The reaction between TnT and phage-displayed peptide may be treated as a reversible noncovalent complex formation . According to the induced fitting model, the interaction between the ligand and its binding site on the protein surface requires energy to deform structures and fit them in proper orientation and distance . However, if the interaction is strong enough, the energy released during the process of complex formation is higher than the energy required for complex dissociation. The reaction scheme of a reversible complex formation may be written as in Equation . According to the mass action law, increasing ligand concentration causes a rise in receptor saturation. In the case of a monovalent receptor (complex stoichiometry 1:1), the reaction of receptor saturation shown in Eq.1 is sufficient, while polyvalency of the receptor imposes the existence of multiple stages. In order to represent the saturation of n-valent receptor 𝑛, equations have to be written as in Eq.2, where 𝑖 refers to subsequent numbers from 1 to 𝑛. The exact formulas for each stage are written in Supplementary Materials (Eq. S1-S5).