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We present a simple yet accurate numerical approach to compute the freeenergy of binding of multivalent objects on a receptor-coated surface. Themethod correctly accounts for the fact that one ligand can bind to at most onereceptor. The numerical approach is based on a saddle-point approximation tothe computation of a complex residue. We compare our theory with the powerfulValence-Limited Interaction Theory (VLIT) (J. Chem. Phys. 137, 094108(2012), J.Chem. Phys. 138, 021102(2013)) and find excellent agreement in the regime wherethat theory is expected to work. However, the present approach even works forlow receptor/ligand densities, where VLIT breaks down.

Simple approach for calculating the binding free energy of a multivalent particle