The inside of a cell is extremely crowded. We will try to gainsome insight for exactly how crowded by considering some numbersthat are estimates of the situation in the common bacterium E.coli. One can estimate the total number of proteins present ina cell in several ways. For example, one can measure the dry massof a cell (the amount of material left once the cell is dried out),analyze the composition to determine what fraction is amino acids,estimate the average molecular weight of a protein, and use allthese numbers to calculate the total number of protein moleculespresent. Alternatively, one can use experimental analysis todetermine the approximate amount of proteins present in a sampleconsisting of a known number of cells. All of these methods agreethat a typical E. coli bacterial cell contains about 3 x106 proteins.
a) We can estimate the volume of an E. colicell to be about 1 µm3, that is, equivalent to a cube of1 µm on each side. Convert that volume to liters, and assumingthere are 3 x 106 total proteins present, calculate thetotal molar concentration of proteins contained in a bacterialcell.
b) Take the reciprocal of the molarconcentration obtained in part a, and convert units to find thenumber of cubic nanometers per protein molecule.
c) One way to think about the volume perprotein molecule found in part b is that if you divided up thetotal volume of the cell into tiny cubes, with each cube having thevolume found in part b, then on averge, each cube would contain oneprotein. The length of each side of one of these cubes would justbe the cube root of the volume per protein molecule. Further, thelength of each side of the cube is an estimate of thecenter-to-center separation distance of each protein molecule. Fromthe volume per protein obtained in part b, use this approach toestimate the center-to-center distance between protein molecules(on average) in an E. coli cell.
d) Averaged across a cell's inventory ofproteins, the average protein molecular weight is about 30000 gramsper mole (i.e., 30 kiloDaltons). For proteins, an average massdensity is found of about 1.4 g/cm3. Use these numbers,after appropriate unit conversions, to calculate the average volumeof a protein molecule in cubic nanometers. Compare this number tothe value obtained in part b, and estimate what fraction of thetotal volume of a cell is filled with proteins.
