Fluorescence anisotropy

Become fluorophores excited with linearly polarized light, the rays - also from linearly polarized light - with few exceptions. This phenomenon is called fluorescence polarization.

Are the fluorophores move and not fixedly mounted in space, so the fluorescence polarization is affected by the rotation of the mobile fluorophore, that is through the rotational diffusion constant: The lifetime of the excited state, which is the time between the absorption of a photon and emission of a photon, the so-called fluorescence lifetime, is indeed very small - it is in the nanosecond range - but the average rotation speed of the moving fluorophores is usually large enough that it has an influence on the measured fluorescence polarization.

Determination of fluorescence polarization

Measurement-based basic structure

The excitation light is linearly polarized with a polarizer and is then incident on the sample. The emission light is with a second polarizer - analyzer - analyzes. For this purpose, the intensity of the emitted light is measured at two positions of the analyzer relative to the position of the polarizer:

Polarization anisotropy, the total intensity

The difference D between and is used as a measure of the degree of polarization of emission light.

If D is equal to zero, the rotation speed of the studied fluorophores is so fast that stochastically distributed within the fluorescence lifetime of the excited fluorophore, the orientations of the fluorophores: It is then measured completely unpolarized emission light.

D is equal to one, the rotation speed of the examined fluorophores is so slow that there is not change in the fluorescence lifetime of the excited fluorophore, the orientation of the fluorophore: The polarization of the excitation light is maintained in the emission light. However, the emission light to the same angle as the excitation light to be emitted by the fluorophore. This is usually not the case, that is, there is an intrinsic rotation of the emitted light to the light absorbed by the fluorophore, although it does not rotate.

The difference D is always normalized by a factor. Here, two different values ​​have been established, which differ in their normalization: the polarization P and the anisotropy A.

The polarization P is defined as:

The weighting factor G is a separately determining factor devices. The measured values ​​and deviate from the ideal values ​​, since the sensitivity ratio of the detector system for parallel and perpendikuläre radiation may be different. Ideally G = 1

The anisotropy of A is defined as:

The total intensity S is defined as:

The meter factor G is:

The G- factor is determined before the actual measurement using a fluorescent sample. The two intensities and are doing exactly the opposite as the intensities and provides:

Correlations between polarization and anisotropy

Made between the polarization and anisotropy, the following relationships:

The polarization and the anisotropy can thus be transformed into one another directly.

Heterogeneous fluorophore populations

Are different fluorophore populations are present, a mixed polarization or a Mischanisotropie is measured.

For the mixed polarization, the following relationship can be written by Gregorio Weber:

Here, the polarization of the fluorophore population and the ith fraction of the ith - fluorophore population of the total intensity S:

Because of the relationship between polarization and anisotropy, the Weberian formula can be made for the Mischanisotropie:

A special case of a heterogeneous fluorophore population is when a background intensity from the measured signal is to be deducted:

The intensities of the parallel and perpendikulären the background radiation in a separate measurement must be determined.

Dependence of the fluorescence polarization of the mobility of the fluorophore

The dependence of the fluorescence polarization of the mobility of the fluorophore when the fluorescence measurement was derived from the stationary Francis Perrin 1926 on the theory of Brownian motion. Named after him Perrin equation describes the relationship between the measured polarization and the fluorescence lifetime and the rotational relaxation time. The Perrin equation is:

Here, the intrinsic polarization of the stationary fluorophore.

Because of the relationship between the polarization P and the anisotropy A - and the relationship between the rotational relaxation and the rotational correlation time - can the Perrin equation can be rewritten to:

Here is the intrinsic anisotropy of the fluorophore immovable, analogous to.

It is usually the following representation the Perrin equation preferred because it is more compact compared to the original formulation of the equation:

The fluorescence lifetime is a solid material size for each fluorophore, if there is no dynamic quenching processes. If so, that is, when the fluorophores practically no longer rotate ( for example, in a highly viscous solution ), then the intention of the quotient to one, that is, A is equal to the intrinsic anisotropy A0. If on the other hand, that is, the rotation of the fluorophores is infinitely fast, then the anisotropy A is also striving to 0 because and only values ​​greater than zero and can accept the same because of the linear relationship of the Perrin equation, it follows that the anisotropy A, only values ​​between zero and the intrinsic anisotropy A0 can assume. Analogous is that the polarization P can also only assume values ​​between zero and the intrinsic polarization P0.

For a spherical molecule in aqueous solution can be prepared for the rotational correlation time, the following relationship:

Here, the viscosity of the solvent, T being the temperature, R is the gas constant and V is the molecular volume of the fluorophore. From the Perrin equation, the general contexts follow these conditions:

• The anisotropy of A increases when the volume of the fluorophore increases.
• The anisotropy of A increases when the viscosity of the solvent increases.
• A anisotropy decreases as the temperature increases.
• A anisotropy decreases as the fluorescence lifetime increase.