One of the most important aspects of understanding cell biology is to appreciate the scale of the cell. The following problems are geared to start developing this sense of scale. You should not need a calculator to solve them. Use scientific notation and round the answers up to 2 significant digits, i.e.. round 3.1415 to 3.1 or 5.03x10¹¹ to 5.0x10¹¹.
Hint - convert the starting units to match the final units and always follow the units through the equation.
1. A typical cell is 10 µm across. For simplicity, let's assume that the cell is a cube. A phospholipid is composed of a glycerol (C₃(H₂O)₃) head group with two fatty acid tails and a phosphate containing polar group. Assuming that the cross sectional area of the phospholipid is the same as the rectangular shape of three 3 carbon >C< connected by single bonds. Carbon >C< has a diameter D of 0.2 nm and a single bond is 0.15 nm in length. How many phospholipid molecules would make up the lipid bilayer that covers our typical 10 µm cell?
2. A typical cell is 10 µm across. For simplicity, let's assume that the cell is a cube. If 72% of the mass of the cell is water H₂O and the density of the cell is 1 g/cm³ (the same as water), how many moles of water are in a cell? How many molecules of water H₂O is this? If the pH of the cytoplasm is 7.0, how many H₃O⁺ ions are there in the cell?
3. A typical cell is 10 µm across. For simplicity, let's assume that the cell is a cube. The protein concentration C in a cell is about 20 mg/ml. If the molecular weight of a average protein is 50,000 Daltons, how many protein molecules are there in a typical cell?
4. The average protein is 50,000 Daltons. The average molecular weight of an amino acid is 110 Daltons. How many amino acids are there in an average protein? How long would the mRNA that encodes the average protein have to be? (Assuming that there is no un-translated RNA at the ends of the mRNA.) If the human genome is 3x10⁹ nucleotides long, how many genes can we theoretically encode? A newt has 3x10¹⁰ nucleotides per genome and the lily has almost 10¹¹ nucleotides per genome. Why do we observe this apparent discrepancy in genome size? Explain your answer.
5.Double-stranded DNA has a diameter of 2 nm. Each turn of the helix is 3.4 nm in length and requires 10 base pairs. The human genome is 3x10⁹ base pairs long distributed over 22 autosomal chromosomes and one 1 sex chromosome. Since most cells are diploid (there are two 2 copies of the genome), there are a total of 44 autosomal and 2 sex chromosomes. This is true for all cells, except the germ cells, such as eggs and sperm. How long (in mm) would the chromosomal DNA in a germ cell be if it was stretched out. What size cube (in µm) could you pack all the DNA of a diploid cell into? Is it possible to pack all this DNA into this space?