25. The two charts below are for an uninhibited enzyme E with Michaelis-Menton kinetics. The enzyme has a V_max= 600 and a K_M = 50. E catalyzes a reaction in which compound C is converted to compound H. . Write your answers below the charts.
a. Describe the interaction(s) of a mixed inhibitor X with E, C, and H.
    You may find it helpful to write a simple diagram that represents their interactions.
b. Define α or α′ for X, and write the modified Michaelis-Menton equation that shows
     the effect of X on E.
c. Add a line to each graph to show the effect of adding X. Describe X's effect for the
     Michaelis-Menton graph.

        a. A mixed inhibitor (I) associates with E to form an EI complex and with the enzyme–substrate complex to form an ESI complex:

        b. , where K_i = the dissociation constant for the EX complex.
    , where K_i′ = the dissociation constant for the ECX complex.

        c. See the dashed line on each graph.
    X increases K_M (usually, although it may decrease) and decreases V_max.
    For the Michaelis-Menton graph, the added line should not approach V_max.
    For the Lineweaver-Burk graph, the added line should intersect the first line, but not
     on the y axis.

26. The diagram on the left below represents an intermediate in the reaction catalyzed by enolase. In the reversible reaction 2-phosphoglycerate D phosphoenolpyruvate (PEP).
a. Either write a sentence describing the difference between substrate and product or
    draw the structures of substrate and product.
b. What co-factor(s) are required by enolase? Classify each as prosthetic or co-substrate.
c. Name the amino acid residues in the active site and explain why they are required
    for catalysis. This should include the type of mechanism enolase uses.

        a. This is the reaction:
    Water is removed from carbons 2 and 3 of 2-phosphoglycerate.

        b. Two Mg²⁺ ions are prosthetic co-factors.

        c. Lysine and glutamate side chains are required in the active site, functioning as base
     and acid, respectively. That is, first lysine accepts H⁺ from carbon 2, and then the
     glutamic acid side chain donates H⁺ to the O that becomes water. This is acid-base
     catalysis.

27. The chart on the right represents the effect of increasing [S] for an allosterically regulated enzyme in the absence of modulators. Assume that V_max= 300.
a. Which is the more appropriate term to use for this enzyme–K_M or K_0.5 ?
    Explain the difference between the two terms and the reason for your choice.
b. Give an approximate value for your answer to part a.
c. Add a line to the chart to represent the effect of adding an allosteric inhibitor.
     What change, if any, occurs to your answer to part b?
d. What type of inhibition (competitive, uncompetitive, or mixed) does allosteric
    inhibition resemble? Describe one similarity.

        a. K_0.5 is the more appropriate term. This refers to [S] when v₀ = ¹/₂ V_maxfor enzymes
    that do not have Michaelis-Menton kinetics. K_M = [S] when v₀ = 1/₂ V_maxfor enzymes
     that do have Michaelis-Menton kinetics. Allosterically regulated enzymes nearly
    always have cooperative binding of substrate (a sigmoidal graph) and therefore do
    not have Michaelis-Menton kinetics.

        b. about 30

        c. The value increases. The curve you add should still be sigmoidal and still approach
    the same V_max.

        d. Allosteric inhibition resembles mixed inhibition, because the inhibitor binds at
    a site that is not the active site, and it can bind to either E or ES.
    Allosteric inhibition resembles competitive inhibition because the K_M is increased,
    but the V_maxremains the same.
    Basically, you could answer either as long as you provided a logical reason that was
    consistent with both types of inhibition.

28. The protein segment below is the consensus sequence recognized and modified by protein kinase C (PKC), an enzyme involved in covalent modification. It also includes a substrate of trypsin, a serine protease with a specificity pocket for positively-charged side chains. Trypsin is involved in proteolysis.
a. Circle the side chain that is the most likely substrate for PKC and describe what
    happens to it and to the protein as a result of the reaction catalyzed by PKC.
b. Draw an arrow to a peptide bond that is a trypsin substrate and describe what
    happens to it and to the protein as a result of the reaction catalyzed by trypsin.
c. Assume that the protein containing this segment can be activated by either PKC or
    trypsin. How can the activation be reversed or ended in one case? (Your choice of
    either PKC or trypsin)

        a. The side chain is phosphorylated, becoming larger and negatively charged. This
    causes a change in conformation of the protein and therefore a change in activity.

        b. There are actually three peptide bonds that could be trypsin substrates, indicated
    by the three arrows. Any one is acceptable. Hydrolysis causes separation of the
    protein into two separate parts, which would change activity.

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