Question

You have come down with a nasty cold and would like to understand why the virus that infected you is making you feel so lousy. With a few basic facts, given here within the problem, you can show that each infected cell is now very full of virus particles, resulting in your current condition. a. Given that a typical cell is about 10 μm in diameter, calculate its volume in liters. b. Find the concentration (in Molarity) of a single virus within that cell. c. Find the concentration (in Molarity) of 100 virus particles within that cell. d. Find the concentration (in Molarity) of 5*104 (50,000) virus particles — a typical number produced by a viral infection — within that cell. e. If each virus particle is 100 nm in diameter, calculate the “excluded volume” — the space occupied by those 5*104 virus particles. Compare this to the volume of the cell. In other words, what fraction of the cells total volume is being occupied by the virus particles? f. Calculate the average distance between virus particles (hint; in lecture, we did a similar calculation for gas molecules and started out with the inverse of the particle number density (N/V).

Answer 1

A. Calculate the volume of the cell in cm³, which is equivalent to mL.
10 µm = 10^-3 cm. The volume of the cell is (10^-3 cm)³ = 10^-9 mL
Since the density of the cell is 1 g/cm³, a cell weighs 10^-9 g.

B. Molar concentration is to divide the total number of virions per ml by Avogadro number.

For example: your have 1.2*10^13 virions/ml

Molar concentration = 1.2*10^13 / 6.023*10^23 = 0.19*10^-9 = 0.19*10^-19 mole per ml; for lit, 0.19nM.

C. If one million virions are added to one million cells, the MOI is one. If ten million virions are added, the MOI is ten. Add 100,000 virions, and the MOI is 0.1. The concept is straightforward.