Question

In bacteria, a ribosome synthesizes a protein containing 300 amino acids from mRNA in 20 seconds. If the average lifetime of an mRNA is 2 minutes, the number of ribosomes that can translate a single mRNA containing 1350 nucleotides is .............

Hint:

To estimate ribosome loading, divide mRNA length by ribosome footprint (≈75 nt).

Answer 1

Correct Answer: 4

Step 1: Determine translation speed. 
300 amino acids are synthesized in 20 s. 
Thus, ribosome speed = \[ \frac{300\ \text{aa}}{20\ \text{s}} = 15\ \text{aa/s} \] Step 2: Estimate protein length from nucleotide count. 
1350 nucleotides = \[ \frac{1350}{3} = 450\ \text{codons (amino acids)} \] Step 3: Time required to translate one protein. 
\[ t = \frac{450\ \text{aa}}{15\ \text{aa/s}} = 30\ \text{s} \] Step 4: mRNA lifetime. 
mRNA lifetime = 2 minutes = 120 seconds. 
Step 5: Number of ribosomes translating simultaneously. 
In bacteria, ribosomes initiate one after another during translation. Number of ribosomes = \[ \frac{120\ \text{s}}{30\ \text{s}} = 4 \] Step 6: Consider ribosome spacing. 
Length of coding region = 1350 nt. One ribosome occupies ~75 nt. Maximum packing: \[ \frac{1350}{75} = 18\ \text{ribosomes} \] Step 7: Conclusion. 
Thus, a maximum of 18 ribosomes can translate the mRNA.