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Overview

The dissociation constant K_d describes the equilibrium between the bound and unbound state. Therefore, the K_d value is a measure of the affinity of a binding site to a ligand. This constant is independent of the concentrations of the interaction partners.

In contrast, the EC₅₀ describes the effective dose of ligand at which half of all target molecules are present in the bound state (EC₅₀ stands for half maximal effective concentration).

For interactions that follow a simple 1:1 equilibrium binding model (no cooperativity), the K_d value and the EC₅₀ are connected via the following equation (I).

EC₅₀ = K_d + 0.5 *[Target concentration]         (I)

Therefore, at target concentrations far below the K_d, EC₅₀ and K_d have the same value. However, if the target concentration falls within the range of the K_d or above, K_d and EC₅₀ can differ significantly. Due to this concentration dependence, EC₅₀ values are connected to a specific experimental setup and do not transfer to other methods. 

Example

Suppose a given interaction has a Kd of 11 nM (a high affinity) and the target is present at a concentration of 2 nM. In that case, the interaction is independent of the ligand concentration, and a K_d of 11 nM can be calculated (Figure 1). In this case, since EC₅₀ ~ K_d, the EC₅₀ value would be similar to the K_d. On the contrary, when the target concentration is higher (i.e., 200 nM), a ligand concentration of ~100 nM would be necessary to reach a state where half of all target molecules are in the bound state. The EC₅₀ totals to ~100 nM in this case.

Note that the K_d of this interaction is still 11 nM, as this parameter instead describes the physical strength of a molecular interaction. Due to the difference in the target concentration from the expected K_d (200 nM vs 11 nM), the Dianthus software will not be able to fit a K_d in this case, as shown in Figure 1, right side, light blue line. 

After all, the K_d can also be expressed as a function of the thermodynamic equilibrium of an interaction (ΔG = RT ln(K_d)). The standard definition of the K_d as the ligand concentration at which half of all target molecules are in the bound state only applies at target concentrations well below the K_d, i.e., where K_d ≈ EC₅₀.