404
9 Bioenergetics
K
equib =
p [C F ] |νp|
r [C r ] |ν r | = exp (−g
o /RT ) .
(9.228)
In this way, for biological reactions, concentrations in the law of mass action for
water, hydronium ion, or magnesium ion are not included when calculating the
change in the Gibbs free energy per mole.
Biochemical reactions on Earth occur within water solutions or on boundaries of
macromolecules in contact with water solutions. Active transport can carry reactants
through membranes and along protein ‘highways’, and within capsules. In water
solutions, isolated reactants and products are carried by thermal diffusion. In most
cases, the reactant molecules are far less numerous than water, making the solutions
dilute.
In those cases for which molecules involved in a reaction act independently, the
application of statistical mechanics shows that the law of mass action is expressible
in terms of what are called reaction ‘activities’, a i , for each reactant and product,
rather than concentrations. For dilute solutions with no long-range interactions
between particles, the activities can be expressed in terms of concentrations with
a i = γ i [C i ]/[C
o
i ] ,
where the γ i are called the reaction activity coefficients (note they are unitless),
and [C o
i ] is a standard concentration for molecule kind labeled by ‘i’. Activity
coefficients are found in statistical mechanics from the so-called ‘partition function’
for the system, or modeled from experimental data. The arguments are presented in
Chap. 10.
Even for dilute solutions, if reactant or product molecules become surrounded
by other particles, such as by inhibitors or by ions attracted to participating charged
macromolecules, then the activity coefficients for dilute solutions become less than
one. As an example, we will discuss the Debye–Hückel model in Sect. 10.9.5.
9.21.3 Membrane Dynamics and Active Transport
Equilibrium ideas can be applied to a semi-permeable membrane, such as a cell wall.
Suppose component s is allowed to come into equilibrium across this membrane.
Let the system variables inside the cell be labeled by ‘I ’, and those outside by O.
If some dN k of the molecules of component s move from the inside to the outside,
then the Gibbs free energy for the combined system will change by
dG = (μ
O
k − μ
I
k )dN k .
(9.229)
At equilibrium, dG = 0, and the chemical potentials must balance:
9 Bioenergetics
K
equib =
p [C F ] |νp|
r [C r ] |ν r | = exp (−g
o /RT ) .
(9.228)
In this way, for biological reactions, concentrations in the law of mass action for
water, hydronium ion, or magnesium ion are not included when calculating the
change in the Gibbs free energy per mole.
Biochemical reactions on Earth occur within water solutions or on boundaries of
macromolecules in contact with water solutions. Active transport can carry reactants
through membranes and along protein ‘highways’, and within capsules. In water
solutions, isolated reactants and products are carried by thermal diffusion. In most
cases, the reactant molecules are far less numerous than water, making the solutions
dilute.
In those cases for which molecules involved in a reaction act independently, the
application of statistical mechanics shows that the law of mass action is expressible
in terms of what are called reaction ‘activities’, a i , for each reactant and product,
rather than concentrations. For dilute solutions with no long-range interactions
between particles, the activities can be expressed in terms of concentrations with
a i = γ i [C i ]/[C
o
i ] ,
where the γ i are called the reaction activity coefficients (note they are unitless),
and [C o
i ] is a standard concentration for molecule kind labeled by ‘i’. Activity
coefficients are found in statistical mechanics from the so-called ‘partition function’
for the system, or modeled from experimental data. The arguments are presented in
Chap. 10.
Even for dilute solutions, if reactant or product molecules become surrounded
by other particles, such as by inhibitors or by ions attracted to participating charged
macromolecules, then the activity coefficients for dilute solutions become less than
one. As an example, we will discuss the Debye–Hückel model in Sect. 10.9.5.
9.21.3 Membrane Dynamics and Active Transport
Equilibrium ideas can be applied to a semi-permeable membrane, such as a cell wall.
Suppose component s is allowed to come into equilibrium across this membrane.
Let the system variables inside the cell be labeled by ‘I ’, and those outside by O.
If some dN k of the molecules of component s move from the inside to the outside,
then the Gibbs free energy for the combined system will change by
dG = (μ
O
k − μ
I
k )dN k .
(9.229)
At equilibrium, dG = 0, and the chemical potentials must balance: