Final answer:
About 780,751 times for EcoRI and about 12,500,000 times for FatI. Average fragment size is 4090 base pairs for EcoRI and 255 base pairs for FatI.
Step-by-step explanation:
In a human DNA molecule, about 60% of the base pairs are AT. If the human genome has 3.2 billion base pairs of DNA, we can calculate the number of times the specified restriction sites will be present.
The restriction site for EcoRI is 5’ GAATTC 3’ which means that the enzyme cuts between the G and the A in the sequence. The recognition sequence GAATTC occurs once every 4096 base pairs (6 nucleotides x 4 possibilities). Therefore, in a 3.2 billion base pair DNA molecule, the EcoRI restriction site will be present approximately 780,751 times (3,200,000,000 / 4096).
The restriction site for FatI is 5’ CATG 3’ which means that the enzyme cuts between the A and the T in the sequence. The recognition sequence CATG occurs once every 256 base pairs (4 nucleotides x 4 possibilities). Therefore, in a 3.2 billion base pair DNA molecule, the FatI restriction site will be present approximately 12,500,000 times (3,200,000,000 / 256).
The average size of DNA fragments after cutting with a restriction enzyme can be calculated by subtracting the size of the recognition sequence from the size of the DNA molecule. For EcoRI, the average fragment size will be 4096 base pairs (4096 - 6 = 4090). For FatI, the average fragment size will be 255 base pairs (256 - 1 = 255).