ΕΡΓΑΣΤΗΡΙΟ ΕΝΖΥΜΙΚΗΣ ΤΕΧΝΟΛΟΓΙΑΣ

ENZYME KINETICS

1. 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 K_m.

b) Calculate V_max. 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 K_m.

and K_m 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.

2. 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 K_m and V_max, using a Lineweaver-Burke plot.

b) Suppose the experiment were repeated with five times the amount of

enzyme. How would K_m and V_max 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 K_m and V_max?

3. 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	Lactose and 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?

4. 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 25^oC. You determine the

concentration of nylon at equilibrium is 0.0001M. 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? Explain.

[Substrate] (M)	Velosity (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?

5. 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?