Binding constant (original) (raw)

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Chemical property

The binding constant, or affinity constant/association constant, is a special case of the equilibrium constant K,[_citation needed_] and is the inverse of the dissociation constant.[1] It is associated with the binding and unbinding reaction of molecules. Consider a binding reaction between two molecules, X and Y, which is formalized as:

X + Y ⇌ XY

The reaction is characterized by the on-rate constant _k_on and the off-rate constant _k_off, which have units of M−1 s−1 and s−1, respectively. In equilibrium, the forward binding transition X + Y → XY should be balanced by the backward unbinding transition XY → X + Y. That is,

k o n [ X ] [ Y ] = k o f f [ X Y ] {\displaystyle k_{\rm {on}}\,[{\rm {X}}]\,[{\rm {Y}}]=k_{\rm {off}}\,[{\rm {XY}}]} {\displaystyle k_{\rm {on}}\,[{\rm {X}}]\,[{\rm {Y}}]=k_{\rm {off}}\,[{\rm {XY}}]}

where [X] and [Y] represent the concentration of unbound molecules, while [XU] represents the concentration of bound complexes. The binding constant _K_a is defined by

K a = k o n k o f f = [ X Y ] [ X ] [ Y ] {\displaystyle K_{\rm {a}}={k_{\rm {on}} \over k_{\rm {off}}}={[{\rm {XY}}] \over {[{\rm {X}}]\,[{\rm {Y}}]}}} {\displaystyle K_{\rm {a}}={k_{\rm {on}} \over k_{\rm {off}}}={[{\rm {XY}}] \over {[{\rm {X}}]\,[{\rm {Y}}]}}}.[2]

An often considered quantity is the dissociation constant _K_d ≡ ⁠1/K_a⁠, which has the unit of concentration, despite the fact that strictly speaking, all association constants are unitless values. The inclusion of units arises from the simplification that such constants are calculated solely from concentrations, which is not the case. Once chemical activity is factored into the correct form of the equation, a dimensionless value is obtained. For the binding of receptor and ligand molecules in solution, the molar Gibbs free energy Δ_G, or the binding affinity is related to the dissociation constant _K_d via

Δ G = R T ln ⁡ K d c ⊖ {\displaystyle \Delta G=RT\ln {K_{\rm {d}} \over c^{\ominus }}} {\displaystyle \Delta G=RT\ln {K_{\rm {d}} \over c^{\ominus }}},

in which R is the ideal gas constant, T temperature and the standard reference concentration co = 1 mol/L.

  1. ^ Yartsev, Alex. "Affinity, association constant and dissociation constant | Deranged Physiology". derangedphysiology.com. Retrieved 2024-06-04.[_self-published source?_]
  2. ^ "The Equilibrium Binding Constant and Binding Strength of Proteins (Video) | JoVE". www.jove.com. Retrieved 2024-06-04.[_unreliable source?_]