Kd Binding Affinity Calculator

Calculate dissociation constant Kd, fraction bound, and association rate from binding data.

Concentration of free ligand [L] (nM) (nM)

Dissociation constant Kd (nM) (nM)

Total receptor [R]tot (nM) (nM)

Association rate kon (M⁻¹s⁻¹) (M⁻¹s⁻¹)

Dissociation rate koff (s⁻¹) (s⁻¹)

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What K_d Means Physically

The dissociation constant is the ligand concentration at which half the receptors are occupied. It has units of concentration, and lower means tighter binding.

Fraction bound = [L] / ([L] + K_d) K_d = k_off/k_on

[L] relative to K_d	Fraction bound
0.1 × K_d	9%
K_d	50%
10 × K_d	91%
100 × K_d	99%

The curve is hyperbolic, so saturation is approached slowly. Reaching 91% occupancy requires ten times the K_d; reaching 99% requires a hundredfold. This is why dose-response experiments need concentrations spanning several orders of magnitude around the K_d.

Why Residence Time Often Matters More

The same K_d can arise from fast on and fast off rates, or slow and slow. Residence time — 1/k_off — is frequently the better predictor of drug efficacy in vivo, because a drug that dissociates slowly keeps acting after plasma concentration has fallen.

k_on (M⁻¹s⁻¹)	k_off (s⁻¹)	K_d	Residence time
10⁷	5 × 10⁻²	5 nM	20 s
10⁵	5 × 10⁻⁴	5 nM	33 min

Both rows give identical K_d yet behave completely differently in a patient. Tiotropium's clinical advantage over ipratropium comes largely from residence time rather than affinity, which is why kinetic characterisation has become standard in drug discovery.

Avidity Versus Affinity

A single antibody binding site may have modest affinity, but IgG has two and IgM has ten. Because all arms must release simultaneously for the antibody to dissociate, functional avidity can exceed intrinsic affinity by several orders of magnitude.

This is why IgM works effectively despite low per-site affinity, and why measurements from monovalent fragments differ so markedly from whole-antibody data. Ligand depletion is the other common pitfall: when receptor concentration approaches K_d, free ligand is measurably less than added ligand and the simple equation no longer holds.

Worked Examples

Example 1: Antibody: [L]=10nM, Kd=5nM

Fraction=10/15=66.7% bound

Result: Kd~5nM typical for therapeutic antibody

High affinity: pM-nM range

Example 2: Drug-receptor: kon=1e5, koff=5e-4

Kd=5e-4/1e5×1e9=5nM

Result: Residence time=1/koff=2000s=33min

Long residence time = sustained effect

Example 3: Same affinity, different drugs

k_off 5×10⁻² versus 5×10⁻⁴ at matched K_d

Result: 20 s versus 33 min residence

Identical K_d, completely different clinical behaviour. The slow-dissociating drug continues acting after plasma levels fall.

Example 4: Why IgM works with low affinity

Ten binding sites, modest per-site affinity

Result: Avidity vastly exceeds affinity

All ten arms must release simultaneously for dissociation. The combined effect can be orders of magnitude tighter than any single site.

Common Mistakes

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Assuming saturation near the K_d

That concentration gives only 50% occupancy. Reaching 99% requires a hundredfold higher ligand concentration.

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Comparing drugs by K_d alone

Identical K_d can come from very different rate constants. Residence time often predicts in vivo efficacy better than affinity does.

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Confusing avidity with affinity

Multivalent binding can exceed single-site affinity by orders of magnitude, since all arms must release at once. IgM illustrates this clearly.

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Ignoring ligand depletion

When receptor concentration approaches K_d, free ligand is substantially less than added ligand and the simple binding equation breaks down.

Frequently Asked Questions

Why residence time matters?

Drug effect duration correlates with koff (not just Kd). Same Kd, different kon/koff → different durations. Tiotropium (COPD): very slow koff → 24hr dosing. Short residence time: good for safety (rapid reversibility). Targeted covalent inhibitors: irreversible (koff≈0).

SPR for Kd measurement?

Surface Plasmon Resonance (Biacore): immobilize receptor, flow analyte. Measure real-time binding. Get kon and koff directly. Kd=koff/kon. ITC (Isothermal Titration Calorimetry): also gives ΔH and ΔS of binding thermodynamics.

What does K_d mean?

The ligand concentration at which half the receptors are occupied. Lower values mean tighter binding.

Why does residence time matter?

Because two drugs with identical K_d can have very different dissociation rates. Slow dissociation prolongs action after plasma concentration falls.

What is the difference between affinity and avidity?

Affinity is single-site binding strength; avidity is the combined effect of multiple sites. Multivalent binding can be orders of magnitude tighter.

What is ligand depletion?

When receptor concentration approaches K_d, binding removes a significant fraction of ligand, so free concentration is lower than added and the simple equation fails.