Fluorescence Polarization

Polarization Light is a harmonic electromagnetic wave. When considering its interaction with matter we can in most cases neglect the magnetic part. The plain in which the electric vector E oscillates defines the polarization of light. E B Natural light contains randomly all possible orientations of electric vector Unpolarized (random) light Light propagation direction

Polarizer Common polarizers: an optical component that selects from passing light only the component polarized in a given direction I0 I = I0/2 Polarizer Linear polarized light Unpolarized (random) light Common polarizers: double refracting (birefrigent) calcite (CaCO3) crystals- which refract components of light polarized in two perpendicular planes under different angles filters, which effectively absorb one plane of polarization (e.g., Polaroid type-H sheets based on stretched polyvinyl alcohol impregnated with iodine)

In 1920, F. Weigert discovered that the fluorescence from solutions of dyes was polarized. Specifically, he looked at solutions of fluorescein, eosin, rhodamine and other dyes and noted the effect of temperature and viscosity on the observed polarization. Wiegert discovered that polarization increased with the size of the dye molecule and the viscosity of the solvent, yet decreased as the temperature increased. He recognized that all of these considerations meant that fluorescence polarization increased as the mobility of the emitting species decreased.

- + Polarization and dipole transitions Absorption: The probability of a transition of a molecule between two energetic levels (for example S0  S1) is proportional to cos2f, where f is the angle between the dipole moment of the transition and the direction of polarization of the excitation light. - + potential dipole orientation probability of excitation Photoselection: The phenomenon of anisotropic distribution of orientation of molecules in excited state in the sample caused by the properties of excitation light. Emission of a point dipole is polarized in the direction of the dipole The emitted intensity is proportional to sin2x, where x is the angle between the dipole and the direction of propagation of the emitted light

Polarization in a fluorescence experiment Y X excitation detection I I The polarization state of fluorescence is described by: Polarization Anisotropy is preferred because it contains the total intensity IT Anisotropy

Polarization in a fluorescence experiment Y X excitation detection I I Why is the total intensity IT equal to I + 2 I ??? For the reason of symmetry the component polarized in the X direction and Y direction have the same intensity I, but in the given geometry we detect only the one polarized in X direction. Note: anistropy of a mixture of fluorophores fi – fraction of i-th fluorophore

Next we take an ensemble of molecules with random values of f Polarization in a fluorescence experiment Z Y X excitation detection I I D q I ≈ cos2q I≈ sin2f sin2q f First we consider the simplest case – a single fluorophore with a fixed position of its transition dipole moment Next we take an ensemble of molecules with random values of f Averaging over f: I≈ 1/2 sin2q

Polarization in a fluorescence experiment Y X excitation detection I I D q f Let us consider random orientation of dipole moments – we have to average over q The probability density function of finding an excited molecule with a dipole under the angle q: size of the “cone” for given q photoselection

Polarization in a fluorescence experiment Y X excitation detection I I D q r0 = 0.4 f Let us consider random orientation of dipole moments – we have to average over q

Polarization in a fluorescence experiment Da De q a r0 P0 0.4 0.5 54.7 90 -0.2 -0.333 a excitation I X f I Y detection The derivation was true for molecules with collinear transition dipole moments of absorption and emission, that is however not a general situation. Let us consider an angle a between the two dipoles

Polarization of 2-photon fluorescence Molecules can be excited by a simultaneous absorption of 2 photons. The molecule is excited by energy 2 hnexc. The process is nonlinear – probability of excitation is proportional to Iexc2. hnexc hnem hnem > hnexc hnexc The excitation probability is proportional to cos4q – different photoselection

Polarization of multiphoton fluorescence

Anisotropy and molecular motion So far we have considered “frozen” molecules. However, in reality the molecules are mobile and their rotation changes the orientation of the dipole q. Changes in q are reducing the anisotropy caused by photoselection. Where  is the rotational correlation time (Debye rotational relaxation time) which is the time for a given orientation to rotate through an angle given by the arccos e-1 (68.42o). For a spherical molecule: h – viscosity D – translational diffusion coefficient u – partial specific volume h – degree of hydration For a globular protein:

Temporal decay of anisotropy The temporal decay of anisotropy due to molecular rotations can be investigated by time-resolved fluorescence spectroscopy (like fluorescence lifetimes – TCSPC, frequency domain) It also influences the value of anisotropy measured by steady-state fluorescence spectroscopy: Perrin equation Perrin, F. 1926. Polarisation de la Lumiere de Fluorescence. Vie Moyene des Molecules Fluorescentes. J. Physique. 7:390-401.

E1 Perrin equation for a spherical molecule expressed in terms of P Perrin-Weber plot A plot of 1/P - 1/3 versus T/ predicts a straight line, the intercept and slope of which permit determination of Po and the molar volume (if the lifetime is known). Shown below is such a plot (termed a Perrin-Weber plot) for protoporphyrin IX associated with apohorseradish peroxidase - the viscosity of the solvent is varied by addition of sucrose.

IPA Measuremet of fluorescence anisotropy Z polarizer analyzer V … vertical vertical excitation H … horizontal IVV I X IVV = SV I detection IVH = SH I I Y IVH The plane defined by the direction of excitation and detection (XY) is called horizontal (it is usually horizontal in the experiment). The measured intensities are identified by two indices describing the orientations of the excitation polarizer and analyzer (the polarizer in the detection channel). We have to account for different sensitivities S of detection of individual polarizations

IPA Determination of G factor Z polarizer analyzer V … vertical horizontal excitation H … horizontal IHV I X IHV = SV I detection IHH = SH I I Y IHH In the case of horizontal excitation (excitation light polarized in Y direction), the light polarized in Z and X direction, which we detect are both I !!!

Magic angle If we place no analyzer in the detection pathway, we measure I + I. That is, however, not the total intensity IT = I + 2 I . The fluorescence intensity decays measured in that way may be, therefore, distorted due to anisotropy decay. We can either measure separately I and I and calculate IT. or we can measure with an analyzer oriented under an angle x, for which I would contribute to the passing light with a double weight compared to I I x Magic angle I Note: Even unpolarized excitation causes photoselection, because the light transversally polarized. In that case the maximal anisotropy (for collinear transition dipole moments) r0MAX = 0.2.

E2 Time-resolved fluorescence anisotropy POPOP Note: Scattered light can cause higher anisotropy, because it is completely polarized (rsc = 1). It is necessary to minimize scattering for accurate anisotropy measurement

Polarization methods are ideally suited to study the aggregation state of proteins. Consider, for example, the case of a protein dimer - monomer equilibrium. F Following either intrinsic protein fluorescence (if possible) or by labeling the protein with a suitable probe one would expect the polarization of the system to decrease upon dissociation of the dimer into monomers since the smaller monomers will rotate more rapidly than the dimers (during the excited state lifetime). F F F Lower P Higher P Hence for a given probe lifetime the polarization (or anisotropy) of the monomer will be less than that of the dimer

E3 The polarization/anisotropy approach is also very useful to study protein-ligand interactions in general. The first application of fluorescence polarization to monitor the binding of small molecules to proteins was carried out by D. Laurence in 1952 using Gregorio Weber’s instrumentation in Cambridge. Specifically, Laurence studied the binding of numerous dyes, including fluorescein, eosin, acridine and others, to bovine serum albumin, and used the polarization data to estimate the binding constants.

E3 A typical plot of polarization versus ligand/protein ratio is shown below: In this experiment, 1 micromolar mant-GTPS (a fluorescent, non-hydrolyzable GTP analog) was present and the concentration of the GTP-binding protein, dynamin, was varied by starting at high concentrations followed by dilution. The binding curve was fit to the anisotropy equation (in this case the yield of the fluorophore increased about 2 fold upon binding). A Kd of 8.3 micromolar was found

E4 FPIA – Fluorescence Polarization ImmunoAssay Among the first commercial instruments designed to use a fluorescence polarization immunoassay for clinical diagnostic purposes was the Abbott TDx – introduced in 1981. The basic principle of a polarization immunoassay is to: Add a fluorescent analog of a target molecule – e.g., a drug – to a solution containing antibody to the target molecule Measure the fluorescence polarization, which corresponds to the fluorophore bound to the antibody Add the appropriate biological fluid, e.g., blood, urine, etc., and measure the decrease in polarization as the target molecules in the sample fluid bind to the antibodies, displacing the fluorescent analogs.

E4 + + Fluorophore-linked antigen Antibody High Polarization Unlabeled antigen + Low Polarization