The Hill Model is used for affinity quantification of multivalent interactions and provides information about the degree of Cooperativity. For monovalent interactions and interactions without Cooperativity, the Kd Fit Model is used instead. The Hill fit model uses the equation:

where 

• f(c) is the fraction bound at a given Ligand concentration c

• Unbound is the signal of the Target alone

• Bound is the signal of the Complex

• EC₅₀ is the half-maximal effective concentration

• n_Hill is the Hill coefficient

The reason why the Hill Fit yields an EC₅₀ instead of a K_d is that the Hill Fit is used for interactions with cooperativity and non-1:1 interactions, where the individual binding sites differ in affinity. In these situations, the affinity (K_d) of the individual binding sites cannot easily be determined, but instead, the EC₅₀ is a useful parameter.

The Hill coefficient n_Hill describes the degree of cooperativity of an interaction: n_Hill>1 indicates positive cooperativity (e.g. binding of O₂ to hemoglobin), while n_Hill<1 indicates negative cooperativity (e.g. for some dimeric GPCRs or metabolic Enzymes).

The Hill coefficient is also used to indicate Unspecific/ Promiscuous Binders in small molecule research. Here, n_Hill>1 for protein-small molecule interactions is often used as an indicator for non-1:1 binding stoichiometry, suggesting non-specific interaction effects.

Importantly, the Hill Fit should only be used when the investigated interaction is known to be cooperative or non-1:1. For all other interactions, use the K_d model. Binding curves calculated with the Hill Fit often fit any measured data very well. This does not necessarily mean the interaction shows cooperativity or several binding events. While a Hill coefficient of n_Hill≠1 may indicate cooperativity, this must be confirmed with appropriate experiments. Stoichiometry, for example, can be a factor that can be investigated using a special experimental setup.

Note: The Hill coefficient does not describe the stoichiometry of interaction, but rather its cooperativity. In general, when working with Hill coefficients, one should be cautious with their interpretation.