluchowski analysis to calculate the adsorption and desorption rate, a model of multilayers with decreased molecular areas to allow effective densities greater than a close-packed monolayer, and a concentration-dependent layer thickness.