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PROBLEMS

10.1. Why is mRNA so unstable in most bacteria (half-life of about 1 min)? In many higher
organisms, mRNA half-lives are much longer ( 1 h). Why?

10.2. What would be the consequence of one base deletion at the beginning of the message
for a protein?
10.3. S.B. Lee and J.E. Bailey (“Genetically structured models for lac promoter-operator
function in the E. coli chromosome and in multicopy plasmids: lac promoter function”,
Biotechnology & Bioengineering, 26: 1381 e 1389, 1984) modeled the lac-operon by
including binding of the repressor to a nonspecific binding site in the chromosome (X d ).
Neglecting the binding of inducer to the repressor-operator complex, the equilibria are
given by

>

K 1 E r ð

E r þ m S L 4 S L Þ m (P10.3-1)

K 2 E o E r

E O þ E r 4 (P10.3-2)

S L Þ m K 3 E O E r ð

E O þ E r ð S L Þ m (P10.3-3)

K 4 X d E r

X d þ E r (P10.3-4)

4

K 5 X d E r ð

X d þ E r ð S L Þ m 4 S L Þ m (P10.3-5)

(a) assuming [X d ] T z [X d ], show

S L T ð1 þ K 5 ½X d T Þ

½ E O 1 þ K 4 ½X d T þ K 1 ½

E O T ¼

(P10.3-6)

S L T ð1 þ K 5 ½X d T ÞþK 2 ½

½

1 þ K 4 ½X d T þ K 1 ½ E r T

where K's are equilibrium constants.
(b) Let K 1 ¼ 10 7 mol 1 l, K 2 ¼ 10 12 mol 1 l, K 3 ¼ 10 9 mol 1 l, K 4 ¼ 10 3 mol 1 l,

2 2

10 9 mol 1 l, and [X d ] T ¼ 10 2 mol/l and [E r ] T ¼ 10 8 mol/l. Plot K 5 ¼ 1.5 4 2

the value of the free to total operator ratio (with m ¼ 4), both from Eqn (P10.3-6)