Dissociation Constant

Overview

The dissociation constant (Kd) is the equilibrium constant for the reverse direction of a binding reaction:

RL ⇌ R + L Kd = [R][L] / [RL]

Kd has units of concentration (M, mM, μM, nM, pM). Smaller Kd means tighter binding. It is the most intuitive measure of binding affinity because it equals the free ligand concentration at which half of available sites are occupied — no multiplication or logarithm required.

Kd is the single most-cited number in biophysical characterization of peptide-receptor interactions.

Detailed Explanation

Deriving the half-occupancy point

Define fractional occupancy θ = [RL] / ([R] + [RL]). Substituting the equilibrium expression:

θ = [L] / (Kd + [L])

When [L] = Kd, θ = 0.5. Hence Kd = the free ligand concentration producing 50% receptor occupancy. This is a fundamental rule for interpreting binding and dose-response data.

Relationship to Ka

The association constant Ka is the reciprocal of Kd:

Ka = 1 / Kd

Ka is expressed in M⁻¹. Large Ka = tight binding. Researchers often publish both or one depending on convention; in pharmacology Kd (or its log, pKd) dominates.

Relationship to EC50

For simple systems without spare receptors, functional EC50 approximates Kd. In systems with spare receptors or amplification, EC50 can be substantially lower than Kd — maximal response is achieved when only a fraction of receptors are occupied. This is why Kd and EC50 should not be used interchangeably without checking assay conditions.

Kd vs. IC50

IC50 is the concentration of an inhibitor producing 50% inhibition. For a competitive inhibitor, Cheng-Prusoff conversion relates IC50 to Ki (the Kd for the inhibitor):

Ki = IC50 / (1 + [S]/Km)

This shows why raw IC50 values are condition-dependent — they shift with substrate concentration.

Relationship to Michaelis-Menten kinetics

Km, the substrate concentration at which an enzyme operates at half Vmax, is a kind of apparent Kd for the enzyme-substrate complex — provided catalysis is slow relative to dissociation. In fast-catalyzing enzymes Km can differ from the true Kd.

Measurement

• Saturation binding — radiolabeled ligand, increasing concentrations; fit a hyperbolic binding isotherm to extract Kd and Bmax.
• Competition binding — fixed radiolabeled ligand, displaced by varying cold competitor; Ki calculated via Cheng-Prusoff.
• Surface plasmon resonance — measures kon and koff in real time; Kd = koff/kon.
• Isothermal titration calorimetry — direct thermodynamic measurement; high-quality Kd plus ΔH and ΔS.
• Fluorescence polarization — rapid screening Kd measurements.
• Microscale thermophoresis — small-sample affinity determination.

Typical Kd Ranges

• Strong protein-protein interactions: pM – nM
• Antibody-antigen: pM – nM
• Enzyme-substrate affinity: typically μM
• Peptide hormone-receptor (native): 0.1 – 100 nM
• Allosteric modulators: nM – μM
• Weak transient interactions: mM

Kinetic Consequences of Identical Kd

Two ligands can share a Kd of 1 nM but have very different kon and koff values:

• Ligand A: kon = 10⁷ M⁻¹s⁻¹, koff = 10⁻² s⁻¹ (fast on, moderate off)
• Ligand B: kon = 10⁵ M⁻¹s⁻¹, koff = 10⁻⁴ s⁻¹ (slow on, slow off)

Ligand B has a much longer residence time on the receptor and often produces more durable pharmacodynamic effects even though Kd is identical. Residence time has become an important parameter in peptide drug optimization alongside Kd.

Factors Affecting Kd

• Temperature — binding thermodynamics shift with temperature
• pH and ionic strength — influence electrostatic contributions and zwitterion character
• Conformational state of receptor — inactive vs. active conformation, receptor trafficking status
• Presence of cofactors, lipids, or modifications
• Allosteric modulators changing the orthosteric Kd via the allosteric site

Relevance to Peptide Therapeutics

A peptide's Kd is a first-order predictor of:

• Effective dose range
• Fraction of receptors occupied at clinical concentrations
• Likelihood of displacing endogenous ligands
• Competition with competing therapies

Targeting Kd values appropriate for the therapeutic context — not simply the lowest achievable — is a hallmark of sophisticated peptide design.

Summary

Kd is the dissociation constant — a direct, universally understood measure of binding strength. Its numerical value and its kinetic decomposition into kon and koff sit at the foundation of every quantitative description of peptide pharmacology.