Fluorescence resonance energy transfer (FRET) is a biophysical technique important for measuring nanometer scale distances and changes occurring within the distance in biological systems. It analyses the macromolecular interactions between florescent molecules which are close in nature. Kinetics of association / dissociation between biological macromolecules can be carried out by this technique. The distance between the interacting molecules is calculated by FRET analysis. This transfer of absorbed light energy between two chromophores is radiationless. The distance of the molecules is measured by optical diffraction limited resolution. Single strands of dye labelled DNA strands is hybridized and the optical properties of the double standard is measured fluorescence spectroscopy.
Absorption and fluorescence
An atom or molecule is moved into a higher state by absorption of a photon of suitable wavelength. This excitation makes the shift of the atom or molecule from its ground state s0 to the higher energy state s1. The de -excitation will occur in one of the following process.
- Heat: Collision of the molecule with environment leads to release this energy (photon) as a form of heat energy. It is a radiationless process.
- Fluorescence: The photon is directly emitted back due to the transition of the molecules from excited state to ground state. The energy released as fluorescence is generally less than that of absorbed energy, a small part of the energy s released as heat (stokes shift).
- Phosphorescence: The molecule undergoes a radiationless transition to a triplet state (T1). In a different step the molecule returns to a ground state by emission of a proton.
- Energy Transfer: The excited molecule (donor) transfers the energy directly to a nearby molecule (acceptor). The acceptor molecule is excited electronically. This transfer is radiationless can occur as Forster or as Dexter transfer. This is the basic principle behind FRET analysis.
Energy transfer mechanisms
Radiative energy transfer
The mechanism of energy transfer from the donor molecule to the acceptor is a two- step process. The Donor molecule from its excited state returns to a ground state by release of a photon. In the second step, the photon released from donor molecule excites the acceptor molecule. Now the acceptor molecule is transferred to the excited state. This mechanism is called trivial form energy transfer.
The efficiency of this process depends on the following four parameters:
- the quantum yield DΦe of D* for emitting a photon
- the number density nA of ground state A molecules that can absorb the emitted photon
- the absorption cross section A or the probability with which A will absorb an emitted photon
- the overlap of the fluorescence emission spectrum of D* and the absorption (or excitation) spectrum of A.
Radiationless energy transfer
A mechanism of radiationless transfer of this energy can also happen. The transfer of energy from donor molecule, D, to the acceptor molecule, A, the energy can also be transferred in a radiationless way. This can occur in two ways:
- a) by collision (more precisely: by exchange interaction) (Dexter energy transfer)
- b) by Coulomb interaction (Forster energy transfer)
In case of Dexter energy transfer, the excited electron orbitals of the Donor molecule collide with the electronic orbitals of the Acceptor molecule. The result is the transfer of the electronic orbitals. The collision changes the spin in both acceptor and donor molecule.
3D* + 1A → 1D + 3A*
For Dexter transfer mechanism to occur the distance between the donor and acceptor molecules should be very small. Spin interaction decays exponentially with the increase in distance between the acceptor and donor molecules. It occurs efficiently within a distance of 1 mm. This makes Dexter mechanism of energy transfer inapplicable for laboratory experiments.
The Forster mechanism can occur for large distances and thus it is useful in laboratory applications. The two step process of donor de-excitation and acceptor excitation is explained as coulombic dipole- dipole interactions. A direct collision of donor and acceptor molecule is not required. This mechanism can be explained Molecular broadcaster (D) and receiving molecule (A).
Fermi’s Golden Rule
The rate constant kr for spectroscopic transition described by perturbation theory can be expressed by Fermi’s “Golden Rule”:
Here, is the density of the final states relevant for the transition (i.e. the density of isoenergetic donor acceptor states)
i is the wave function of the initial state
f is the wave function of the final state
h is the interaction operator.
The probability for a radiative transition between an excited state and the ground state is given by the
transition dipole moment R. It is defined as:
R=∫φ2 * ⋅er⋅φ1dV (2)
Here, φ1 is the electronic wavefunction of the molecule in the excited state
φ2 is the conjugate complex wavefunction of the molecule in the ground state
e is the electric charge
r is the spatial coordinate.
In a slightly simplified view, the integral ∫φ2 * ⋅er⋅φ1dV describes the displacement of the charge distribution between ground and excited states upon inducing an optical transition by the alternating electromagnetic field of the light wave. The transition dipole moment of the donor can now interact in a radiationless way with the transition dipole moment of the acceptor. Thus, a transfer of the excitation energy between the two molecules can take place. Classically, the interaction energy between two dipoles is given by:
Edipole−dipole= κ/4πϵ0(μDμA/ r3DA)
κ is a geometric factor (depending on the orientation of the dipoles with respect to each other)
ε0 is the electric field constant (8,854*10-12 F/ m )
μD is the value of the electric dipole moment of the donor
μA is the value of the electric dipole moment of the acceptor
rDA is the (mean) distance between the dipoles.
If all constants are combined in a single constant one obtains the Forster radius r0, and becomes the following relationship which is also known as Forster equation:
The Forster radius is the distance at which 50% of the excited donor molecules will be deactivated by the Forster mechanism. Forster radii are characteristic for a specific donor acceptor pair and are compiled in the literature for several such pairs. The Forster equation is useful when measuring the energy transfer efficiency E, i.e. the portion of all photons absorbed by the donor which have been transferred to the acceptor. The energy transfer efficiency is given by:
It can be determined from the relative donor fluorescence yields in presence (FDA) and in absence (FD) of the acceptor:
Forster energy transfer in biophysical chemistry
Since the method is dependent on forster radius of the Forster mechanism and Forster radii typically. The entire process is dependent of the dimensions of biologically relevant macromolecules (20-90 A). Thus this method is ideally suitable for analysis of steric information about such molecules. The method is therefore applicable to measuring distances well below the diffraction limited spatial resolution in optical spectroscopy corresponding to 200 nm for short wave visible (blue) light. Many proteins, DNA structures, the thickness of biological membranes and distances between subunits of large proteins re in the size of a typical Forster radii. Any variation of the distance between donor and acceptor will change the FRET efficiency E which can then be used for the determination of molecular structures. For example, if a protein is labelled with matching donor and acceptor dyes at different positions, structural changes of the molecule (e.g. due to solvation effects) can easily be monitored. To this end the energy transfer efficiency must be determined in the presence and in the absence of the acceptor. If the Forster radius of the donor acceptor pair used is known, then the distance between donor and acceptor can be calculated from at any time.
The source for the excitation light can be a high pressure xenon lamp. A fluorescence spectrometer uses two monochromators, the first one is for the excitation light and the second one for the emitted fluorescence light. Two beam paths for excitation and emission are normally oriented perpendicular to each other in order to minimize the influence of scattered excitation light. Since the fluorescence light is weak and emitted isotropically in all directions, special mirrors are required for the collection of as many photons as possible. The emitted light is normally registered by a photomultiplier. While a normal UV/VIS spectrometer is usually designed in a two beam configuration, fluorescence spectrometers are usually one-beam devices. Another important difference concerns the slit widths of the monochromators. For UV (VIS absorption spectroscopy it is desirable to use as narrow a slit as possible (e.g. 1 nm), for optimum spectral resolution. In fluorescence spectroscopy slit widths are generally larger (e.g. 2 to 5 nm for the excitation light, 5 to 20 nm for the emitted fluorescence), so that sufficiently much light can be collected by the detector. The somewhat lower spectral resolution is tolerable as fluorescence spectra of dissolved molecules in the liquid phase are generally spectrally broad and only weakly structured. Note that fluorescence spectroscopy can be performed in two modes:
a.) For a fixed excitation wavelength an emission spectrum is measured.
b.) For a fixed emission wavelength an excitation spectrum is measured.
It is also possible to scan both excitation and emission wavelengths, resulting in an array of spectra known as two-dimensional spectra.
The goal of the experiment is to determine the energy transfer efficiency of a matching pair of donor and acceptor dyes (the donor (D) Cy3 and the acceptor (A) Cy5) after hybridized of dye labelled single DNA strands.
The donor strand sequence is
CCC AAA CTA AAC TTA ACT AAA CTA AAC CCC
and the acceptor strand sequence is
GGG TTT GAT TTG AAT TGA TTT GAT TTG GGG
Note that here for reasons of clarity the second strand is not written in the usual notation from the 5´ end to the 3´ end.
- A stock solutions (ca. 10μM) of both labelled and unlabelled single strand DNA solutions. From these, first all possible combinations of DNA double strands need to be hybridised: a) donor/acceptor (Cy3/Cy5), b) donor/naked (Cy3/N), c) acceptor/naked (Cy5/N), d) naked/naked (N/N).
- Register absorption spectra of all double strands using a UV/VIS absorption spectrometer. This will allow you a) to exactly determine the concentration of the solutions and b) to choose the best excitation wavelength for the fluorescence measurements. You will also need to monitor two reference spectra of the cuvette, one of the cuvette filled with buffer solution only, and another one for the empty (airfilled) cuvette. Thus, altogether you will register six absorption spectra.
- Register two fluorescence spectra for each of the dye containing double strand solutions (Cy3/Cy5, Cy3/N, and Cy5/N), one for the absorption maximum lAA of the acceptor and one for the absorption maximum lD A of the donor. This will result in a set of also six fluorescence spectra.
- Determine the Forster radius experimentally and theoretically and compare the values to each other. From the measured absorption and fluorescence spectra of donor and acceptor dyes you can calculate the overlap integral of eq. which will in turn let you determine a theoretical value for the Forster radius from the optical properties of the individual dyes. Experimentally, the Forster radius can be obtained from the measured energy transfer efficiency and the known geometry of the hybridized double strands.
With respect to
1) The sample preparation
Sample preparation requires the use of micropipettes (Eppendorf pipettes). Mix 30 μL of each single strand solution in a micro test tube that can be used for the Peqlab Primus 25 thermocycler. Place the four mixtures into the thermocycler. Switch the thermocycler on, select and start the program by pressing the RUN button. First, the samples will be kept at a temperature of 25 °C for 30 s, then they will be heated to 95 °C for 2 minutes, next they will slowly be cooled to 25 °C at a rate of 0.2 °C/s, and last they will be kept at 25 °C for another 8 minutes. After passing this procedure which will take about 20 minutes the samples will be hybridized.
With respect to
2) Registration of absorption spectra
The optical cuvette has an optical path length of 3 mm. Prior to each use it needs to be thoroughly cleaned. Remove any remaining liquid from the cuvette using the micropipette set to a volume of ca. 80 μL and return it to the micro test tube. Then fill the cuvette with 100 μL double-distilled water (ddH2O). Clean the cuvette by repeated (three times) aspirating and dispensing of the pipette tip. Pour the water out and remove the remaining water from the bottom of the cuvette with the micropipette. Repeat this procedure three times with ddH2O and another three times with ethanol. After drying the cuvette with nitrogen it is ready to be refilled with the next sample. Take care when changing pipette tips in order not to contaminate or dilute the samples. Do not touch the optical surface of the cuvette with your fingers, and make sure you leave a small air bubble in the cuvette when applying the stopper. Try to avoid too many cleaning steps of the cuvette by taking absorption and fluorescence spectra of the same sample. Only the first dye containing sample you will have to prepare twice as you do not yet know the absorption maximum of the second dye that you need to know for the fluorescence measurements as the second excitation wavelength. Register the six absorption spectra as described in appendix 1 in the wavelength range from 200 nm to 750 nm. Do not use the automatic background correction, as manual background correction (and its discussion) will be part of the data analysis. Save the data on a memory stick or the like.
With respect to
3) Registration of fluorescence spectra
Determine the wavelengths λAA and λAD of the acceptor and donor absorption maxima from the double strands consisting of one naked and one dye labelled strands each. Use λAA and λAD as excitation wavelengths for the registration of fluorescence emission spectra for all three dye containing double strand solutions. .
Data analysis and discussion
1) Display the absorption spectra graphically. Perform the background correction for the absorption spectra of the dye containing double strands and display the background corrected spectra in the relevant wavelength range.
Determine the concentrations c of your samples. Use the Lambert-Beer law
with the decadic molar absorption coefficients
εD = 150000 M−1cm−1 for Cy3 (at 550 nm) and
εA = 250000 M−1cm−1 for Cy5 (at 650 nm).
Here, A is the absorbance,
ε is the decadic molar absorption coefficient,
s is the absorption path length,
c is the concentration,
It is the intensity of the transmitted radiation, and
I0 is the intensity of the incoming radiation.
Estimate the relative and absolute concentration of 1:1 (Cy3/Cy5) complexes.
2) Display the fluorescence spectra graphically. Determine the energy transfer efficiency. FDA and FD are integrated fluorescence intensities of the donor-naked hybrid and the donoracceptor hybrid. Comparing the amplitudes of the fluorescence spectra at their respective maxima yields an approximate value for the ratio FDA/FD, but is not exact enough since the two fluorescence spectra overlap. Suggest a better procedure for determining this ratio.
3) Evaluate the spectral overlap integral J. In the integral, the fluorescence spectrum of the donor needs to be normalized with respect to its area ,such that
This sum represents the overlap integral J. The unit of J is a length to the power of 6 per amount of substance, e.g. cm6/mol, L/(mol-cm3)-nm4, L/mol-cm3, or the like. Use the overlap integral to calculate the Forster radius r0. How much smaller would J be if the donor fluorescence spectrum and the acceptor absorption spectrum were shifted further apart by 50 nm? What would be the effect on the Forster radius and the energy transfer efficiency?
4) Estimate the distance rgeo between the two dyes of the donor acceptor pair from the geometry of the Cy3/Cy5 double strand. Use a value of 0.34 nm as the mean distance between two neighbouring base pairs. Then use the energy transfer efficiency E determined in 2) and the Forster radius r0 determined in 3) to obtain an experimental value for the distance between the two dyes. Discuss discrepancies. Instead of using the value of 0.34 nm per base pair one can also measure the distance for a known DNA structure using a visualization program such as VMD. Choose a suitable structure from the PDB protein data base and print a view where the start and end points of your distance measurements have been marked.
5) The DNA strands used could easily be labelled with Cy3 and Cy5 at other base pairs than the ones you have been working with. List expected energy transfer efficiencies for at least five other distances.