Association entropy in adsorption processes

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, ΔS°, have been derived from the root-mean-square fluctuations in protein crystals, suggesting ΔS°≃ -50 e.u., i.e., TΔS°≃ -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane, obtaining TΔS°≃ -1.7 kT ≃ -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much 'softer'.