Chapter 2 – Orientation for the Bio-Curious 55
QUESTIONS
2.1
In a reversible isomerization reaction between two isomers of the same molecule,
explain what proportion of the two isomers might be expected to exist at chemical
equilibrium, and why. In an autocatalytic reaction, one of the reacting molecules itself
acts as a catalyst to the reaction. Explain what might happen with a small excess of
one isomer to the relative amounts of each isomer as a function of time. How is this
relevant to the d/l isomers amino acids and sugars? Discuss how might evolution
affect the relative distribution of two isomers? (For a relevant, interesting read, see
Pross, 2014.)
2.2
Staphylococcus aureus is a spherical bacterium of 1 μm diameter, which possesses just
one circular chromosome. A common form of this bacterium was estimated as having
1.2% of its cellular mass taken up by DNA.
a
What is the mass of the cell’s chromosome?
b
The bases adenine, cytosine, guanine, and thymine have molecular weights of
0.27, 0.24, 0.28, and 0.26 kDa, respectively, excluding any phosphate groups. The
molecular weight of a phosphate group is 0.1 kDa. Estimate the contour length of
the S. aureus genome, explaining any assumptions.
2.3
The primary structure of a human protein compared to that of budding yeast,
S. cerevisiae, which appears to carry out the same specific biological function, was
found to have 63% identical sections of amino acids based on short sequence sections
of at least five consecutive amino acids in length. However, the respective DNA
sequences were found to be only 42% identical. What can account for the difference?
2.4
The cell doubling time, a measure of the time for the number of cells in a growing
population to double, for E. coli cells, which is a rich nutrient environment, is 20 min.
What rate of translation of mRNA into amino acids per second can account for such
a doubling time? How does this compare to measured rates of mRNA translation?
Comment on the result.
2.5
What is the relation between force and its potential energy landscape? Why is it more
sensible to consider the potential energy landscape of a particular force first and then
deduce the force from this, as opposed to considering just a formulation for the force
directly?
2.6
What are the van der Waals interactions, and how do these relate to the Lennard–
Jones potential? Rewrite the Lennard–Jones potential in terms of the equilibrium dis
tance rm in which the net force is zero and the depth of potential parameter is in Vm,
which is the potential energy at a distance rm.
2.7
A DNA molecule was found to have a roughly equal mix of adenine, cytosine, guanine,
and thymine bases.
a
Estimate the probability for generating a mismatched base pair in the DNA double
helix, stating any assumptions you make. (Hint: use the Boltzmann factor.) When
measured in a test tube, the actual mismatch error was found to be 1 in 105.
Comment on the result.
b
In a living cell, there is typically one error per genome per generation (i.e., per cell
division). What error does this equate to for a human cell? How, and why, does
this compare with the value obtained earlier?
2.8
Calculate, with reasoning, the free energy difference in units of kBT required to trans
locate a single sodium ion Na+ across a typical cell membrane. Show, by considering
the sodium ion to be a unitary charge q spread over a spherical shell of radius r, that
the activation energy barrier required to spontaneously translocate across the lipid
bilayer of electrical relative permittivity εr is given by q/8π rεrε0. (Note, this is known
as the “electrical self energy”). There is an initial concentration of 150 mM of sodium
chloride both inside and outside a roughly spherical cell of diameter 10 μm, with a
sodium ion diameter of 0.2 nm. The cell is immersed in a specific kinase inhibitor
that prevents ATP hydrolysis, which is normally required to energize the pumping
of sodium ions across the cell membrane through sodium-specific ions channels (see
Chapter 4), and the cell is then suddenly immersed into pure water. Calculate the