Question

Calculate the frequency of b cells specific for antigen a on day 36 if the antibody concentration on day 36 is about 8 × 103. (for practice doing calculations with proportions, try this exercise. for practice doing calculations with numbers written in scientific notation, try this exercise.)

Answer 1

-The number of B cells producing the antibody is proportional to the concentration of that antibody.

-On day 16, one out of  100000 B cells are specific for antigen A
\frac{1}{100000} = 1 x 10⁻⁵ B cells

- on day 16, Antibody concentration is  2 × 10¹= 20 Antibodies
- on day 36, antibody concentration 8 × 10³.= 8000

20 antibodies ------------ 1 x 10⁻⁵ B cells
8000 antibodies--------------x

x= (8000 x 1 x 10⁻⁵)/ 20
x= 4x10⁻³ or 1 in 250 are B cells specific for antigen A