the evanescent field K ev is given by By tracking the angle at which we monitor resonance (SPR angle) during exposure to an adhe-

w 0

K s =

K ev = K s sin θ =

exposure to the molecule helps us to define the where w 0 is the frequency of incident light, η g

amount of adsorbance The gradient (first derivathe refractive index of the dense medium (e.g.

tive) gives additional indications for the rate of glass), θ the angle of incidence of the light and

adsorption [2].

c the speed of light in vacuum. The wave vector of a surface plasmon K sp is different and can be

2.1 The Necessity of the Prism

approximated by the following equation: To be able to observe a maximum Surface Plas-

K sp ≈

field f s (see Figure 3) has to be equal. This is no the case if we have no high refractive prism

Where m is the dielectric constant of the metal above the metall film. It can be visualized by

film and η s is the refractice index of the dielec-Figure 3, where the two lines representing f sp

tric medium [5]. At a specific angle of incidence and f s don’t cross each other, because of:

the evanescent wave of the incoming light couples with the free oscillating electrons also called

f sp < f s .

plasmons in the metal film. This effect reaches it maximum when

If we do use an high refractive prism we will

Through this effect energy of the incident light is transfered to the metal film during the reflection, decreasing the the intensity of the outgoing light detectable by a 2D array of charge coupled detectors (CCD).

Equation (1) reveal that K ev is dependent from the refractive index of the medium above the metall film. Thus, if the refractive index η g

because both frequencies can cross each other visuallized by Figure 4.

Figure 2: An SPR adsorption profile, [2]

2.2 Adsorptions Kinetics

above the silver or gold surfaces changes by ab-sorption of a protein layer, the angle where we

The diffussion process of an adsorbate on the can observe a plasmon phenomenon will change.

surface is slower than the intrinsic adsorp-

2

dissociation constant, [A] is the concentration Figure 4: Frequency with an high refractice

of the ligate solution, [B] is the concentration of prism, [6]

free ligand and [AB] the concentration of the bound ligate-ligand complex. The maximum change in the SPR angle (R max ) is proportional tion kinetics. Therefore it represents the rate-

to the total ligand concentration ([B]+[AB]), determining factor. Karlsson et al. was able

R max −R is proportional to the free ligand con-

to show that diffusion kinetics are dependent on

centration [B] and [A] may be considered as a the flow rate while intrinsic kinetics are not en-

constant (C) since the free ligate is constantly abling us to determine a mass transport limita-

refilled under flow conditions. Thus we can tion by changing the flow rate of the system [7].

write equation (8) as The kinetics of diffusion can be appoximated by

the equation below describing the rate of diffusion j d :

j d =

stants. The slope of each concentration plot (k s ) where D is the diffusion coefficient, x d the

is then plotted against the ligate concentration boundary layer thickness, k m the mass transfer

(C), which will give us a linear dependence decoefficient, [A] b bulk concentration of the an-

scribed by the following equation:

alyte and [A] s the surface concentration of the − k s = K a C + K d .

analyte [3]. Equation (6) can be arranged under conditions of a general flow cell to:

By determining the slope and the y-axis intercept we get K a and K d . We can also simplify

k m =

C of the analyte to zero and get:

where ν is the velocity or flow rate, L is the dR/dt = -K d R . (12)

distance between inlet into flow cell and sampling area and h is the height of the flow cell.

Which enables us to calculate the dissociation

At the beginning of a ligand-ligate adsorption

constant more precisely. This simplification can

process the kinetics are diffusion limited. With

be made if the bound [AB] complex is in a buffer

increasing adsorptions the number of free bind-

solution, leading to a very low concentration C

ing sites represented by free ligands for the ligate

[2].

reduces. Finally the observed binding rate will eventually reflect that of the intrinsic kinetics

3 Biological Applications

(the binding rate). By increasing the diffusion rate and reducing the rate of binding we will go from a diffusion-limited rate to an intrinsic re-The use of SPR methods for biological probaction rate. As we can see from equation (7) lems was mainly driven by Nylander et al. and

3