What is the molecular weight of an mRNA that codes for the protein of molecular weight 75,000 kDa? (Assume the molecular weight of an amino acid residue is 120 Da)
The correct answer and explanation is:
Let’s analyze the problem step-by-step:
Given:
- Protein molecular weight (MW) = 75,000 kDa
- Molecular weight of an amino acid residue = 120 Da
- Want: Molecular weight of the mRNA coding for this protein
Step 1: Understand units and convert if necessary
- 1 kDa (kilodalton) = 1000 Da (daltons)
- Protein MW = 75,000 kDa = 75,000 × 1000 = 75,000,000 Da
Step 2: Calculate the number of amino acids in the protein
Since each amino acid residue weighs about 120 Da: Number of amino acids=Protein MW in DaMW per amino acid residue=75,000,000 Da120 Da/residue=625,000 residues\text{Number of amino acids} = \frac{\text{Protein MW in Da}}{\text{MW per amino acid residue}} = \frac{75,000,000 \text{ Da}}{120 \text{ Da/residue}} = 625,000 \text{ residues}
Step 3: Calculate the length of the mRNA (in nucleotides)
- Each amino acid is coded by 3 nucleotides (a codon) in mRNA.
Number of nucleotides=625,000×3=1,875,000 nucleotides\text{Number of nucleotides} = 625,000 \times 3 = 1,875,000 \text{ nucleotides}
Step 4: Calculate the molecular weight of the mRNA
- Average molecular weight of a nucleotide in RNA is about 330 Da (this includes the ribose sugar, phosphate group, and base).
MW of mRNA=number of nucleotides×MW per nucleotide=1,875,000×330=618,750,000 Da\text{MW of mRNA} = \text{number of nucleotides} \times \text{MW per nucleotide} = 1,875,000 \times 330 = 618,750,000 \text{ Da}
Step 5: Convert the mRNA molecular weight into kDa
618,750,000 Da=618,750,0001000=618,750 kDa618,750,000 \text{ Da} = \frac{618,750,000}{1000} = 618,750 \text{ kDa}
Final answer:
The molecular weight of the mRNA is approximately 618,750 kDa.
Explanation (about 300 words):
Proteins are polymers made of amino acids, and the molecular weight of a protein depends on the number of amino acid residues it contains and the average weight of each residue. Here, the protein has a molecular weight of 75,000 kDa, which is extremely large (typical proteins are usually in the tens or hundreds of kDa range, so this is a hypothetical large protein).
First, converting 75,000 kDa into daltons (Da) gives 75 million daltons. Given that each amino acid weighs about 120 Da, dividing the total protein mass by 120 gives the number of amino acids in the protein chain. This yields 625,000 amino acids — a very large polypeptide.
Each amino acid in a protein is encoded by a sequence of three nucleotides (a codon) on the messenger RNA (mRNA). Therefore, the length of the mRNA sequence required to code for this protein is three times the number of amino acids, equaling 1,875,000 nucleotides.
Next, to find the molecular weight of the mRNA, we use the average molecular weight of a single nucleotide, which is about 330 Da. This accounts for the nitrogenous base, sugar, and phosphate group. Multiplying the total number of nucleotides by 330 Da gives the total mass of the mRNA.
Converting back to kilodaltons for ease of comparison gives about 618,750 kDa, which is roughly 8 times larger than the protein molecular weight. This makes sense because nucleotides are smaller individually than amino acids, but there are three nucleotides per amino acid, and the overall weight accumulates accordingly.
Thus, the mRNA molecule coding for this large protein would have an enormous molecular weight of approximately 618,750 kDa.