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2.5 Physical Quantities in Biology
Worked Case Example 2.3: Intracellular Concentrations
In one experiment, the numbers of 40 different protein molecules per cell were estimated
from a population of many E. coli bacteria and found to have mean values in the range
9–70,000 molecules per cell. (An E. coli cell is rod-shaped approximated for much of its
cell cycle as a cylinder of length 2 μm capped at either end with a hemisphere of diam
eter 1 μm.)
a
What is the volume of a single E. coli cell in L?
b
What does the mean data for protein numbers suggest in the range of molarity values
for different proteins in units of nM?
c
What is the smallest nonzero protein molarity you might measure if you had the
sensitivity to perform the experiment on just a single cell with arbitrarily high time
resolution?
d
How does this compare with the molarity of pure water (hint: what is the formal def
inition of molarity)?
Answers:
a
The volume of the cell Vc = {(1.0 × 10−6 × 0.5)2 × (2.0 × 10−6)} + {2 × 2 × π × (1.0 ×
10−6 × 0.5)3/3} = 1.0 × 10−18 m3 = 1.0 × 10−15 L.
b
The number of moles for total number of n molecules is n/(6.022 × 1023).
Thus, the range in number of moles for proteins studied is {9–70,000}/(6.022 ×
1023) = 1.5 × 10−23 to 1.2 × 10−19 mol.
Thus, the range in molarity is {1.5 × 10−23 to 1.2 × 10−19}/(1.0 × 10−15) = 1.5 × 10−8 to
1.2 × 10−4 M = 18–120,000 nM.
c
For a single-cell measurement with high time resolution, one might be able to
detect the presence of just a single protein molecule in a cell since expression
from a single gene is stochastic. This minimal nonzero molarity = {1/(6.022 ×
1023)}/(1.0 × 10−15) = 1.7 nM.
d
Water has molecular weight equivalent to 18 Da (i.e., 18 g, each molecule
consisting of 1 atom of oxygen, atomic mass 16 g, and 2 atoms of hydrogen,
atomic mass 1 g). The mass of 1 L of water is 1 kg; thus, the number of moles in 1
L of water is 1/(0.018) ≈ 56 M.
2.6 SUMMARY POINTS
◾Carbon chemistry permits catenated compounds that form the chemicals of life.
◾Biology operates at multiple length and time scales that may overlap and feedback
in complex ways.
◾The cell is a fundamental unit of life, but in general it needs to be understood in the
context of several other cells, either of the same or different types.
◾Even simple cells have highly localized architecture, which facilitates specialist bio
logical functions.
◾The most important class biomolecules are biological catalysts called “enzymes,”
without which most chemical reactions in biology would not happen with any
degree of efficiency.
◾The shape of molecules is formed from several different forces, which leads to
differences in their functions.
◾The key process in life is the central dogma of molecular biology, which states
that proteins are coded from a genetic code written in the base pair sequence
of DNA.