Shortcut Methods and Tricks to Solve Numerical Problems in Biotechnology

1. DNA Replication:

• To calculate the minimum number of nucleotides that must be added during one round of replication to synthesize two molecules of DNA, you can use the formula:

Minimum number of nucleotides = (Length of DNA molecule) x (Number of new strands)

• In this case, the length of the DNA molecule is 100,000 base pairs, and we need to synthesize two new strands. Therefore, the minimum number of nucleotides required is:

Minimum number of nucleotides = (100,000 base pairs) x (2 strands) = 200,000 nucleotides

2. Gene Expression:

• To determine the number of amino acids produced from the translation of a gene, you can use the formula:

Number of amino acids = (Length of coding region) / 3

• In this case, the length of the coding region is 1,500 nucleotides. Since there are three nucleotides per codon, which codes for one amino acid, we can calculate the number of amino acids as follows:

Number of amino acids = (1,500 nucleotides) / 3 = 500 amino acids

3. Transcription:

• To find the number of mRNA molecules produced in an E. coli cell if each of its 4,000 genes is transcribed into a single mRNA molecule, you can simply multiply the number of genes by 1:

Number of mRNA molecules = (Number of genes) x (1 mRNA molecule per gene)

• Therefore, the number of mRNA molecules produced will be:

Number of mRNA molecules = (4,000 genes) x (1 mRNA molecule per gene) = 4,000 mRNA molecules

4. Translation:

• To determine the time required for a ribosome to translate a protein that is 500 amino acids long, you can use the formula:

Translation time = (Protein length) / (Translation rate)

• Given the average translation rate in prokaryotic cells is 20 amino acids per second, and the protein is 500 amino acids long, the translation time can be calculated as:

Translation time = (500 amino acids) / (20 amino acids/second) = 25 seconds

5. DNA Restriction Enzymes:

• To calculate the number of recombinant DNA molecules formed when a vector DNA of 5,000 base pairs is ligated with restriction fragments of an average size of 1,000 base pairs, you can use the formula:

Number of recombinant DNA molecules = (Vector DNA size) / (Fragment size)

• Therefore, the number of recombinant DNA molecules formed will be:

Number of recombinant DNA molecules = (5,000 base pairs) / (1,000 base pairs) = 5 recombinant DNA molecules

6. PCR (Polymerase Chain Reaction):

• To determine the total amount of DNA after 30 cycles of PCR, you can use the formula:

Total DNA amount = (Initial DNA amount) x (2^Number of cycles)

• Given the initial DNA amount is 0.1 ng and there are 30 cycles of PCR, the total DNA amount can be calculated as:

Total DNA amount = (0.1 ng) x (2^30) = 1.07 x 10^9 ng

7. Protein Purification:

• To calculate the purification yield, you can use the formula:

Purification yield = (Final protein yield) / (Starting material)

• In this case, the starting material is 100 mg of crude cell extract, and the final yield of the purified protein is 10 mg. Therefore, the purification yield is:

Purification yield = (10 mg) / (100 mg) = 0.1 or 10%

8. Electrophoresis:

• To determine the apparent mobility of DNA fragments in electrophoresis, you can divide the distance migrated by the time taken for migration:

Apparent mobility = (Distance migrated) / (Time taken)

• Given that the DNA fragments migrate 10 cm in a 2-hour electrophoresis on a 20 cm gel, the apparent mobility is:

Apparent mobility = (10 cm) / (2 hours) = 5 cm/h

9. Southern Blot Hybridization:

• To find the number of probe molecules bound to each DNA fragment during Southern blot hybridization, you can use the following calculation:

Number of probe molecules per fragment = (Probe size) / (Average fragment size)

• In this case, the probe size is 500 nucleotides, and the average fragment size is 1,000 base pairs. Therefore, the number of probe molecules bound to each DNA fragment is:

Number of probe molecules per fragment = (500 nucleotides) / (1,000 base pairs) = 0.5 probe molecules

10. Northern Blot Hybridization:

• To determine the number of probe molecules bound to each mRNA molecule during Northern blot hybridization, you can calculate:

Number of probe molecules per mRNA = (Probe size) / (mRNA region complementary to probe)

• Since the probe is complementary to a 1,500-nucleotide region of the mRNA, and the probe size is 500 nucleotides, the number of probe molecules bound to each mRNA molecule is:

Number of probe molecules per mRNA = (500 nucleotides) / (1,500 nucleotides) = 0.33 probe molecules