Zinc is a voltage-dependent blocker of native and heterologously expressed epithelial Na⁺ channels

Abstract

Zn²⁺ (1–1,000 μM) applied to the apical side of polarized A6 epithelia inhibits Na⁺ transport, as reflected in short-circuit current and conductance measurements. The Menten equilibrium constant for Zn²⁺ inhibition was 45 μM. Varying the apical Na⁺ concentration, we determined the equilibrium constant of the short-circuit current saturation (34.9 mM) and showed that Zn²⁺ inhibition is non-competitive. A similar effect was observed in Xenopus oocytes expressing αβγrENaC (α-, β-, and γ-subunits of the rat epithelial Na⁺ channel) in the concentration range of 1–10 μM Zn²⁺, while at 100 μM Zn²⁺ exerted a stimulatory effect. The analysis of the voltage dependence of the steady-state conductance revealed that the inhibitory effect of Zn²⁺ was due mainly to a direct pore block and not to a change in surface potential. The equivalent gating charge of ENaC, emerging from these data, was 0.79 elementary charges, and was not influenced by Zn²⁺. The stimulatory effect of high Zn²⁺ concentrations could be reproduced by intra-oocyte injection of Zn²⁺ (~10 μM), which had no direct effect on the amiloride-sensitive conductance, but switched the effect of extracellular Zn²⁺ from inhibition to activation.

Appendix

Correction of conductances in oocyte recordings

Consider the oocyte as a sphere of radius R. Two forces govern ion movement across the membrane and in the thin shells of fluid surrounding it: the electric field E and the concentration gradient dc/dx. The drift speed (s) for electric conduction of an ion is proportional to its mobility u:

$$ s=uE $$

(1)

Since the main voltage drop is across the membrane itself, the electric field intensity in the extracellular and intracellular fluid is less than 10 V/m, thus the drift speed for Na⁺ in solution (u=5.19×10⁻⁸ m² s⁻¹ V⁻¹ at 25°C) is less than 0.5 μm/s. For a thin layer of thickness Δx located in the immediate vicinity of the membrane, the mass conservation law expresses the amount of Na⁺ accumulated or depleted during a short time interval Δt as the difference between the amount transported across the membrane and the amount gained or lost by diffusion, according to Fick's first law:

$$ 4\pi R^2 \Delta x\Delta c = I_{{\rm{Na}}} \Delta t/F - 4\pi \left( {R \pm \Delta x} \right)^2 D_{\rm{s}} {{\Delta c} \over {\Delta x}}\Delta t $$

(2)

where Δc represents the variation in concentration during Δt,I _Na the Na⁺ current across the oocyte membrane, R the oocyte radius, F Faraday's constant and D _S the diffusion coefficient. Therefore:

$$ \Delta c = {{{{I_{{\rm{Na}}} } \over F}\Delta t} \over {4\pi R^2 \Delta x + 4\pi \left( {R \pm \Delta x} \right)^2 {{D_{\rm{s}} \Delta t} \over {\Delta x}}}} $$

(3)

is proportional to the current. For Δx=1 μm, Δt=0.2 ms (equal to the sampling interval used for recordings), and an oocyte radius R=0.6 mm, we can calculate the proportionality factor, knowing the diffusion coefficient for Na⁺ at 25°C (D _S=1.33×10⁻⁹ m² s⁻¹):

$$ \Delta c = {\rm{0}}{\rm{.0000458}} \cdot I_{{\rm{Na}}} $$

(4)

Using this relationship, we built a numeric integration algorithm to correct the values of conductance derived from the currents recorded during the voltage step protocols. For each integration step, Δc values were computed and used to update Na⁺ concentrations and then the Na⁺ driving force. The driving force was used within the next integration step to calculate the conductance. The resulting values were additionally corrected for each voltage step of the protocol by proportionality factors representing the relative values of initial conductances.

Calculation of the surface potential

The Grahame equation (1947) [17], a generalization of the Gouy (1911)-Chapman (1913) equation, relates the surface potential Ψ₀ to the surface charge density σ and the bulk concentrations c _k of various ionic species of valence z _k present in the surrounding solution:

$$ \sigma ^2 = 2\varepsilon _{\rm{r}} \varepsilon _0 {\rm{RT}}\sum\limits_{\rm{k}} {c_{\rm{k}} \left[ {\exp \left( {z_{\rm{k}} F\psi _0 /{\rm{RT}}} \right) - 1} \right]} $$

(5)

where ε_r and ε₀ represent the relative and absolute dielectric constants of the solvent, respectively, R the perfect gas constant, T the absolute temperature, and F Faraday's constant.

Independently, the surface charge density can be expressed, like the concentration of a complex into a chemical reaction, by the Langmuir adsorption isotherm:

$$ \sigma = zS{c \over {c + K_{\rm{d}} }} $$

(6)

where S represents the maximal binding site density multiplied by the elementary charge, and K _d the dissociation constant of the ion from the surface. In the presence of multiple ion species the formula becomes more extended, due to competition for binding sites, but it has been proved that monovalent cations have a small contribution. As for multivalent cations, they interact mainly with PS, which represents 10–20% of the lipid contents in biomembranes. The PS dissociation constants are 120–250 mM for Mg²⁺, 83 mM for Ca²⁺, 25 mM for Ni²⁺, 1 mM for Be²⁺ and 0.02 mM for Gd³⁺ [6, 23], while for zwitterionic phospholipids they are higher at physiological pH (e.g. for phosphatidylcholine 556 mM for Mg²⁺ and 370 mM for Ca²⁺ [23]), indicating a weaker interaction with these residues. In the case of a main divalent cation (Ca²⁺) and an additional multivalent cation I acting as a competitive inhibitor, the apparent dissociation constant of the main cation changes with [I]:

$$ K_{\rm{d}}^{\rm{*}} = K_{\rm{d}} \left( {1 + \left[ I \right]/K_{\rm{d}}^{\rm{I}} } \right) $$

(7)

For a single ion species, Eqs. 5 and 6 can be easily combined:

$$ \sigma ^2 = {{z^2 S^2 } \over {\left( {c + K_{\rm{d}} } \right)^2 }} = 2\varepsilon _r \varepsilon _0 {\rm{RT}}c\left[ {\exp \left( {zF\psi _0 /{\rm{RT}}} \right) - 1} \right] $$

(8)

and the unknown surface charge density σ eliminated. Then Ψ₀ can be directly expressed as a function of the ionic concentration c (or, better, of the ionic activity):

$$ \psi _0 = {{{\rm{RT}}} \over {zF}}\ln \left[ {1 + {{z^2 S^2 } \over {2\varepsilon _{\rm{r}} \varepsilon _0 {\rm{RT}}}}{{c^2 } \over {\left( {c + K_{\rm{d}} } \right)^2 }}} \right] $$

(9)

Now we can introduce numeric values for the parameters. Using a maximal monovalent charge density S=0.2 C/m² [6], which is equivalent to 1 elementary charge/80 Å² and in agreement with the mean area per phospholipid found in different bilayer models [28], the equation becomes (at room temperature):

$$ \psi _0 = 12.5\ln \left[ {1 + 22800{{c^2 } \over {\left( {K_{\rm{d}} + c} \right)^2 }}} \right] $$

(10)

The electrical distance of block

Let us consider the epithelial Na⁺ channel as a transmembrane pore. If we assume a single binding site for Na⁺ within the pore, the kinetics of ion passage can be expressed in a similar way to that of a chemical reaction:

$$ \left[ {{\rm{Na}}^ + } \right]_{\rm{o}} \mathrel{\dynrightleftarrows {k_1 }{k_{ - 1} }} \left[ {{\rm{Na}}^ + - C} \right]\mathrel{ \dynrightleftarrows {k_2 }{k_{ - 2} }} \left[ {{\rm{Na}}^ + } \right]_{\rm{i}} $$

(11)

According to a kinetic equation:

$$ {{{\rm{d}}\left[ {{\rm{Na}}^ + - C} \right]} \over {{\rm{d}}t}} = \left[ {{\rm{Na}}^ + } \right]_o \left[ C \right]k_1 + \left[ {{\rm{Na}}^ + } \right]_{\rm{i}} \left[ C \right]k_{{\rm{ - 2}}} - \left[ {{\rm{Na}}^ + - C} \right]\left( {k_2 + k_{{\rm{ - 1}}} } \right) $$

(12)

where the population of unoccupied channels, [C], can be expressed as a function of the total population of channels, [C]₀

$$ \left[ C \right] = \left[ C \right]_0 - \left[ {{\rm{Na}}^ + - C} \right] $$

(13)

Therefore, at equilibrium, the channel occupancy by Na⁺ is:

$$ \left[ {{\rm{Na}}^ + - C} \right] = {{\left[ C \right]_0 \left( {\left[ {{\rm{Na}}} \right]_{\rm{o}} k_1 + \left[ {{\rm{Na}}} \right]_{\rm{i}} k_{{\rm{ - 2}}} } \right)} \over {k_2 + k_{{\rm{ - 1}}} + \left[ {{\rm{Na}}} \right]_{\rm{o}} k_1 + \left[ {{\rm{Na}}} \right]_{\rm{i}} k_{{\rm{ - 2}}} }} $$

(14)

If Na⁺ outflow through the channel is very low compared to the inflow, we can omit [Na]_ik₋₂ and write the Na⁺ inward current as:

$$ I_{{\rm{Na}}} = Fk_2 \left[ {{\rm{Na}}^ + - C} \right] = {{Fk_2 \left[ C \right]_0 \left[ {{\rm{Na}}^ + } \right]_{\rm{o}} } \over {\left[ {{\rm{Na}}^ + } \right]_{\rm{o}} + {{k_2 + k_{{\rm{ - 1}}} } \over {k_1 }}}} $$

(15)

Under the action of a non-competitive blocker B, the total population of available channels will be reduced with the amount of blocked channels, to:

$$ \left[ C \right]_0 - {{\left[ C \right]_0 \left[ B \right]k_1^{\rm{B}} } \over {\left[ B \right]k_{\rm{1}}^{\rm{B}} + k_{{\rm{ - 1}}}^{\rm{B}} }} = {{\left[ C \right]_0 } \over {1 + \left[ B \right]{{k_1^{\rm{B}} } \over {k_{{\rm{ - 1}}}^{\rm{B}} }}}} $$

(16)

where k ₁ ^B and k ₋₁ ^B represent the blocking and unblocking rates, respectively, and [B] the concentration of blocker. Each of these two rates can be described in terms of the free energy barrier, according to the Arrhenius formula (developed later by Eyring):

$$ k_1^{\rm{B}} = B_1 e^{{\rm{ - }}\Delta {\rm{G}}_{\rm{1}} {\rm{/RT}}} \;{\rm{and}}\;k_{{\rm{ - }}1}^{\rm{B}} = B_{{\rm{ - 1}}} e^{{\rm{ - }}\Delta {\rm{G}}_{{\rm{ - 1}}} {\rm{/RT}}} $$

(17)

where ΔG ₁ and ΔG _-1 represent the Gibbs free energy barriers for entering and leaving the blocking site in the absence of transmembrane electric field, B ₁ and B _-1 are specific constants, R the ideal gas constant, and T the absolute temperature. If the blocker enters the pore to a site located at a certain fraction δ of the total length of the transmembrane electric field, the work required for the charge movement up to the point of maximal free energy, located at another fraction length of the transmembrane field, α, will be added to the energy barrier:

$$ k_1^{\rm{B}} = B_1 e^{{{{\rm{ - }}\Delta {\rm{G}}_{\rm{1}} {\rm{ - zF}}\alpha {\rm{V}}} \over {{\rm{RT}}}}} \;{\rm{and}}\;k_{{\rm{ - 1}}}^{\rm{B}} = B_{{\rm{ - 1}}} e^{{{{\rm{ - }}\Delta {\rm{G}}_{{\rm{ - 1}}} {\rm{ + zF}}\left( {{\rm{\delta - \alpha }}} \right){\rm{V}}} \over {{\rm{RT}}}}} $$

(18)

Therefore, the ratio of currents or conductances in the presence and in the absence of the blocker becomes a function of the transmembrane potential V and of the electrical distance of the blocking site δ:

$$ {{I_{{\rm{Na}}}^{\rm{B}} } \over {I_{{\rm{Na}}} }} = {1 \over {1 + \left[ B \right]{{B_1 } \over {B_{{\rm{ - 1}}} }}e^{{{{\rm{\Delta G}}_{{\rm{ - 1}}} {\rm{ - \Delta G}}_{\rm{1}} {\rm{ - zF\delta V}}} \over {{\rm{RT}}}}} }} $$

(19)