211G A20 -Biology Math Problems Assignment

13 Jun 211G A20 -Biology Math Problems Assignment

Question
Course Number: 211G A20
Course Name: Online – Cellular and Organismal Biology
Instructor: Catherine Hartkorn

Individual/Partner Project – Biology Math Problems Assignment
Write out your calculations and explanations for ALL problems.
Please do ask me for help on these if you need it.

Problem Set 1 – Problems on Biomolecules (2 problems):
1. The sequence of amino acids of the enzyme lysozyme is known. Below is a list of amino acids
and the number of each in the lysozyme molecule.
Type

Molecular Weight

Number in Lysozyme

Alanine

89

12

Arginine

174

11

Asparagine

132

13

Aspartic acid

133

8

Cysteine

121

8

Glutamic acid

147

2

Glutamine

146

3

Glycine

75

12

Histidine

155

1

Isoleucine

131

6

Leucine

131

8

Lysine

146

6

Methionine

149

2

Phenylalanine

165

3

Proline

115

2

Serine

105

10

Threonine

119

7

Tryptophan

204

6

Tyrosine

181

3

Valine

117

6

Questions:
a. What is the average molecular weight of the 20 amino acids?
b. What is the molecular weight of lysozyme?
c. What is the average molecular weight of the amino acids in lysozome?
d. How many S-S bonds are possible in lysozyme?
(hint: look at the structures of each amino acid, and figure out which of these have sulphurs
that are FREE to form bonds).
e. Is the net charge on lysozyme positive or negative?
(hint: again, look at the structures of each amino acid, and figure out which of these are
neutral, which are positively charged, and which are negatively charged; then add up the
individual charges for each amino acid to get the net charge of this protein)

2. Proteins (both enzymatic and structural) play a significant role in maintaining the pH in a cell.
Seven of the 20 amino acids commonly found in proteins have an ionizable group. These
groups (side chains) determine the charge on the protein and buffer the cytoplasm of the cell
that contains it.
Populations of proteins that contain ionizable side chains have a probability of being “charged”
or not. The probability of a side chain being charged is related primarily to the side chain
chemistry and the pH of the cellular compartment; other usually less important factors are
temperature, ionic strength, and bulk microenvironments.
The ratio of the charged to uncharged side chains is usually symbolized by K:
K=c/u
where c is the proportion of charged side chains and u is the proportion of uncharged side chains
(so that c + u = 1).
In the laboratory, the pH of a protein’s environment can be altered so that we have equal
numbers of charged and uncharged molecules. We call the pH at which K is 1 (equal number of
charged and uncharged side chains) the pK of the side chain.

Below is a list of the seven amino acids whose charge is altered by the cellular pH:
Acidic

pK

Basic

pK

Aspartic acid

3.87

Lysine

10.53 Cysteine

8.33

Glutamic acid

4.25

Arginine

12.48 Tyrosine

10.07

Histidine

Polar

pK

6.00

Cell compartments can vary in pH from about 4.0 to 8.5, but the pK values of the various amino
acids remain fixed. When the pH of the environment is not equal to the pK of the side chain,
the proportion of charged and uncharged side chains changes to as to satisfy the equation:
pH = pK + log ( c / u )
As an example, for aspartic acid in a protein with a pH environment of 3.87, pH = pK,
so log (c/u) = 0. Consequently, (c/u) = 10 ^ 0 = 1, and c = u. However, when the pH and the
pK are different, the term log (c /u) will not be zero and the ratio (c/u) will be different from 1.
Questions:
a. The pH of healthy cell cytoplasm varies from 7.2 to 7.4. Using this information, and the
information above, complete the following table:

Amino acid in protein

pK of the side chain

Percent Charged at pH Percent Charged at pH
= 7.2
= 7.4

Aspartic acid

3.87

?

?

Histidine

6.0

?

?

Cysteine

8.33

?

?

Arginine

12.48

?

?