Enzyme Biochemistry Practice Problems

You are a research scientist studying a novel enzyme X, and you want to characterize this new enzyme. You measure the velocity of the reaction with different substrate concentrations and get the following data:
```
    [substrate] (mM)                Initial Velocity (mmol/min)
---------------------------------------------------------------------
             3.0                            10.4
             5.0                            14.5
            10.0                            22.5
            30.0                            33.8
            90.0                            40.5
```
- a) Graph the above data. From the graph, estimate KM.
- b) Calculate Vmax. Show any equations and calculations.
- c) Is X an allosteric enzyme? Explain.
- d) You decide to do this experiment again, but this time with only one third of the enzyme X concentration used in the first experiment. Draw a new graph on the same graph that you did the first graph on. Estimate Km and Vmax from the new graph.
- e) You wish to find the amino acid sequence of the enzyme X. What methods might you use to determine this? Name at least three.
Five reaction mixtures containing 10 x 10-9 M of an enzyme are made up with five different substrate concentrations and the initial rates of the reactions were measured:
- a) Determine Km and Vmax, using a Lineweaver-Burke plot.
  0
- b) Suppose the experiment were repeated with five times the amount of enzyme. How would Km and Vmax be affected?
- c) A poison is added to the reaction mixture that is known to bind the enzyme at a site different from where the substrate binds. The poison and the substrate can bind the enzyme simultaneously but the poison prevents the formation of product. Qualitatively, how does the poison affect Km and Vmax?
In certain bacteria, the biosynthesis of aromatic amino acids (phenylalanine, tyrosine, and tryptophan) proceeds by a branched pathway where some intermediates are used to make more than one amino acid. The pathway and some key intermediates are shown below.

This pathway is regulated by feedback inhibition at enzymes a through e. For parts a through e, list the intermediates and products shown which you might expect to be inhibitors of each enzyme. Explain your answer briefly.
Lactose is a disaccharide found in milk. Although in the United States we are told that milk, it does a body good, many adults throughout the world get sick from drinking milk because they cannot digest lactose. Lactose intolerance varies markedly among various human populations. (For example, only about 3% of people of Danish descent are lactose intolerant, compared with 97% of people of Thai descent.) When someone who is lactose intolerant ingests milk, the lactose accumulates in the lumen of the small intestine because there is no mechanism for uptake of the disaccharide. This causes abdominal distension, cramping, and watery diarrhea.
- a) Why can't lactose diffuse across the membranes of the intestinal epithelial cells in the absence of a carrier-mediated uptake system?
- b) Why does the accumulation of sugar (or any solute) in the intestinal lumen cause an influx of water that leads to watery diarrhea?
  Adults who can drink milk can do so because of the enzyme lactase which is located on the outer surface of epithelial cells lining the small intestine. Lactase hydrolyzes lactose into its two component monosaccharides, glucose and galactose. Both glucose and galactose can cross the epithelial cells, and therefore do not cause illness.
- c) Based on your knowledge of transport across cell membranes, propose a mechanism by which galactose is transported into the intestinal epithelial cells. (Making a diagram will help you visualize the mechanism better). (There are several possible solutions - you only need to propose one.)
  
  You decide to study lactase further, and see whether it can also cleave other common disaccharides, such as maltose. (Maltose = glucose + glucose.) You find that maltose is NOT cleaved by lactase, and furthermore, maltose appears to have some kind of inhibitory effect on lactase's ability to cleave lactose.
- d) Is maltose a more likely candidate for competitive or noncompetitive inhibition of lactase? Explain.
  
  In order to confirm your hypothesis in part (d), you quantitatively study the kinetics of lactase with lactose alone, and in the presence of both lactose and maltose. You measure the initial velocity of the reaction (rate at which lactose is cleaved) at varying concentrations of substrate. The data is given below.
```
  [Lactose] moles/liter                   Velocity  (moles/min)
------------------------------------------------------------------            
                                       lactose only   with maltose
------------------------------------------------------------------
  0.3 x 10-5                              10.4          4.1
  0.5 x 10-5                              14.5          6.4
  1.0 x 10-5                              22.5          11.3
  3.0 x 10-5                              33.8          22.6
  9.0 x 10-5                              40.5          33
```
- e) Graph 1/V vs. 1/[S] for lactase both with and without maltose. Does your graph confirm or contradict your prediction in part (d)? Why?
You notice one day a slimy patch of goo on your carpet. It seems as if the goo is eating away at your carpet. Being an awesome biologist, you figure out it's bacteria feeding off your carpet. But wait, your carpet is made of nylon! How can this be? Perhaps the landfill and nuclear power plant next to your house has something to do with it...
You set out to determine how the bacteria can live off of nylon since nothing known can. You scrape some off the bug-infested carpet and take it to your lab. You culture large quantities of the bacteria and painstakingly purify a protein with the ability to cleave the nylon. You name the newly discovered enzyme Leggsase. Nylon is a polymer made up of many repeating subunits (like the polysaccharides). It looks like this:

The squiggly lines at the ends indicate that this same unit is repeated many times in both directions. The arrow points to the bond that is cleaved to break up the nylon polymer.
- a) Just how good is the enzyme? If we just put nylon in water, the rate at which this bond will cleave is about 1 per year. In the presence of the enzyme, it's about 100 per second. What is the increase in the rate of the reaction?
- b) You make a solution that is 0.1M in nylon. You add some enzyme and allow the reaction to reach equilibrium at 25oC. You determine the concentration of nylon at equilibrium is .0001M. i) What is the equilibrium constant for the reaction?
  
  ii) What is the change in free energy (Delta G) in kcal/mol? Is this an exergonic or endergonic reaction?
- c) You set up you assay system and collect data on the rate of the reaction as a function of the substrate concentration. (Data on next page) i) Graph rate vs substrate concentration for this enzyme reaction.
  ii) Is this likely to be a single- or multi-unit enzyme (see page 128-9 in Purves)? Explain.
```
 [Substrate] M           Rate sec-1
------------------------------------
      0                       0
      1                      2.9
      2                      6.4
      3                      9.1
      4                      12.0
      5                      14.6
      6                      17.2
      7                      18.7
      8                      19.5
      9                      19.9
      10                     20.0
```
- d) Since the world probably wouldn't like to have this bacteria eating up all the nylon around, you decide to make a bunch of money by discovering an inhibitor to it. You discover that a dipeptide, Gly-Gly, is a fair inhibitor of Leggsase.
  i) Draw the structure of the dipeptide (for yourself) and explain why it would inhibit Leggsase.
  
  ii) Is this likely to be a competitive or non-competitive inhibitor? Explain.
- e) You are so good, you even get crystals of Leggsase. Through the wonders of X-ray crystallography, you are able to determine the exact molecular structure of Leggsase. The active site seems to be in the middle of a long shallow grove on one face of the protein. What kinds of amino acids (polar, charged, hydrophobic, small, large, etc.) would you expect to line this groove? Why?
A mutation that changes an alanine residue in the interior of a protein to a valine residue is found to lead to a loss of activity. However, activity is restored when a second mutation at another position changes an isoleucine residue to a glycine residue. How might this second mutation lead to a restoration of activity?

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