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.

Kinetic titration
Kinetic titration

Reaction equation

Reaction equation
Reaction equation

Differential equation

Differential equation
Differential equation

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 modal also contains terms for mass transport, drift and bulk refractive index mismatches.

Numeric model

Numeric model
Numeric model

Parameter setup

Name Fit Allow Neg. Keyword Initial value Units
kaglobalNoNo1e5M-1 s-1
kdglobalNoNo1e-3s-1
RmaxlocalNoNoYMaxRU
ktglobalNoNo2e7RU M-1 s-1
RI1localYesNo0RU
RI2localYesNo0RU
RI3localYesNo0RU
RI4localYesNo0RU
RI5localYesNo0RU
ConcNoNoYesM
ton1NoNoYess
ton2NoNoYess
ton3NoNoYess
ton4NoNoYess
ton5NoNoYess
c-timeNoNoYess
FNoNoYes
DriftLocalYesNo0RU 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

NameValueUnits
kakaM-1s-1
kdkds-1
KDkd/kaM
RmaxRmaxRU
ktktRU M-1s-1
RI1RI1RU
RI2RI2RU
RI3RI3RU
RI4RI4RU
RI5RI5RU
DriftDriftRU 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
2
4
8
16
32
Kinetic titration
Simulation

References

(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).