1. Because G binds to C more strongly than A binds to T, the melting temperature should increase with the fraction of G/C pairs along the backbone of a sequence.

a. Plot the melting temperature as a function of G/C content for a 60 base pair sequence by varying the number of G/C pairs between 15 and 45 bases. Plot the melting temperature versus the fraction G/C content. Does the melting temperature depend linearly on the fraction of G/C pairs, and if so, what is the slope and the intercept? Make sure you show the sequences you used.

b. compare the melting temperature of the original strand (60 bases, 30 C/G bases) at different concentrations of salt, NaCl, up to physiological salt concentration (0.15 M NaCl).

2. To support 25 cycles of PCR in which you start with a single double strand where each strand is 4000 bases, what concentration of each nucleotide would you need to start with assuming each of the nucleotides is distributed throughout the DNA randomly? Assume 1 ml of solution is the total volume.

3. A 3700 bp sequence is digested with two separate restriction enzymes, KpnI and EcoR1. When digesting with KpnI, all EcoR1 sites are left in tact. Similarly, when digesting with EcoR1, all KpnI sites are left in tact. In the following, the results of two separate digestions are written. Assume each enzyme cuts with a staggered cut. What are the locations of the KpnI and EcoR1 sites on the 3700 bp original sequence?

KpnI digestion:
100 bp, no intact EcoR1 site, 5′ staggered end, 3′ staggered end.
500 bp sequence, with intact EcoR1 site 200bp from 5′ end, 5′ blunt end, 3′ staggered end.
1400 bp sequence, 2 intact EcoR1 sites 200bp and 800 bp from 5′ end, 5′ staggered end, 3′ staggered end.
500 bp, no intact EcoR1 site, 5′ staggered end, 3′ blunt end.
500 bp, intact EcoR1 site 300 bp from the 5′ end, 5′ staggered end, 3′ staggered end.
700 bp sequence, no intact EcoR1 site, 5′ staggered end, 3′ staggered end.

EcoR1 digestion
600 bp sequence, no intact KpnI site, 5′ staggered end, 3′ staggered end.
1300 bp sequence, two intact KpnI sites, 300 bp and 1000 bp from the 5′ end, 5′ staggered end, 3′ staggered end.
1100 bp, one intact KpnI site 600 bp from the 5′ end, 5′ staggered end, 3′ blunt end.
200 bp, no intact KpnI site, 5′ blunt end, 3′ staggered end.
500 bp sequence, two intact KpnI sites, one 200 bp and one 300 bp from the 5′ end, 5′ staggered end, 3′ staggered end.