Förster Radius Calculator

A Förster Radius Calculator is a scientific tool used in biochemistry, biophysics, and materials science to determine a critical distance for a phenomenon called Förster Resonance Energy Transfer (FRET). FRET is a process where energy is transferred non-radiatively (without light) from an excited "donor" molecule to a nearby "acceptor" molecule. The Förster radius, designated as R₀, is the specific distance between a donor and an acceptor at which this energy transfer process is 50% efficient. By calculating R₀, scientists can use FRET as a "molecular ruler" to measure nanometer-scale distances and conformational changes within proteins, DNA, and other macromolecules, providing invaluable insights into biological processes.

The Förster Radius Calculator Formula Explained

The Förster radius (R₀) is determine by the spectral properties of the donor and acceptor molecules and the environment they are in. The calculation is based on Förster's theory.

First, an intermediate value is calculated:
R₀⁶ = (8.79 × 10⁻²³) × κ² × QD × J / n⁴

Then, you take the sixth root to find R₀:
R₀ = [(8.79 × 10⁻²³ × κ² × QD × J) / n⁴]^(1/6)

Key Variables

• R₀: The Förster radius in centimeters (cm). This result is almost always converted to nanometers (nm) or angstroms (Å) for practical use.
• κ² (kappa squared): The orientation factor. It describes the relative orientation in space between the donor and acceptor dipoles.
• QD: The quantum yield of the donor fluorophore. This is a dimensionless number between 0 and 1 that represents the efficiency of the donor's fluorescence process.
• J: The spectral overlap integral. This value quantifies the degree of overlap between the donor's emission spectrum and the acceptor's absorption spectrum, measured in units of M⁻¹ cm⁻¹ nm⁴.
• n: The refractive index of the medium separating the donor and acceptor.

Typical Values for Förster Radius Calculator

This table provides common values and ranges for the parameters used in the R₀ calculation, which can help in setting up an experiment or verifying results.

How to Calculate the Förster Radius: A Practical Example

Let's calculate R₀ for a common FRET pair, Cy3 (donor) and Cy5 (acceptor), under typical biological conditions.

Step 1: Gather the known parameters.

• Orientation Factor (κ²): We assume the molecules are randomly orient in solution, so κ² = 2/3.
• Donor Quantum Yield (QD): The quantum yield for Cy3 is approximately 0.3.
• Spectral Overlap Integral (J): For the Cy3-Cy5 pair, a typical literature value is J = 9.8 × 10¹⁴ M⁻¹cm⁻¹nm⁴.
• Refractive Index (n): The experiment is in an aqueous buffer, so we use n = 1.33.

Step 2: Calculate the R₀⁶ term.
R₀⁶ = (8.79 × 10⁻²³) × (2/3) × 0.3 × (9.8 × 10¹⁴) / (1.33)⁴
R₀⁶ = (1.72 × 10⁻⁸) / 3.11 ≈ 5.53 × 10⁻⁹ cm⁶

Step 3: Calculate R₀ by taking the sixth root.
R₀ = (5.53 × 10⁻⁹)^(1/6)
R₀ ≈ 0.000053 cm

Step 4: Convert the result to a more useful unit.
Since 1 cm = 10⁷ nm, we convert the result to nanometers.
R₀ = 0.000053 cm × (10⁷ nm / 1 cm)
R₀ ≈ 53 nm

Therefore, the Förster radius for this Cy3-Cy5 pair under these conditions is approximately 53 nm.

Frequently Asked Questions (FAQs)