398
9 Bioenergetics
V Na = 61.5 mV. The Nernst–Planck equation balances the diffusion of ions across
a membrane in one direction with the forced motion due to the electric field across
the membrane carrying the ions in the opposite direction. As we have noted, for
living cells, transport of ions across cell membranes involve very few ions compared
to the number in the liquid near the membrane. This means that the concentrations
of the ions do not significantly change near the nerve cell membrane due to ion
transport, except after very long times of nerve cell firing.
A nerve membrane sustains a potential difference of about V = −70 mV using
ion pumps. (The interior of the cell has a lower potential than the outside.) Ninety
percent of the energy used by the brain is for these sodium pumps. A resting brain
uses about 20 W. An active brain can require 100 W.
The value of V across a cell membrane comes from not only the concentrations
of the various ions, but also the permeability of a variety of ion channels. (See the
Goldman–Hodgkin–Katz equation (9.180).)
9.21.1 Equilibrium of Chemical Reactions
If a system has a number of particle species, the amount of any one component in
one phase can change due to phase changes or by a chemical reactions. As such a
change progresses, small changes in the number of a certain species of molecules
M i must be in proportion to the stoichiometric coefficients ν i , (See Eq. (9.208))
dN i = ν i dξ
(9.213)
where dξ measures the progress of the reaction.
At constant temperature and pressure, the Gibbs free energy changes only by
changes in the particle numbers:
dG| T ,p =
μ i dN i .
(9.214)
For a reaction,
dG| T ,p = dξ
μ i ν i
(9.215)
At equilibrium, the Gibbs free energy reaches a minimum, so at equilibrium, we
have the condition
μ i ν i = 0 .
(9.216)
If the reactants and products are each in an ideal gaseous state, then the chemical
potentials are expressible in terms of the partial pressures p i = N i k B T /V as
9 Bioenergetics
V Na = 61.5 mV. The Nernst–Planck equation balances the diffusion of ions across
a membrane in one direction with the forced motion due to the electric field across
the membrane carrying the ions in the opposite direction. As we have noted, for
living cells, transport of ions across cell membranes involve very few ions compared
to the number in the liquid near the membrane. This means that the concentrations
of the ions do not significantly change near the nerve cell membrane due to ion
transport, except after very long times of nerve cell firing.
A nerve membrane sustains a potential difference of about V = −70 mV using
ion pumps. (The interior of the cell has a lower potential than the outside.) Ninety
percent of the energy used by the brain is for these sodium pumps. A resting brain
uses about 20 W. An active brain can require 100 W.
The value of V across a cell membrane comes from not only the concentrations
of the various ions, but also the permeability of a variety of ion channels. (See the
Goldman–Hodgkin–Katz equation (9.180).)
9.21.1 Equilibrium of Chemical Reactions
If a system has a number of particle species, the amount of any one component in
one phase can change due to phase changes or by a chemical reactions. As such a
change progresses, small changes in the number of a certain species of molecules
M i must be in proportion to the stoichiometric coefficients ν i , (See Eq. (9.208))
dN i = ν i dξ
(9.213)
where dξ measures the progress of the reaction.
At constant temperature and pressure, the Gibbs free energy changes only by
changes in the particle numbers:
dG| T ,p =
μ i dN i .
(9.214)
For a reaction,
dG| T ,p = dξ
μ i ν i
(9.215)
At equilibrium, the Gibbs free energy reaches a minimum, so at equilibrium, we
have the condition
μ i ν i = 0 .
(9.216)
If the reactants and products are each in an ideal gaseous state, then the chemical
potentials are expressible in terms of the partial pressures p i = N i k B T /V as