Logarithmic interpretation of this case might also be considered (Eq. S26). Friguet's model and the model presented in this work are focused on a linear approximation of the signalconcentration function. However, this work extends the original Friguet model with calculations for non-monovalent systems, which has not been analysed earlier. To our knowledge, it is the first attempt to comprehensively study relations between a receptor (a phage exposing specific peptides) and ligands (target protein) at the equilibrium stage during an ELISA test. It is important to mention that only for linear approximation it is possible to present the 𝑎 𝑎 0 ratio independent from 𝑐 0 𝑀13 . This fact is a significant advantage due to difficulties in precise measuring of physical phage particle concentration. As a substitute, a biological titre of phages (in plaque-forming units per millilitre) is used in the literature and this work. Another attempt to develop a method enabling more accurate determination of phage concentration was spectrophotometrically measuring phages' ssDNA in the sample . This method is not recommended for phage samples obtained via PEG precipitation . The true physical concentration may be determined via mass spectrometry under the assumption of a certain pVIII protein number per virion. Nevertheless, during ELISA, one also measures a signal from phage particles unable to infect bacteria and/or activate dye metabolism, which may cause a difference between physical phage concentration and biological titre. Also, Friguet's original paper avoids the requirement of antibody concentration, which enables calculations for impure antibodies (with mixed specificity). The ratio 𝑎 𝑎 0 (Eq.7) refers to the signal measured of TnT and phage mixture (𝑎) and the signal recorded in the absence of soluble TnT (𝑎 0 ) and is necessary for the determination of the ratio