Problem Set 2 (due Wed May 14, 2014).
1. Write the sequence of the complementary DNA strand and RNA transcription product for each of the following
using the standard 5’ ? 3’ notation (ie write each sequence so it begins with the 5’ residue) (2pts each).
a. 5’-GATCAA-3’
b. 5’-TCGAAC-3’
c. 5’-ACGCGT-3’
d. 5’-TACCAT-3’
2. The composition of one of the strands of a DNA duplex contains 30% of A and 24% of G.
a. What is the percentage of T in this same strand if it contains the same percentage of T and C?
b. What is the percentage of T and C in the complementary strand?
c. What is the percentage of A and G in the complementary strand?

3. Two complementary DNA oligonucleotides (strands A and B) have the following nucleotide sequence.
Strand A sequence: 5’-AAATAAAAT-3’
Strand B sequence: 5’-ATTTTATTT-3’
DNA duplex of Strands A and B:
a. What is the calculated extinction coefficient at 260 nm (?260 in units of M-1 cm-1) for each single-stranded
oligonucleotide (strands A and B) (hint: use website tool: http://www.scripps.edu/california/research/dnaprotein-research/forms/biopolymercalc2.html)
b. The optical density at 260 nm (A260) of a solution of Strand A was measured to be 0.1 and A260 of Strand B
was measured to be 0.077. What is the molar concentration of each solution (hint: A260 =
?260[oligonucleotide]pathlength and pathlength is 1 cm)?
c. Equal amounts of strand A and Strand B were mixed together and annealed to form duplex DNA. What is
the expected A260 for the duplex solution if ?260 of the duplex is assumed to be the sum of ?260 from each
strand?
d. The actual A260 of the duplex solution was measured to be 0.12. How does the experimental value of A260
compare to the expected A260 value in part c, and give a molecular interpretation to explain why they might
be different?
e. What is the enthalpy of duplex formation (?H?), assuming that the hydrogen bonds (from Watson-Crick base
pairs) are the only source of the enthalpy (hint: assume each H-bond has dissociation energy of 10 kJ/mol)?

f.

If the melting temperature of the DNA duplex was measured to be 333 K, what is ?S? for the duplex
formation (hint: assume both ?S? and ?H? are temperature independent)?

g. What is ?G? and Keq for duplex formation at 298 K?
h. The equilibrium constant for duplex formation nearly doubles when the temperature is decreased to 4 ?C.
Explain the steep temperature dependence of duplex formation using the Le Chatelier principle.

4. A DNA duplex encodes a vast amount of information.
a. How many different 8-mer sequences of DNA are possible? In other words, how many different sequences
can be generated by the four different nucleotides connected 8 at a time (hint: there are 16 possible
dinucleotides and 64 possible trinucleotides).
b. How many bits of information are stored in an 8-mer DNA sequence? In the human genome sequence that
contains 2.9 x 109 bases? [hint: a bit specifies 2 bases and a second bit specifies the other two; so, a single
DNA base pair stores 2 bits (22 = 4 possible sequences), a dinucleotide stores 4 bits (24 = 16 possible
sequences), and a trinucleotide stores 6 bits (26 = 64 sequences)]
c. Compare the number of bits encoded by the human genome with the amount of information that can be
stored on a 1 gigabyte thumb drive. (hint: a byte is equal to 8 bits)
5. An enzyme with a Km value of 3.9 x 10-5 M is treated with an initial substrate concentration of 0.035 M. The
initial rate (v0) of the enzyme catalyzed reaction is 6.2 micromolar product formed per minute (v0 = 6.2 ?M/min)
at an initial substrate concentration of 0.035 M, and the total enzyme concentration ([E]0) is 0.1 ?M.
Assuming Michaelis-Menton Kinetics:
a. Calculate the value of Vmax (hint: Vmax = v0 when the enzyme is saturated with substrate).
b. What is the concentration of product formed after 5 min (assume the enzyme remains saturated with
substrate during this period) and explain any assumptions about whether the reaction is zero-order or firstorder?
c. Calculate the catalytic turnover number ( kcat ?

Vmax
) in units of min-1?
[E ]0

d. Calculate the catalytic efficiency (kcat/KM) in units of M-1 s-1?

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