A bar chart in a research paper reports the effective viscosity felt by three…

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

Life at Thermal Energy, Ch Random walks, diffusion and the crowded cell

Problem

A bar chart in a research paper reports the effective viscosity ηeff\eta_{\rm eff} felt by three different probes diffusing in Escherichia coli\textit{Escherichia coli} cytoplasm. These values were obtained by measuring each probe's diffusion coefficient DD in the cytoplasm and then reading off the viscosity that the Stokes-Einstein relation D=kBT/(6πηeffa)D = k_BT/(6\pi\eta_{\rm eff}a) would require, using each probe's known radius aa. The three bars are: a small metabolite, radius a=0.36 nma = 0.36\,\mathrm{nm}: ηeff=1.2 mPa s\eta_{\rm eff} = 1.2\,\mathrm{mPa\,s}green fluorescent protein (GFP), radius a=2.4 nma = 2.4\,\mathrm{nm}: ηeff=10 mPa s\eta_{\rm eff} = 10\,\mathrm{mPa\,s}a ribosome-sized complex, radius a=12 nma = 12\,\mathrm{nm}: ηeff=40 mPa s\eta_{\rm eff} = 40\,\mathrm{mPa\,s}Take kBT=4.11×10−21 Jk_BT = 4.11\times10^{-21}\,\mathrm{J} (298 K). ((a)) State, in words, the trend the chart shows and what it says about the common misconception that crowding slows every molecule by the same factor. ((b)) Using the chart's value of ηeff\eta_{\rm eff} for GFP, predict DD for GFP in cytoplasm from the Stokes-Einstein relation, and compare it with the measured value D=7.7×10−12 m2 s−1D = 7.7\times10^{-12}\,\mathrm{m^2\,s^{-1}} quoted for GFP in E. coli\textit{E. coli}.

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