Thanks a lot for your insightful comment. I think you are right that there're errors in my calculations. Based on your comment, the correct calculations should be:
- Step 2: The blood contains about 10⁷ B-cells per mL of blood at any time, which can produce antibodies up to a concentration of 100,000 ng/ml, capable of neutralizing 10⁴ antigens.
- Step 3: Each vaccine may have up to about 100 antigens. This means that an infant can respond to 100 vaccines -- calculated by dividing 10⁴ antigens capable of being neutralized by 10² antigens per vaccine -- at any time.
- Step 4: But to be conservative, each antigen typically has 10 epitopes. Epitopes are parts of the antigen that the antibody can bind to. Each vaccine, thus, has 100*10 = 10³ epitopes. This means an infant can still respond to 10 vaccines at any time.
- Step 5: Therefore, if 5 vaccine shots were administered at a single visit, it would use up half of the immune system at a given time.
But I am still conflicted about the calculations because they arrived at a different conclusion than Offit et al., who wrote:
"""
If we assume that 1) approximately 10 ng/mL of antibody is likely to be an effective concentration of antibody per epitope (an immunologically distinct region of a protein or polysaccharide), 2) generation of 10 ng/mL requires approximately 10^3 B-cells per mL, 3) a single B-cell clone takes about 1 week to reach the 10^3 progeny B-cells required to secrete 10 ng/mL of antibody (therefore, vaccine-epitope-specific immune responses found about 1 week after immunization can be generated initially from a single B-cell clone per mL), 4) each vaccine contains approximately 100 antigens and 10 epitopes per antigen (ie, 10^3 epitopes), and 5) approximately 10^7 B-cells are present per mL of circulating blood, then each infant would have the theoretical capacity to respond to about 10 000 vaccines at any one time (obtained by dividing 10^7 B cells per mL by 10^3 epitopes per vaccine).
"""
I think Offit et al. used B-cell clones as the numerator and vaccine antigens as the denominator. But I'm not sure if B-cell and B-cell clone concentrations are the same. I think I need more time to read about this. But if you have any comments, I'd love to hear it, thanks again and my apologies for the long response.
