1. Cell sizes. To appreciate the differences in cell size, consider the following specific examples. Escherichia coli, a typical bacterial cell, is cylindrical in shape, with a diameter of about 1 Ám and a length of about 2 Ám. As a typical animal cell, consider a human liver cell, which is roughly spherical in shape and has a diameter of about 20 Ám. And for a typical plant cell, consider the columnar palisade cells located just beneath the upper surface of many plants. These are cylindrical in shape, with a diameter of about 20 Ám and a length of about 35 Ám.
(A) Calculate the approximate volume of each of these three cell types in cubic micrometers. (Recall that V = pr2h for a cylinder and that V = 4pr3/3 for a sphere.)
(B) Approximately how many bacterial cells would fit in the internal volume of a human liver cell?
(C) Approximately how many liver cells would fit inside a palisade cell?
2. To get some feeling for the differences in size of various cellular structures, it is useful to compare the structures on a macroscopic scale. Listed below is a variety of structures, with their approximate dimensions. To compare their dimensions on a macroscopic scale, assume that each structure has been magnified a million-fold, using a scale such that 1 nm is represented by 1 mm. On this scale, a prokaryotic ribosome has a diameter of 25 mm, and is therefore the size of a large marble. Convert each of the other dimensions to this macroscopic scale, and suggest a physical object that has approximately the same dimensions.
1. Eukaryotic ribosome (Where proteins are made): 30 nm
2. Mitochondrion (Where chemical energy is released): 1 x 2 Ám
3. Chloroplast (Which traps light energy): 2 x 8 Ám
4. Nucleus (Control center of the cell): 6 Ám in diameter
5. Liver cell: 20 Ám in diameter
6. Chicken egg: 4 x 6 cm
7. Human being: 1.8 m tall
3. On the same macroscopic scale as in question 2, what would be the dimensions of the following?
(A) a typical cell membrane: 8 nm wide
(B) the thickness of Glad wrap: 10 Ám
4. What would be the dimensions E. coli and the palisade cell in question 1, if they were placed on the same macroscopic scale as the cell structures in question 2 (i.e., if they were magnified a million-fold)?
5. How many cell membranes would have to be aligned side by side before the structure could be seen with the light microscope? How many with the electron microscope? (Assume a typical membrane to be about 8 nm wide.) (The limit of resolution for a light microscope is 200 nm and for an electron microscope 0.1-0.2 nm.)