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The Statistical Basis of Bioenergetics
10.3 Speculate on how the possible protein foldings in present life forms has been
restricted by evolution.
10.4 Describe how the attachment of a small molecule to the surface of a larger
molecule can increase the rate of the reaction of the smaller molecule with another
smaller molecule.
10.5 Outline a computer program that finds possible foldings of a given short
sequence of amino acids forming a protein in a biological cell.
10.6 Consider a molecule in an NMR machine that has four separated hydrogen
protons whose spins are effectively uncoupled to neighboring atoms. Being spin
1/2 particles, they are allowed by quantum theory to have only two measurable
orientations with the external magnetic field, aligned or anti-aligned. With four
arrows indicating spin, show the possible configurations of the proton spins. In an
NMR magnetic field of B = 1.2 T, the energy of the anti-aligned spins are higher
than the aligned. If the environmental temperature is T = 37 ◦ C, what is the fraction
of the aligned protons at equilibrium.
10.7 On the International Space Station, astronauts use an airlock to enter and
exit at the beginning and end of spacewalks. The pressure in the airlock is first
lowered from 1 to 0.694 atm, and the air enriched with oxygen, to reduce the
nitrogen dissolved in the astronaut’s blood. The astronaut spends the ‘night’ in this
chamber. After the astronaut puts on his spacesuit (containing pure oxygen), the
airlock drops pressure to 0.293 atm, the pressure that the spacesuit can sustain in the
vacuum of outer space. Finally, the airlock is evacuated and the astronaut can exit to
space. If the volume of the airlock chamber is 34 cubic meters, how much does the
temperature of the air in the chamber drop during the drop of pressure from 0.694
to 0.293 atm, assuming no heat input, and starting T i = 25 ◦ C?
10.8 Estimate the reduction in oxygenated hemoglobin while smoking a cigarette
which produces 100 ppm of carbon monoxide gas.
10.9 What is the expected relative fluctuation (N/N ) in water molecule number
in a nanoscale volume of water of size V = 10(nm)
3 and at body temperature of
37 ◦ C.
10.10 The result of hydrolysis of the AT P in our cells is the release of energy,
which is used to promote other reactions. In the process, ADT and inorganic
hydrogen phosphate H 3 PO 4 are produced. The symbol P i (‘inorganic phosphate’)
will be used for H 3 PO 4 . Under standard conditions (T s = 25 ◦ C, p s = 10 5 N/m 2 ,
pH = 7.0, [AT P ] = 1 M, [ADP ] = 1 M, [P i ] = 1 M), the available
energy per mole is the change in the Gibbs free energy per mole for the reaction
AT P → ADP + P i , which is found to be g o = −30.5 kJ/mol. In an intracellular
environment, g o varies between −28 to −34 kJ/mol, depending on the pH and
the concentration of Magnesium ions. If, in the cell, [AT P ] = 1.4 mM, [ADP ] =
0.5 mM, and [P i ] = 1.2 mM, what is the range of the Gibbs free energy per mole
released?
The Statistical Basis of Bioenergetics
10.3 Speculate on how the possible protein foldings in present life forms has been
restricted by evolution.
10.4 Describe how the attachment of a small molecule to the surface of a larger
molecule can increase the rate of the reaction of the smaller molecule with another
smaller molecule.
10.5 Outline a computer program that finds possible foldings of a given short
sequence of amino acids forming a protein in a biological cell.
10.6 Consider a molecule in an NMR machine that has four separated hydrogen
protons whose spins are effectively uncoupled to neighboring atoms. Being spin
1/2 particles, they are allowed by quantum theory to have only two measurable
orientations with the external magnetic field, aligned or anti-aligned. With four
arrows indicating spin, show the possible configurations of the proton spins. In an
NMR magnetic field of B = 1.2 T, the energy of the anti-aligned spins are higher
than the aligned. If the environmental temperature is T = 37 ◦ C, what is the fraction
of the aligned protons at equilibrium.
10.7 On the International Space Station, astronauts use an airlock to enter and
exit at the beginning and end of spacewalks. The pressure in the airlock is first
lowered from 1 to 0.694 atm, and the air enriched with oxygen, to reduce the
nitrogen dissolved in the astronaut’s blood. The astronaut spends the ‘night’ in this
chamber. After the astronaut puts on his spacesuit (containing pure oxygen), the
airlock drops pressure to 0.293 atm, the pressure that the spacesuit can sustain in the
vacuum of outer space. Finally, the airlock is evacuated and the astronaut can exit to
space. If the volume of the airlock chamber is 34 cubic meters, how much does the
temperature of the air in the chamber drop during the drop of pressure from 0.694
to 0.293 atm, assuming no heat input, and starting T i = 25 ◦ C?
10.8 Estimate the reduction in oxygenated hemoglobin while smoking a cigarette
which produces 100 ppm of carbon monoxide gas.
10.9 What is the expected relative fluctuation (N/N ) in water molecule number
in a nanoscale volume of water of size V = 10(nm)
3 and at body temperature of
37 ◦ C.
10.10 The result of hydrolysis of the AT P in our cells is the release of energy,
which is used to promote other reactions. In the process, ADT and inorganic
hydrogen phosphate H 3 PO 4 are produced. The symbol P i (‘inorganic phosphate’)
will be used for H 3 PO 4 . Under standard conditions (T s = 25 ◦ C, p s = 10 5 N/m 2 ,
pH = 7.0, [AT P ] = 1 M, [ADP ] = 1 M, [P i ] = 1 M), the available
energy per mole is the change in the Gibbs free energy per mole for the reaction
AT P → ADP + P i , which is found to be g o = −30.5 kJ/mol. In an intracellular
environment, g o varies between −28 to −34 kJ/mol, depending on the pH and
the concentration of Magnesium ions. If, in the cell, [AT P ] = 1.4 mM, [ADP ] =
0.5 mM, and [P i ] = 1.2 mM, what is the range of the Gibbs free energy per mole
released?