Fluorescence correlation spectroscopy (FCS) on a fluorescently tagged cytoplasmic protein
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Biophysics & Medical Physics · Physical foundations of the living cell
Forces, Machines and Signals, Ch Diffusion: friction, capture and the crowded cytoplasm
Problem
Fluorescence correlation spectroscopy (FCS) on a fluorescently tagged cytoplasmic protein, with a correlation time of 1ms, reports D=2.5μm2s−1. Fluorescence recovery after photobleaching (FRAP) on the same protein, with a recovery time of 1s, reports D=0.5μm2s−1. A researcher argues: "since the two methods disagree by a factor of five, the protein must exist as two distinct populations, each diffusing normally, a fast free pool and a slow bound pool, and FCS and FRAP are simply weighting the two pools differently."
((a)) Assuming instead that the protein undergoes anomalous subdiffusion, ⟨r2⟩∝tα, with a single exponent α, and that each method reports the apparent diffusion coefficient D(t)∝tα−1 evaluated at its own characteristic time, find the value of α consistent with the two measurements.
((b)) State whether the two-population explanation is required by the data, given this value of α.