A single quantum-dot-labelled receptor is tracked diffusing in a cell membrane; its…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Biophysics & Medical Physics · Physical foundations of the living cell

Forces, Machines and Signals, Ch Diffusion: friction, capture and the crowded cytoplasm

Problem

A single quantum-dot-labelled receptor is tracked diffusing in a cell membrane; its one-axis mean square displacement is measured at three lag times. Data: t=0.10 st=0.10\,\mathrm{s}, ⟨x2⟩=0.040 μm2\langle x^2\rangle=0.040\,\mathrm{\mu m^2}; t=1.0 st=1.0\,\mathrm{s}, ⟨x2⟩=0.40 μm2\langle x^2\rangle=0.40\,\mathrm{\mu m^2}; t=10 st=10\,\mathrm{s}, ⟨x2⟩=4.0 μm2\langle x^2\rangle=4.0\,\mathrm{\mu m^2}. ((a)) Find the anomalous exponent α\alpha from the log-log slope between the extreme points, and check the middle point against it. ((b)) Compute the apparent diffusion coefficient at each of the three lag times and comment on what you find. ((c)) State whether this receptor's motion is anomalous, and name one single-particle-tracking artefact that could push a fitted α\alpha slightly below 11 even for an ordinarily diffusing receptor.

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