Intracellular Mg<Superscript><Emphasis Type="Bold">2+</Emphasis></Superscript> Influences Both Open and Closed Times of a Native Ca<Superscript><Emphasis Type="Bold">2+</Emphasis></Superscript>-activated BK Channel in Cultured Human Renal Proximal Tubule Cells

M. Kubokawa; Y. Sohma; J. Hirano; K. Nakamura; T. Kubota

doi:10.1007/s00232-005-0802-3

The Journal of Membrane Biology

September 2005, Volume 207, Issue 2, pp 69–89 | Cite as

Intracellular Mg²⁺ Influences Both Open and Closed Times of a Native Ca²⁺-activated BK Channel in Cultured Human Renal Proximal Tubule Cells

Authors
Authors and affiliations

M. KubokawaEmail author
Y. Sohma
J. Hirano
K. Nakamura
T. Kubota

Article

Received: 01 December 2004

Revised: 20 October 2005

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4 Citations

Abstract

Effects of intracellular Mg²⁺ on a native Ca²⁺-and voltage-sensitive large-conductance K⁺ channel in cultured human renal proximal tubule cells were examined with the patch-clamp technique in the inside-out mode. At an intracellular concentration of Ca²⁺ ([Ca²⁺]_i) of 10⁻⁵–10⁻⁴ M, addition of 1–10 mM Mg²⁺ increased the open probability (P_o) of the channel, which shifted the P_o –membrane potential (V_m) relationship to the negative voltage direction without causing an appreciable change in the gating charge (Boltzmann constant). However, the Mg²⁺-induced increase in P_o was suppressed at a relatively low [Ca²⁺]_i (10^−5.5–10⁻⁶ M). Dwell-time histograms have revealed that addition of Mg²⁺ mainly increased P_o by extending open times at 10⁻⁵ M Ca²⁺ and extending both open and closed times simultaneously at 10^−5.5 M Ca²⁺. Since our data showed that raising the [Ca²⁺]_i from 10⁻⁵ to 10⁻⁴ M increased P_o mainly by shortening the closed time, extension of the closed time at 10^−5.5 M Ca²⁺ would result from the Mg²⁺-inhibited Ca²⁺-dependent activation. At a constant V_m, adding Mg²⁺ enhanced the sigmoidicity of the P_o–[Ca²⁺]_i relationship with an increase in the Hill coefficient. These results suggest that the major action of Mg²⁺ on this channel is to elevate P_o by lengthening the open time, while extension of the closed time at a relatively low [Ca²⁺]_i results from a lowering of the sensitivity to Ca²⁺ of the channel by Mg²⁺, which causes the increase in the Hill coefficient.

Keywords

Ca²⁺-activated K⁺ channel Intracellular Mg²⁺ Open probability Gating kinetics Kidney Proximal tubule

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Notes

Acknowledgement

We gratefully acknowledge Prof. K. L. Magleby (University of Miami) for providing the program for analyzing 2-D dwell-time. This study was partly supported by a grant from the Japan Society for the Promotion of Science to Y.S. (15590196).

Appendix 1

SIMPLIFICATION OF THE GATING MODEL

Rothberg & Magleby (1999, 2000) proposed a general 50-state two-tiered gating model of BK channels consisting of 25 closed states on the upper tier and 25 open states on the lower tier, which could approximate both dwell-time distributions from low to high Ca²⁺_i. To analyze the effects of Mg²⁺ on the gating of RPTEC BK channels, we employed this model but reduced the number of states.

We recorded the single-channel current for 2-D dwell-time distribution analysis at a fixed voltage of 15 mV (Fig. 8). At a fixed voltage, the original two-tiered kinetic model involved five states in the open and closed tiers, respectively (Rothberg & Magleby, 1999, 2000) (see the gray + black part in scheme A-1). Under all the conditions of [Ca²⁺]_i and [Mg²⁺]_i adopted in this study, the 1-D open- and closed-time distributions could be fitted by two and three exponential components, respectively (see Figs. 6A and 9). Therefore we reduced the states in the model to two open and three closed states because of minimal numbers of underlying 2-D exponential components. This means that we omitted the states with a very low occupancy probability and/or very short mean lifetime under the experimental conditions used for the kinetic analysis. Because we used relatively high concentrations of Ca²⁺_i at which P_o was ∼0.3, the reduced two-tiered two-open and three-closed state model might correspond to the right end (higher Ca²⁺ concentration end) of the Rothberg & Magleby model (see the black part in scheme A-1). Open image in new window

AN ITERATIVE ESTIMATION OF RATE CONSTANTS

To estimate the rate constants in gating model I from the 2-D dwell-time distribution, we employed an iterative simulation method similar to that described by Magleby & Weiss (1990).

First, an idealized single-channel current including 300,000 opening-closing event pairs was generated according to the proposed gating scheme I, with no noise and an unlimited time resolution. The idealized single-channel current was sampled at 10 kHz by superimposing Gaussian noise (Press et al., 1992) and low-pass filtered at 2 kHz with a digital Gaussian filter (Colquhoun & Sigworth, 1995). The amplitude of the Gaussian noise was adjusted to show a root-mean-square amplitude in the final output similar to that observed in closed states in our experimental current recordings (∼0.8 pA_p-_p at 2 kHz filtered). The durations of open and closed intervals in the simulated single-channel currents were measured with a half-amplitude threshold analysis and binned into the 2-D dwell-time histograms in a manner identical to that used to analyze the experimental data.

The most likely rate constants were determined from direct likelihood comparisons of the simulated 2-D dwell-time distribution with the 2-D dwell-time distribution best-fitted to the experimental 2-D dwell-time distribution. The fitting of data was restricted to intervals with a duration greater than two-fold the dead times. To simplify the writing, the text will refer to the fitting of the (smoothed) 2-D dwell-time distributions (surface plots) presented in the figures (see Method), when, in reality, the non-smoothed 2-D frequency histograms were fitted.

Note that the simplification we performed on the general 50-state two-tiered scheme of BK channel gating and original 2-D dwell-time analysis described by Rothberg & Magleby (1999, 2000) should somehow reduce the accuracy of estimates of model parameters.

Appendix 2

AN OPEN CHANNEL Mg²⁺-BINDING SCHEME FOR Mg²⁺-DEPENDENT ACTIVATION

To qualify the interaction of Mg²⁺ with the BK channel from the P_o data with and without Mg²⁺, we employed a simple gating scheme in which Mg²⁺ could bind to the channel in its open conformation and stabilize it, as follows:

$$\mathop {\rm{C}}\limits^{{\rm{(closed)}} \atop \vdots} \mathop{\longleftrightarrow}\limits^{\beta}_{\alpha} {\rm{O}} + \mathop{\rm{Mg}^{2 +}}\limits^{\hskip-16pt{{\rm{(open)}} \atop \vdots}} {\mathop{\longleftrightarrow} \limits_{k_{{\rm{off}}} }^{k_{{\rm{on}}} }} {\rm{O}} \cdot \mathop{\rm{Mg}^{2 +}}\limits^{\hskip-16pt{{\rm{(Mg-open)}} \atop \vdots}}$$

(Scheme B-1)

According to the open-channel stabilization scheme B-1, the open probability in the presence of Mg²⁺ (P_oMg) is derived as follow:

$$ P_{\rm oMg} = P_{{\rm o}(0{\rm Mg})} + {1 - P_{\rm o}(0{\rm Mg}) \over {1 +\left( {K_{\rm Mg}} \over {[{\rm Mg}^{2 +}]} \right)}} $$

(B1)

where P_o(0Mg) is the open probability in the absence of Mg²⁺ and K_Mg is the apparent dissociation constant of Mg²⁺ binding to the channel, described as follows:

$$ K_ {\rm Mg} = {\left( 1 \over P_{{\rm o}(0{\rm Mg})} \right) \cdot \left(K_{\rm off} \over K_{\rm on} \right) = {K_{\rm Mg}^0 \over P_{{\rm o}(0{\rm Mg})}}} $$

(B2)

where K_Mg⁰ is the value of K_Mg under the conditions where the open probability is equal to 1 in the absence of Mg²⁺.

From Eq. B2

$$ \eqalign{\log K_{\rm Mg} &= \log K_{\rm Mg}^0 - \log P_{{\rm o}(0{\rm Mg})} = \cr &\log K_{\rm Mg}^0 - \log P_{\rm min}} $$

(B3)

where P_min is the open probability in the absence of Mg²⁺ used in Eq. 4

Therefore K_Mg is in inverse proportion to P_o(0Mg) in the open-channel stabilization scheme B-1. This means that the log-log plots of K_mg against P_min should show a slope of −1, which is consistent with our experimental data (Fig. 7 A, B).

In the case where state-independent binding of Mg²⁺ opened the closed channel and stabilized the open channel, K_Mg should be independent of P_o(0Mg) (equation not shown). Assuming that Mg²⁺ could bind to the channel in its closed conformation and open the channel, K_Mg should be described as follows (derivation not shown):

$$ \eqalign{\log K_{\rm Mg} = \log K_{\rm Mg}^0 -\log P_{{\rm o}(0{\rm Mg})} =\cr \log K_{Mg}^0 - \log (1 - P_{\rm min} )} $$

(B4)

In this case, the log-log plots of K_Mg against P_min should show a positive slope, which is inconsistent with our experimental data (Fig. 7A, B).

Appendix 3

A TWO-TIERED, 10-STATE GATING SCHEME FOR REPRODUCING Mg²⁺-INDUCED ENHANCEMENT

To reproduce the Mg²⁺-induced enhancement of P_o, we developed a two-tiered, 10-state Monod-Wyman-Changeux gating scheme (Cox et al., 1997) with the assumption of a competitive inhibition of the binding of Ca²⁺ to the high-affinity Ca²⁺ sites by Mg²⁺ in closed channels (Eq. C8) and a mutual binding of Mg²⁺ to the low-affinity Mg²⁺/Ca²⁺ sites in open channels (Eq. C9). Open image in new window

where C_i and O_i, are closed and open channels with a number i (0–4) of Ca²⁺ (or Mg²⁺) ions binding to the BK channel; α_c and β_c, and α₀ and β₀ are the apparent binding and unbinding rates of Ca²⁺ to BK channels in closed and open states; γ_i and δ_i are transition rates from O_i, to C_i and from C_i, to O_i.

Derivation of the Apparent On-Rate of Ca²⁺ Binding under Competitive Inhibition by Mg²⁺

Assuming competitive inhibition between Ca²⁺ and Mg²⁺ as below: Open image in new window

$$ [{\rm EMg}] + [{\rm E}] + [{\rm ECa}] =[{\rm E}_0], $$

(C1)

$$ k_{{\rm off}({\rm Ca})} \cdot [{\rm ECa}] = k_{{\rm on}({\rm Ca})} \cdot [{\rm Ca}^{2+}] \cdot [{\rm E}], $$

(C2)

$$ k_{{\rm off}({\rm Mg})} \cdot [{\rm ECa}] = k_{{\rm on}({\rm Mg})} \cdot [{\rm Mg}^{2+}] \cdot [{\rm E}], $$

(C3)

From Eqs. |C1|–|C3|,

$$ [{\rm E}] = {[{\rm E}_0] \over 1 +{[{\rm Ca}^{2+}] \over K_{\rm Ca}} + {[{\rm Mg}^{2+}] \over K_{\rm Mg}}} $$

(C4)

Where

$$ K_{\rm Mg} = k_{{\rm off}({\rm Mg})} /k_{{\rm on}({\rm Mg})}; K_{\rm Ca} = k_{{\rm off}({\rm ca})} /k_{{\rm on}({\rm Ca})} $$

The apparent on-rate of Ca²⁺ binding in the presence of Mg²⁺, α, is described by:

$$\alpha = k_{{\rm on}({\rm Ca})} \cdot [{\rm Ca}^{2+}]\cdot [{\rm E}] = k_{{\rm on}({\rm Ca})} \cdot [{\rm Ca}^{2+}] \cdot \left({[{\rm E}_0]\over {1 +{[{\rm Ca}^{2+}]\over K_{\rm Ca}} + {[{\rm Mg}^{2+}]\over K_{\rm Mg}}}} \right) $$

(C5)

In the absence of Mg²⁺, Open image in new window

the on-rate of Ca²⁺ binding α⁰, is described by:

$$ \alpha^0 = k_{{\rm on}({\rm Ca})} \cdot [{\rm Ca}^{2+}] \cdot [{\rm E}] = k_{{\rm on}({\rm Ca})} \cdot [{\rm Ca}^{2+}] \cdot \left({[{\rm E}_0]} \over {1 + {[{\rm Ca}^{2+}] \over {K_{\rm Ca}}}} \right),$$

(C6)

Therefore, from Eqs. C5 and C6,

$$ \alpha = \alpha^0 \cdot [{\rm Ca}^{2+}] \cdot \left(1 +{{[{\rm Ca}^{2+}]} \over K_{\rm Ca}} \over {1 +{[{\rm Ca}^{2+}] \over K_{\rm Ca}} + {[{\rm Mg}^{2+}] \over K_{\rm Mg}}} \right), $$

(C7)

Thus, the apparent Ca²⁺ -binding rate to the high-affinity Ca²⁺ sites in closed channels, α_c, is calculated as below:

$$ \alpha_c = \alpha _c^0 \cdot [Ca^{2+}] \cdot \left(1 + {{[{\rm Ca}^{2+}]} \over K_{\rm Ca}({\rm C})} \over {1 + {[{\rm Ca}^{2+}] \over K_{\rm Ca}({\rm C})} + {[{\rm Mg}^{2+}] \over K_{\rm Mg}({\rm C})}} \right), $$

(C8)

where α _c ⁰ is the apparent rate constant for the binding of Ca²⁺ to BK channels in a closed state without Mg²⁺; and K_Ca(C) (= β_c/α_c) and K_Mg(c) are dissociation constants for the binding of Ca²⁺ and Mg²⁺ to BK channels in the closed state.

The apparent Ca²⁺ binding rate to the low-affinity Mg²⁺/Ca²⁺ sites in open channels, α_o, is calculated as below:

$$ \alpha_{\rm o} = \alpha_{\rm o}^0 \cdot \left( {[{\rm Ca}^{2+}]} + [{\rm Mg}^{2+}] \right), $$

(C9)

where α _o ⁰ is the rate constant for the binding of Ca²⁺ and Mg²⁺ to BK channels in an open state.

Calculation of P_O in Scheme C-1

P_o is calculated by using the Q-matrix method (Colquhoun & Hawkes, 1995). Values of the parameters (Table 3) were determined from our P_o–[Ca²⁺]_i data (Fig. 4A) referring to the values reported by Cox et al. (1997).

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M. Kubokawa
- 1
Email author
Y. Sohma
- 2
- 3
J. Hirano
- 1
K. Nakamura
- 1
T. Kubota
- 2

1.Department of Physiology II, School of MedicineIwate Medical UniversityMoriokaJapan
2.Department of PhysiologyOsaka Medical CollegeTakatsukiJapan
3.John M. Dalton Cardiovascular Research CenterUniversity of Missouri-ColumbiaColumbiaUSA

Intracellular Mg²⁺ Influences Both Open and Closed Times of a Native Ca²⁺-activated BK Channel in Cultured Human Renal Proximal Tubule Cells

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Intracellular Mg 2+ Influences Both Open and Closed Times of a Native Ca 2+ -activated BK Channel in Cultured Human Renal Proximal Tubule Cells

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Intracellular Mg²⁺ Influences Both Open and Closed Times of a Native Ca²⁺-activated BK Channel in Cultured Human Renal Proximal Tubule Cells