Math/bio problem

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 Polar pK Aspartic acid 3.87 Lysine 10.53 Cysteine 8.33 Glutamic acid 4.25 Arginine 12.48 Tyrosine 10.07

Histidine 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 = 7.2

Percent Charged at pH = 7.4

Aspartic acid 3.87 ? ? Histidine 6.0 ? ? Cysteine 8.33 ? ? Arginine 12.48 ? ?