Cell cycle and number of ribosomes
Read the paper "Ribosome content and the rate of growth of Salmonella
typhimurium" by R.E. Ecker and M. Schaechter (Biochim. Biophys. Acta
76,275,1963 ).
(a) The authors show that their data can be fit by a simple assumption that
the rate of production of soluble protein, \(P\) is proportional to the number
of ribosomes. But this leaves out the need for the ribosomes to also make
ribosomal protein, in an amount, \(R\). The simplest assumptions are that the
total protein production rate, \(\mathrm{d} A / \mathrm{d} t,\) is proportional
to the number of ribosomes, and the total amount of non-ribosomal protein
(also knows as soluble protein) needed per cell is independent of growth rate.
Given these assumptions, how would the ratio \(R / A\), with \(A\) the total
protein content, depend on the growth rate? Does this give a maximum growth
rate? If so, what is it?
(b) With a 3000 s division time for \(E .\) coli, about \(25 \%\) of its protein
is ribosomal. Note that the microbe Salmonella typhimurium considered here is
very similar to \(E .\) coli. Using these numbers and your results from above,
what fraction of the protein would be ribosomal for the highest growth rate
studied in the paper? How does this compare to their measured ratio of
ribosomes to soluble protein, \(R / P\) at these growth rates? How does the
predicted \(R / P\) at high growth rates change if you now assume that
\(\mathrm{d} P / \mathrm{d} t\) is proportional to \(R\) as they did in the paper?
(c) Another factor that needs to be taken into account is the decay of
proteins. If all proteins decayed at the same rate, \(\gamma\) how would this
modify your results from
(a)? How does the predicted functional from of R/A versus growth rate change?
Explain why the data rule out \(\gamma\) being too large and hence infer a rough
lower bound for the lifetime, \(1 / \gamma,\) of "average" proteins.