## Surface Plasmon Resonance imaging (SPRi)

## How can I recover affinity values from the kinetic curves?

- Kinetics parameters
**k**is the association rate constant (M_{a}^{-1}-s^{-1}), in some cases, it is also called**k**_{on}**k**is the dissociation rate constant (s_{d}^{-1}), in some cases, it is also called**k**_{off}

SPR kinetics data (interactions) can be modeled simply in order to evaluate the affinity between 2 molecules. The model generally used supposes that the reactions involve one ligand (L) and one analyte (A) which interact with a **1:1 stoichiometry**:

This model gives the following formula for our interaction kinetic curves, one for the association response (R_{a}) and one for the dissociation response (Rd), the response being in our case the reflectivity variation:

R_{a}(t)=R_{eq}•(1-exp[-k_{obs}•(t-t_{0})]) (association)

R_{d}(t)=R_{d}(t_{1})•exp[-k_{off}•(t-t_{1})] (dissociation)

with k_{obs} = k_{a}•C_{i}+k_{d}, the **observed** on-rate constant of the response during association, C_{i} the injected analyte concentration and k_{offf} = k_{d}, the off-rate constant of the response during dissociation, t_{0} and t_{1} are indicating respectively the beginning of the association and of the dissociation.

Briefly, the kinetics parameters k_{a} and k_{d} are calculated by fitting each part of the interaction (association and dissociation) with a mono-exponential curve, preferentially by using the ScrubberGen software (Scrubber-based).

- Affinity parameters
**K**is the affinity constant (M_{A}^{-1})**K**is the equilibrium constant (M)_{D}

Knowing the kinetics parameters, the affinity constant between 2 molecules can be deduced:

K_{A} = 1/K_{D} = k_{a}/k_{d}

The affinity parameters can also be calculated from equilibrium values with a Langmuir fit.