DƯỢC LÍ Goodman & Gilman's The Pharmacological Basis of Therapeutics 12th, 2010

accordance with its concentration gradient. The driving
force for this type of transport therefore is stored in the
electrochemical potential created by the concentration
difference of S 2
across the plasma membrane. For
example, an inwardly directed Na + concentration gradient
across the plasma membrane is created by Na + ,
K + -ATPase. Under these conditions, inward movement
of Na + produces the energy to drive the movement of a
substrate S 1
against its concentration gradient by a secondary
active transporter as in Na + /Ca 2+ exchange.
Depending on the transport direction of the solute, secondary
active transporters are classified as either symporters or antiporters.
Symporters, also termed co-transporters, transport S 2
and S 1
in the
same direction, whereas antiporters, also termed exchangers, move
their substrates in opposite directions (Figure 5–4). The free energy
produced by one extracellular sodium ion (Na + ) is given by the difference
in the electrochemical potential across the plasma membrane:
⎛ C
Δ = E F + RT In⎜
⎝ C
Na,
i
μ Na m
(Equation 5–4)
The electrochemical potential of a non-ionized compound Δμ s
acquired from one extracellular Na + is less than this value:
(Equation 5–5)
Therefore, the concentration ratio of the compound is given by the
following equation:
(Equation 5–6)
Assuming that the concentration ratio of Na + is 10 and that E m
is
–60 mV, ideally, symport of one non-ionized organic compound with
one Na + ion can achieve a 100-fold difference in the intracellular
substrate concentration compared with the extracellular concentration.
When more than one Na + ion is coupled to the movement of
the solute, a synergistic driving force results. For the case in which
two Na + ions are involved,
S
i
S
o
S
i
S
o
⎛ C
≤ ⎜
⎝ C
⎛ C
≤ ⎜
⎝ C
Na,
o
Na,
i
Na,
o
Δ μ + Δμ
≤ 0
2
⎞ ⎛ −2E F⎞
m
⎟ exp⎜
⎠ ⎝ RT ⎟
⎠
(Equation 5–7)
In this case, the substrate ideally is concentrated intracellularly 1000-
fold relative to the extracellular space under the same conditions.
The Na + /Ca 2+ antiporter shows the effect of this dependence in the
square of the concentration ratio of Na + ; Ca 2+ is transported from the
cytosol (0.1 μM < [Ca 2+ ] < 1 μM) to the plasma [Ca 2+ ] free
~1.25 mM.
KINETICS OF TRANSPORT
s
Na,
o
Na,
i
The flux of a substrate (rate of transport) across a biological
membrane via transporter-mediated processes
Na
⎞
⎟
⎠
⎞ ⎛ − E F⎞
m
⎟ exp⎜
⎟
⎠ ⎝ RT ⎠
is characterized by saturability. The relationship
between the flux v and substrate concentration C in a
transporter-mediated process is given by the Michaelis-
Menten equation:
V
v =
K
C
+ C
(Equation 5–8)
where V max
is the maximum transport rate and is proportional
to the density of transporters on the plasma
membrane, and K m
is the Michaelis constant, which
represents the substrate concentration at which the flux
is half the V max
value. K m
is an approximation of the dissociation
constant of the substrate from the intermediate
complex. When C is small compared with the K m
value,
the flux is increased in proportion to the substrate concentration
(roughly linear with substrate concentration).
However, if C is large compared with the K m
value, the
flux approaches a constant value (V max
). The K m
and
V max
values can be determined by examining the flux at
different substrate concentrations. The Eadie-Hofstee
plot often is used for graphical interpretation of saturation
kinetics. Plotting clearance v/C on the y axis and
flux v on the x axis gives a straight line. The y intercept
represents the ratio V max
/K m
, and the slope of the line is
the inverse of the K m
value:
v
C
(Equation 5–9)
Involvement of multiple transporters with different
K m
values gives an Eadie-Hofstee plot that is curved.
In algebraic terms, the Eadie-Hofstee plot of kinetic
data is equivalent to the Scatchard plot of equilibrium
binding data.
Transporter-mediated membrane transport of a
substrate is also characterized by inhibition by other
compounds. The manner of inhibition can be categorized
as one of three types: competitive, noncompetitive,
and uncompetitive.
Competitive inhibition occurs when substrates
and inhibitors share a common binding site on the transporter,
resulting in an increase in the apparent K m
value
in the presence of inhibitor. The flux of a substrate in
the presence of a competitive inhibitor is
V C
max
v =
(Equation 5–10)
K I K C
m( 1 + /
i) +
where I is the concentration of inhibitor, and K i
is the
inhibition constant.
max
m
Vmax
C
= −
K K
m
m
95
CHAPTER 5
MEMBRANE TRANSPORTERS AND DRUG RESPONSE