Download 1) Draw a reaction diagram for the conversion of molecule A into B

BIBC 102, Metabolic Biochemistry
Problem Set 1
Randy Hampton
1) Draw a reaction diagram for the conversion of molecule A into B. At the conditions of
the reaction, the free energy change DG of going from A to B is –26kJ/mole.
a) Indicate where the free energy change for the reaction appears.
b) Show where the activation energy for the reaction is indicated.
c) Why can’t we assign a value for the DG‡ from knowing the DG?
2) In class, we saw that the effect of changing the activation energy on a rate constant is
-(DG‡/RT)
predicted by the equation k= (kT/h)e
Note the left "k" is the rate constant,
and the right "k" (in boldface) is the Boltzmann constant.
a) using this equation, determine what the ratio of k is for the forward and reverse
reactions for the problem above.
b) why don’t you need to know the activation energy to determine this? Justify
your answer.
c) from this information, determine the ratio of A to B that must exist for the
system to be in equilibrium
3) You determine a Lineweaver-Burke plot for an enzyme you are studying and discover
that it is curved! What that means, you realize, is that the “constants” that would define a
line, are not staying constant. This sounds familiar.
a) Assuming that “Km” changes with substrate concentration, figure out what
shape a Lineweaver-Burke plot would have for an enzyme showing cooperativity,
that is, the substrate improves the enzymes’ function at high substrate
concentrations.
Your enzyme has a native molecular weight of 100,000 (this can be measured by a variety
of techniques). A different preparation of the enzyme made in your lab in harsher
conditions has a native molecular weight of only 25, 000. When you determine the
Lineweaver-Burke plot for this preparation, it is a straight line!.
b) Draw a Lineweaver-Burke plot for this more familiar case, showing the numerical
features of the graph that make it useful.
c) propose an explanation for these observations based on ideas of protein structure.
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BIBC 102, Metabolic Biochemistry
Problem Set 1
Randy Hampton
Fall 2004
4) 18) The kcat for catalase is 40,000,000 or 4 x 107 (sec-1). The reaction catalyzed by this
enzyme is:
H2O2
H2O +1/2O2
Suppose that a sample of catalyase is running at its maximal rate, and that will continue for
the duration of your experiment. Answer these questions
a) What is the saturated rate of water production per molecule of enzyme? How
about the saturated rate of O2 production?
b) If a micromole of catalase is operating at maximal velocity, what mass of 02
(grams) is generated per hour?
c) How long does it take a molecule of saturated catalase to convert peroxide to
water and oxygen?
d) suppose that the same experiment is performed as in a, but a sample of 3
micromoles is saturated. What is the rate of substrate conversion in mole/sec? How
about the rate of water molecules converted per molecule of catalase?
e) Can you tell what concentration of peroxide results in 50% maximal rate for a
given sample of catalase with the information? Justify your answer.
5) There is a class of enzymes called cysteine protesases that specifically cleave
polypeptides in a manner very similar to the serine protease chymotrypsin that we
discussed in class. In particular there is a histidine that works together with the cysteine to
promote nucleophilic accack of a specific peptide bond in the active site.
a) first look up the structures of cysteine and serine, and note the similarities in their
structure, using a picture (Although I wouldn’t make you memorize these, I promise
you it will benefit you as biologist and/or physicians to learn the structures of these
molecules)
b) write the mechanism by which serine attacks a generic peptide bond. You don’t
need any “catalytic triad” stuff (yet). I am just interested in you showing the
electron pushing of a nucleophilic attack.
c) Now, do the same with cysteine. You can see that this replacement on the
cysteine proteases makes a lot of sense.
d) Draw a little diagram of what you might imagine a cysteine protease would look
like if it is set up the same way as a serine protease. Show the histidine, apartate,
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BIBC 102, Metabolic Biochemistry
Problem Set 1
Randy Hampton
Fall 2004
the location of the “oxyanion hole” and the specificity pocket that in the case of
serine proteases determines their high specificity for peptides bonds next to aromatic
amino acid residues.
6) Phosphate is covalently added to proteins to regulate their function in many instances in
biology. Protein phosphorylations are catalyzed by members of a large class of enzymes
termend protein kinases. The phosphate is provided by ATP. Frequently the R group of
serine is the recipient of this modification.
a) Write the reaction showing transfer of ATP to the serine R group. For this
reaction, you don’t need to “push electrons”. Just show reactants and products.
Do draw the serine R group.
Now we will consider the hydrolysis of phosphoserine to remove the added phosphate.
Protein dephophorylations is catalyzed by enzymes termed protein phsophatases. In this
reaction, water is used to break the “phosphoester” bond. Note that this is not the exact
reverse of the protein kinase reaction.
b) Writing the structure of the phosphoylated serine R group, show the hydrolysis of
the phosphoserine back to regular old serine.
7) The standard free energy DG’O for ATP hydrolysis to ADP and Pi is -30.5 kJ/mole.
The complete reaction is
ATP + H2O
ADP + Pi
a) Write out the equation for the actual free energy at any concentration of the
reactants and products, at standard conditions (the reason for the ‘)
b) Compute the true DG for the case in which the ATP, and ADP and the Pi are all
at 1M concentrations
c) Compute the true DG for when all three molecules are at 0.01 M concentrations
d) In a neuron, the concentrations of the ATP , ADP and Pi is 2.59, 0.73, and 2.72
mM. Calculate the actual free energy change for hydrolysis of ATP at these
concentrations
e) Now do the same for and E. coli cell, where the three concentrations (same
order) are 7.9, 1.04 and 7.9
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