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Figure 12. A variable intrapore
energy well model. (A) Two energy wells, designated c and e, in
the pore of ROMK2. Both are
shallow such that most K+ ions
pass through the channel easily
(left). However, when the inner
well (e) deepens, a permeating
K+ ion is trapped (right). (B) Energy profiles for K+ trapped in
the deep well at 0, −100, and
−300 mV (top) under the condition of 110 K+ solution. The fractional distance refers to the fraction of the transmembrane electric field sensed, with the
extracellular and intracellular
boundaries set at 0 and 1, respectively. (C) Energy barriers as a
function of voltage under the
condition of 110 K+ solution. As
the membrane potential becomes more negative, the
heights of the outer (ΔU2, solid
line) and inner (ΔU3, broken line)
barrier increase and decrease, respectively. A trapped ion preferentially crosses the outer barrier
between 0 and −110 mV and the
inner barrier between −110 and
−300 mV (dotted line).
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Figure 13. Hypothetical mechanism for the variable energy
well. The pore of ROMK2 has a
binding site comprised of four
identical elements that can
move in a radial direction. The
elements may move toward a cation occupying the binding site to
coordinate and trap the ion, closing the channel.
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Figure 1. ROMK2 has two closed and one open states. (A) Single-channel K+ currents in a cell-attached patch from a Xenopus oocyte expressing ROMK2. Pipette solution contained the control solution. High bath K+ (110 mM) depolarized oocytes, and the voltage at the left of each record is the negative of the applied pipette
potential and is presumed to approximate the potential difference
across the patch (oocyte relative to pipette). Upward deflections
from the closed state (dashed line) correspond to inward K+ current. The long closures at −120 mV appear to be longer than
those at −80 and −200 mV. (B) Histogram of closed times at −100
mV. The histogram is fit with two exponential distributions with
time constants of 1.4 and 47 ms. 99% of closures are accounted for
by the short time constant. (C) Histogram of open times at −100
mV. The histogram is fit with one exponential distribution with a
time constant of 17 ms.
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Figure 2. Voltage dependence of mean closed and open time.
(A) Closed times. The smooth lines are fitted lines with Eq. 6. The
best-fit values for the long closed state are ΔU2 = 15 kBT, δ2 =
−0.30, ΔU3 = 20 kBT, and δ3 = 0.26 (top line). The best-fit values
for the short closed state are ΔU2 = 12 kBT, δ2 = −0.33, ΔU3 = 15
kBT, and δ3 = 0.33 (bottom line). Data represent means ± SEM for
five to eight experiments. (B) Open times. The line is fitted with
Eq. 4. The best fit values were ΔU1 = 3 kBT and δ1 = 0.24. The
value of A was set to 0.90 based on the result of Fig. 10 C. Data represent means ± SEM for five to eight experiments.
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Figure 10. Effect of K+ concentration on the gating of ROMK2.
(A) Single channel K+ currents
with 10, 110, and 500 K+ solutions in the pipette. V = −120
mV. (B) Mean open times with
10 (▪), 110 (•), and 500 (▴) K+
solutions in the pipette plotted as
functions of voltage. The data
were fit with Eq. 4. The best fit
values were ΔU1 = 3.4 kBT and δ1
= 0.20. The values of A for 500,
110, and 10 K+ were 1.37, 0.90,
and 0.42, respectively. Data
points represent 3 (500 K+), 3
(10 K+), and 5–13 (110 K+) experiments. (C) Mean closed
times with 10 (▪), 110 (•), and
500 (▴) K+ in the pipette plotted
as functions of voltage. The 110
K+ data contain data from experiments with 110 K+, 1 Cs+, 0.1
Cs+, 0.01 Cs+, 10 Na+, and 10 Li+
solution. The data were fit simultaneously with Eq. 6. The best fit
values are ΔU2 = 12 kBT, δ2 =
−0.24, and δ3 = 0.42. The values
of ΔU3 are 14, 15, and 18 kBT for
500, 110, and 10 K+, respectively.
Data points represent 3 (500
K+), 3 (10 K+), and 5–13 (110
K+) experiments.
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Figure 3. Ba2+ increases the number of long closures. (A) Single-channel K+ currents with 0.5, 0.05, and 0.005 mM Ba2+ in the
pipette. The voltage was −60 mV in each case. (B) Histogram of
closed times with 0.05 mM Ba2+ at −60 mV. The line represents
the best fit with two exponential distributions with time constants
of 0.9 ms (31% of closures) and 31.5 ms (69% of closures). (C)
Histogram of open times with 0.05 mM Ba2+ at −60 mV. The line
represents the best fit with one exponential with a time constant of
5.4 ms. (D) Blocking rates, kblock, and unblocking rates, kunblock, as a
function of Ba2+ concentration at −60 mV. kblock was calculated
with Eq. 8. The line for the kblock is the best fit with the function,
kblock = A · [Ba2+]o, where A is 1.94 · 106 s−1 M−1. kunblock was obtained from the inverse of long closed time. The line for the kunblock
represents the mean value of 29 s−1. Data are from four, four, and
six experiments with 0.5, 0.05, and 0.005 mM Ba2+, respectively.
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Figure 4. Ba2+ shows biphasic
voltage-dependent off rates. (A)
Single-channel K+ currents with
0.005 mM Ba2+ solution in the pipette. There are more long closures compared with those with
control solution as shown in Fig.
1 A. The durations of long closures at −120 mV appear to be
longer than those at −60 and
−200 mV. (B) Histogram of
closed times with 0.005 mM Ba2+
at −100 mV. The line represents
the best fit with two exponential
distributions with time constants
of 1.0 ms (63% of closures) and
49.8 ms (37% of closures). (C)
Histogram of open times with
0.005 mM Ba2+ at −100 mV. The
line represents the best fit with
one exponential with a time constant of 8.5 ms. (D) Blocking
rates of Ba2+ as a function of voltage. Eq. 3 was used to fit the data.
The best-fit values were ΔU1 = 6
kBT and δ1 = 0.40. Data represent means ± SEM for three to
six experiments. (E) Mean dwell
time of long closures as a function of voltage. The data were fit
with Eq. 6 (solid line). The values
of the best fit were ΔU2 = 15 kBT,
δ2 = −0.24, ΔU3 = 21 kBT, and δ3
= 0.28.
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Figure 5. EDTA eliminates long closures. (A) Single channel K+
currents with 5 mM EDTA in the 110 K+ solution. The long closures were rarely seen. (B) Closed-time histogram at −80 mV. The
histogram was fit well with one exponential distribution with a
time constant of 1.0 ms. (C) Open-time histogram at −80 mV. The
histogram was fit well with one exponential distribution with a
time constant of 17 ms.
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Figure 6. Voltage dependence of mean closed and open time
with EDTA. (A) Closed times. The lines are fit with Eq. 6. The best-fit values were ΔU2 = 12 kBT, δ2 = −0.24, ΔU3 = 15 kBT, and δ3 =
0.42. Data represent means ± SEM for three to six experiments except −40 mV (n = 1). (B) Open times. The line is obtained from
Eq. 4. The best-fit values are ΔU1 = 3.3 kBT and δ1 = 0.20. The
value of A was set to 0.90 based on the result of Fig. 10 C. Data are
from the same experiments as in A.
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Figure 7. 10 mM Rb+ + 110 mM K+ solution in the pipette. (A)
Closed-time histogram at −100 mV. A single exponential did not
adequately describe the histogram. (B) A good fit to the data in A
was obtained with two exponential distributions with time constants of 0.3 ms (74%) and 1.9 ms (26%). (C) Voltage dependence
of longer short closed times. The values of the best fit obtained
with Eq. 6 were ΔU2 = 13 kBT, δ2 = −0.10, ΔU3 = 16 kBT, and δ3 =
0.18. Data from three experiments. (D) Voltage dependence of
shorter short closed times. The values of the best fit obtained with
Eq. 6 were ΔU2 = 10 kBT, δ2 = −0.15, and ΔU3 = 16 kBT. δ3 was set
to be 0.2. Data from three experiments.
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Figure 8. Effect of Rb+ only
(110 Rb+) solution in the pipette. (A) Closed-time histogram at −100 mV. The histogram was well described by one
exponential distribution with a
time constant of 0.65 ms. (B)
Voltage dependence of closed
times. The values of the best fit
obtained with Eq. 9 were ΔU2 =
11 kBT, δ2 = −0.15, and ΔU3 =
17 kBT. δ3 was set to be 0.2. Individual data from two experiments are shown.
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Figure 9. The effect of Cs+ on
the mean open time and single
channel current. (A) Currents
with 1 mM Cs+ solution in the pipette. (B) Voltage dependence
of mean open time. Data from
four to five experiments. (C)
Voltage dependence of single
channel current. The line is the
best fit with Eq. 10 to the data
from −20 to −120 mV. Best fit
values were Ki = 16.4 mM and δ
= 0.60. Data from four to five experiments.
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Figure 11. Rate of entering the short closed state as functions of
voltage (A) and current amplitude (B). Symbols are 110 K+ (♦),
500 K+ (□), 10 K+ (▴), 1 Cs+ (○), 0.1 Cs+ (▪), 0.01 Cs+ (▵), 10
Na+ (×), and 10 Li+ (⋄). The straight line in B is a linear regression line with slope of 23 and y intercept of 17 (correlation coefficient = 0.985).
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