• TRUMP's between-the-lines module has determined that there are no hidden messages in the text, and that this is not a cryptogram. You will have to deduce the rules.
• TRUMP's Watson & Crick module has determined that one of the rules pertains to two of the bases, and each of the other two rules pertains to one of the other two bases.
• TRUMP's elementary module has dtermined that one base always comes in an odd number, another comes in an even number, and the other two never co-occur.
• TRUMP's central dogma module has determined that it may be helpful to line the strips up alphabetically before you attempt to deduce the amino acid encoding scheme.
• TRUMP's AAAARGH module has determined that AAAAAAAAA = A, AAAAAAAHH = B, AAAAAAAII = C, AAAAAHHHH = D, etc.
• TRUMP's ribosome module has determined that the first protein is PHENOMENON and the last is ADDENDUM.
• TRUMP's cloning module has determined that you need to find a way of cloning this singularly unusual set of proteins.
• TRUMP's plurality module has determined that you'll observe some interesting phenomena (but no seraphim) in the end(s).

Solution

The text explains what to do, and there are no hidden messages. The first step is to infer the rules for what can pair with what; they turn out to make sense, in an oblique way:

1. The number of aerines is always odd. (air = unstable)
2. The number of terrines is always even. (earth = stable)
3. Hydrine and ignine never coexist. (water vs. fire)

A little math demonstrates that this narrows it down to 25 possible combinations, which, when they're ordered alphabetically, stand for the letters A-Y:

AAAAAAAAA   A
AAAAAAAHH   B
AAAAAAAII   C
AAAAAAATT   D
AAAAAHHHH   E
AAAAAHHTT   F
AAAAAIIII   G
AAAAAIITT   H
AAAAATTTT   I
AAAHHHHHH   J
AAAHHHHTT   K
AAAHHTTTT   L
AAAIIIIII   M
AAAIIIITT   N
AAAIITTTT   O
AAATTTTTT   P
AHHHHHHHH   Q
AHHHHHHTT   R
AHHHHTTTT   S
AHHTTTTTT   T
AIIIIIIII   U
AIIIIIITT   V
AIIIITTTT   W
AIITTTTTT   X
ATTTTTTTT   Y

Fill in the blanks to complete the following string of "proteins":

PHENOMENON SERAPH CHILD PERSON BATHTUB NUCLEUS ADDENDUM

Before Leeloo got away, Mactilburgh was about to describe cloning the proteins themselves. All of the proteins are singular nouns, and most of them have irregular plurals:

PHENOMENA
SERAPHIM
CHILDREN
PEOPLE
BATHTUBS
NUCLEI
ADDENDA

The ends of these words spell AMNESIA, hence the discussion of memory in the letter. (One of Ian's only pet peeves about sci-fi movies is that cloned characters mysteriously retain their memories.)

(A piece of trivia: In fact, only Snakes on a Plane ever received this puzzle.)