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The plasma cell in our body produces antibodies at a rate of 2000 molecules/s. How many picograms (pg) of antibodies can it produce per day?

Assume that each IgG heavy chain and light chain mRNA molecule can be used to initiate translation at a rate of 0.5/s and elongate at a rate of 10 amino acids/s. The heavy chain and light chain transcripts are 1000 bp and 500 bp, respectively.

Estimate the copy number of mRNAs for the heavy chain and light chain, and the transcription rate of the heavy chain and light chain genes. You can assume the half-life of IgG mRNAs is 2 hours. Note that the plasma cell has only one copy of functional heavy chain and light chain genes due to allele inactivation to prevent one cell from producing two different kinds of antibodies.

Answer :

To estimate the copy number of mRNAs for the heavy chain and light chain, we need to consider the transcription rate and the half-life of IgG mRNAs. The transcription rate can be calculated by dividing the rate of translation initiation (0.5/s) by the average time it takes to initiate translation, which is the inverse of the rate of translation initiation (1/0.5 = 2 s). Therefore, the transcription rate is 0.5/s / 2 s = 0.25 transcripts/s.

Assuming a half-life of 2 hours for IgG mRNAs, we can calculate the number of mRNAs at steady state by multiplying the transcription rate by the half-life. 0.25 transcripts/s * 2 hours * 3600 s/hour = 1800 transcripts.

Since each mRNA molecule corresponds to one antibody molecule, the copy number of mRNAs represents the number of antibody molecules produced. Therefore, the plasma cell can produce approximately 1800 molecules of antibody per day.

To estimate the amount of antibody produced in picograms (pg) per day, we need to know the molecular weight of an antibody molecule. Let's assume an average molecular weight of 150 kDa for IgG antibodies. This corresponds to 150,000 g/mol.

Given that Avogadro's number is approximately 6.022 × 10^23 molecules/mol, we can calculate the number of moles of antibody produced per day by dividing the number of molecules by Avogadro's number: 1800 molecules / 6.022 × 10^23 molecules/mol = 2.99 × 10^-21 moles.Finally, to convert moles to grams, we multiply by the molecular weight: 2.99 × 10^-21 moles * 150,000 g/mol = 4.48 × 10^-15 grams, which is equivalent to 4.48 pg.Therefore, the plasma cell can produce approximately 4.48 picograms of antibody per day.

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