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Fluorescence correlation spectroscopy (FCS) can reveal molecular dynamics information on small biological molecules by monitoring their time correlated
fluorescence fluctuations at thermal equilibrium. FCS involves exciting a fluorophore with a laser beam and collecting the molecule’s fluorescence emission
using single photon detectors. Polarized excitation light can be used to polarize both the excitation and the emission of the fluorophore. By measuring the
fluorescence fluctuation due to changes in the polarization of the molecule, one can extract information on the molecule’s rotational dynamics. The molecule’s
rotation dynamics can reflect the sample’s molecular composition and interactions as well as the local microscopic environment of the fluorescent molecule. It
is important to be able to control the polarization of the excitation light precisely with polarized FCS as well as other techniques exploiting the polarization of
fluorophores. A recent study suggests that delivering accurately controlled polarized light to a sample is difficult due to the depolarization effect of a dichroic
mirror used in the system. The work suggests a method to correct for this depolarization effect using a combination of a half-wave plate and a quarter-wave
plate. Using this methods we were able to achieve the desired linear polarization of light and eliminate depolarization artifacts at the sample. With this preliminary
result, further study will include deriving a mathematical model to deliver circularly polarized light to the sample and demonstrate the capability of FCS to measure
rotational dynamics of fluorescent protein molecules such as green fluorescent protein (GFP) or enhanced green fluorescent protein (EGFP.)
Fluorescence Correlation Spectroscopy (FCS)
We use fluorescence fluctuation spectroscopy which exploits spontaneous fluctuation of phototon intensity from a sample as molecules move in and out of
sub-femtoliter observation volume to study molecular dynamics. (Figures 1 and 2.)
Figure 1: Fluctuation of fluorescence intensity can be attributed to translational or rotational diffusion or chemical, conformational, or photophysical changes of
the molecules. (Figure 1a; Pabit, et al., 2008) Data analysis using mathematical models such as the autocorrelation function (equation 1; Figure 2) or the
crosscorrelation function (FCCS) give quantitative information about the molecules (Thompson, 1991; Hess, et al., 2002.)
Figure 2: (left) Schematic diagram of observation volume (red sphere) defined by a focal point of the excitation laser beam. The random fluctuation in fluorescence
intensity (middle) is recorded by single photon detectors. We can calculate the autocorrelation function (equation 1) from this fluctuation and compare it with
various established models to study molecular dynamics. The shape and the decay pattern of the autocorrelation function depend on the rate of the diffusion
of molecules. Therefore, it provides ways to determine binding interactions, diffusion coefficients, and reaction kinetics.
What is polarized light?
Figure 3: Light can be described as a transverse electromagnetic wave which has two orthogonal components: Ex and Ey (figure 4, left.) The two components
of natural light have random phase and magnitude difference. A linear polarizer polarizes natural light by letting in only the component of light that is parallel
to its transmission axis.
How do we change the polarization of light?
Figure 4: (a) Once light is polarized, we can change it direction of polarization using a half-wave plate, a quarter-wave plate, or a combination of both. The two
orthogonal components of light will propagate with different speeds within the wave plates. The thickness of wave plates is accurately controlled so that when
the light emerges, the phase difference between the two components changes. A half-wave plate (λ/2 plate) will introduce a phase difference of π radians and
a quarter-wave plate (λ/4 plate) will introduce a phase difference of π/2 radians. (b) As a result, if incoming light makes an angle α with the fast axis of a half-wave
plate, the polarization of the emerging light will be 2α. A quarter-wave plate will turn linearly polarized light into circularly polarized light, or vice versa.
Polarized Fluorescence Spectroscopy (FCS)
The idea to apply FCS to investigate rotational dynamics was introduced in the 1970’s (Aragón, et al., 1976; Kask, et al., 1987.) Polarized excitation via
photoselection and polarized emission and its detection are shown in figure 5. The change in polarization results in the fluctuation of fluorescence. The
resulting autocorrelation function reflects the rotation dynamics of a molecule.
Figure 5: (a) In this diagram, the polarization of excitation light is parallel to the y-axis. The electric dipole of a fluorophore (μ) makes the angle θ1 with the
polarization direction of the excitation light. The excitation probability of the fluorophores in the observation volumes is proportional to cos2 θ1. This phenomenon
is called photoselection (Lakowicz, 2006.) If the molecule rotates by θ2-θ1 during relaxation, the emission polarization direction will now be θ2. (b) The polarization
of the emission light can be detected when a polarizer is placed in front of a photo detector. A polarizing cube beamsplitter transmits a component of light that
is parallel to its optic axis and reflects the component that is perpendicular.
Depolarization effect of dichroic mirror
Delivering accurately controlled polarization of excitation light is important in polarized FCS and scanning optical microscopy studying anisotrophic structure of a
sample. A previous study shows that this task is hindered by the depolarization effect of a dichroic mirror which is an important component of epi-illuminated
microscopy (Dong, et al.) A dichroic mirror introduces an arbitrary phase delay to the incoming light and causes alteration of the polarization of the incoming
beam (figure 6.) In addition, the dichroic mirror causes intensity variance depending on the polarization direction of the transmitted beam. This preliminary study
was aimed to correct this depolarization effect of the dichroic mirror.
The standard two-photon FCS experimental setup (Pabit, et al., 2008) shown in figure 7 is used. A polarizing beamsplitter cube and wave plates (λ/4 and λ/2 plates)
are used for polarized FCS.
In this preliminary experiment to compensate the depolarization effect of a dichroic mirror, we used a thin film sample with fluorescent molecules aligned in a single
direction. We placed polarization optics along the beam path as suggested in a previous study by Dong, et al.
In future studies, two photomultiplier tubes (PMTs) or avalanche photodiodes (APDs) will be used as a single photon detector and a polarizing beam splitter cube
will be placed before the detectors to separate the polarization of emitted fluorescence (figure 5b.) We will use fluorescent proteins such GFP or EGFP in viscous
soluations such as glycerol to study the rotational dynamics.
Figure 7: A setup of a typical FCS experiment. A λ/2 plate, a λ/4 plate, and a polarizing beam splitter are used for polarized FCS experiments. An excitation light
is reflected to the sample by a dichroic mirror. The fluorescent emission is then transmitted through the same dichroic mirror and is detected by the photon
detectors. This signal is correlated using a correlator.
Figure 8: A λ/2 plate and a λ/4 plate are placed along the laser beam path before the scanning mirrors to manipulate the polarization of the excitation light.
The polarization of excitation light can be changed by rotating the fast axis (shown as a dotted line in the figure) of the wave plates. We placed a liner polarizer
in the place of the objective lens (not shown) to measure the polarization of the excitation light in the sample. As a control, we change the polarization of the
excitation light from 0 to 180 degrees using the λ/2 plate only. The average intensity of fluorescence for each excitation polarization angle is measured using
a PMT.
Our preliminary results show that we are able to deliver the desired polarization of excitation light to the sample by introducing an additional phase delay using
λ/2 and λ/4 plates to cancel out the depolarization effect of the dichroic mirror (figure 9.)
Figure 9: The plot shows fluorescence intensity measured by a PMT versus polarization direction of the excitation light. The theoretical prediction (blue circle) was
made based on the relationship I=Imaxcos2θ where I is the fluorescence intensity, Imax is the maximum intensity, and θ is the angle between the polarization
direction of the excitation light and the electric dipole of a fluorophore. In this prediction, Imax is set to 281 kHz which is the maximum intensity from the experiment
with depolarization compensation (red square.) For both the theoretical prediction plot and the compensated plot, the x-axis refers to the direction of the
polarization of the excitation light at the sample. In the case of the plot with the compensation (green triangle,) the x-axis refers to the angle of the λ/2 plate.
Both the data with and without compensation are normalized. However, in a non-ideal situation, the intensity at θ=90° is not 0 Hz due to optical distortion such
as the depolarization effect of the high numerical aperture objective lens used in the experiment.
Future Directions:
1. Derivation of a mathematical model to deliver circularly polarized light to the sample
2. Setting up a second microscope for the experiment
3. Demonstrating the capability of FCS to measure molecular rotational dynamics using fluorescent proteins such as GFP or EGFP.
This material is based upon work supported by the Howard Hughes Medical Institute under Grant No. 52005873 and the Jackson Award for Undergraduate
Research in Physics and Astronomy from Emory University’s Department of Physics. Thanks to Dr. Keith Berland for his continuous support and to the rest
of the Biophotonics lab members for their guidance.
-Aragón, S.R. and Pecora, R. (1976). Fluorescence correlation spectroscopy as a probe of molecular dynamics. J. Chem.. Phys. 64 (4): 1791-1803.
-Bacia, K., Kim, S., and Schwille, P. (2006). Fluorescence cross-correlation spectroscopy in living cells. Nature Methods. 3 (2): 83-89.
-Hess, S.T., Huang, S., Heikai, A.A., and Webb, W.W. (2002). Biological and chemical applications of fluorescence correlation spectroscopy. Biochemistry.
41 (3): 697-705.
-Kask, P., Piksarv, P., Mets, Ü, Pooga, M, and Lippmaa, E. (1987). Fluorescence correlation spectroscopy in the nanosecond time range: rotational diffusion of
bovine carbonic anhydrase B. Eur. Biophys. J. 14: 257-261.
-Lakowicz, J.R., Fluorscence Anisotrophy. In: Principles of Fluorescence Spectroscopy. 3rd edition. New York: Springer Science+Business Media. p.353-382.
-Pabit, S., and K. Berland (2008). Two Photon Fluorescence Correlation Spectroscopy. Handbook of Biological Nonlinear Optical Microscopy (B. Masters and
P.So, Ed.) In Press
-Thompson, N.L. (1991). Fluorescence Correlation Spectroscopy. In: Lakowicz, J.R., editor. Topics in Fluorescence Spectroscopy. New York: Plenum Press.
p.337-378.
-Personal communication with Chen-Yuan Dong from Department of Physics, National Taiwan University
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