Biacore X100 reference portal

Definition of affinity

The steady state phase (seen as a constant signal) provides information on the affinity of the interaction i.e. the strength of the binding. The affinity can also be determined from kinetic measurements. For a simple interaction, the equilibrium constant K_D is the ratio of the rate constants k_d/k_a.

Affinity from steady-state

The value of the equilibrium dissociation constant (K_D) is obtained by fitting a plot of response at equilibrium (R_eq) against the concentration. Steady-state affinity measurements are not affected by mass transport limitations since they are based on report points taken at equilibrium. To obtain a robust fit to a plot of R_eq against C for affinity determination, it is important that the range of analyte concentration is wide enough to reveal the curvature of the plot in full. In particular, if the highest concentration is too low in relation to the calculated K_D value, the reported values will be uncertain even if the fit is apparently good and the chi-squared value is low.

Plot of response at equilibrium (R_eq) against the concentration

At steady-state, the net rate of complex formation is zero:

so

Rearranging and setting R=R_eq (the equilibrium response level) gives:

Setting k_d/k_a=K_D (the equilibrium dissociation constant) gives

The model calculates the equilibrium dissociation constant K_D for a 1:1 interaction from a plot of steady state binding levels (R_eq) against analyte concentration (C). The equation includes a term for the bulk refractive index contribution RI, which is assumed to be the same for all samples. This term simply serves as an offset on the R_eq-axis.

The model parameters are:

		Obtained from
KD	Equilibrium dissociation constant (M)	Fitted
Rmax	Analyte binding capacity of the surface (RU)	Fitted
Offset	Bulk refractive index contribution in the sample	Fitted

Note that reported K_D values that are higher than half the highest analyte concentration used should be treated with caution. If the response against concentration plot does not flatten out sufficiently because the concentrations are not high enough in relation to the K_D value, the reported value may be unreliable.

In practice, it can be difficult to reach steady state particularly at the lower concentrations. If steady state is not reached the affinity will be underestimated – the extent of the error depends on how far from steady state the interaction is. In such cases, kinetic analysis can be more appropriate.

Affinity from kinetic analysis

The affinity constant K_D is also obtained from kinetics analysis as the ratio of the rate constants k_a and k_d:

K_D = k_d / k_a

Should I determine affinity from steady-state or kinetics?

Ideally, values determined from kinetics and from steady state measurements should be the same. In practice, these approaches are generally applicable in different situations that are often mutually exclusive: kinetics analysis can be used for sensorgrams that contain kinetic information but do not necessarily reach steady state, while determination from steady state measurements is most useful for interactions where the kinetics are too fast to measure with confidence but steady state is reached with relatively short injection times. If the interaction is a 1:1 binding but does not reach steady state, a more reliable value for KD may be obtained from kinetic evaluation.

Data series that contains kinetic information but does not reach steady state

Data series that reaches steady state but is too fast to resolve kinetics