Q.57 A protein has three identical sites arranged at the vertices of an equilateral triangle. If one site is filled with a dye (donor), the measured quantum yield (ϕD) is 0.5. Filling one site with a donor dye and a second site with an acceptor dye results in ϕD of 0.25. The measured ϕD of one site filled with donor and the other two sites filled with acceptor dye (rounded off to three decimal places) is ____________.
Three-Site Equilateral Triangle Dye Transfer Calculation
FRET Model Basics
Quantum yield ϕ_D equals the intrinsic yield times the fraction of excitations not transferred: ϕ_D = ϕ_0 × (1 - total transfer probability), where ϕ_0 = 0.5 from single-donor case. Transfer probability to one acceptor is β, so with one donor and one acceptor, ϕ_D = 0.5 × (1 – β) = 0.25, giving β = 0.5.
Two-Acceptor Calculation
With one donor and two acceptors, transfers are independent due to identical sites/distances: total transfer = β + β = 2β = 1.0. Thus, ϕ_D = 0.5 × (1 – 1.0) = 0.000 (exact; rounded to three decimals as 0.000).
GATE Biotechnology 2023 Question Context
This GATE Biotechnology 2023 question tests FRET quenching in multi-site protein labeling, key for quantum yield protein dye interactions and spectroscopy. Students preparing for IIT JAM or CSIR NET often encounter such problems on fluorescence resonance energy transfer (FRET) in biomolecules.
Core Concept: FRET in Symmetric Sites
In an equilateral triangle setup, donor-acceptor distances are equal, so transfer efficiency β is identical pairwise. Single donor ϕ_D = 0.5 sets baseline ϕ_0. Donor + one acceptor drops to 0.25, confirming β = 0.5 via ϕ_D = ϕ_0 (1 – β).
For donor + two acceptors, no transfer overlap assumed (common in such models), total quenching = 2β = 1, so ϕ_D = 0.
Step-by-Step Solution
- Intrinsic yield: ϕ_0 = 0.5
- One acceptor: 0.5(1 – β) = 0.25 → β = 0.5
- Two acceptors: 0.5(1 – 2×0.5) = 0.000
No options given (numerical answer type); value is 0.000.
Exam Relevance
Perfect for quantum yield measurement in competitive biotech exams—practice similar FRET efficiency calculations for GATE BT, IIT JAM, CSIR NET preparation.
