Abstract

A florescence spectrometer was constructed with the goal of determining binding affinities of protein-ligand complexes, such as phalloidin and F-actin, via fluctuation correlation. The spectrometer was successfully aligned so as to excite the calibration dye, Rhodamine 6G, and pass the refined fluorescence beam to a photon counting head. Several difficulties, including sources of background light, deterioration rate of calibration samples, apparatus alignment, and challenges finding the sample focal point were encountered. In tandem, these issues barred goal achievement; however, acquisition of data from an outside experiment allowed for confirmation of calibration theory. It was determined for the data set provided that the effective volume of excitation was 0.28±0.13 fL, which is within a sigma from the provided value of 0.20 fL. This confirms that the theory herein is correct for calibration of the apparatus.

Introduction

Ligand-protein reactions may be characterized by their binding affinities. This affinity has important consequences, as in the case of phalloidin, where the toxin’s high binding affinity to F-actin prevents depolymerization, destroying liver cells and resulting in death. To determine this binding affinity, fluorescence spectroscopy may be used. Fluorescence is the emission of light following the excitation and relaxation of a molecule due to incident light. Light emitted in fluorescence is of a longer wavelength than the excitation light, a result of the non-radiative transitions of the excited electron to lower energy states before its return to the ground state. This principle allows for the separation by wavelength of excitation and emission light. The goal of this experiment is to build a fluorescence spectrometer, calibrate it with a solution of Rhodamine 6G, and use it to determine the binding affinity of the phalloidin/F-actin complex.

Theory

Diffusion

In fluctuation correlation spectroscopy (FCS), light is emitted from fluorescently tagged molecules in a sample volume. These molecules are freely diffusing through a solvent and thus their motion is Brownian, where irregular motion of particles in solution is due to random thermal interactions with the solvent molecules. Einstein showed that the irregular motion of particles in solution is due to random thermal interactions with the solvent molecules^[1]. Solvent molecules have a two-fold effect on solute particles, acting as both a driving force for fluctuations, and a dampening force for particle motion. Using this information, the Stokes-Einstein relation

...1

in which R is the radius of the suspended particle, D is the translational diffusion coefficient, k_b is Boltzmann’s constant, T is the temperature in Kelvin, and

is the viscosity of the solvent. It may then be derived that the mean-squared displacement increases linearly over time and is proportional to the translational diffusion coefficient

...2

These results are fundamental to the underpinnings of fluctuation correlation spectroscopy and form the foundation for the analysis of the experimental data.

Correlation of Fluctuations

The statistical fluctuations of Brownian motion lead to fluctuations in fluorescence intensity, producing a noise signal of photon counts. From equations 1 and 2, it is seen that the larger a particle, the smaller its mean squared displacement will be in a given time. Thus larger molecules take longer to move through the sample volume and therefore the photons emitted as a result of their fluorescence will be detected for a longer period of time. It follows then that the intensity peaks due to the passing of larger molecules will be greater in width than those peaks which occur as a result of the passing of smaller molecules.

These width variations are then analyzed using by autocorrelation (autocorrelation theory was drawn from the primary paper of reference^[2] being used to build the apparatus). The autocorrelation function measures the overlap of a function with itself after a given time lag,

. The normalized autocorrelation function for the experiment is shown below in equation 3, giving the autocorrelation, G(), in terms of the fluorescence intensity as a function of time, F(t).

...3

In the case of this experiment, solving for F(t) and

in terms of the spatial integration of concentraiton fluctuations (derived by Fick^[3]), weighted by a volume sensitivity function, yields equation 4, the autocorrelation for translational diffusion^[4][5].

...4

are volumetric parameters to be determined through calibration, as outlined in the primary paper of reference^[2].

In a system in which both free and protein-bound fluorescently-tagged ligand are present, two correlation times of translation diffusion may be found, which arise from fluorescing species of significantly different masses. The observed autocorrelation function for such a system, G(

) is given by the superposition of the autocorrelation function for each state, G() and G(), is given in equation 5

...5

where f is the fraction of bound ligands in the reaction^[2]. The [original] figure below shows how different superpositions of

and (boundary curves) give varied in-between values for (inside curves).

Binding Affinity

In a ligand-protein reaction, the ligand has a far different coefficient of diffusion than the ligand-protein complex (when the protein is several times more massive than the ligand). Thus, using fluorescently tagged ligands, the change in the diffusion coefficient may be used to find the fraction of ligands, f, that are bound, and thus the binding affinity of the ligand.

The superposition of autocorrelations in %REFLATEX{5}% allows for the calculation of f in a given solution. If protein concentration is varied, then f may be fit as a function of protein concentration. This allows for determination of the dissociation constant of the two species, seen in equation 6.

...6

Thus, with the association constant simply being the inverse of the dissociation constant, the binding affinity of the two species may be determined.

Methods

Apparatus

The 5mW, 532 nm laser is reduced in power to around 100 µ­W as it passes through a polarizer set to reduce photo-bleaching of the fluorescent tags. The beam is passed through the first spatial filter, which uses a 10x objective and 25µm pinhole. Due to imperfections the air and surfaces enountered by the beam, the objective focusing of the laser creates a Fourier transform intensity distribution centered around the Gaussian component of the beam, which is subsequently filtered to only pass the Gaussian component of the beam by the pinhole. The beam is then made parallel once again as it is passed through lens 1. The beam is cut in width by an iris to so as to avoid unnecessary background light from laser reflection later in the apparatus. Excitation (laser) light is then reflected by the dichroic mirror, and focused through the 100x oil immersion objective, through immersion oil onto the sample.

The fluorescent emission light is collected by the objective and, due to its longer wavelength, is passed through the dichroic mirror. The second spatial filter (this time a 10x objective with a 50 µm pinhole) cuts out any fluorescence that isn’t from within the effective excitation volume. This beam then passes through a series of three lenses (necessary due to geometrical constraints and materials at hand) to become parallel and small enough in diameter so as to fit within the detection window on the photon counting head after passing through a color filter that removes any remaining laser light. The photon counting head allows for single-photon detection, so that fluctuations caused by molecules entering and exciting the excitation volume are detectable. The photon counts are passed along through a DAQ card to a computer that collects and processes the information in a !LabVIEW program.

Sample Making

A typical sample cell was constructed by placing two strips of double-sided, 2mm thick tape parallel on a microscope slide. A cover slip was then placed over these strips of tape to create a channel. Solutions of Rhodamine 6G (R6G) were prepared via a series dilution using micropipettes, and solution of desired concentration was added to the channel. The channel was then sealed by applying nail polish.

Data Collection

The Hamamatsu H6240-01 was supplied by a 5 volt power source for data acquisition. To obtain adequate data, minimization of background light sources was required. To these ends, all lights were turned off, including the computer monitor. The door frame was covered to avoid ambient light entering from the hallway. All other sources of electronic light (blinking power buttons on computers, the voltage source display, cell phones) were covered. Boxes and black paper were used to minimize ambient laser light pick-up by the counting head. Lastly, movement during data collection was avoided, as alteration of ambient laser light distribution was detectable due to movements near the laser.

Results & Discussion

Experimental Results

The sample was successfully placed within the focus of the objective, by using a 100 mM solution of !R6G in order to find the position of the sample that passed the maximum fluorescence intensity through the spatial filter by eye (as shown below, where left to right is the sample being moved towards the camera, which is placed in the position of the photon counting head in the apparatus diagram).

Due to either excessive background noise or imprecision in the placement of samples within the sample holder, the autocorrelations, taken at a sampling frequency of 100 kHZ over a time period of one minute, for samples containing water, 1 nM R6G, 10 nM R6G, and 100 nM R6G, all shown below, are nearly identical, rather than showing the

behavior expected from equation 4 or the expected from Rhodamine 6G.

After a reduction in noise from approximately 240,000 counts a second to around 10,000 counts a second, an attempt was made to find the focus by slowly sweeping through the range of the sample holder. As can be seen, the results were inconclusive.

Finally, the samples were placed by eye approximately within the focus of the objective and the average photon count per second at each concentration was recorded yielding the following table:

Time constraints prohibited any further attempts at proper calibration.

Calibration Data Analysis

Calibration data for a fluctuation correlation spectrometer using the dye Alexa 488 was obtained from Professor Mueller's lab. With this data the autocorrelation was able to be generated and fit according to equation 4, with a gamma correction factor of 0.237 given to us by Professor Mueller's lab, using matlab. The results may be seen below.

From this fit and the known diffusion coefficient of Alexa 488 of 435 /s ^[6], we were able to obtain the volumetric constants =0.36±0.078m

and

=0.62±0.27m, giving an effective volume of 0.28±0.13 fL which was within one sigma of the given value of 0.20 fL. The fit parameters and the values calculated from the fit are summarized in the table below.

Conclusions

A fluorescence spectrometer was built with the goal of determining the binding affinity of phalloidin to F-actin. In tandem, an array of difficulties barred this goal from being reached. However, calibration data acquired from the Mueller lab allowed the calibration theory to be tested. It was determined for the data set provided that the effective volume of excitation in the sample was 0.28±0.13 fL, which is close to the provided value of 0.20 fL. If future work on this apparatus surmounts the aforementioned difficulties and allows for detection of fluorescence and accurate calibration, determination of accurate binding affinities would attainable.

Acknowledgements

We would like to thank our TAs, instructors, and peers of MXP II for guidance, and the Department of Physics & Astronomy for its resources. A special thanks goes out to Issac from Professor Mueller’s lab, the data from whom made our analysis possible. Thanks also goes to the authors of our primary paper of reference^[2], for instructions within the paper, as well as providing us with model !LabVIEW software upon request, which helped us to build our own software, built upon work by Kurt Wick. Lastly, deep gratitude is extended to our advisor, Prof. Elias Puchner, for his many hours of assistance.

References

[1] A. Einstein. Ann. Phys, 17, 549-549-560 (1905).

[2] Rieger, Nienhaus, Rocker. “Fluctuation correlation spectroscopy for the advanced physics laboratory.” Am. J. Phys. 73, 1129 (2005); doi: 10.1119/1.2074047.

[3] Fick, Adolf. “Ueber Diffusion.” Annalen der Physik , 1855 , 59.

[4] S. R. Aragon and R. Pecora, “Fluorescence correlation spectroscopy as a probe of molecular dynamics,” J. Chem. Phys. 64, 1791-1803 (1976).

[5] R. Rigler, U. Mets, J. Widengren, and P. Kask. “Fluorescence correlation spectroscopy with high countrate and low background: analysis of translational diffusion,” Eur. Biophys. J. 22, 169-175 (1993).

[6] Petrášek ; Schwille. “Precise Measurement of Diffusion Coefficients using Scanning Fluorescence correlation Spectroscopy.” Biophys J., 2008, 94(4), 1437-1448.