396
9 Bioenergetics
Life systems on Earth have learned to use catalysts, inhibitors, enhancers,
regulators, chaperones, etc., to control reaction rates. A catalyst is a substance which
becomes chemically involved in one or more reactions, increasing one or more
reaction rates. After a finite sequence of reactions, the catalyst is restored, ready
to take part in a repeat performance. Biochemical enzymes are an example of a
catalyst. There may also be temporary inhibitors that attach to a catalyst to slow
or stop its catalytic action, or attach to a reactant to slow or stop a reaction; or
enhancer proteins that facilitate catalysts; or parallel reactions that change the pH;
or mechanisms that carry reactants together.
As a reaction proceeds near equilibrium, with fixed temperature and pressure,
δG =
J
μ J δN J .
(9.205)
But the number of molecules of one type may change because of the reaction.
As type J molecule is consumed by a given reaction, the amount of some other
type K in the reaction must also change. From the definition of the stoichiometric
coefficients, this observation can be expressed as: δN J /ν J = δN K /ν K , J = K.
To see this ratio condition in an example, consider again the oxidation of water
2 H 2 + O 2 → 2 H 2 O ,
(9.206)
taking place in a gas with a large number of each molecule. If just one oxygen
molecule reacts with two hydrogen molecules to make two molecules of water, then
the amounts of each molecule change by: δN 1 = −2, δN 2 = −1, and δN 3 = +2.
This means
δN 1
−2
=
δN 2
−1
=
δN 3
+2
.
(9.207)
In the general case,
δN 1
ν 1
=
δN 2
ν 2
= · · · = δξ ,
(9.208)
where we have introduced a value for the common ratio, with the name δξ . The value
of δξ characterizes the progress of the reaction, and is the stoichiometric fraction of
the number of any one type of molecule that has engaged in the reaction after a short
time.
The ‘rate of the reaction’ is δξ/δt, with values being the number of particles
involved per unit time t. For example, if δξ/δt were N particles per second, then
Nν r of molecules of reactants of type r have reacted with Nν p of type p product
molecules each second. In the reaction rate, the detailed time-dependent dynamics
of the molecular interactions come to play, including the interactions with other
materials.
9 Bioenergetics
Life systems on Earth have learned to use catalysts, inhibitors, enhancers,
regulators, chaperones, etc., to control reaction rates. A catalyst is a substance which
becomes chemically involved in one or more reactions, increasing one or more
reaction rates. After a finite sequence of reactions, the catalyst is restored, ready
to take part in a repeat performance. Biochemical enzymes are an example of a
catalyst. There may also be temporary inhibitors that attach to a catalyst to slow
or stop its catalytic action, or attach to a reactant to slow or stop a reaction; or
enhancer proteins that facilitate catalysts; or parallel reactions that change the pH;
or mechanisms that carry reactants together.
As a reaction proceeds near equilibrium, with fixed temperature and pressure,
δG =
J
μ J δN J .
(9.205)
But the number of molecules of one type may change because of the reaction.
As type J molecule is consumed by a given reaction, the amount of some other
type K in the reaction must also change. From the definition of the stoichiometric
coefficients, this observation can be expressed as: δN J /ν J = δN K /ν K , J = K.
To see this ratio condition in an example, consider again the oxidation of water
2 H 2 + O 2 → 2 H 2 O ,
(9.206)
taking place in a gas with a large number of each molecule. If just one oxygen
molecule reacts with two hydrogen molecules to make two molecules of water, then
the amounts of each molecule change by: δN 1 = −2, δN 2 = −1, and δN 3 = +2.
This means
δN 1
−2
=
δN 2
−1
=
δN 3
+2
.
(9.207)
In the general case,
δN 1
ν 1
=
δN 2
ν 2
= · · · = δξ ,
(9.208)
where we have introduced a value for the common ratio, with the name δξ . The value
of δξ characterizes the progress of the reaction, and is the stoichiometric fraction of
the number of any one type of molecule that has engaged in the reaction after a short
time.
The ‘rate of the reaction’ is δξ/δt, with values being the number of particles
involved per unit time t. For example, if δξ/δt were N particles per second, then
Nν r of molecules of reactants of type r have reacted with Nν p of type p product
molecules each second. In the reaction rate, the detailed time-dependent dynamics
of the molecular interactions come to play, including the interactions with other
materials.