Question

In a FRET experiment designed to monitor conformational changes in T4 lysozyme, the fluorescence intensity fluctuates between 5000 and 10,000 counts per second. Assuming that 7500 counts represents a FRET efficiency of \(0.5,\) what is the change in FRET pair separation distance during the reaction? For the tetramethylrhodamine/texas red FRET pair employed \(r_{0}=50 . \AA\)

Short answer

Given a range of fluorescence intensities from a FRET experiment monitoring conformational changes in T4 lysozyme, determine the change in FRET pair separation distance during the reaction if the FRET efficiency is 0.5 at 7500 counts and the Förster distance (𝑟₀) is 50 Å.

Step-by-step solution

Calculate the FRET efficiencies at other intensity values

Calculate the FRET efficiency at both ends of the intensity range, 5000 and 10000 counts. We can use the ratio of the counts to estimate the corresponding FRET efficiencies. For 5000 counts: \[ E_1 = \frac{5000}{7500} \cdot 0.5 \] For 10000 counts: \[ E_2 = \frac{10000}{7500} \cdot 0.5 \] Calculate \(E_1\) and \(E_2\):

Calculate separation distances at each FRET efficiency

Using the formula for FRET efficiency (\(E\)) and the given \(r_0 = 50 \AA\), calculate the separation distances (\(r\)) at each FRET efficiency: \[ E = 1 - \frac{1}{(1 + (\frac{r}{r_0})^6)} \] Solve for \(r_1\) and \(r_2\) at each FRET efficiency: For \(E_1\): \[ r_1 = r_0\sqrt[6]{\frac{1}{1 - E_1} - 1} \] For \(E_2\): \[ r_2 = r_0\sqrt[6]{\frac{1}{1 - E_2} - 1} \] Calculate \(r_1\) and \(r_2\):

Find the change in FRET pair separation distance

Finally, we can calculate the change in FRET pair separation distance during the reaction as the difference between the separation distances at both FRET efficiencies: \[ \Delta r = r_2 - r_1 \] Calculate \(\Delta r\):

Key concepts

Förster Resonance Energy Transfer

Förster Resonance Energy Transfer (FRET) is a powerful technique used to investigate proximity between two molecules, often within the range of 1 to 10 nanometers. It relies on the non-radiative energy transfer from a donor molecule, which is excited by an external light source, to an acceptor molecule within its proximity. The efficiency of this energy transfer (\(E\)) is highly sensitive to the distance between the two molecules, making FRET a useful tool for probing molecular interactions such as protein conformational changes.

The basic principle behind FRET is that the donor molecule, usually a fluorescent dye, absorbs a photon and reaches an excited state. Instead of releasing the energy as emitted light, it transfers the energy to the nearby acceptor molecule, if it lies within a certain critical distance known as the Förster radius or \(r_0\). The acceptor molecule can then emit fluorescence at a longer wavelength, which can be measured. Dyes or proteins with intrinsic fluorescence properties can be used as donors and acceptors in these experiments.

Fluorescence Intensity

In the context of FRET, fluorescence intensity is a crucial measurement that reflects the amount of emitted light from the acceptor fluorophore upon energy transfer from the donor. Intensity fluctuations can indicate changes in distance between the donor and acceptor molecules. For instance, as molecules move closer together, the fluorescence intensity typically increases due to higher FRET efficiency, and conversely, the intensity drops when they move further apart.

Quantifying fluorescence intensity provides valuable information on the molecular environment and is especially important in calibrating FRET experiments. It can help in determining the FRET efficiencies (\(E\)) by comparing the measured intensities to known standards or reference measurements. For example, in the exercise provided, a known FRET efficiency corresponding to a specific fluorescence intensity allows us to estimate the efficiencies at other intensities.

Protein Conformational Changes

Proteins are dynamic entities that undergo conformational changes as part of their biological function. These changes can involve shifts in the protein's secondary, tertiary, or quaternary structures and are essential for processes such as enzyme catalysis, signal transduction, and molecular recognition.

Monitoring conformational changes in proteins is crucial for understanding their function and interaction with other molecules. FRET is particularly well-suited for this purpose as it can detect changes in the distance between specific parts of a protein or between the protein and a binding partner. By labeling strategic sites on the protein with a FRET pair—a donor and an acceptor—the distance-dependent changes in energy transfer can reveal significant insights into the protein's structural dynamics during different biological processes.

FRET Pair Separation Distance

The separation distance between the donor and acceptor in a FRET experiment, often denoted as \(r\), is a key determinant of the energy transfer efficiency. As the separation distance changes, usually due to molecular movements or conformational alterations, the efficiency of energy transfer between the FRET pair also changes. This dependence of energy transfer on \(r\) allows researchers to calculate the physical distance between donor and acceptor molecules using the FRET efficiency values.

Typically, using the known Förster radius (\(r_0\)) and the measure of FRET efficiency, researchers can apply the FRET efficiency formula to calculate the separation distance between the FRET pair. A high FRET efficiency suggests that the molecules are close, within the Förster radius, while a low efficiency indicates a larger separation distance. By measuring how the separation distance changes, for example during a biochemical reaction, researchers can quantify the magnitude and dynamics of molecular interactions or conformational shifts.