1. In class we calculated the value of the pressure for which diamond is in equilibrium with graphite. Suppose that you are working for a company that wants to make diamond and they determine that they need a chemical potential of -80 kJ/mol for the reaction. What pressure does this correspond to?

 

2. Calculate a.) the activation energy and prefactor for the Arrhenius rate constant for the unfolding of the protein "foldase" given the data in the table. b.) Using the fraction folded determine the folding rate constant at each temperature. c.) Finally, use the data to determine DH^o and DS^o for the unfolding reaction.

T (K)	kobs (unfolding)	Fraction folded
280	1450	0.84
290	2420	0.70
300	3936	0.50
310	6180	0.31
320	9470	0.18

 

 

3. A pharmaceutical company is investigating a new lead for a drug known as Cureall. The drug binds to the active site of enzyme Blahase, which tends to make sick people feel lousy if it is not inhibited. The binding equilibrium is known to be:

1. Determine the binding (association) enthalpy for Cureall and Yuckose, respectively, with Blahase.

 

DH^o (1) = _________________. DH^o (2) = _________________.

2. Determine the binding (association) entropy for Cureall and Yuckose, respectively, with Blahase.

 

DS^o (1) = _________________. DS^o (2) = _________________.

3. Cureall is a mimic for a carbohydrate, but it is a floppy molecule (i.e. it has many ether linkages and there any many possible conformations of the drug in solution). Your boss asks you to explain the sign of the entropy of binding of the drug.

 

 

 

4. Ascertain whether the drug binds more tightly than the native substrate Yuckose at body temperature.

e.) The pharmaceutical company states that the concentration of the drug Cureall can be as high as 10^-8 M while the native substrate has a concentration of 10^-6 M (1 micromolar). Assuming these concentrations and an enzyme concentration of 10^-6 M determine the effect of inhibitor on the enzyme kinetics at 290 K. The enzyme turnover number (i.e. the rate constant k_b) is 1000 s^-1 at 290 K. The binding half-life for the substrate Yuckose is 69.3 milliseconds. NOTE: The binding constants above are association constants. K_I for inhibition is usually reported as a dissociation constant (K_I = 1/K_a for 1).

K_M = ___________________. V_max = ___________________________.

V = ______________________________ for [S] = 10^-6 M.

V_I = ______________________________ for [S] = 10^-6 M and for [I] = 10^-8 M.

The rate slows by a factor of:

V/ V_I = ________________________________.

f.) Assuming the same concentrations as above determine the effect of inhibitor on the enzyme kinetics at 310 K. At this temperature the enzyme turnover number (i.e. the rate constant k_b) is unchanged at 10³ s^-1 and the binding half-life for the substrate Cureall is 6.93 milliseconds.

K_M = ___________________. V_max = ___________________________.

V = ______________________________ for [S] = 10^-6 M.

V_I = ______________________________ for [S] = 10^-6 M and for [I] = 10^-8 M.

Hint: use

Experts suggest that an inhibitor should lower the enzyme rate by at least a factor 100 to be an effective drug. Should Smartmoney, Inc. invest in Cureall?

1. The enzyme convertase is inhibited by a non-competitive inhibitor that binds to an allosteric binding site with an association constant of K_a = 10⁴ M^-1. Convertase is observed to have a maximal velocity of 10.0 mmol/min for the conversion of sugar to carbohydrate. At a sugar concentration of 10^-6 M the rate is 5.0 mmol/min.

1. Determine K_M for convertase.
2. Determine effect on the maximal rate if the inhibitor concentration is 10^-2 M.

K_M = ___________________.

V_max,I = _____________________________

In the presence of an inhibitor we have:

1. According to the chemiosmotic theory, an electrochemical proton gradient is used to synthesize ATP in mitochondria. The enzyme that does this is located on the inside of the mitochondrial membrane. The oxidation of carbohydrates and fats is used to pump protons outside the mitochondrial membrane until the steady state membrane potential is –140 mV and the pH gradient is DpH = 1.5 units. Inside the mitochondrion, pH = 7.0, [ATP] = 1 mM, [P_i] = 2.5 mM, [ADP] = 1mM, and T = 310 K and the standard free energy change is (DG^o = 31 kJ/mol).

1. A. How much free energy is required to synthesize ATP inside the microchondria?
2. B. How much free energy is made available by moving one mole of protons from the outside to the inside? Is this enough to drive ATP synthesis?
3. C. How many protons must be translocated per ATP synthesized?

1. Calculate the surface tension of a liquid if the capillary rise in a tube of radius 100 m is 0.1 m and the density is 0.8 gm/cm³.

 

2. Myoglobin is a skeletal protein that binds oxygen. The standard free energy for the reaction

Myoglobin + O₂ à Oxymyoglobin

Is DG^o = -30.0 kJ/mol at 298 K and pH 7. The standard state of O₂ is the dilute solution molarity scale; therefore the concentration of O₂ must by in units of molarity (M). What is the ratio (oxymyoglobin)/(total myoglobin) in an aqueous solution at equilibrium with a partial pressure of oxygen P(O₂) = 30 Torr? Assume ideal behavior of O₂ gas and that Henry’s law holds for O₂ dissolved in water (The Henry’s Law Constant is K(O₂) = 43 x 10³ atm).

 

 

3. A. Determine the solution concentration of oxymyoglobin given that the extinction coefficient is 180,000 M^-1cm^-1 at the peak of the Soret band (l_max = 418 nm). The absorbance of the sample is 0.3 in a 1 millimeter pathlength cell.

B. Assuming that the photolysis yield for MbO₂ à Mb + O₂ is F_photolysis = 0.75 and that the absorbance of Mb is 0.1 at 418 nm, calculate the largest possible change in absorbance that can occur for laser photolysis of oxymyoglobin.

 

4. How many photons of light strike a molecule on average if the wavelength of the radiation is 500 nm and the total energy per unit area is 1 nanoJoule/mm² and the concentration of molecules is 1 mM in a 1 mm cuvette?

1. Briefly describe the procedure used in the Polymerase Chain Reaction (PCR). Include the name of a commonly used polymerase and describe its properties.
2. What is an oncogene? Describe how an oncogene can lead to the formation of a cancer cell.
3. What is a reverse transcriptase? Describe one application of a reverse transcriptase.
4. Describe viral membrane fusion. Give one example of a virus that uses membrane fusion to enter a cell.
5. What is gene therapy? Describe one drug delivery method that has been used for gene therapy studies.
6. What is Green Fluorescent Protein? Why is this protein useful as tool in studies of cell biology?