COVID-19 vaccination second doses: why two doses and why the specified interval?

Question

Certain COVID-19 vaccines such as the Pfizer BioNTech and Moderna are specified to be administered in two doses separated by a 21 and 28 day interval, respectively. My questions are:

1. Why administered in two doses versus (perhaps) one larger dose? Some vaccines are "single dose" but some are not. What is going on biologically/biochemically that requires or favors a two-dose regimen and why does this not apply in the case of single-dose vaccines? Does it relate to the "platform" (mRNA vs adenovirus, etc.)?
2. Why the specified interval? How was it determined that 21 or 28 days would be the optimum interval between doses? What is going on in the body at or about 21 or 28 days that makes it optimal to administer a second dose at that time but not sooner or later?
3. Why is there a difference in interval between the Pfizer at 21 days and Moderna at 28 days?

Answer 1

From an article in JAMA

When the [Pfizer and Moderna] vaccines were first tested, a relatively weak immune reaction was found within a few weeks after people received the first dose of vaccine, followed by a strong reaction when a second dose was given.

Multiple doses are not uncommon in vaccinations. Shingrix, a shingles vaccination is also two dose, as are HPV vaccines.

Additional Information:

Successful immunization depends upon immune memory and vaccine immunization schedules (i.e. the number of doses and the time elapsed between doses) that are designed to generate optimal immune memory. [...] Memory is evoked as a consequence of initial or primary immunization, which elicits a primary immune response. This “priming” enables the immunized individual to mount a more potent and rapid response to subsequent challenges with the same antigen. The response to each subsequent immunization (secondary, tertiary, etc.) thus increases in intensity [of immune response].