FRET Index Folding Dynamics

Fluorescence Anisotropy and Polarization to Detect Internal Protein Motions

When plane polarized light is used to excite a fluorophore and linearly polarized components of the emission are detected, information can be obtained about the size, shape, and flexibility of proteins or other macromolecules. Fluorescent polarization techniques can be used to monitor the binding of small molecules to proteins and other macromolecules, to study conformational changes in proteins, and to study the self-association of peptides and proteins.

In the case of linearly polarized excitation, those molecules whose absorption oscillators are oriented parallel to the direction of polarization will be preferentially excited. This will result in highly polarized fluorescence if the molecule do not rotate during the interval between the absorption and emission of light. If the molecule is free to rotate, the orientation of the absorbing molecules will be partially randomized. This results in partial depolarization. That is to say the rotational relaxation time is much shorter than the fluorescence decay time. The molecular orientation effectively becomes randomized before fluorescence occurs. If the fluorescence lifetime is known and the depolarization is measured, one can calculate the amount of Brownian rotation. This latter parameter is a valuable indicator of size, shape, and flexibility of the fluorescent moiety.

Depolarization of the emitted light is due then to protein rotation. It can be measured in the steady state when the depolarization is determined by both the rate of rotation and the fluorescent lifetime. To separate the two phenomena, measurements are made as a function of the temperature and viscosity of the solvent which directly affect only the rate of rotation. Alternatively, the fluorescent lifetime can be measured directly, as can the rate of depolarization after a very short pulse of polarized exciting light.

Depolarization measurements give the rate of the rotation of the entire protein molecule only when the fluorophores are rigid parts of the molecule. In reality, individual groups in a protein molecule also rotate. For example the side chains of the residues on the surface of a protein rotate about their single bonds independently at a more rapid rate than the entire molecule moves. There may be also be varying degree of flexibility between different parts of a protein, especially between independent domains. The rate at which a molecule rotates is very sensitive to its shape.

Excitation of rigid fluorophores with polarized light leads to preferential absorption by fluorophores with transition dipoles oriented parallel to the polarization direction. In the absence of molecular motion, the fluorescence will show linear polarization. Typically proteins rotate in solution within times of 10 to 100 nsec. Typical fluorescence decay times are in the range of 1 to 30 nsec. Thus the extent of polarization observed in solution will depend critically on the relative rates of fluorescence decay and molecular rotation.

The degree of fluorescence polarization, P is defined as:

  where I_para is the fluorescence intensity measured polarized parallel to the absorbed plane-polarized radiation, and I_perp is that perpendicular to the absorbed radiation.

If the emission is completely polarized in the parallel direction then P = 1. If the light is totally polarized in the perpendicular direction then P = -1. The theoretical limits of polarization are thus +1 to -1. In solution, these limits are not realized. Fluorescence is usually seen to be only partially polarized or completely unpolarized. The absorption of polarized light by a fluorophore is greatest when the plane of polarization is parallel to a particular axis of the fluorophore. Generally, the fluorophore will be randomly oriented. The probability of absorption in this random but stationary arrangement causes the polarization of the fluorescence to be less than 1/2. Any P less than 1 is referred to as fluorescence depolarization.

In the case of like fluorophores, depolarization may be affected both by the motion of the absorber and by energy transfer between the fluorophores. If the emitter is rotating very rapidly, which creates a substantial change in orientation during the lifetime of the excited state, the polarization will be decreased further. Resonance energy transfer occurs with highest frequency between molecules having parallel dipoles. The energy transfer between identical fluorophores results from the fact that resonance energy transfer also occurs between nonparallel dipoles, which leads to depolarization. This type of depolarization is highly concentration dependent because the efficiency decreases with the sixth power of distance between the fluorophores.

Several types of motions contribute to the fluorescence depolarizationin proteins:

• Motion out the point of attachment of the fluorophore to the protein, 10^-9 sec
• Torsional and hinge motions of protein domains, 10^-9 sec
• Global rotational diffusion of the whole molecule, 10^-9 - 10^-8 sec

The limiting or intrinsic polarization, P_o, is the polarization in the absence of rotation that would be observed if the absorbing molecule was immobilized and far from other molecules. Technically, P_o is the polarization that is observed observed when the fluorophore is in a solvent of very high viscosity and very low concentration. At very high viscosity and high concentration, the effect of energy transfer is primarily detected. At low viscosity and low concentration, the effect of molecular motion is primarily detected. In general:

where phi is the angle between the absorption and emission dipoles.

Additional depolarization occurs if the dipole rotates through an angle omega:

where P is the observed polarization. Thus the total depolarization is dependent on an intrinsic factor P_o and an extrinsic factor omega.

The observed depolarization is related to the excited state lifetime and the rotational diffusion of the fluorophore. For a spherical molecule the following relationship holds:

where t_r is the rotational relaxation time, V is the molar volume of the rotating unit, R is the universal gas constant, T the absolute temperature and eta is the viscosity. t_r is the time for a given orientation to rotate through an angle given by arccos e^-1 (ie, 68.42^o).

Using this relationship, the polarization can be written as:

where t is the excited state lifetrime. A plot of 1/P - 1/3 versus T/eta (Perrin-Weber plot) is a staight line. Its slope and intercept permits determination of the molar volume and P_o.

The relationship (Perrin equation) can also be written as :

from which it appears that if we know the intrinsic polarization, the observed polarization, and the excited state lifetime, we can determine the rotational relaxational time. This parameter will give information then on either the molecular volume or size of the rotating unit or the viscosity of the medium (for example the viscosity of the membrane in which the protein is embedded).

Deviations from linearity (downward curvature) in the Perrin equation indicates multiple rotational modes. This may be due to local mobility of the fluorophore about its point of attachement. Also it may be due to domain movements or movement of part of the protein. Local motion usually cannot be detected with non-covalent associations of fluorophores and proteins, since the extrinsic fluorophore is ordinarily held via not one but a few points of attachment.

Fluorescence Anisotropy

Another measure of the polarization of fluorescence is the emission anisotropy, wich is defined as:

The physical interpretation of the emission anisotropy is similar to that of the degree of polarization. In analogy to polarization, the theorethical limits of anisotropy are +1 to -0.5. The advantage of the anaisotropy is that its time dependence is determined only by the rotational motion of the fluorophore. The time dependence of the degree of polarization is determined both by the fluorescence lifetime, and the rotational motion. Also, unlike polarization, the fluorescence anisotropy function is directly additive. This arises from the fact that the term I_para + 2I_perp represents the total emission intensity.

In terms of anisotropy, the Perin equatuion can be written as:

where r_o is the limiting anisotropy, and r is related to P by:

To measure these parameters in proteins, one can follow either the intrinsic fluorescence of tryptophan, tyrosine, NADH, FAD, porphyrines, or the fluorescence of extrinsic probes associated with the protein either covalently (for example dansyl or fluorescein) or non-covalently (for example ANS or MANT).

Phosphorescence Anisotropy

Phosphorescence anisotropy can be used to detect slow molecular mortions in proteins. Extrinsically labelled membrane proteins and the cytoskeletal components are particularly well suited for determining the segmental or internal motion of these proteins. This is because their correlation times are within the phosphorscence time frame. When a protein is embedded in a viscous memrane, the global motion is slowed by at least 3 order of magnitude and occurs on the 10^-6 to 10^-3 timescale. Thus fluorescence polarization cannot be used to determine the rotational diffusion coefficienr of an intrinsic membrane protein. The lower lifetime of decay from the triplet state can be used successfully. The time-resolved phospohorescence anisotropy decay is measured in the same way as time-resolved fluorescence. Eosyn and erythrosin are the most successfull phosphoresscence probes.

The uniaxial the rotational diffusion coefficient (ie. the motion is about the normal to the bilayer surce) is very dependent on the size of of the rotating unit. Thus it is ideally suited to determine the associationof membrane proteins either with themselves with other memrane proteins or with cytoskeletal proteins. In contrast the translational or lateral diffusion coefficient is not effected greatly by protein association within the membrane. If the membrane protein exists as a single species, the uniaxial rotation results in two correlation times. If it is adimer or higher polymer, two correlational times are expected for each species. For example, erythrocyte band-3 (a membrane protein) exhibits 3 correlation times. The shortest is 12-30 msecond, which is consistent with a dimer. This motion is not affected by crosslinking of band-3 with monoclonal antibodies. Therefore, this represents the flexibility near the site of labeling of band-3 with the phophoressecence probe. The amplitudes of the two remaining correlational times 200 and 300 millisecond vary greatly upon addition of monoclonal antibody. These correlation times represent the global motion of the molecule.

Here is a list of some proteins (mostly membrane proteins and proteins of the cytoskeleton) that have been studied with phosphorsecence anisotropy:

• cytochrome b5
• cytochrome c
• cytochrome p-451
• erythrocyte band 3
• mitochondrial f1-atpase
• sr atpase
• egf receptor
• fc receptor
• acerylcholine receptor
• ldl receptor
• actin
• spectrin
• viral fusion protein

Internal Motions of IgG

Fluorescence techniques have been used to explore several different aspects of the IgG structure. Measurements of FRET distances were described on a previous page. Results obtained with fluorescence polarization using the same IgG derivatives are briefly summarized here.

Fluorescence polarization was used to determine whether the three components of the antibody structure move independently relative to the motion of the overall molecule. The figure (left) graphically defines the possible internal motions of IgG in terms of rotational angles and axes.

Antibodies that specifically bind the fluorophore dansyl-L-lysine were used in these experiments. The emission anisotropy of the dansyl bound to intact antibody, to F(ab')₂ and to Fab was measured. Only in the case of the Fab fragment can the data be described by a single rotational correlation time. The data indicate that Fab rotates as a single rigid body unit with a rotational correlation time time of 33 nsec. Such a long correlation time indicates that the Fab fragment is not spherical. The rotational correlatuion time is consistent with with a structure that is a prolate ellipsoid of revolution having an axial ratio of 2.

The decay of anisotropy for the intact IgG molecule can be analyzed in terms of two exponential decays. The rotational correlation time for the IgG molecule is 168 nsec. This is much longer than anticipated for a sphere indicating an asymmetrical structure. The fraction of the decay due to segmental motion was found to be 0.56. This suggests that the Fab portion of the molecule can rotate both independently of the overall molecule and with the overall molecule. The results obtained with the dansyl bound to F(ab')₂ also indicate that considerable flexibility arises from the segmental motion of the Fab's. The hapten itself is bound rigidly to the binding site and undergoes no significant rotation independent of that of the Fab.

FRET Index Folding Dynamics

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