Polymer-tethered ligand-receptor interactions between surfaces II.

In this paper, we analyze the thermodynamics of interactions between surfaces mediated by polymer-tethered ligand-receptor binding. From statistical thermodynamics calculations, we obtain an effective two-dimensional binding constant reflecting contributions from the microscopic binding affinity as well as from the conformation entropy of the polymer tethers. The total interaction is a result of the interplay between attractive binding and repulsion due to confinement of the polymer chains. We illustrate the differences between three scenarios when the binding molecules are (1) immobile, (2) mobile with a fixed density, and (3) mobile with a fixed chemical potential (connected to a reservoir), which correspond to different biological or experimental situations. The key features of interactions, including the range of adhesion (onset of binding) and the equilibrium separation, can be obtained from scaling analysis and are verified by numerical solutions. In addition, we also extend our method of treating the quenched case with immobile ligands and receptors developed in a previous paper [Martin, J. I.; Zhang, C.-Z.; Wang, Z.-G. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2621-2637] as a density expansion in terms of both ligand and receptor densities. Finally, we examine several cases having ligand-receptor pairs with different tether lengths and binding affinities, and/or nonbinding linear polymers as steric repellers. Such systems can exhibit complex interactions such as a double-well potential, or a bound state with an adjustable barrier (due to the repellers), which have both biological and bioengineering relevance.