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Exponential Decay

The mathematical function describing how fluorescence intensity decreases over time after excitation.

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Definition
After pulsed excitation, a population of identical fluorophoresLoading... exhibits exponential intensity decay: I(t) = I0 × e-t/τ. The time constant τ (fluorescence lifetimeLoading...) is the time at which intensity reaches 1/e (~37%) of its initial value. FRETLoading... causes the donor decay to accelerate (shorter τ), providing the physical basis for quantitative interaction measurement.
I(t) = I₀ × e^(-t/τ)
Fundamental decay equation
τ = 1/e time
37% remaining intensity
Multi-exponential
Complex samples have multiple components
FRET shortens τ
Faster decay = energy transfer

Understanding Decay Curves

Fluorescence decay reflects the statistical nature of excited state relaxation. Each fluorophore has a probability of emitting at any moment, leading to exponential population decay.

Visualizing the decay curve reveals:

  • Faster decay (steep curve) = shorter lifetime = FRET occurring
  • Slower decay (gradual curve) = longer lifetime = no FRET
  • Multiple slopes = multiple populations with different lifetimes

TCSPCLoading... instruments measure these nanosecond-scale decays by building histograms of photon arrival times.

Simplified

What It Shows: After you excite a fluorophore, it glows and then fades. The decay curve shows how fast it fades.

FRET Connection: If FRET is happening, the donor fades faster because energy is leaving through a second pathway (transfer to acceptor).

Analysis Approaches

Two main approaches extract lifetime from decay data:

Curve Fitting: Fit the decay to I(t) = ΣAie-t/τi to extract lifetime components. Requires assumptions about number of components.
Phasor AnalysisLoading...: Transform decay to frequency domain, mapping to a point on the phasor plot. Position reveals lifetime without fitting. Points inside the semicircle indicate multi-exponential decay.

Both approaches quantify the same underlying physics—the rate of excited state decay—using different mathematical frameworks.

Simplified

How to Analyze: Two approaches:

  1. Fit an exponential curve to the data (traditional)
  2. Transform to phasor coordinates (modern, fit-free)

Both give you the lifetime, just using different math.

Clinical Relevance

  • Quantitative FRET: Lifetime change from exponential decay analysis enables numerical FRET efficiency calculation
  • Fit-free methods: Phasor analysis bypasses fitting artifacts for robust clinical applications
  • Multi-component resolution: Separates bound vs unbound populations in heterogeneous tissue
  • QF-Pro foundation: All FLIM-FRET measurements ultimately derive from exponential decay analysis

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