A small signalling molecule of radius diffuses in water

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 small signalling molecule of radius a=0.50 nma = 0.50\,\mathrm{nm} diffuses in water. Use kBT=4.11 pN nmk_BT = 4.11\,\mathrm{pN\,nm} and η=0.89 mPa s\eta = 0.89\,\mathrm{mPa\,s} at 25∘C25^\circ\mathrm{C}, and kBT=4.28 pN nmk_BT = 4.28\,\mathrm{pN\,nm} and η=0.69 mPa s\eta = 0.69\,\mathrm{mPa\,s} at human body temperature, 37∘C37^\circ\mathrm{C}. ((a)) Predict DD at 25∘C25^\circ\mathrm{C} and at 37∘C37^\circ\mathrm{C}. ((b)) Predict the time for the molecule to diffuse 10 μm10\,\mathrm{\mu m} at each temperature, treating the crossing as one-dimensional. ((c)) By what factor does raising the temperature from 25∘C25^\circ\mathrm{C} to 37∘C37^\circ\mathrm{C} speed up this crossing?

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