Reference no: EM132726270

Homework 1:

Question 1. The forward rate constant for an uncatalyzed reaction is 10^-4 s^-1; an enzyme binds to the transition state of this reaction with the free energy ΔG = -50 kJ/mol; temperature = 300K.
a) Find the kcat.
b) Assuming that the enzyme can be represented by a sphere with r = 5 nm and the substrate can be represented by a sphere with radius r = 2 nm, determine the rate of this reaction in sucrose solution with viscosity of 3 cP. The substrate concentration is 100 mM, the enzyme concentration is 1 nM. Quarter of all collisions result in a complex formation.

• Viscosity has no effect on the enzyme motions involved in catalysis and that due to steric restrictions only 25% of collisions between the enzyme and substrate result in productive collision (i.e. in the formation of the ES complex).
• From an orthogonal experiment you know that once bound, the substrate undergoes chemical transformation (i.e. dissociation rate constant of the substrate from the ES complex (k-1) is negligibly small when compared to kcat)
• To determine the overall reaction rate you will need to take into account both catalyzed and uncatalyzed reactions
• Debye-Smoluchowski equation for the second order association rate:

Question 2. Reaction A has an activation energy of 150kJ/mol and pre-exponential factor of 10¹⁴ s^-1. Reaction B has an activation energy of 60kJ/mol and pre-exponential factor of 10¹² s^-1. Temperature is 300K. Calculate activation enthalpy and entropy. Compare the transition states of the two reactions.

Homework 2:

Given:
1. A popular restriction enzyme binds its specific sequence at 37°C and 100 mM NaCl with an observed equilibrium association constant Kobs=1011M-1. Four ion pairs were implicated in the stability of the specific enzyme/DNA complex.

Based on the analysis of model compounds, the ΔG of formation of 1 ion pair with phosphate in 1M salt is +0.2 kcal/mol.

ΨdsDNA=0.88

Using polyelectrolyte theory:

(a) Calculate the Kobs and Kd(obs) at 200 mM and 1M NaCl

(b) Calculate the non-electrostatic contribution to the free energy of this interaction
Hint: total free energy of binding can be calculated form the intrinsic binding constant K; it will have an electrostatic component (contribution of the four ion pairs) and a non- electrostatic component, which you need to find.

(c) dsDNA may be protected from activity of the restriction enzyme by methylation (attachment of a methyl group to one of the phosphates, which results in removal of one negative charge from the recognition sequence). Calculate the association constant for hemi-methylated sequence (one methyl group is added, and therefore one ionic interaction is removed) at 37°C and 100mM NaCl. Assume that biding to the hemi-methylated sequence does not change the non-electrostatic component of the binding energy and that the electrostatic component scales linearly with the number of contacts.

(d) Plot the dependence of the LogKobs vs. Log [Na+] for the non-methylated and hemi-methylated DNA

Question 2. Intrinsic fluorescence quenching was used to measure the dissociation constants (Kd) of glucose binding to the enzyme glucokinase at different temperatures. This was done for wildtype (wt) and mutant (mt) forms of the enzyme and with and without 20% glycerol in the buffer. The table below contains the Kd values determined under each condition.

Temp (°C)	wt Kd (mM)	wt+glycerol Kd (mM)	mt Kd (mM)	mt+glycerol Kd (mM)
44		1.03
39	1.56	1.08	1.09	0.80
34	1.66	1.21	1.20	1.08
25	2.75	1.83	1.80	1.02
16	5.38	2.19	2.53	1.14
11	5.53		2.85

(a) Use the data in the table above to create a van't Hoff plot. Print and attach this plot.

(b) Determine ΔH and ΔS for the binding of glucose to glucokinase. Report values for the wildtype and mutant enzymes, with and without glycerol.

(c) From the calculated ΔH and ΔS values and the van't Hoff plot, what can be determined about the thermodynamic signature of glucose binding to glucokinase? What can be determined from the effects of the mutation and glycerol?

Attachment:- biophysical chemistry homework.rar