Fluorescence anisotropy or fluorescence polarization is the phenomenon where the light emitted by a fluorophore has unequal intensities along different axes of polarization. Early pioneers in the field include Aleksander Jablonski, Gregorio Weber, and Andreas Albrecht. The principles of fluorescence polarization and some applications of the method are presented in Lakowicz's book.
Definition of fluorescence anisotropy
The anisotropy (r) of a light source is defined as the ratio of the polarized component to the total intensity ():
When the excitation is polarized along the z-axis, emission from the fluorophore is symmetric around the z-axis(Figure). Hence statistically we have . As , and , we have .
Principle – Brownian motion and photoselection
In fluorescence, a molecule absorbs a photon and gets excited to a higher energy state. After a short delay (the average represented as the fluorescence lifetime ), it comes down to a lower state by losing some of the energy as heat and emitting the rest of the energy as another photon. The excitation and de-excitation involve the redistribution of electrons about the molecule. Hence, excitation by a photon can occur only if the electric field of the light is oriented in a particular axis about the molecule. Also, the emitted photon will have a specific polarization with respect to the molecule.
The first concept to understand for anisotropy measurements is the concept of Brownian motion. Although water at room temperature contained in a glass to the eye may look very still, on the molecular level each water molecule has kinetic energy and thus there are many collisions between water molecules in any amount of time. A nanoparticle (yellow dot in the figure) suspended in solution will undergo a random walk due to the summation of these underlying collisions. The rotational correlation time (Φr), the time it takes for the molecule to rotate 1 radian, is dependent on the viscosity (η), temperature (T), Boltzmann constant (kB) and volume (V) of the nanoparticle:
The second concept is photoselection by use of a polarized light. When polarized light is applied to a group of randomly oriented fluorophores, most of the excited molecules will be those oriented within a particular range of angles to the applied polarization. If they do not move, the emitted light will also be polarized within a particular range of angles to the applied light.
For single-photon excitation the intrinsic anisotropy r0 has a maximum theoretical value of 0.4 when the excitation and emission dipoles are parallel and a minimum value of -0.2 when the excitation and emission dipoles are perpendicular.
where β is the angle between the excitation and emission dipoles. For steady-state fluorescence measurements it is usually measured by embedding the fluorophore in a frozen polyol.
Taking the idealistic simplest case a subset of dye molecules suspended in solution that have a mono-exponential fluorescence lifetime and r0=0.4 (rhodamine 6g in ethylene glycol made to have an absorbance of ~0.05 is a good test sample). If the excitation is unpolarized then the measured fluorescence emission should likewise be unpolarized. If however the excitation source is vertically polarized using an excitation polarizer then polarization effects will be picked up in the measured fluorescence. These polarization artifacts can be combated by placing an emission polarizer at the magic angle of 54.7º. If the emission polarizer is vertically polarized there will be an additional loss of fluorescence as Brownian motion results in dye molecules moving from an initial vertical polarized configuration to an unpolarized configuration. On the other hand, if the emission polarizer is horizontally polarized there will be an additional introduction of excited molecules that were initially vertically polarized and became depolarized via Brownian motion. The fluorescence sum and difference can be constructed by addition of the intensities and subtraction of the fluorescence intensities respectively:
Dividing the difference by the sum gives the anisotropy decay:
The grating factor G is an instrumental preference of the emission optics for the horizontal orientation to the vertical orientation. It can be measured by moving the excitation polarizer to the horizontal orientation and comparing the intensities when the emission polarizer is vertically and horizontally polarized respectively.
G is emission wavelength dependent. Note G in literature is defined as the inverse shown.