Biology Reference
In-Depth Information
direction of reducing the perturbation), since, if L and P are increased in Scheme
7.2
,
the perturbation will shift the equilibrium from left to right and the quotient, [L'
P']/
∙
[L][P], in Eq.
7.3
will decrease making
G more negative (or less positive).
The binding process in Scheme in
7.2
can be altered in two distinct ways:
D
1. By changing the concentrations of the interacting molecules, that is, L, P, and
L'
P', and
2. By changing the structures of the interacting molecules thereby changing their
binding affinities for ligands as reflected in the standard Gibbs free energy
change,
∙
G
0
.
D
The first mechanism of changing binding equilibria may be referred to as the
“concentration effect” (which is global affecting all interacting molecules more or
less simultaneously and the second mechanism as the “structure effect”) (which can
be localized to individual molecules). The concentration effect will be manifested
through the quotient term in Eq.
7.3
, and the structure effect will be exerted through
the changes in the standard Gibbs free energy levels,
G
0
, of interacting molecules.
D
At equilibrium,
D
G
¼
0. So, Eq.
7.3
can be rewritten as
G
0
D
¼
RT log K
(7.4)
e
D
G0
=
RT
K
¼
(7.5)
where K is the equilibrium constant defined as [L'
P']/([L][P]). Equation
7.5
indicates that the equilibrium constant of a ligand-binding process is the exponen-
tial function of the standard Gibbs free energy change associated with that process.
As evident in Eq.
7.3
,
∙
G
0
can become equal when [L'
D
G and
D
P'], [L] and [P]
∙
G
0
can be experimentally determined by measur-
are unity (e.g., 1 mol/L). Thus,
D
ing
'P', L, and P at 1 mol/L. Similarly,
the kinetics (i.e., rate) of the ligand-binding process, Scheme
7.2
, is determined by
both the concentrations of the chemical species involved, that is, [L] and [P], and
the Gibbs free energy change,
D
G while keeping the concentrations of L
∙
G
{
, between the initial and the transition state of the
system (assuming that the rate of de-binding is negligible) according to Eq.
7.6
:
D
z
=
RT
Ae
D
G
k
¼
(7.6)
where k is the
rate constant
(i.e., the rate at unit concentrations of chemicals involved)
for the binding process, Scheme
7.2
, and A is the “pre-exponential factor” that reflects
the molecular motions at the transition state (Laidler 1965; Kondepudi and Prigogine
1998, pp. 237-239). Please note that Eq.
7.6
indicates that the
rate constant
,k,of
binding is an exponential function of the
Gibbs free energy of activation,
G
{
,
whereas Eq.
7.5
indicates that
the equilibrium constant, K,
of the same process is an
exponential function of the
standard Gibbs free energy change,
D
G
0
.
The Gibbs free energy changes accompanying the binding process represented
by Scheme
7.2
are diagrammatically presented in Table
7.1
. The
x
-axis is the
D
