Virtual_Lab__Enzyme_Controlled_ReactionsWorksheet1_Which_of_the

Virtual Lab: Enzyme Controlled Reactions

Worksheet

1. Which of the following does NOT apply to an enzyme:

a. Catalyst

b. Inorganic

c. Protein

d. All of the above apply to an enzyme

2. When an enzyme catalyzes a reaction:

a. Substrate(s) bind in the active site

b. Products bind in the active site

c. The shape of the enzyme remains unchanged

d. The enzyme is consumed by the reaction

3. Which of the following would interfere most with the ability of an enzyme to catalyze a reaction?

a. Reduced concentration of substrate available

b. Reduced concentration of product available

c. Increased concentration of substrate available

d. A change in the pH

4. Feedback mechanisms regulate the rate of enzyme activity, effectively “turning off” an enzyme in a reversible way until more product is needed. Which of the following would be most effective as a feedback mechanism?

a. Reduced concentration of product

b. Increased concentration of substrate

c. A change in pH

d. Temporary binding of a non-substrate molecule in the active site

5. Which of the following statements is accurate in describing the activity of the lactase enzyme?

a. Lactase can function equally effectively at many different pH levels

b. The shape of lactase does not change during the reaction

c. Lactase is converted to glucose and galactose by the reaction

d. One lactase enzyme can catalyze many reactions

6. Look up and write in the following definitions as they apply to chemical reactions:

a. Catabolic

b. Anabolic

c. Endergonic

d. Exergonic

7. Is the action of the enzyme illustrated in the video:

a. Anabolic or catabolic?

b. Endergonic or exergonic?

8. Endergonic or exergonic? Is the action of lactase:

a. Anabolic or catabolic?

b. Endergonic or exergonic?

9. Why is enzyme activity similar to, but not exactly like, a “Lock” and “Key”?

Table 1: Record your data on the number of product molecules formed per minute obtained from the virtual lab.

# Product Molecules/minute at:

Amount of Substrate (Lactose)	pH 3	pH 5	pH 7	pH 9	pH 11
0.5 g	19	39	72	45	24
1.0 g	39	81	145	91	49
2.0 g	82	168	300	189	103
4.0 g	96	198	350	223	121
8.0 g	96	198	350	223	121

10. What substrate amount was required to achieve the maximum reaction rate?

11. At what pH level did the maximum reaction rate occur?

12. Why was there no increase in the reaction rate with 8.0 g. of substrate as compared to 4.0 g. of substrate? What would you need to add to see an increase in the reaction rate with 8.0 g. of substrate?

13. In the graph you created in the lab simulation with your data:

a. What is represented by the green line?

b. what is the optimal pH for lactase enzyme activity?

14. Consider only the experiment you conducted with 0.5 g. of lactose.

a. What is the independent variable?

b. What is the dependent variable?

14. The maximum rate of this reaction is 350 molecules product/minute. List two changes you could make in the experimental conditions or variables that would increase this reaction rate. Explain why each change you listed will increase the reaction rate.

MATH 464

HOMEWORK 4

SPRING 2013

The following assignment is to be turned in on Thursday, February 14, 2013.

1. Let X be a discrete random variable on a probability space (Ω,F,P). Let g : R → R be a function and set Y = g(X), i.e. Y : Ω → R is defined by

Y (ω) = g(X(ω)) for all ω ∈ Ω .

Prove that Y is a discrete random variable.

2. Let 0 < p ≤ 1 and consider a function X with range {1, 2, 3, · · ·} and corresponding numbers

P(X = k) = p(1 −p)k−1 for any integer k ≥ 1 .

Prove that X is a discrete random variable by showing that the sum of the above probabilities is 1. This is the geometric random variable with parameter p.

3. Let X be a Poisson random variable with parameter λ > 0. Compute the following:

a) P(2 ≤ X ≤ 4) b) P(X ≥ 5) c) P(X is even)

give each answer in exact form and, with the choice of λ = 2, give a decimal approximation to the above which is accurate to 3 decimal places.

4. Let X be a discrete random variable whose range is {0, 1, 2, 3, · · ·}. Prove that

E(X) = ∞∑ k=0

P(X > k) .

5. Compute the expected value of the geometric random variable with pa- rameter 0 < p ≤ 1. Hint: Use problem 4 above.

6. Let X be a binomial random variable with parameters 0 ≤ p ≤ 1 and n > 0 an integer. For any 0 ≤ k ≤ n, denote by Pk = P(X = k). Compute

2 SPRING 2013

the ratio Pk−1 Pk

for 1 ≤ k ≤ n.

Show that this ratio is less than one if and only if k < np + p. This shows that the most probable values of X are those near np.

7. Let X be a Poisson random variable with parameter λ > 0. Let g : R → R be the function g(x) = x(x− 1). Set Y = g(X). Find E(Y ).

8. Let X be a function whose range is {1, 2, 3, · · ·}. Consider the values

P(X = n) = 1

n(n + 1) for any n ≥ 1 .

Does this function X define a discrete random variable? If so, what is E(X)?

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