A student is asked to find the number of molecules of a signalling protein present at…

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 The scales of life and the thermal energy

Problem

A student is asked to find the number of molecules of a signalling protein present at a concentration of 500 μM500\,\mathrm{\mu M} inside one Escherichia coli cell of volume 1 fL1\,\mathrm{fL}. Their working, copied exactly, is: "V=1 fL=1×10−15 LV = 1\,\mathrm{fL} = 1\times10^{-15}\,\mathrm{L}. Since 1 L=1 m31\,\mathrm{L} = 1\,\mathrm{m^3}, take V=1×10−15 m3V = 1\times10^{-15}\,\mathrm{m^3}. Concentration c=500 μM=0.5 mM=0.5 mol m−3c = 500\,\mathrm{\mu M} = 0.5\,\mathrm{mM} = 0.5\,\mathrm{mol\,m^{-3}}. Copy number n=cNAV=0.5×6.02×1023×1×10−15=3.0×108n = cN_AV = 0.5 \times 6.02\times10^{23} \times 1\times10^{-15} = 3.0\times10^{8} molecules." ((a)) Identify the error in this working. ((b)) Give the correct copy number.

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