Opposing gates model for voltage gating of gap junction
channels
Ye
Chen-Izu1,
Alonso P.
Moreno2, and
Robert A.
Spangler3
1 Department of Physiology, University of Maryland School of
Medicine, Baltimore, Maryland 21201; 2 Department of
Medicine, Krannert Institute of Cardiology, Indianapolis, Indiana
46202; and 3 Department of Physiology and Biophysics, State
University of New York at Buffalo, Buffalo, New York 14214
 |
ABSTRACT |
Gap junctions are intercellular channels that link the cytoplasm
of neighboring cells. Because a gap junction channel is composed of two
connexons docking head-to-head with each other, the channel voltage-gating profile is symmetrical for homotypic channels made of
two identical connexons (hemichannels) and asymmetric for the heterotypic channels made of two different connexons (i.e., different connexin composition). In this study we have developed a gating model
that allows quantitative characterization of the voltage gating of
homotypic and heterotypic channels. This model differs from the present
model in use by integrating, rather than separating, the contributions
of the voltage gates of the two member connexons. The gating profile
can now be fitted over the entire voltage range, eliminating the
previous need for data splicing and fusion of two hemichannel
descriptions, which is problematic when dealing with heterotypic
channels. This model also provides a practical formula to render
quantitative several previously qualitative concepts, including a
similarity principle for matching a voltage gate to its host connexon,
assignment of gating polarity to a connexon, and the effect of docking
interactions between two member connexons in an intact gap junction channel.
connexin; cell signaling; mathematical model
 |
INTRODUCTION |
GAP JUNCTIONS ARE
INTERCELLULAR channels that directly link the cytoplasm of
adjacent cells. Cell-cell communication via gap junctions has been
recognized to play important roles in many physiological processes,
such as impulse propagation in the heart and neurons, nutrient supply
in the lens, pattern formation during development, and regulation of
cell growth and transformation (for reviews see Refs. 3,
5, 25, and 27). The gap junction channels also provide a unique system for the study of
structure-function relationships of protein molecules, because their
structure is unique among ion channels. A gap junction channel is
composed of two connexons that protrude from two neighboring cells and dock with each other via their extracellular loops (13,
32). Each connexon is made of 6 connexin subunits, of which 18 different isoforms have been identified and cloned. Each connexin forms channels with distinctive properties, including single-channel conductance (33), channel permeability (9, 12,
14), gating response to pH (18, 19), and
voltage-sensitive gating (22). Gap junction voltage gating
is the most extensively characterized fingerprint for channels made of
various connexin types. Because the two connexons that constitute a gap
junction are oriented as mirror images of each other in an intact
channel, a homotypic channel made of two identical connexons has a
symmetrical structure (32), whereas a heterotypic channel
made of two different connexons has an asymmetric structure.
Consequently, the channel voltage-gating profile, which is the
relationship between channel conductance and transjunctional voltage
(Vj), is largely symmetrical for homotypic channels across positive and negative voltage ranges but asymmetric for
heterotypic channels.
Alterations in channel protein structure, by molecular techniques or by
pairing connexons in various combinations, often lead to changes in the
channel voltage gating (24, 26, 30, 34). To study the
structure-function relationship, Spray, Harris, and Bennett (15,
28) developed a quantitative (S-H-B) model for the channel
voltage gating, in which a single Boltzmann function was used to
characterize a symmetrical voltage-gating profile. Later, use of the
S-H-B model was extended to also describe the asymmetric gating of
heterotypic channels. The common practice is to splice the
voltage-gating profiles into two segments in the positive and negative
voltage (Vj) ranges or at the
Vj of peak conductance (17, 20, 22, 26,
34, 37). Each of the two data segments is then fitted to a
single Boltzmann function. In the case of the homotypic channels that
are fully open at Vj = 0 mV, each connexon
contributes to one-half of the voltage-gating profile, so it is
reasonable to splice the gating profile at
Vj = 0 mV. However, if the gating profiles
of two connexons overlap, with a voltage range in which neither
connexon is fully conducting, the contributions of two member connexons
are integrated and, therefore, cannot be separated at
Vj = 0 mV. It is equally arbitrary to
separate the gating profile of a heterotypic channel at the Vj of peak conductance. Moreover, when the
gating profile is spliced to two segments and each is fitted
independently to a single Boltzmann function, the intersection of the
two fitting curves often produces an odd point with a discontinuous
first derivative that clearly does not reflect a physical reality. This
discontinuity reveals the problem inherent in the practice of adapting
the S-H-B model to heterotypic channels. Recently, Vogel and Weingart
(35) presented a detailed model using four conductance
states and two voltage gates to describe an intact gap junction
channel. Their model included many variations that could arise in gap
junction conduction. However, because their mathematical description
was given in general form (consisting of
13 free parameters), it does
not provide a practical formula to characterize the real experimental
data of macroscopic currents.
Here we present a simple four-state model to integrate the contribution
of the two member connexons in an intact gap junction channel. This
model employs three new considerations: 1) thermodynamic self-consistency in the Gibbs free energy of the system, 2)
assumption of one open channel conductance and one residual conductance
value for an intact channel, and 3) simplification afforded
by assuming independent or contingent gating. [This assumption was
first proposed by Spray et al. (29); here we translate it
into a new mathematical formula.] This model provides a practical
formalism for fitting the experimental data of macroscopic currents
over the entire voltage range in the voltage-gating profile,
eliminating the need for arbitrary data splicing and fusion of two
hemichannel descriptions. The model also helps to render several
previously qualitative concepts in quantitative terms, particularly
those relating to matching a voltage gate to its host connexon and
defining the docking interaction between two hemichannels.
 |
METHODS |
Expression of gap junctions composed of homotypic and heterotypic
connexins.
The experimental data used here for model fitting were previously
published, and the methods used in obtaining these data have been
described elsewhere (see footnotes in Table
1). Connexin30 (Cx30), connexin26 (Cx26),
and connexin32 (Cx32) were expressed in Xenopus oocytes
(11); connexin43 (Cx43) and connexin45 (Cx45) were
expressed in N2A cells (20). Briefly, when
Xenopus oocytes are used to express connexin cRNAs, the
endogenous connexin38 (Cx38) is first suppressed by preinjection with
an antisense oligonucleotide to the 5' end of Xenopus Cx38
3-4 days before injection with exogenous connexin RNA, as
previously described (2). The follicular membranes of the
oocytes were removed before injection. The inner vitelline membranes
were removed 1 day after the injection of RNA, and the oocytes were
paired in an agar well to force close contact with each other. Gap
junction conductance between paired oocytes was measured after
24-48 h of incubation at room temperature. The oocytes were
maintained in L-15 medium (GIBCO). The solution was changed
twice per day to prevent contamination.
The connexin RNA was prepared using the in vitro transcription methods
previously described (2). The integrity of synthesized RNA
was verified by agarose gel electrophoresis. The concentration of the
RNA was estimated by ultraviolet absorption at 260 nm, with purity
assessed by the 260 nm-to-280 nm ratio.
Dual-cell voltage clamp.
The experiments on the gap junctions expressed in Xenopus
oocytes were performed on an electrophysiology setup containing the
following instruments: two Geneclamp500 amplifiers, a Digidata 1200 analog-to-digital converter, a VA-100 analog-to-digital recorder, a JVC
video recorder, and a personal computer. pClamp6 (Axon Instrument) was
used for data acquisition. Dual-cell voltage-clamp techniques were used
to measure the gap junction coupling between cell pairs. To increase
input resistance of cells, micropipettes were filled with a patch
solution containing cesium (130 mM CsCl, 0.5 mM CaCl2, 10 mM HEPES, 10 mM EGTA, pH 7.2). During recording, cells were kept at
room temperature in a cesium-containing solution (160 mM NaCl, 7 mM
CsCl, 2.0 mM CaCl2, 0.6 mM MgCl2, 10 mM HEPES,
pH 7.4). The cells in a pair, cell L and cell R,
were individually voltage clamped. The holding potential for both cells
was
60 mV, close to the cell resting potential.
Vj steps were delivered to cell R,
while the voltage was held constant in cell L. The evoked
current in cell L was then recorded as the transjunctional current.
Data analysis.
We used pClamp6, Excel (Microsoft), and Prism (GraphPad Software) for
data analysis. The current decay due to voltage gating was best fitted
to exponential functions. The initial current was then obtained by
extrapolation to time 0; the steady-state current was
obtained as the offset of the exponential fitting at infinity.
Vj was obtained as the potential difference
between the two voltage electrodes. The initial conductance
(Gi) and the steady-state conductance
(Gss) were calculated from the initial and the
steady-state current, respectively, as the ratio of current to voltage.
In plotting the relationship between conductance and voltage, the sign
of Vj is referenced to the cytoplasmic side of
CxR in a connexon pair denoted CxL/CxR (CxL in cell L; CxR in cell R).
 |
RESULTS |
Voltage gating of gap junctions.
A homotypic gap junction channel made of two identical connexons has a
largely symmetrical voltage-gating profile. Figure 1A shows the currents through
homotypic Cx30 channels evoked by Vj steps from
105 to +105 mV in 10-mV increments (published initially in Ref.
11). The currents are largely symmetrical for positive and
negative voltage ranges. The currents reach an initial maximum and then
decay to a steady-state level during the maintained voltage step,
revealing the voltage-gating phenomenon. We calculated
Gi and Gss from the
current-voltage relationship and normalized the Gi and Gss of each cell
pair to the interpolated value of its Gi at
Vj = 0 mV, so that data from cell pairs
with different coupling levels can be compared. Predictably, homotypic
gap junctions, such as those composed exclusively of Cx30, exhibit a
symmetrical gating profile (Fig. 1B).

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Fig. 1.
Transjunctional currents and conductance of gap junction
channels. A: macroscopic currents through homotypic
Cx30/Cx30 channels, evoked by transjunctional voltage
(Vj) steps from 105 to +105 mV in 10-mV
increments from a holding potential of 0 mV. Both cells were held at
60 mV at resting condition. Cx, connexin; I, current;
t, time. B: relationship between averaged channel
conductance and Vj of Cx30/Cx30 channel (17 cell
pairs). This channel has a largely symmetrical voltage-gating profile.
Gi, initial conductance;
Gss, steady-state conductance.
C: macroscopic currents through heterotypic Cx30/Cx32
channels evoked by the same voltage-clamp protocol used in
A. D: relationship between averaged channel conductance and
Vj of heterotypic Cx30/Cx32 channel (21 cell
pairs). Cx30/Cx32 channel has a distinctively asymmetric voltage-gating
profile.
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A heterotypic channel made of two different connexons often has an
asymmetric gating profile. Figure 1C shows the currents through heterotypic Cx30/Cx32 channels, which present a dramatic asymmetry in the voltage-gating profile (Fig. 1D). Stepping
to negative voltages greater than
40 mV evoked large currents that decayed to smaller steady-state currents over time; stepping to more
positive voltages evoked much smaller currents that showed little
decay. This marked rectification of Gi in the
gating profile is similar to that reported in heterotypic pairings of
Cx32 with other connexons, e.g., Cx26/Cx32 (2), Cx46/Cx32,
and Cx50/Cx32 (37).
The voltage dependence of Gi should reflect, in
principle, the voltage dependence of the single-channel
conductance, because the initial open probability
(Po,i) is a constant value, fixed by the
holding potential (0 mV in most experiments). The voltage dependence of
Gss, however, is determined not only by
single-channel conductance, but also by changes in the channel
open probability (Po) due to voltage gating. The
present study is focused on modeling this steady-state voltage
gating of homotypic and heterotypic gap junction channels.
Opposing gates model for gap junction voltage gating.
Our model assumes that each member connexon contributes one voltage
gate, and therefore two voltage gates in series control the gating of
an intact gap junction channel. The schematic presentation of the model
is shown as
where Ki (i = 1, 2, 3, 4)
is the equilibrium constant for each of the transition processes, with
the forward transition taken in the direction indicated by the long
arrows. A channel can occupy one of the four possible states:
1) O(oo), in which both gates are open, 2)
C1(co), in which gate L is closed and gate
R is open, 3) C2(oc), in which gate
L is open and gate R is closed, and 4) C3(cc), in which both gates are closed. An identical
four-state scheme was proposed conceptually by Moreno et al.
(21), put into a mathematical expression (10,
23), and incorporated into a general model (35).
Here we develop this four-state scheme into a circumscribed
mathematical model by utilizing three considerations: 1)
detailed balance of the state transitions, 2) separation of Po from the macroscopic conductance, and
3) assumption of independent/contingent gating.
The equilibrium constants between the states can be expressed
explicitly in terms of Vj or V (the
subscript j is dropped to simplify notation) as a Boltzmann relation
|
(1)
|
where Ai is the voltage sensitivity
coefficient and Voi is the voltage
for half-maximal conductance. The sign for V is negative for
K1 and K3 but positive
for K2 and K4, because the two voltage gates are oriented as mirror images of each other.
Fundamental thermodynamic considerations, based on the consistency of
free energy change between any two states regardless of the pathway,
require that
K1 · K4 = K2 · K3. Under
this constraint, the probability of a gap junction channel being open
(Po) can be calculated from the equilibrium
distribution among the available states
|
(2)
|
If it is assumed that the channel displays a single-channel
conductance level in the open state, the relationship between the
conductance of a population of gap junction channels and the steady-state Po is
|
(3)
|
where Gmax is the maximum conductance,
Gss is the steady-state conductance, and
Gmin is the minimum conductance (equivalent to
Eq. 5 in Ref. 28). To characterize the voltage
gating, we isolate Po from the other two
factors, namely, single-channel conductance and total number of
channels, by taking a ratio of the above conductance to the initial
conductance. This produces
|
(4)
|
where gn = Gss/Gi is the normalized
steady-state conductance, gmax = Gmax/Gi is the normalized
maximum conductance, and gres = Gmin/Gi is the normalized
residual conductance. Gi denotes the initial
conductance or instantaneous conductance. By definition, gmax
1 and 0
gres
1. Gi might be smaller than
Gmax if some channels are not open at the
initial moment. The gres reflects a persistent
conductance in the closed state that is present in most gap junction
channels studied, unless the channels are closed by phosphorylation or
pathological pH (7, 21). With rearrangement, we obtain the
following equation
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(5)
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The above treatment is based on a simplifying assumption that an
intact gap junction channel has one open channel conductance and one
residual conductance. A more complicated scheme includes one open
channel conductance and one residual conductance for each connexon
(hemichannel), giving rise to four possible conductances corresponding
to the four kinetic states for an intact channel (35).
Multiple single-channel conductances, as determined by single-channel
patch-clamp techniques, have been reported in several gap junction
channels (6, 21, 31). Nonetheless, the available experimental data concerning macroscopic currents do not have sufficient resolution to allow us to distinguish between the available models (as demonstrated later in regard to the independent vs. the
contingent model). As a practical matter, we use the above simplifying
assumption to extend from the original S-H-B model (15,
28) and, at the same time, to avoid the complications in the
general model (35) that cannot be resolved by the
experimental data of macroscopic currents. Although it is relatively
simple, this four-state equilibrium model can accommodate a number of rather complex features that can arise in gap junctions. For example, direct interaction between the connexons, such that the
Po of one gate depends on the state of the
other, would be represented quite simply by a difference between the
appropriate K values, e.g., K1 and
K3. On the other hand, an indirect effect
mediated by changes in the electrical potential profile across the
connexon pair would be modeled by a difference in A in the
exponential expressions for the equilibrium constants.
Contingent gating model.
On the basis of the physical considerations originally proposed by
Harris et al. (15), we further simplify the above scheme to two specific models. The contingent gating model assumes that if one
gate is closed, the other gate must be open. The underlying consideration is that Vj would drop entirely
across the closed gate, so there would be no voltage drop across the
open gate. This assumption, together with the assumption that a gate
has negligible probability of closing in the absence of a voltage drop
across it, leads to K3 = K4 = 0. Under these conditions, we have
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(6)
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Thus we obtain the following equation for the contingent model
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(7)
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Equation 7 contains six free parameters:
A1, A2,
Vo1, Vo2,
gres, and gmax. In the
case of a homotypic channel with two identical gates, we have the
constraint A1 = A2
and Vo1 = Vo2, so
the free parameters are reduced to four. Thus, for homotypic channels, we have
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(8)
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Independent gating model.
The independent gating model assumes that the two voltage gates in a
gap junction channel do not influence each other, through direct
interaction or indirectly through changes in the distribution of
Vj over the two hemichannels. Hence, the
probability of one gate being open is independent of the state of the
other. This assumption leads to K1 = K3 and K2 = K4. Under these conditions
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(9)
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Thus we obtain the following equation for the independent gating
model
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(10)
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Equation 10 also contains six free parameters,
A1, A2,
Vo1, Vo2,
gres, and gmax, for
heterotypic channels. For a homotypic channel, the free parameters are
reduced to four, and we have
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(11)
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For a homotypic channel, the model equations of contingent and
independent models become even functions of voltage,
gn(V) = gn(
V), because of the constraint
A1 = A2 and
Vo1 = Vo2. This symmetry
in the model equations concurs with the symmetrical gating of homotypic channels.
Voltage-gating parameters.
The parameters A and Vo in the
above-mentioned models describe the gap junction channel voltage
gating in terms of the voltage sensitivity and the half-maximal
voltage. However, to relate these functional measures to the
underlying molecular structure, it is preferable to convert these
descriptive parameters to physical terms. If we view voltage gating as
being controlled by a charge movement, or a dipole rotation, in the
channel molecule, the gating can be characterized by the equivalent
gating charge (Q) and the transition energy between open and
closed states (Uo). Q and
Uo are related to A and
Vo as follows
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(12)
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(13)
|
We use the elementary charge (e) for the unit of
Q and millielectron volts (meV) for the unit of
Uo. Q is calculated as the equivalent
net charge involved in the voltage gating, with the assumption that
these charges move across the entire transjunctional electrical field.
To relate Q to the number of charged and polar residues in
the channel molecule, one needs to consider that voltage gating could
involve translocation of positive and/or negative charges and/or dipole
rotation across only a fraction of the potential field because of
structural constraints. Hence, the actual charge involved in gating is
probably larger than Q. During a voltage pulse, external
energy input U(V) causes a shift in the gating state. If U > Uo, the gate
becomes more likely to be in the closed rather than the open state.
Conversely, for U < Uo, the
gate is predominantly open.
The normalized residual conductance, gres = (Gmin/Gi)
1, reflects the remaining conductance when the voltage gates are closed, usually under high voltages. For homotypic channels, the residual conductance has the same value at the positive and negative voltages. For heterotypic channels, the residual conductance could have two
different values. However, in known cases such as heterotypic Cx37/Cx40
(17), Cx26/Cx50, and Cx26/Cx30.3
(Zhu and Nicholson, personal communication), the residual conductance values at the positive and negative voltages are similar. In this model we have made
the simplifying assumption that there is only one
gres value for an intact channel.
The normalized maximum conductance gives the ratio of maximum
conductance to initial conductance, gmax = (Gmax/Gi)
1. If gmax = 1, all the channels are open at the
initial moment of the voltage step. If gmax > 1, some channels are closed. The Po at the
initial moment (Po,i) can be calculated from the
gres and gmax as follows
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(14)
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Example of using the model to characterize voltage gating.
As a simple example, we used the models to characterize the voltage
gating of the homotypic Cx30 channel (Fig.
2A). First, we calculated the
normalized conductance gn(V) from
Gss(V)/Gi(V). The normalization here is performed against the
Gi(V) values at each voltage point
according to the definition of gn (see Eq. 4), different from the prior normalization of conductance to the single Gi at 0 mV for comparing data from
different cell pairs. Because gn reflects the
Po and is dimensionless, the normalization here
also automatically takes into account the different coupling levels. We
used the contingent model (Eq. 8) to fit the data and obtained gating parameters of A = 0.116 mV
1 and Vo = 41.5 mV for each
voltage gate (Table 1). The gres is 25% of the
initial conductance, gres = 0.25. The
gmax is equal to the initial conductance,
gmax = 1.00.

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Fig. 2.
Voltage gating of homotypic and heterotypic channels made
of Cx30 and Cx32. A: conductances of homotypic Cx30/Cx30
channel are shown in
Gi-Vj,
Gss-Vj, and normalized
conductance (gn)-Vj
relationships. Values are averaged data from 17 cell pairs. The
gn-Vj relationship is
fitted to contingent (solid line) and independent (dashed line) models.
The 2 models yield identical fitting curves: solid and dashed lines are
superimposed. Gating parameters from the 2 models also have the same
value up to the 3rd decimal point (Table 1). B:
gn-Vj relationship of
homotypic Cx32/Cx32 channel is well fitted to contingent (solid line)
and independent (dashed line) models. The 2 models yield identical
fitting curves: solid and dashed lines are superimposed. C:
gn-Vj relationship of
heterotypic Cx30/Cx32 channel is also well fitted to contingent (solid
line) and independent (dashed line) models. The 2 models yield
identical fitting curves: solid and dashed lines are superimposed.
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The calculated Po,i is 1.0 for the homotypic
Cx30 channel (Eq. 14). However, the error margin of the
parameters is strongly dependent on the precision of the experimental
data. For example, single-channel measurements showed that
Po,i of the homotypic Cx43 channel is ~0.8
(4, 8). However, the parameters obtained from fitting of
the averaged macroscopic data of Cx43 gave
gres = 0.29 and
gmax = 1.00, which result in a calculated
Po,i of 1.0 (Table 1). The apparent discrepancy
in the Po,i values most likely arises from
errors in the parameters. In the case of Cx43 data, the standard error
of gres is 0.08 and that of
gmax is 0.03. The calculated
Po,i should have a standard error of 0.2 (calculated by deriving the error of Po,i from
that of Gres and Gmax in
Eq. 14 using standard method). Therefore, the
Po,i of 0.8 is within the error margin. We will
not include the detailed statistics of fitting and error estimates,
because we wish to focus on the basic principles and features of the model.
We also used the independent model (Eq. 11) to fit the data
and obtained gating parameters of the same values up to the precision of data (Fig. 2A).
Because of the symmetry in homotypic channel gating, it is no surprise
that the negative values A =
0.116 mV
1
and Vo =
41.5 mV also fit the
voltage-gating profile of Cx30/Cx30. This raises the question of gating
polarity. By convention, a connexon is deemed to have positive gating
polarity if it closes at positive voltages referenced to its
cytoplasmic side or to have negative gating polarity if it closes at
negative voltages (2, 17, 30, 34). Gating polarity cannot
be determined in homotypic channels because of the symmetry in voltage
gating. Consequently, gating polarity can be determined only from
heterotypic pairings (17) or between wild-type and mutant
connexins (34). Application of this strategy (see
DISCUSSION) leads to the assignment of positive gating
polarity to Cx30. We calculate the equivalent gating charge and the
transition energy of Cx30 in its homotypic channel as Q = 3.0 e and Uo = 125 meV (Table
1). These parameters for homotypic Cx30 channel gating are denoted
Cx30(3.0 e, 125 meV) and defined as the reference value of Cx30.
 |
DISCUSSION |
Gating polarity.
After the parameters for the two voltage gates in an intact gap
junction channel are obtained, an immediate question arises: which gate
belongs to which connexon hemichannel? In previous studies,
investigators developed a method to match the gate to its host
connexon. Stated simply, the two gates in heterotypic CxL/CxR channels
are matched with CxL and CxR according to how closely the gating
parameters resemble the reference values of CxL and CxR (22,
34). Here we propose a refinement of the formalism for this
often loosely applied principle.
First, we suggest using the physical parameters Q and
Uo, instead of the descriptive parameters
A and Vo, as the basis for comparison. Because the physical parameters can be better related to
the underlying molecular structure, they make a more meaningful comparison. Some investigators have already used equivalent gating charge to characterize gap junction voltage gating (22, 28, 34). Second, we suggest establishing a hierarchy with
Q as the primary criterion and Uo as
the secondary criterion for comparison. The reason for this is that
docking interaction probably causes less change in Q than in
Uo, because Q is mainly determined by the charged and polar residues in the gating domain, whereas
Uo reflects the energy contribution associated
with not only the gating charges but also the protein conformational
change due to docking.
For example, the two voltage gates in the heterotypic Cx40/Cx37
channels have parameters gate
V(10.5
e, 277 meV) and gate+V(6.3
e, 124 meV) (Fig. 3, Table 1) for gating in the negative and positive voltage ranges,
respectively. The reference value of Cx40 is Cx40(8.0
e, 276 meV) and that of Cx37 is Cx37(6.7 e, 110 meV) (Fig. 3, Table 1). With Q and Uo values for comparison, gate
V should be matched to Cx40 and gate+V to Cx37. Hence, the Cx37 gate closes at positive voltages referenced to its cytoplasmic side, whereas
Cx40 channels close at negative voltages referenced to the Cx37 side,
or in the positive voltage range referenced to its own side. Therefore,
Cx37 and Cx40 have positive gating polarity, in agreement with that
originally assigned by Hennemann et al. (17). We
denote the voltage-gating parameters of the heterotypic Cx40/Cx37
channel as follows: Cx40(10.5 e, 277 meV)/Cx37(6.3
e, 124 meV).

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Fig. 3.
Voltage gating of homotypic and heterotypic channels made
of Cx37 and Cx40. Voltage-gating profiles of homotypic Cx40 channel
(A), homotypic Cx37 channel (B), and heterotypic
Cx40/Cx37 channel (C) are fitted to contingent or
independent model. Symbols, averaged experimental data; lines, fitting
curve from either model. Resulting voltage-gating parameters are listed
in Table 1. In earlier publications (17, 22), homotypic
Cx37 channel gating profile was shown as Gss
(normalized to Gi at 0 mV), instead of
gn (gn = Gss/Gi).
Gss-Vj relationship
seemed best fitted to the sum of 2 Boltzmann functions;
gn-Vj relationship is
best fitted to a single Boltzmann function.
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Another simple example is Cx43/Cx45. The two gates in the
heterotypic Cx43/Cx45 channels have the following parameters:
gate
V(2.3 e, 51 meV) and
gate+V(0.7 e, 89 meV) (Fig.
4, Table 1). The reference
values are Cx43(1.5 e, 92 meV) and Cx45(2.8 e, 29 meV) (Fig. 4, Table 1). With the Q value as the first
criterion, gate
V should be matched to Cx45 and
gate+V to Cx43. Hence, the Cx45 gate closes at
negative voltages referenced to its cytoplasmic side, whereas Cx43
channels close at positive voltages referenced to the Cx45 side, or in
the negative voltage range referenced to its own side. Therefore, Cx45
and Cx43 have negative gating polarity. We denote their gating as
Cx43(
0.7 e, 89 meV)/Cx45(
2.3 e, 51 meV).

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Fig. 4.
Voltage gating of homotypic and heterotypic channels made
of Cx43 and Cx45. Voltage-gating profiles of homotypic Cx43/Cx43
(A), homotypic Cx45/Cx45 (B), and heterotypic
Cx43/Cx45 (C) channels are best fitted to contingent or
independent model. Symbols, averaged experimental data; lines, fitting
curve from either model. Resulting voltage-gating parameters are listed
in Table 1. Homotypic Cx45/Cx45 channel demonstrates a clear case where
initial conductance is smaller than maximum conductance. Only ~63%
of the channels are open at the initial moment. Heterotypic Cx43/Cx45
channel profile clearly shows an "off-center peak."
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In the heterotypic channels Cx40/Cx37 and Cx43/Cx45, the Q
values of the two voltage gates are very different; hence, the gates
can be assigned, using Q as the primary criterion, to their host connexons without much ambiguity. If the Q values of
the two gates are similar, e.g., in Cx26/Cx50 (Table 1), the
Uo values are used to assign the gates to their
host connexons. In the case that the Q and
Uo values of the two voltage gates in a
heterotypic channel are similar, statistical evaluation of the
difference in the parameter values would be necessary. First, the
difference between the Q values should be tested for
statistical significance. If they are insignificant, then the
difference between the Uo values is tested. The
convention and the objective of the "similarity principle" are to
assign the two voltage gates to the two member connexons in a
heterotypic channel in a way that minimizes the changes in Q
(primary criterion) and Uo (secondary criterion).
The heterotypic Cx30/Cx32 channel presents an interesting case. Only
the gate at negative voltages, gate
V, can be
determined; the gate at positive voltages,
gate+V, is absent in the voltage range of
experimentation (Fig. 2B). Although it is possible that
gating might occur at positive voltages outside the experimental
voltage range, evidence has been presented that the gating polarity of
Cx32 is negative (34). If this is the case, then Cx30 and
Cx32 in the heterotypic Cx30/Cx32 channel close at negative voltages,
while neither closes at positive voltages. Presumably, in the voltage
range where both gates are partially closed, the measured conductivity
should reflect the product of open probabilities for the two gates.
This observation is consistent with the behavior of other heterotypic
combinations of Cx32 with connexons of positive gating polarity, e.g.,
Cx26 (2) and Cx46 and Cx50 (36, 37), where
the gate
V closely resembles a Cx32 gating profile.
Docking interaction between two member connexons in an intact
channel.
Two connexons dock through their extracellular loops to form an intact
gap junction channel, although some connexon pairs are incapable of
docking with each other to form functional channels (16, 36,
37). Docking interaction often introduces changes in the
connexon voltage-gating characteristics (for summary see Refs.
5 and 12). Here we propose to measure the changes in the
voltage gating of CxA because of its heterotypic docking
with CxB as the difference between the gating parameters of
CxA in the heterotypic CxA/CxB channel
and the reference value of CxA.
For example, the heterotypic Cx40/Cx37 channel has gating parameters
Cx40(10.5 e, 277 meV)/Cx37(6.3 e, 124 meV). The
reference values are Cx40(8.0 e, 276 meV) and Cx37(6.7
e, 110 meV). Hence, we calculate the docking interaction
between Cx40 and Cx37 as follows: in Cx40, the equivalent gating charge
is increased by 2.5 e (= 10.5 e
8.0 e), and the transition energy is increased by 1 meV (=
277 meV
276 meV); in Cx37, the equivalent gating charge is
decreased by 0.4 e, and the transition energy is increased by 13 meV (Table 1). The above changes in the gating parameters of Cx40
and Cx37 serve to characterize the heterotypic docking interaction, in
reference to the docking interactions of the homotypic channels.
The changes in the Q and Uo
values lead to corresponding changes in the voltage-gating profile. The
functional implication is that the larger the Q value, the
more sensitive the gating in response to voltage change (steeper gating
profile), and the larger the Uo value, the
greater the voltage across the channel needed to close the gate. An
increase of 25 meV in the Uo value causes
an e-fold increase in the equilibrium constant between the
open and closed gating states.
Table 1 lists the voltage-gating parameters of several
representative connexon pairings. The homotypic "reference
values" for nine of the known connexins (i.e., Cx26, Cx30,
Cx30.3
, Cx32, Cx37, Cx40, Cx43, Cx45, and Cx50) are shown.
Heterotypic pairings between positive gating connexins (Cx30/Cx26,
Cx40/Cx37, Cx26/Cx30.3
, and Cx26/Cx50), negative gating connexins
(Cx43/Cx45), and positive and negative gating connexins (Cx30/Cx32), as
well as interactions between
-connexins (Cx40/Cx37 and Cx43/Cx45),
-connexins (Cx26/Cx30, Cx26/Cx30.3
, and Cx30/Cx32), and
- and
-connexins (Cx26/Cx50), are illustrated. The changes in the
voltage-gating parameters of several connexon pairs from their
homotypic docking interaction reveal that some heterotypic docking
causes only slight changes in the voltage gating of member
connexons, e.g., the heterotypic docking of Cx37 and Cx40.
However, some heterotypic docking significantly alters the voltage
gating of member connexons, as in the case of heterotypic docking of
Cx26 with Cx50, Cx30.3
, or Cx50. We speculate that the extent of
alteration in the connexon voltage gating due to docking is dependent
on the rigidity of its docking domain relative to that of the partner.
In summary, the present model is a natural extension of the original
S-H-B model (15, 28). We have added necessary complexity to model the asymmetric gating of a heterotypic channel, mainly by
integrating the two voltage gates from the two hemichannel connexons.
At the same time, we introduce three assumptions to circumscribe the
complexity in a general model (35), so the present model
can be used as a practical tool to fit the experimental data of
macroscopic currents without too much ambiguity. The limitation of the
model comes from its simplifying assumptions. The requirement of
thermodynamic consistency should always hold true. The assumption of an
independent or a contingent model provides a simple mathematical formula. The assumption of one open channel conductance and one residual conductance limits the number of independent parameters in the
fitting equations, so the experimental data can be fitted without
ambiguity. In principle, the above constraints limit the model
application to the channels that have only one voltage gate on each
hemichannel, one single-channel conductance, and one residual conductance. In practice, however, many known channels possess features
that approximate these conditions and, therefore, can be characterized
using the present model. For example, Cx43 has a fast voltage gating
and a slower gating (1, 24). Because the fast gating
happens within milliseconds, the slower gating (~100 times slower)
can be easily separated from the former and characterized using this
model. In another example, the single-channel conductance of Cx43 is
seen as 60 pS in some cells and as 90 pS in others. However, for a
given expression system, the Cx43 channel demonstrates only one
dominant conductance level (21). Hence, the present model
can be used to approximate the gating behavior. The voltage-gating
profiles of all the channels listed in Table 1, except the heterotypic
Cx43/Cx45 channel, demonstrate similar residual conductance levels at
positive and negative voltage ranges. Therefore, the present model can
apply to these channels. In the case of Cx43/Cx45, the voltage-gating
profile shows that gate at the positive voltage range has not reached
the residual conductance level within the experimental voltage range
(Fig. 4C). Recently, using longer voltage steps, we found
that the residual conductance is similar in positive and negative
voltage ranges with a value very close to zero (unpublished data).
Thus this model does not apply to the channels with multiple
single-channel conductance levels, with more than two voltage gates, or
with two different residual conductance levels. Nor does the model
attempt to describe the kinetic behavior of channels. The present model
aims to describe the steady-state properties of the voltage gating at
the level of macroscopic currents. The model sets consistent
criteria to characterize the gating of heterotypic and homotypic
channels in a comprehensive and intuitive way. The model also provides
a practical formalism for fitting the voltage-gating profile over the
entire voltage range, eliminating the previous need for data splicing.
Hence, this model presents a useful tool for quantitatively
characterizing the voltage gating of a population of gap junction channels.
 |
ACKNOWLEDGEMENTS |
We thank Dr. Bruce J. Nicholson for substantial input into the
writing of the manuscript and for sharing the experimental data on
Cx26, Cx30.3
, and Cx50; Dr. Thomas M. Suchyna for sharing the
experimental data on Cx37/Cx40; and Drs. Leighton T. Izu and Edward G. Lakatta for comments on the manuscript.
 |
FOOTNOTES |
Y. Chen-Izu was supported, in part, by National Cancer Institute Grant
CA-480490 (to Bruce J. Nicholson) and by the Interdisciplinary Training
Program in Muscle Biology, Department of Biochemistry and Molecular
Biology, University of Maryland School of Medicine. A. P. Moreno
was supported, in part, by National Heart, Lung, and Blood Institute
Grant HL-63969 and an Indiana University Research Venture Award.
Address for reprint requests and other correspondence: Y. Chen-Izu, Dept. of Physiology, University of Maryland School of Medicine, 655 W. Baltimore St., Baltimore, MD 21201-1559 (E-mail: ychen005{at}umaryland.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 1 February 2001; accepted in final form 11 July 2001.
 |
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