Hill Model

The Hill fit is used for affinity quantification of multivalent interactions and provides information about the degree of Cooperativity. For monovalent interactions and interactions without cooperativity the K_d 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 F_norm signal of the Target Bound is the F_norm signal of the Complex EC₅₀ is the half-maximal effective concentration and n_Hill is the Hill coefficient.

The Hill Fit yields an EC₅₀ instead of a K_d because 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 be easily determined while 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 as an indicator for Unspecific/Promiscuous Binders binders in small molecule research. Here, n_Hill>1 for protein – small molecule interactions is often used as indicator for non-1:1 binding stoichiometry, suggesting non-specific interaction effects.

Importantly, the Hill Fit should only be used in TRIC data evaluation 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 will often fit any measured data however, this does not necessarily mean that the interaction shows cooperativity, or several binding events. While a Hill coefficient of n_Hill ≠1 may indicate cooperativity, this has to be confirmed with appropriate experiments. Stoichiometry, for example, can be a factor in this that can be investigated with TRIC using a special experimental setup.

Note that the Hill coefficient does not describe the stoichiometry of an interaction but rather it’s cooperativity. When working with Hill coefficients, the data should be interpreted carefully.