Simple approach for calculating the binding free energy of a multivalent   particle
  We present a simple yet accurate numerical approach to compute the free energy of binding of multivalent objects on a receptor-coated surface. The method correctly accounts for the fact that one ligand can bind to at most one receptor. The numerical approach is based on a saddle-point approximation to the computation of a complex residue. We compare our theory with the powerful Valence-Limited Interaction Theory (VLIT) (J. Chem. Phys. 137, 094108(2012), J. Chem. Phys. 138, 021102(2013)) and find excellent agreement in the regime where that theory is expected to work. However, the present approach even works for low receptor/ligand densities, where VLIT breaks down. 
Nicholas B. Tito, Stefano Angioletti-Uberti, and Daan Frenkel
cond-mat.soft