⚖️ Steady State Check

"Should I wait for equilibrium?" In SPR and BLI flow systems, the association phase plateaus when binding and dissociation balance — this plateau is called steady state (dR/dt ≈ 0) and equals the thermodynamic equilibrium response Req. The two terms are used interchangeably here. The most common mistake with high-affinity binders is reading endpoints before this plateau is reached, then fitting a Langmuir isotherm to those under-saturated values and reporting a falsely weak KD.

Reaching 95% of equilibrium takes ~3 time constants (3/kobs ≈ 3τ, where τ = 1/kobs); reaching 99% takes ~5τ. For tight binders near KD, kobs ≈ kd, so τ can be hours.

Model assumptions: This simulation uses ideal 1:1 pseudo-first-order kinetics and assumes (i) no mass-transport limitation, (ii) no rebinding during dissociation, (iii) constant analyte concentration throughout the injection, and (iv) a fixed Rmax independent of concentration. Real sensorgrams that deviate from these predictions may indicate one of those effects rather than a tool error.

What to do when equilibrium isn't reached: (a) extend the injection time, (b) raise analyte concentration to increase kobs = kaC + kd, (c) switch to single-cycle or multi-cycle kinetic fitting, or (d) report an apparent KD with the caveat that it is an upper-bound estimate. See also: Equilibrium Analysis and 1:1 Langmuir Model.

1.0 × 10^5 M⁻¹s⁻¹
1.0 × 10^-3 s⁻¹
10 pM1 nM100 nM10 µM
100 nM

Time to 95% Equilibrium

4.5 min
✅ Routine: Use Equilibrium Analysis (≤10 min)

Calculated as 3 / (ka×C + kd). Thresholds: ≤10 min = routine equilibrium; 10–60 min = long injection may work; >60 min = equilibrium impractical, use kinetic fitting instead.

What if you read endpoints instead of waiting for equilibrium?

A common mistake: fitting a Langmuir isotherm to endpoint values from an association phase that hasn't reached steady state. The curves below show what your sensorgram looks like — dashed lines mark the true equilibrium level (Req).

2.0 min
1.0 nM
2.5 nM
5.0 nM
10 nM
20 nM
50 nM
1.0e+2 nM
True Req

True KD

10.0 nM

kd / ka

"KD" from Endpoints

135 nM

+1249% error (13.5× weaker)

Apparent Rmax: 78.4 RU vs true 50 RU

At t = 2 min, the highest-concentration curve (best case) reaches 73% of its Req — lower concentrations reach less.

Langmuir Isotherm: True Equilibrium vs Endpoint Values

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