Biochemistry/Chemistry 440b

Fall 2014

Solutions to Exam 2 1. Lipid shape refers to the relative nearest neighbor spacing required for optimal

thermodynamic interactions between the non-polar alkyl chains on one hand, and the polar head groups on the other. When these are matched, the lipid is cylindrical in shape. This favors the bilayer geometry. If the head group requires a much larger space, a spherical micelle shape is favored, as is the case for many detergents. If the head groups require a small space between neighbors, as when they interact with each other, the hexagonal micelle geometry is preferred.

2. A colligative effect is one that under ideal conditions depends only on the number concentration of a solute (molarity or molality) and not on the type or molecular size of the solute. Osmotic pressure, boiling point elevation, freezing point depression and vapor pressure are all colligative effects. Non-ideal effects often modulate the measurements.

3. The DNA cooperative unit is about 300 or so basepairs. When DNA melts, it does so in units of about 300 basepairs that form bubbles or loops in the DNA. These units melt in all-or-nothing fashion, i.e., cooperatively.

4. a)

b) The unfolded protein has a larger solvent accessible non-polar surface area, which

results in ordered water molecules adjacent to this surface. It takes extra heat to break these non-covalent bonds between water molecules as the temperature is raised. Hence, the value of PC is larger for the unfolded protein than for the folded protein, which does not have as much organized water around non-polar surfaces.

c) The definition of the heat capacity (constant pressure) is

1

PP

H CT

=

From this it follows that

PP

H CT

=

Therefore: 2 1 2 1

( )T T PH H C T T = +

This means that the positive value of PC means that the value of H will increase as the

temperature is increased 2 1( )T T>

d) The vant Hoff enthalpy measures the heat per mol of the cooperative unit undergoing the transition (protein unfolding). Calorimetric enthalpy is normalized per mol of whatever was placed in the sample compartment.

Since 2o ocal vHH H = , it is plausible that the cooperative unit consists of half of the protein. Perhaps the protein has two similar or identical domains that unfold separately as cooperative units.

5. a) Start with the following equation:

[ ]11.7 log[ ]

ln( / 4) [ ]

oXY

m oT XY

B HT Na

R C A S++ = +

+ +

We know that the total strand concentration is 50TC M= and we need to calculate the enthalpy

and entropy terms from the Table of basepair parameters. These are tabulated for log[ ] 1Na M+ = .

For the oligonucleotide duplex:

5- A C G G T G T 3 3- T G C C A C A 5 From the Table of enthalpy and entropy values:

0 = 0 + [0 + 0 + 0 + 0 + 0 + 0 ]+ 0

oH = 0.2+[-8.8-10.6-8.0-8.4-8.4-8.4] +4.4= -48 kcal/mol

2

0 = 0 + [0 + 0 + 0 + 0 + 0 + 0 ] + 0+ 0 ooligoS = -5.7+[-22.7-27.2-19.9-22.4-22.4-22.4]-0.0 +13.8= -128.9 cal/(mol-deg)

0osymS = because the oligonucleotide is not self-complementary

Now we can find the melting temperature at 1 M NaCl.

= 0

4 + 0 = 480001.98 ln 0.000054 128.9 317.4 44.3oMT K C= =

b)

Now we can correct for 0.05M [NaCl]: log [+] = 11.7.

Thus TM2 - TM1=11.7(log[Na+ ]2 - log[Na+ ]1)=11.7log([Na+ ]2/[Na+ ]1) at 0.05M [NaCl]: TM2 = TM1 +11.7log([Na+ ]2/[Na+ ]1)= 44.3+11.7log(0.05)= 44.3 -15.2= 29.2o C

c) By reducing the DNA concentration, the TM will decrease. This can be seen by looking at the equation, or just by realizing that by mass action, lowering the concentration of double strand DNA will shift the equilibrium to favor the single strands:

strand 1 + strand 2 [strand 1 strand 2]

3

6. Relaxed form means no supercoils and all B DNA double strand. We also know that k w rL T W= + . a)

8000 76210.50762

w

r

k

T

WL

= =

=

=

b) The linking number must remain the same since the plasmid remains sealed. The twist is reduced by removing 200 basepairs of B DNA and converting it to single strand. The underwinding of the DNA must be offset by the formation of positive supercoils.

7628000 200 743

10.5762 743 19

k

w

r

L

T

W

=

= =

= =

c) Adding the topoisomerase reduces the writhing number to zero, but the twist remains the same.

08000 200 743

10.5743

r

w

k

W

T

L

=

= =

=

d) Removing the topoisomerase locks the linking number at 743. Removing the single-strand binding protein results in the entire plasmid being B-DNA. This introduces negative supercoils since the linking number is less than the twist number. There are 19 negative supercoils that result.

7438000 76210.5743 762 19

k

w

r

L

T

W

=

= =

= =

4

7. Stability is defined as water oU UG G . We get this from the equation, recognizing that at 50% unfolded, 0ureaUG = .

[ ]urea waterU UG G m urea =

For protein 1:

0 1.9(3.9)

7.41 kcal/mol

waterU

waterU

GG=

=

For protein 2:

0 2.1(3.9)

8.19 kcal/mol

waterU

waterU

GG=

=

a) Protein 2 is more stable than protein 1 by 8.19 7.41 0.78 = kcal/mol at 25oC b) The two proteins do not necessarily have the same TM values. The TM

depends on the values of and o oU UH S which we do not know.

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