Kinetic titration

Kinetic titration

The kinetic titration (single cycle kinetics) is useful with interactions which are difficult to regenerate or when regeneration is detrimental to the ligand (1). In addition, it can be used to determine the concentration and kinetic range of an interaction. During the kinetic titration, the analyte is injected from a low to high concentration with short dissociation times in between and a long dissociation time at the end. The short and long dissociation times will speed up the injection sequence. All the analyte injections are analysed in the same sensorgram with a special equation for kinetic titration. The model is based on the one to one binding interaction and is limited to five analyte injections (2). A mass transfer component (kt) and drift are added in de model.

Reaction equation

Reaction equation
Reaction equation

Differential equation

Differential equation
Differential equation
L concentration of free ligand in RU
A concentration of free analyte in M
LA concentration of ligand-analyte complex in RU
ka association rate constant in M-1s-1
kd dissociation rate constant in s-1

Response calculation

Response calculation
Response calculation

Because it is not possible to solve this type of injection with a differential model, a numeric model is used. In the numerical model each analyte injection is individually fit, and the total response calculated. The numerical model also contains terms for mass transport, drift and bulk refractive index mismatches.

Numeric model

Numeric model
Differential equation
LA concentration of ligand-analyte complex in RU
RI refractive index in RU
$x injection time x
kt mass transport coefficient
F Dilution factor
Conc concentration of free analyte in M
ka association rate constant in M-1s-1
kd dissociation rate constant in s-1
A Analyte concentration in RU
L Ligand concentration in RU

Parameter setup
Name Fit Allow Neg. Keyword Initial value Units
ka global No No 1e5 M-1 s-1
kd global No No 1e-3 s-1
Rmax local No No YMax RU
kt global No No 2e7 RU M-1 s-1
RI1 local Yes No 0 RU
RI2 local Yes No 0 RU
RI3 local Yes No 0 RU
RI4 local Yes No 0 RU
RI5 local Yes No 0 RU
Conc No No Yes M
ton1 No No Yes s
ton2 No No Yes s
ton3 No No Yes s
ton4 No No Yes s
ton5 No No Yes s
c-time No No Yes s
F No No Yes
Drift Local Yes No 0 RU s-1

Although in the parameter table the RI and Drift are locally fit, they are in the model set to a constant of zero. It is better to start to fit the curves without these parameters. When the kinetic parameters are known, then it is possible to add refractive index bulk effect or drift.

Report setup
Name Value Units
ka ka M-1s-1
kd kd s-1
KD kd/ka M
Rmax Rmax RU
kt kt RU M-1s-1
Drift Drift RU s-1

Below an example of a sensorgram generated with the differential equations from above.

Simulation parameters sensorgram
Concentration (nM) ka (M-1s-1) kd (s-1) RMax (RU)
local global global global
- 6.94 105 4 10-4 36


(1) Dougan, D. A. et al - Effects of substitutions in the binding surface of an antibody on antigen affinity. Protein Eng 11: 65-74; (1998). Goto reference
(2) Karlsson, R. et al - Analyzing a kinetic titration series using affinity biosensors. Analytical Biochemistry 349: 136-147; (2006).