From the Vollum Institute, Oregon Health Sciences University, Portland, Oregon 97201-3098
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ABSTRACT |
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Voltage-gated Ca2+ channels select Ca2+ over competing, more abundant ions by means of a high affinity binding site in the pore. The maximum off rate from this site is ~1,000× slower than observed Ca2+ current. Various theories that explain how high Ca2+ current can pass through such a sticky pore all assume that flux occurs from a condition in which the pore's affinity for Ca2+ transiently decreases because of ion interactions. Here, we use rate theory calculations to demonstrate a different mechanism that requires no transient changes in affinity to quantitatively reproduce observed Ca2+ channel behavior. The model pore has a single high affinity Ca2+ binding site flanked by a low affinity site on either side; ions permeate in single file without repulsive interactions. The low affinity sites provide steps of potential energy that speed the exit of a Ca2+ ion off the selectivity site, just as potential energy steps accelerate other chemical reactions. The steps could be provided by weak binding in the nonselective vestibules that appear to be a general feature of ion channels, by specific protein structures in a long pore, or by stepwise rehydration of a permeating ion. The previous ion-interaction models and this stepwise permeation model demonstrate two general mechanisms, which might well work together, to simultaneously generate high flux and high selectivity in single file pores.
Key words: Ca2+ channel; ion channel; permeation; selectivity; single file pores ![]() |
INTRODUCTION |
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Ca2+ channels choose Ca2+ over Na+ at a ratio of 1,000:1
(Hess et al., 1986) because of an intrapore, high affinity
Ca2+ binding site (Kd = 0.7 µM Ca2+). In the absence
of Ca2+, Na+ and other monovalent ions pass freely
through Ca2+ channels, but they are blocked when external Ca2+ concentration rises above 1 µm (Kostyuk et
al., 1983
; Almers et al., 1984
). Block depends on membrane voltage (Lansman et al., 1986
; Fukushima and
Hagiwara, 1985
; Lux et al., 1990
), as required of a site
within the pore (Woodhull, 1973
), and on the direction of ion movement (Kuo and Hess, 1993a
, 1993b
), as
required of a site within a multi-ion pore (Hille and
Schwarz, 1978
). The maximum off rate from a micromolar binding site in free solution is ~103 ions per second, yet picoampere currents (over 106 Ca2+ ions per
second) pass through Ca2+ channels. This is a specific
example of a general problem of channel permeation:
how high flux can occur through a channel that selects
its preferred ion with an intrapore binding site. This
cannot happen in a rigid pore with just a single binding site because, as affinity for an ion increases, the ion's
exit rate decreases in exact proportion to the increased
occupancy of the site (Bezanilla and Armstrong, 1972
).
The gross discrepancy between flux and binding in
Ca2+ channels makes them a valuable system for exploring this problem. Several theories of Ca2+ channel
permeation have been proposed and they share an essential feature: when Ca2+ ions bind to the channel, the
pore's affinity for Ca2+ diminishes, thereby promoting
high Ca2+ flux. Here, we describe a model that generates high flux without such changes in affinity, thereby
demonstrating a second general mechanism.
The most widely known Ca2+ channel model proposes a pair of high affinity intrapore binding sites
through which ions move in single file (Hess and Tsien,
1984; Almers and McCleskey, 1984
). Previously, single
file models had successfully described permeation in
K+ channels (Hille and Schwarz, 1978
), gramicidin
channels (Andersen and Procopio, 1980
), and Na+
channels (Begenisich, 1987
). In such models, ions hop
sequentially from one site to the other following two
rules: (a) an ion cannot bind to a site already occupied
by another; (b) an ion cannot pass over a site without
binding to it (Hille, 1992
). The same rules govern movement of ions through semiconductor crystals (Shockley et al., 1952
). Thus, such models explore whether this
simple physical precedent can explain the relatively
complex selectivity and permeation of ion channel
proteins.
Although high fluxes are impossible with just a single
high affinity binding site, they can occur when there
are two sites because, when both are occupied, the adjacent ions can repel each other. Specifically, Ca2+ affinity diminishes 20,000-fold when two ions are in the
model pore compared with when one ion is present
(Hess and Tsien, 1984; Almers and McCleskey, 1984
).
Electrostatic repulsion between Ca2+ ions ~10 Å apart
is sufficient to generate this change in affinity, but it is
not the only mechanism possible. Competition for
binding moieties between two Ca2+ ions in a multiply
occupied channel has been suggested as an alternate
mechanism (Armstrong and Neyton, 1991
; Yang et al., 1993
), as has long-lived conformational changes triggered by Ca2+ binding in a single ion pore (Lux et al.,
1990
; Mironov, 1992
).
Two observations indicate that the pore of the Ca2+
channel contains only a single high affinity binding
site, rather than the two suggested by the traditional
model. (a) Single point mutations of critical glutamate
residues simply shift the pore's affinity for Ca2+, whereas
micromolar binding should still be present if there were
two independent sites with the same affinity (Yang et al., 1993; Kim et al., 1993
; Ellinor et al., 1995
). (b) As judged
from the voltage dependence of Ca2+ block, Ca2+ binds
to the same pore location whether it arrives from the
outside or the inside solution (Kuo and Hess, 1993a
; but a
different voltage dependence was found by Rosenberg
and Chen, 1991
). These experiments prompted us to
quantitatively evaluate a model, mentioned briefly in
Almers and McCleskey (1984)
, that uses only one high
affinity intrapore site and needs no ion-ion interactions
or transient decreases in Ca2+ affinity. Using rate theory calculations for single file pores, we test the ability
of this mechanism to fit published data regarding: (a)
selectivity of Ca2+ over monovalent ions, (b) selectivity
of Ca2+ over Ba2+, (c) sigmoidal current-voltage (I-V)1
curves, and (d) block by Cd2+.
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METHODS |
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Calculations were done using rate theory models written in Visual Basic 2.0 in which two different kinds of ions move through pores in single file via either two or three binding sites. In such
models, the rate that an ion moves from one site to another equals the product of the rate constant for the transition and the
probability that the site is occupied by that ion. The rate constant
(r) diminishes exponentially as the energy of transition (G) increases relative to the average kinetic energy of an atom (kT): r = e
(G/kT), where k is the Boltzmann constant, T is the temperature, and
, the fastest possible reaction rate, is taken to be the
atomic vibration frequency (5.8 × 1012 s
1 = kT/h, where h is
Plank's constant). G is the sum of the chemical and electrical potential energies that affect the ion movement: G = Gb
Gs + z
Vm, where Gb is the energy of the barrier to be overcome, Gs is
the energy of the present binding site, z is the ion's charge, and
is the fraction of the membrane voltage (Vm) traversed by the ion
in passing from the site to the barrier. If desired, rate constants
can be adjusted with a "repulsion factor" to reflect negative interaction between ions that occupy adjacent sites. (We used the factor only to reproduce earlier repulsion-dependent models and
raised the factor to an exponent of the product of the valences of
the adjacent ions, as appropriate for electrostatic repulsion (see
Almers and McCleskey, 1984
).)
The energies of barriers and binding sites are all adjustable parameters, but critical ones are determined (or at least constrained) by known data. Outer barriers limit entry to the pore,
so they must respect the diffusion limit. A typical diffusion limit
for a small ion is 109 M1 s
1 (Hille, 1992
); this corresponds to an
energy barrier of 8.7 kT (= ln[109/5.8 × 1012]). The energies of
some binding sites can be obtained from apparent dissociation
constants (Kd) by G =
kT ln (Kd).
The concentration of Ca2+ that causes half block of monovalent ion current provides a close approximation of the energy of
the highest affinity Ca2+ binding site in the pore since block is
caused by entry of a single Ca2+ into the pore; for example, a
half-blocking concentration of 1 µM suggests a binding energy of
14 kT (= ln10
6). The concentration of Ca2+ that causes half-maximal Ca2+ current provides an approximation of the energy
of the lowest affinity site since saturation of current reflects filling
of the pore; half saturation at 10 mM suggests a binding energy
of
4.5 kT (= ln10
2). The locations of sites and barriers within
the electric field can also be free parameters, but we just arranged them symmetrically.
The barrier and site energies determine the individual rate
constants and these, together, determine the probabilities that sites are occupied by the different ions. Each site has three possible states: unoccupied or occupied by one of the two ions. Therefore, the two-site pore can exist in 9 (32) possible states and the
three-site pore can exist in 27 (33). The probabilities of occupancy of the different states of the pore were calculated through
their steady state kinetic equations, in which the rates of creation
and loss of the state are equal. For example, the steady state of a
two-site channel having ion B in the left site and ion A in the
right is described by dPBA/dt = 0 = r1P0A + r2PB0 r
1PBA
r
2PBA, where r1 and r
1 are rate constants for entry and exit, respectively, of ion B to the left site, r2 and r
2 are rate constants for
entry and exit of ion A to the right site, and PBA, P0A, and PB0 are
the probabilities that the channel exists in these three states (0 indicates an unoccupied site). Together with the conservation equation (the sum of all probabilities equals 1), there are 9 and
27 independent kinetic equations for the two- and three-site pores, respectively. These equations were solved for the state probabilities in 9 × 9 and 27 × 27 matrices by Gauss elimination. Numbering the states in base 3 greatly eased bookkeeping and
troubleshooting for this operation.
Current for each ion was calculated as the net flux (rate constant × state probability) over the second energy barrier times the ion's charge. Calculation of currents carried by extracellular Na+ and Ca2+ through a single site pore used the formula for a
weighted rectangular hyperbola, as would be appropriate for
competitive binding at a single site enzyme (Hille, 1992):
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where Imax is the maximum current of the indicated ion and K is the ion's dissociation constant from the site.
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RESULTS |
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Choosing Ca2+ over Na+
From a physiological perspective, the selectivity of Ca2+
over Na+ is the most important feature of the Ca2+
channel pore; it allows the channel to preferentially
pass Ca2+ despite the 100-fold concentration advantage
held by Na+. The two essential features of this selectivity are: (a) Na+ (and other inorganic monovalents)
pass freely through the channel when Ca2+ is absent,
but their currents are blocked by micromolar Ca2+; (b)
high Ca2+ flux occurs at millimolar Ca2+ and there is
no inward Na+ flux at these concentrations. These
properties are evident in the data points in Fig. 1 B
(scaled and replotted from Almers et al., 1984), which
show combined Na+ and Ca2+ current through Ca2+
channels over a 1,000,000-fold range of extracellular
[Ca2+]. There is a broad minimum between 10
6 and
10
3 M Ca2+; Na+ carries the current below and Ca2+
carries it above this range. In practice, fitting this data
is the primary challenge of the modeling; once successful, the same model easily fits a variety of other Ca2+
channel data.
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Both the traditional, two-site repulsion-dependent
model (Fig. 1 A, left) and the new model (Fig. 1 A, right)
fit the data in Fig. 1 B (broken and solid curves). However, a pore with only a single high affinity binding site
exhibits appropriate block of Na+ current by micromolar Ca2+, but no significant Ca2+ flux as [Ca2+] rises further (Fig. 1 B, dashed curve). As discussed above, high
Ca2+ flux occurs in the repulsion model because off
rates increase when both sites are simultaneously occupied by Ca2+ ions. In contrast, off rates are unaffected
by multiple occupancy in the other model. This new
model has a single high affinity site, two flanking low affinity sites, and allows no repulsion between ions. We
will call this the "step model" because the low affinity
sites essentially provide stairsteps of potential energy that speed exit from the pore (see DISCUSSION). The inset
shows the contributions of the individual ions to the total
current in the step model in the vicinity of 104 M Ca2+.
Fig. 1 C plots the probability that the step model pore is
occupied in various ways as Ca2+ concentration changes.
Block of Na+ current occurs as occupancy of the high
affinity site by Ca2+ (one Ca curve) increases when Ca2+
rises to the micromolar range. Ca2+ flux occurs at still
higher Ca2+ concentrations as the probability increases
that two or three Ca2+ ions simultaneously occupy the
pore. Most directly, inward Ca2+ flux parallels the occupancy of the internal low affinity site. This occurs as the
external Ca2+ concentration becomes significant compared with the site's dissociation constant, which is 18 mM Ca2+. Although the occupancy plots for the step
model are qualitatively similar to those for the repulsion model (Almers and McCleskey, 1984), the effects
of multiple Ca2+ occupancy are different. An ion at one
site of the step model does not affect an ion at another
site through remote forces.
Choosing Ca2+ over Ba2+
Ca2+ channels generally pass greater Ba2+ currents
than Ca2+, but they choose Ca2+ when both ions are
present. The key features of Ca2+/Ba2+ permeation
are: (a) pure Ba2+ currents are larger and saturate at
higher concentrations than pure Ca2+ currents (Hess
et al., 1986); (b) Ba2+ blocks monovalent currents at
~50× higher concentration than does Ca2+ (Kostyuk
et al., 1983
); (c) Ca2+ blocks Ba2+ current, and does so
more strongly than would occur through simple competition for a single site. The powerful block of Ba2+
current by Ca2+ can manifest itself as an "anomalous
mole fraction effect" in which current carried by mixtures of Ca2+ and Ba2+ having constant total divalent
ion concentration exhibit a minimum at low [Ca2+]
(Hess and Tsien, 1984
; Almers and McCleskey, 1984
;
Friel and Tsien, 1989
; but Yue and Marban, 1990
, saw
no Ca2+/Ba2+ anomalous mole fraction effect).
The data points in Fig. 2 A (replotted from Hess et
al., 1984) give unitary Ca2+ () and Ba2+ (
) current
amplitudes from cardiac Ca2+ channels as a function of
divalent ion concentration. Being actual single channel
amplitudes (rather than the scaled whole cell currents of Fig. 1 B), these data test whether the step model can
quantitatively fit observed single channel flux. The
Ca2+ (solid curve) and Ba2+ (dashed curve) currents calculated from the model (inset) reproduce the key features of the data
Ba2+ current has higher amplitude
and higher half-saturation than Ca2+ current. The energies for Ca2+ in the model were adjusted to give a
good fit to this cardiac Ca2+ channel data and they differ only slightly from those used to fit skeletal muscle
data in Fig. 1. The Ba2+ and Ca2+ models differ only in
the energy of the binding sites. Ba2+ energies for the
high and low affinity sites correspond to Ba2+ concentrations that cause half-block of monovalent currents
(35 µM, Kostyuk et al., 1983
) and half-saturation of
Ba2+ current (28 mM, Hess et al., 1986
), respectively.
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Fig. 2 B shows the predicted anomalous mole fraction behavior when the total divalent ion concentration
is 10 mM. Net current passes through a minimum as
the Ca2+:Ba2+ ratio changes because Ca2+ is so effective
at blocking Ba2+ current. For example, there is virtually
no current carried by 5 mM Ba2+ when 5 mM Ca2+ is
present. Fig. 1 B shows a similar, but far more dramatic, U shape because the difference in affinities between
Ca2+ and Na+ is far greater than between Ca2+ and
Ba2+. (As seen experimentally [Friel and Tsien, 1989],
the mole fraction curve no longer passes through a
minimum at high divalent ion concentrations [data not
shown]. In this respect, a nearly saturated multi-site
pore behaves like a single site pore; presumably, this is
because only a single site at a time is unoccupied in the
near-saturated pore.)
Sigmoid I-V Curves
The current-voltage curve of Ca2+ channels exposed to
physiological ionic concentrations has a rich array of
features that further illustrate the role of Ca2+ block in
selectivity against monovalent ions: (a) current reverses at positive potentials, but not nearly as positive as the
equilibrium potential for Ca2+ (Fenwick et al., 1982;
Lee and Tsien, 1984
); (b) the outward current is carried by intracellular monovalent cations (Lee and Tsien, 1984
; Hess et al., 1986
), and these are far more
permeant than extracellular monovalents (Yamashita
et al., 1990
); (c) despite their impermeability, extracellular monovalents at physiological concentrations block
currents carried by divalent ions (Polo-Parada and
Korn, 1997
); (d) the I-V curve is sigmoid in the vicinity of the reversal potential (Fenwick et al., 1982
; Lee and
Tsien, 1984
). The step model generates each of these
features (Fig. 3).
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In the absence of Ca2+, the single Ca2+ channel I-V
curve is linear and reverses at 0 mV (Rosenberg and
Chen, 1991); the model does the same (not shown). As
extracellular Ca2+ concentration increases, the reversal
potential becomes more positive and the curve becomes more and more sigmoid near the reversal potential (Fig. 3 A). Sigmoidicity, a region of low conductance, occurs when the pore is more likely occupied by
just a single Ca2+ ion (occupancy plot not shown).
When sufficiently positive voltages force the final Ca2+
ion outward from the pore, monovalent cations pass
freely outward. Thus, sigmoidicity in the I-V curve reflects block of the pore by single Ca2+ ions.
Fig. 3 A (inset) shows how much of the net current is
carried by each of the individual ions near the reversal
potential when [Ca2+]out is 10 mM (0 [Ca2+]in). Although Na+ is at the same concentration (140 mM) inside and out, it only carries outward current; clearly, internal Na+ is more permeant than external in the
model. This point was demonstrated in elegant experiments showing that internal Na+ affects the reversal potential of Ca2+ channels far more than external Na+
(Yamashita et al., 1990). In the step model, a change in
Na+ concentration that causes a 2-mV shift if made extracellularly causes a 27-mV shift if made intracellularly
(Fig. 3 B). With respect to monovalent cations, Ca2+
channels are outward rectifiers because of the presence
of an extracellular blocking ion, Ca2+. Intracellular
Na+ is more permeant than extracellular because of
the difference in Ca2+ concentration inside and out. As
shown previously by Hille and Schwarz (1978)
, such
asymmetry requires neither an asymmetric energy profile nor ionic repulsion.
Block of inward Ca2+ current by 140 mM extracellular Na+ is reproduced (compare solid and dashed curves,
Fig. 3 B). As was suggested by Polo-Parada and Korn
(1997), this block is caused by competition between
Na+ and Ca2+ at the external, low affinity binding site.
Block by Cadmium
Cd2+ is one of several polyvalent cations that block Ca2+
channels at very low concentrations (Hess et al., 1986).
The data points in Fig. 4, replotted from Ellinor et al.
(1995)
, show that Cd2+ blocks monovalent ion currents
at ~200-fold lower concentrations than divalent ion
currents. The data is fit by assuming that Cd2+ binds to
the selectivity site far more strongly than does Ca2+
(
24 kT for Cd2+ [Fig. 4, inset] vs.
15.5 kT for Ca2+).
The difference in blocking concentrations for Li+ and
Ba2+ currents is due to their differences in binding to
this site (
10.3 kT for Ba2+ and
5 kT for Li+).
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DISCUSSION |
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This paper asks how a million Ca2+ ions can pass
through a Ca2+ channel in a second when its pore contains a binding site having a maximum off rate of a
thousand per second. This is a specific example of a
general problem: how channels pass high flux if they select their preferred ion with a binding site. All previous models assumed that one Ca2+ ion diminishes the
affinity of the pore for others and that Ca2+ flux ensued
from this low affinity state. The suggested mechanisms for this negative interaction between ions are electrostatic repulsion (Hess and Tsien, 1984; Almers and McCleskey, 1984
), competition for binding moieties (Armstrong and Neyton, 1991
; Yang et al., 1993
; Ellinor et
al., 1995
), and Ca2+-induced conformational changes
(Mironov, 1992
; Lux et al., 1990
). The step model described here does not allow one ion to alter another's
binding to other sites, yet it fits the wide variety of Ca2+
channel permeation data; most importantly, submicromolar Ca2+ blocks current carried by monovalent ions
and Ca2+ above a millimolar generates picoampere, saturable Ca2+ flux. The calculations demonstrate that
ion-ion interactions are not required to generate high
flux in pores that tightly bind their preferred ion. Kiss
et al. (1998)
demonstrates that the same principle fits
data from K+ channels. Below, we describe the mechanism that underlies the model, evidence that supports
its plausibility, and alternate interpretations of it.
Mechanism
The model has a simple mathematical explanation and a physical mechanism that is part of everyday experience. Fig. 5 shows the potential energies of Ca2+ in a single-site pore (A), the repulsion model (B), and the step model (C). The energy of the strongest binding site in each model (arrow 1) determines block of foreign ions by micromolar Ca2+. The energy of the highest barrier to exit the pore (arrow 2) limits Ca2+ flux. In a single-site pore, the rate-limiting exit barrier increases as the selecting binding well deepens. This pictorially represents why an increase in selectivity is expected to decrease flux.
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The repulsion and step models provide two ways of separating the energies that control binding and flux. In the repulsion model (Fig. 5 B), double occupancy (right) of the pore diminishes affinity of the binding sites. Dissociation constants for Ca2+ change from 0.5 µM to 10 mM when the pore goes from singly occupied to doubly occupied. Whether the mechanism is electrostatic repulsion, competition, or conformational changes, Ca2+ flux occurs from this state of shallow binding wells.
In the step model (Fig. 5 C), flux occurs from low affinity sites that are built into the energy profile; therefore, there is no need for multiple occupancy to alter
binding affinities. The essence of the mathematics is
trivial: because the energies that control binding and
flux are similar in the two viable models, binding and
flux are similar. The physical mechanisms of permeation differ, but with the arrows having roughly similar
length in the two models, the calculations come out approximately the same. In both the repulsion and step
models, exit from the pore occurs from a site of ~4
kT. This is ~100 millielectronvolts (Fig. 5 A, scale bar),
the energy imparted to a single charge by the 100-mV driving force typical of biological membranes. Regardless of the permeation mechanism, it seems that the final site before escape from a pore must have an energy
no more negative than such a "biological" magnitude.
The step used in the model more or less cuts the exit
barrier into two halves. The physical mechanism that
causes the profound increase in flux with just a twofold
change in barrier height is analogous to stairsteps.
Imagine a wall, a gravitational potential energy barrier,
2 m high. Flux of people over it is exceedingly low because only the most talented can leap 2 m. Now, place a 1-m step in front of it. Most of us can easily step up that
meter, and then the next, so flux over the wall increases dramatically. The increase in flux is disproportional to the change in limiting barrier height because
the number of people that can hurdle a gravitational
barrier decreases nonlinearly with increasing height. Similarly, the number of atoms with sufficient kinetic
energy to surpass a chemical potential energy barrier
decreases exponentially with increasing height. Once it
has reached the intermediate step, an atom faces the
next barrier with no memory of the energy expended in reaching there because atoms thermally reequilibrate at the atomic vibration frequency (kT/h = 5.8 × 1012 s1). Therefore, steps of chemical potential energy
speed reaction rates much as stairsteps of gravitational
potential energy speed traffic over obstacles.
Although remote interactions between ions do not
occur in the step model, multiple occupancy by Ca2+ is
required for significant Ca2+ flux. The rate constant for
exit of Ca2+ from one of the low affinity sites in Fig. 1
over the exit barrier to the outside is 5 × 106 per second (=[kT/h]exp [14]). If ions went directly from
the high affinity site to the exterior, the rate constant
would be 50 per second (=[kT/h]exp
[25.5]). As
large as this difference is, it is insignificant if the pore is
singly occupied. With just a single ion in the pore, the
probability of occupying one of the low affinity sites is
10
5 that of occupying the high affinity site (Plow/Phigh = exp
[Glow
Ghigh]). This exactly negates the advantage in rate constant since flux equals the product of
the occupancy probability and the rate constant. Significant flux occurs only when there is high occupancy of
the escape site by Ca2+. This occurs when extracellular
[Ca2+] becomes significant compared with the site's
dissociation constant (18 mM). Ca2+ flux is entirely
driven by Ca2+ concentration and its effect on occupancy of the pore.
Plausibility
Ca2+ channels clearly have only a single high affinity
binding site within their pore (Yang et al., 1993; Kim et
al., 1993
; Ellinor et al., 1995
). This selectivity site appears to be flanked by other binding sites because: (a)
extracellular monovalent ions inhibit exit of Ca2+ from
the high affinity site to the outside and intracellular ions inhibit exit to the inside (Kuo and Hess, 1993b
);
(b) extracellular Na+ diminishes inward Ca2+ and Ba2+
current, suggesting that the ions compete for a low affinity entry site that is on the outside of the selectivity
site (Polo-Parada and Korn, 1997
); (c) in the presence
of extracellular Ca2+, monovalent ions are far more
permeant from the inside than the outside (Yamashita
et al., 1990
), suggesting an internal entry site at which
monovalents compete favorably with Ca2+ because of
the low intracellular Ca2+ concentration. These findings suggest that the Ca2+ channel is a multi-site pore
that has a single high affinity site that is flanked by others of lower affinity. This image of the Ca2+ channel
pore has potential energy steps built into it. Any such step of potential energy must contribute to generating
high Ca2+ flux.
Although our calculations show that appropriately designed potential energy steps are sufficient to fit critical Ca2+ channel data, the steps need not be the only factor. Ion-ion interactions are physically reasonable because both electrostatic repulsion and competition for binding moieties are plausible when identical ions simultaneously occupy a pore. The ionic repulsion model and the step model both quantitatively fit the same Ca2+ channel data; at most, this demonstrates that these mechanisms make sense, not that they are real. The reality of Ca2+ channel permeation might involve a combination of the mechanisms that have been theoretically explored in isolation, or, perhaps, some mechanism that has been overlooked.
Steps Might Not Be Sites
The literal interpretation of an energy diagram is that
each well corresponds to a discrete binding site that
should be evident in the three-dimensional structure of
the protein's pore. Surely, this must be the case with
the high affinity site, which consists of a cage of four
glutamates (Yang et al., 1993; Kim et al., 1993
). However, physical interpretation of the low affinity sites is ambiguous. It may be that the Ca2+ ion can experience
steps of potential energy without explicit binding sites
built into the protein. For example, ion channels appear generally to have wide entrance vestibules that
may be on either side of a narrow, short pore (Miller,
1996
). Weak ion binding within the vestibule might be
able to provide the same favorable energy steps provided by discrete sites in a long pore. Indeed, placement of the model's low affinity sites at the very edge of
the electric field, the location of the vestibules, gives qualitatively similar results as those shown. If one literally interprets the steps as sites in the vestibules, the
model suggests that a vestibule serves as an energy "plateau" from which Ca2+ can rapidly enter the pore over
a low energy barrier. However, literal interpretation is
dangerous; the low affinity sites are just a mathematical
artifice for showing that steps of potential energy, no
matter what their cause, can speed flux.
A different interpretation of the low affinity sites is
suggested by a previous case in which stairsteps of potential energy were invoked in the ion transport literature. Eigen and Winkler (1971) and Chock et al.
(1977)
asked how entry of ions to binding sites on carriers could be diffusion limited when the ions had to undergo complete dehydration, which is normally an exceedingly slow process. The paradox is solved through
stepwise replacement of water molecules by coordinating ligands on the carrier; in essence, the carrier catalyzes dehydration of the ion, step by step. This same
phenomenon must occur with channels, where entry is
generally diffusion limited (e.g., Lansman et al., 1986
)
despite the need for nearly complete dehydration
(Hille, 1971
).
Might stepwise rehydration of an exiting ion also occur? This seems probable, not just possible. A Ca2+ ion
coordinates to seven or eight electronegative oxygen
ligands at a time (Falke et al., 1994). Outside the pore,
water molecules provide this coordination. At the selectivity site, negative carboxyl oxygens on four glutamates
contribute to coordination, thereby forming a stronger
bond (Yang et al., 1993
; Kim et al., 1993
). Unless the
Ca2+ ion bursts from the glutamate cage immediately
into water, there must be intermediate lower affinity
states in which the glutamates are replaced by less negative moieties. One possibility would be stepwise replacement of the four carboxyls by water molecules, a mechanism consistent with the proposed flexibility of the
glutamate residues (Yang et al., 1993
; Ellinor et al.,
1995
). Any such event would provide a step of potential
energy in the Ca2+ ion's travel, even though it need not
be a discrete binding site in the channel structure. In
this manner, stepwise rehydration might provide a path
for rapid exit from a pore just as stepwise dehydration
surely provides the path for rapid entry. By showing that even a single energy step can be sufficient, our calculations suggest the feasibility of this simple mechanism of permeation.
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FOOTNOTES |
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Address correspondence to Ed McCleskey, Vollum Institute L-474, O.H.S.U., Portland, OR 97201-3098. Fax: 503-494-6972; E-mail: mccleske{at}ohsu.edu
Received for publication 25 August 1997 and accepted in revised form 12 November 1997.
Permeation programs are available online at http://www.ohsu.edu/vollum/mccleskey/We thank Dr. Ted Begenisich for providing the computer programs on which ours were modeled, and Jack Kaplan, Steve Korn, and Masoud Zarei for helpful comments on the manuscript.
This work was supported by a grant from the National Institute of Drug Abuse.
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Abbreviation used in this paper |
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I-V, current-voltage.
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