Chemistry 440B

First examination

Thursday October 14, 2004

10:00 am – 11:50 am, 124 Burrill Hall

Make sure that your name is included on each booklet of answers handed in. Show all work in the test booklet. Circle all answers and put units on all answers. 1. Thioredoxin is a small monomeric protein (108 residues) whose stability has been

examined using guanidine hydrochloride (GuHCl) denaturation. In one experiment, an arginine was substituted for a buried leucine (L72R). Remarkably, the resulting enzyme is still active. However, the data below indicate an effect on stability. (15 pts)

The data above can be fit to a linear relationship, below:

∆G˚GuHCl = ∆Go

U - m [GuHCl]

where ∆Go

U refers to the stability (folded ⇔ unfolded) in the absence of

denaturant and ∆G˚GuHCl quantifies the unfolding measured as a function of the

concentration of [GuHCl]. The following data were obtained: [GuHCl] yielding 50% unfolding m (kcal/mol) wildtype: 2.65M 5.1 L72R mutant 1.54M 5.9 (a) What is the value of ∆∆GU due to this amino acid substitution? (10 points) (b) Both ∆Go

U and Tm are viewed as measurements of protein stability. These experiments yield ∆Go

U. Can Tm be computed from the value of

∆GoU? If not, what other data are required? (5 points)

2. The transfer free energy of a family of lipid-soluble drugs from water to the interior of a cell membrane was determined to follow the relationship

AreamolcalG o

trans *20900)( −=∆ , if the Area is in Angstroms2 ( 2oA )

If the dosage of the drug is sufficient to maintain the concentration in the water phase (e.g., blood serum) at 0.2 µg/liter, what hydrophobic surface area of the drug molecule is required to assure that the concentration of drug that partitions into the cell membrane is 1.8 µg/liter at 37oC? Assume the drug has a molecular weight of 500. (15 pts) 3. Two proteins are unfolded by thermal denaturation and by chemical denaturation using urea. The values obtained by either method for each protein for ∆Go

U is +12 kcal/mole at 25o (for the equilibrium: F↔U). Hence, by this measure, the two proteins are equally stable at 25oC. Remarkably, the two proteins unfold upon thermal denaturation at very different temperatures. (20 pts) Protein 1: Tm=55oC, ∆Ho

U(at Tm) = +100 kcal/mole Protein 2: Tm=95oC, ∆Ho

U (at Tm) = +75 kcal/mole a) Explain quantitatively why these two proteins have such different thermal stabilities when measured by their Tm values? (10 pts) b) What are the values of ∆Ho

U for each protein at 25oC? (10 pts)

4. The Table below (Table I) shows the concentrations of some of the metabolites of the glycolytic pathway in the intact human erythrocyte (red blood cell). Similar values are found in other cells. The second Table (Table II) shows the values for ∆Go' for some of the reactions of glycolysis. Using the information in these Tables, answer the following questions. (20 pts)

a. Which two of the reactions use the NAD+/NADH couple as an electron acceptor? (5 pts)

b. Given that Eo' (Em,7) for the NAD+/NADH couple is -320 mV, what is the E' value for this couple involved in the two reactions? (10 pts)

c. What value can you calculate for ∆G' for ATP hydrolysis at the concentrations found in the cell (the fifth reaction in Table II)? (5 pts)

d. What is the value for ∆G' for the glucose-6-phosphate phosphatase reaction (the second reaction in Table II)? (5 pts)

Table I Steady-state concentrations of intermediates of glycolysis in

the human erythrocyte (red blood cell). Intermediate Concentration

(µM) Glucose 5,000 Glucose 6-phosphate (G-6-P) 83 Fructose 6-phosphate (F-6-P 14 Fructose 1,6-bisphosphate (F-bis-P) 31 Dihydroxyacetone phosphate (DHAP) 138 Glyceraldehyde 3-phosphate (Gly-3-P) 18.5 3-phosphoglycerate (3-PGA) 118 2-phosphoglycerate (2-PGA) 29.5 Phosphoenolpyruvate (PEP) 23 Pyruvate 51 Lactate 2,900 ATP 1,850 ADP 138 Phosphate 1,000

Table II Values for ∆Go' and ∆G' for some reactions of glycolysis (assume pH 7.0, 298o K) ∆Go' ∆G' (kJmol-1)

glucose + ATP glucose-6-P + ADP -16.74 - glucose-6-P + H2O glucose + phosphate -13.81 -

gly-3-P + NAD+ + Pi 1-3 diphosphoglycerate + NADH + H+ 6.28 - 1-3 diphosphoglycerate + ADP 3-PGA + ATP -18.83 0.8

ATP + H2O ADP + phosphate -30.54 - pyruvate + NADH + H+ lactate + NAD+ -25.10 0

5. Calculate the work available from the following reactions: (25 pts) Transfer of 1 mol electrons a) from succinate to O2 (as air) under conditions at succinate:fumarate ratio of 1.0 at pH 6.5 (13 pts) b) from succinate to cyt c, at succinate:fumarate ratio of 10, ferri- cyt c:ferrocyt c of 10. (6 pts) c) from ferrocyt c to O2 (as air), with ferrocyt c:ferricyt c ratio of 10. (6 pts) Assume pH = 7.0 unless otherwise indicated, temperature = 25o C. Em,pH7 value for the fumarate, 2H+/succinate couple is 20 mV, with z=2; E m,pH7 for the O2, 4H+/H2O couple is 820 mV, with z=4; E m,pH7 for ferricyt c/ferrocyt c is 250 mV, with z=1. (Hint, - remember that the standard state for a gas is a pressure of 1 atms; you may assume that the partial pressure of O2 in air is 0.2 atms)

VALUES FOR RT EXPRESSED IN DIFFERENT UNITS. T T 2.303RT/F 2.303RT RT 2.303RT RT Co K (mV) (kcal/mol) (kcal/mol) (kJ/mol) (kJ/mol) 0 273 54.22 1.250 0.543 5.227 2.270 10 283 56.20 1.296 0.563 5.418 2.353 20 293 58.18 1.341 0.582 5.609 2.436 25 298 59.19 1.364 0.593 5.706 2.478 30 303 60.16 1.387 0.602 5.800 2.519 37 310 61.56 1.419 0.616 5.934 2.577 Useful Physical Constants. Avogadro's number N 6.02 x 1023 mol-1

Boltzman's constant k 1.381 x 10-23 J K-1

Gas constant ( N x k ) R 8.314 J mol-1 K-1

1.987 cal mol-1K-1

Planck's constant h 6.626 x 10-34 J sec electron charge e 1.602 x 10-19 C Faraday constant ( N x e ) F 9.649 x 104 C mol-1 9.649 x 104 J mol-1 V-1

23.06 kcal mol-1 V-1

velocity of light c 2.998 x 108 m sec-1

(1 cal = 4.184 joule (J) ) Useful equations: Thermodynamic relationships Standard equation for ∆G', using the equation for pyruvate dehydrogenase as an example:

]][[]][[ln'

NADHpyruvateNADlactateRTGG o

+

+∆=′∆ Equations relating ∆G to ∆E:

pHmoo

moo

EzFEzFG

EzFEzFGEzFG

,'' ∆−=∆−=∆

∆−=∆−=∆

′∆−=′∆ Equations relating E', Eo' and pH

][][ln

)('

n

zno

AHA

zFRTEE

−−

+=′ npHzF

RTEE oo 303.2' −=

General thermodynamic relationships: ∆U = w + q Under reversible conditions ∆U = wmax + qrev ∆U = ∆A + T∆S ∆A = ∆U - T∆S ∆G = ∆H - T∆S ∆H = qp

∆U = qv dH = CPdT dU = CVdT For general reaction: aA + bB cC + dD

ba

dco

BADCRTGG

}{}{}{}{ln' +∆=′∆

∆Go(denaturant) = ∆Go

(H2O) – m[Denaturant] eq

o KRTG ln−=′∆

van’t Hoff relationship Gibbs-Helmholtz equation (temp. dependence of ∆Go) R

SRTHK

oo ∆+

∆−=ln

For dissociation of weak acid

][][log10 AH

ApK−

+= pH For redox half-cell: AHn A-(n-z) + nH+ + ze ][

][ln)(

'

n

zno

AHA

zFRTE

−−

+=′E

npH

zFRTEoo 303.2' −=E

∆Go(T) = ∆Ho(Tm) [ 1 - T/Tm ] + ∆CP( T - Tm) + ∆CPTln(Tm/T)

, AH A- + H+

-

∆G' = -zF∆E' ∆Go' = -zF∆Eo' ∆Go = -zF∆Eo

Chemical potential of A

solute) nonidealfor dilution highat or solute, ideal(for ]ln[

ln

ART

aRToA

aoAA

+=

+=

µ

µµ

Electrochemical potential of Az

ψµµ zFAA +=

where ψ is the electrostatic potential of the phase containing A For transport of a neutral species, A 1

212

][][ln

AART

nGG A =∆=

∆=′ −µ∆

For transport of a charged species, Az

)12(

1

2)12(

)12(12)12(

][][ln −

+

+−

−−−

∆+=∆

∆+∆=∆=∆

=′

∆ ∆=

ψµ

ψµµ∆

µ

zFAART

zFnGG

nG

z

z

A

AA

A

Equilibrium condition

2

1)12(

][][ln +

+− =∆ z

z

AA

zFRTψ

For transport of protons

where Z = 2.303RT/F, which has a value ~59 mV at 298 K

)12()12()12(

)12(ppmf −−−

− ∆−∆=∆

=∆=+ pHZ

zFH ψ

µ