# Course Number: 211G A20 Course Name: Online – Cellular and Organismal Biology Instructor: Catherine Hartkorn Individual/Partner Project – Biology Math Problems Assignment Write out…

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.
To solve the problems in this problem set, you will need to review (or look up, if you cannot remember) some geometry formulas.
Problem Set 2 – Problems on Cell Structures and Membranes (3 problems):
3. Lysosomes are little sacs of acid in a cell. Their pH is about 5, and an electron micrograph suggests they have a diameter of 0.5 μm. The increased hydrogen ion concentration inside lysosomes is due to the pumping of hydrogen ions across the lysosomal membrane from the surrounding cytosol, which has a pH of 7.2.
a. Assuming that a lysosome has the shape of a sphere and that there is no buffering capacity inside the lysosome, how many hydrogen ions were moved to the inside of the lysosome to lead to an internal pH of 5?
(hint: first determine the volume of a lysosome in liters, then determine [H+] in moles/L in a lysosome at each pH (5 and 7.2), then determine the number of moles of hydrogen ions at each pH, and finally determine and compare the number of hydrogen ions at each pH).
4. Liposomes are laboratory-prepared artificial membranes. Liposomes can be made in a variety of sizes and can be made so that they have transmembrane proteins, which form membrane. Contents of the liposomes can also be known.
For example, let’s say that one lab makes liposomes that are spheres with the diameter of 4 μm and that each liposome has an average of ten protein pores. Each liposome has an internal potassium ion concentration of 100 mM. Each protein pore transports 3x 10^6 potassium ions per second. The pores stay open an average of 0.3 second and stay closed an average of 2 seconds; so, each pore opening and closing cycle takes about 2.3 seconds.
a. Assuming that a liposome has the shape of a sphere, how many potassium ions are in a liposome initially?
(hint: the method here is similar to what you used to solve problem 3 above, except find the volume of a liposome in μm^3 and the [K+] in mol/μm^3)
b. How much time is required for the potassium ions in the liposome to reach equilibrium with their environment? Assume that this environment is relatively large and potassium-free.
(hint: before calculating the total time it would take to reach this equilibrium, think about how many potassium ions would need to leak out of the liposome in order to reach this equilibrium – all of them, half of them, none of them, why?)
5. Glycophorin is a single-pass transmembrane protein in red blood cells (RBCs). The protein component of glycophorin is 131 amino acids long and binds carbohydrates on the outside (noncytoplasmic side) of glycophorin. Then, approximately 100 modified sugar residues are attached near the end of each glycophorin; these account for about 60% of this macromolecule’s mass. The average molecular weight of an amino acid is 130 daltons.
a. What is the average molecular weight (in daltons) of each modified sugar residue on the glycophorin?
b. An RBC contains an average of 6 x 10 ^5 glycophorin molecules. How many modified sugar residues are found attached to glycophorins in one RBC?
c. How many grams does the protein component of glycophorin weigh in one RBC?

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