Optional Practice Problems Lectures 1-4 (amino acids/peptides, pH and pK: Enzyme Kinetics) for Module 1

Biomolecular Chemistry 704 2007



1. a) Glycylglycine, a dipeptide, can be used as a buffer in solution. It is a good buffer near pH 3 and near pH 8. Which functional groups on this dipeptide can act as buffers and what are their pK's? _____________
b) A 0.1 M glycylglycine solution at pH 3.8 could act as a buffer. What percent of the carboxyl group would be in the ionized form? _____________ What percent of the amino group would be in the ionized form? _____________ Which functional group of glycylglycine is acting as a buffer in this solution?_____________

2. Draw the structure of the following pentapeptide as it exists at pH 7. Draw each bond and hydrogen in the structure.

serylaspartylphenylalanylarginyllysine (ser-asp-phe-arg-lys)





3. For the R groups in the pentapeptide listed in #3 above indicate whether it is a) acidic, basic, or uncharged; b) polar or nonpolar (hydrophobic); c) aromatic or nonaromatic. (Each group needs three labels.)

4. What is the net charge of the peptide drawn in #3 above at a) pH=7 and b) pH=12? If a group carries a partial charge at the above pH's calculate the fraction in the charged form. Use the approximate pKa's given in Module 1 p. 7 for all the side chain groups with acid/base properties as well as the alpha carboxyl and alpha amino groups on the C terminus and N terminus of the peptide. Note amide bonds like the peptide bond and the side chains of glutamine and asparagine do not have a pK.


Amino Acids and Peptides--Reference---Notes on how to study:

1. Realize that every amino acid has the same basic formula, except proline (for proline see p 5).

Learn the basic structure of the amino acids and then learn their individual R groups.


2. Understand that every individual amino acid has acid-base properties and can act as a buffer. Know the pK's of the alpha-carboxyl (~2) and alpha-amino groups ~(9) if the free amino acid not part of the peptide. (p. 7) of the module gives the pK's of these groups when these are at then end of a peptide of any size. [As an exercise show the above stucture at physiological pH, pH 7.4.]

3. Learn the R group -side chains for each amino acid listed in lecture 1, p. 5 of the module, by recognizing key functional groups. Be able to recognize the key properties of the R groups; polar (hydrophilic), nonpolar (hydrophobic), acidic, basic or neutral. By knowing the properties of the various amino acids it will be easier to remember them not simply memorize their structures.

4. Know which R group-side chains have acid-base properties and can act as a buffer. Know the approximate value of the pK's of these groups. These are listed on page 7 of the module. If there are side chains that do not have a pK in this table --these side chains are always neutral except in very special circumstances which will be indicated.

5. The R groups with acid-base properties will be 50% ionized (charged) at a pH equal to the pKa for that particular functional group. This group will also be 50% unionized (uncharged-neutral) at a pH equal to the pKa for that particular functional group.

6. Know what happens to the R groups with pKa values when the pH is above or below or equal to the pK. A particular functional group with a pKa will be either neutral (no charge) or charged (ionized) depending on pH. Any one particular functional group only has one charged form depending on whether it is an acidic or basic group.

Note: the conjugate base form can be represented by B- or A-

The Henderson-Hasselbalch equation,
pH = pKa + log A-/HA, can tell you about the conjugate base and weak acid (protonated form) forms of a weak acid group.
A-/HA= conjugate base form/weak acid form

or

pH = pKa - log HA/A-, can tell you about the weak acid(protonated) and conjugate base forms of a weak acid group. HA/A- = weak acid form/conjugate base form

a) At pH's above the pK, the R group will be less protonated (less H+). It will lose the proton (an hydrogen without an electron) and exist in the conjugate base form for that particular group. A CONJUGATE BASE CAN ACCEPT A PROTON.

b) At a pH equal to the pK, half of the molecules will have the proton on that group and half of the molecules will exist without the proton on that particular group. Therefore at a pH equal to the pK, a group will exist 50% in its acid form and 50% in its base form.

c) At pH's below the pK, the R group will be more protonated (more H+). The particular group with acid-base properties will gain the proton and exist in its conjugate acid form. THE ACID FORM CAN DONATE A PROTON.

7. As an exercise draw the free amino acids glutamic acid, histidine, arginine, and tyrosine as they would exist at pH 2, pH 12 and at physiological pH. [Note all of the alpha-carboxyl and alpha-amino groups will have the same structure at a particular pH in each amino acid. It is the R-group which will be different at each pH.]

8. Learn how to draw peptides (p.8 of Module 1). Each amino acid contributes unit to the backbone of a peptide or protein. When drawing a peptide always draw the basic backbone first. Then try filling in the amino acid R group. Notice that the formation of the peptide bond causes the loss of any acid-base (charge) properties of the alpha-amino and alpha-carboxyl group. In a peptide of any size however there can be a terminal amino group and a terminal alpha-carboxyl group which will have acid-base properties. The peptide bonds are "*" in the structure below.


Enzyme Kinetics

1. a. You have measured the velocity of an enzymatic reaction at three substrate concentrations and have obtained the following results:

 
v (nmoles/min) [s] (mM)
33.3 
55.5 
71.4
0.10 
0.25 
0.50
Graph the data and determine the Km and the Vmax. Show your work. Be sure to give the units or dimensions, not just a number.

2. On the graphs below are plots of data obtained with different types of enzyme solutions and varying [s]. The questions below will describe situations which might have given the data depicted by the graph. Indicate after each question the appropriate graph which should be looked at and the parameters asked for.
competive inhibitor graph  V vs S graph
Sigmoidal curve for allosteric enzyme non competitive graph or irreversible or two different conc. of enzyme

A. Which graph depicts a velocity vs. substrate concentration for an allosteric enzyme with more than one subunit._______ Indicate the maximal velocity for the amount of enzyme used to make this plot.______________

B. Which graph most likely depicts a velocity vs substrate concentration for 1 mg of an enzyme which follows Michaelis-Menten Kinetics. __________ Indicate the value for Km and Vmax. _______________________________

C. Which graph shows a reciprocal plot (Lineweaver-Burk) of the effects of [s] on velocity for two different amounts of the same enzyme? _______ If one of the lines on the graph was from the data used to get your answer for B, what was the amount of enzyme used to get the other line?____________

D. Which graph shows a reciprocal plot (Lineweaver-Burk) of the effects of [s] on velocity for an enzyme with and without an irreversible inhibitor present? __________ What is the % inhibition shown? _________

E. Which graph shows a reciprocal plot (Lineweaver-Burk) of the effects of [s] on velocity for an enzyme with and without a competitive inhibitor present?________. What is the Ki for this inhibitor if the inhibitor concentration is 1 mM? ________

F. Which graph shows a reciprocal plot (Lineweaver-Burk) of the effects of [s] on velocity for an enzyme with and without inhibitor present, where that, in the presence of that inhibitor, shows that the degree (%) of inhibition changes (either inhibits more or less) with increasing substrate concentration?________.

3. You investigate a reversible inhibitor of acid phosphatase. This is done by measuring the rate at two substrate concentrations, a low concentration and a high concentration. The following data is obtained:
Low [S]
rate with no inhibitor present 0.0364 micromoles/min
rate with inhibitor A present 0.0308 micromoles/min

High [S]
rate with no inhibitor present 0.2000 micromoles/min
rate with inhibitor A present 0.1000 micromoles/min

Indicate the type of inhibitor and give enough of the reasoning to convince us you are not guessing.


 
 
 
Last Updated 8/15/07 vh