Colloidal quantum dots (QDs) conjugated to antibodies are used to fluorescently tag cell-surface or intracellular biomarker proteins for microscopy, because their inorganic semiconductor core resists photobleaching far longer than organic dyes. But single QDs exhibit photoluminescence intermittency ("blinking"): under continuous excitation each dot randomly switches between bright (ON) and dark (OFF) states, with dwell-time durations that follow a truncated power law rather than exponential (Poisson) statistics:
P(τ_on) ∝ τ_on^(−α) for τ_min ≤ τ_on ≤ τ_max
P(τ_off) ∝ τ_off^(−α) for τ_min ≤ τ_off ≤ τ_max
This is generated per instance by inverse-transform sampling of the truncated power law:
u ~ Uniform(0,1)
τ = ( τ_min^(1−α) + u·(τ_max^(1−α) − τ_min^(1−α)) )^(1/(1−α))
A steeper exponent α produces mostly short dwell times (rapid flicker); a shallower α allows rare, very long ON or OFF excursions — the long-tailed behaviour that distinguishes QD blinking from simple dye photophysics. Meanwhile the organic-dye control population decays smoothly and irreversibly by photobleaching:
I_dye(t) = I₀ · exp(−k·I_exc·t)
- Excitation intensity — scales the dye photobleaching rate constant and overall emitted brightness of both populations.
- Blink exponent α — reshapes the QD on/off dwell-time power law; higher α ⇒ shorter, more frequent switches.
- Biomarker density — number of labeled receptor sites rendered on the simulated membrane patch.
- Time acceleration — compresses a multi-second imaging session into a few seconds of playback.
Real-world relevance: this trade-off — QD photostability vs. blinking-induced signal gaps — governs single-molecule tracking and long-term biomarker imaging protocols, where blinking can be mitigated by shell engineering (e.g. thick-shell "giant" QDs) or software gap-bridging, while photobleaching sets the practical imaging duration for conventional dyes.