About a new method to measure fractional Ca²⁺ currents through ligand-gated ion channels

The Journal of General Physiology recently published a paper (Elenes et al., 2009) describing a novel electrophysiological approach to measure the Ca²⁺-carried current through ligand-gated channels. The method proposed is based on the assumption that all permeant ions compete for a single binding site, which controls permeation and is implemented by fitting single-channel data obtained at different extracellular Ca²⁺ concentrations ([Ca²⁺]_o) to derive values for the fractional Ca²⁺ current, i.e., the percentage of the total current carried by Ca²⁺ ions.

The fractional Ca²⁺ current values obtained are not too different from some of those found for the rat NR1-NR2A NMDA receptor or the human adult acetylcholine receptor (AChR) using the fluorometric method proposed by Zhou and Neher (1993). In contrast, the values found for the fetal and adult mouse AChR (19.3 and 16.3%) are at odds with the values present in the literature (∼2 and ∼4%, respectively) (Villarroel and Sakmann, 1996; Ragozzino et al., 1998; Fucile et al., 2006). In particular, the fractional Ca²⁺ current values for the mammalian fetal AChR calculated using different experimental approaches are all comprised between 2.0 and 3.4% (Decker and Dani, 1990; Vernino et al., 1994; Villarroel and Sakmann, 1996; Ragozzino et al., 1998; Fucile et al., 2006).

Of note, the discrepancy is such that either the values of Elenes et al. (2009) or the previously published values are wrong. Here, we point out some issues that may have influenced the estimates by Elenes et al. (2009).

The authors decompose the total current (i_total) flowing through the AChR channel as the sum of a lumped current representing Na⁺, K⁺, and Mg²⁺ ions (i_Na⁺_−Mg²⁺) plus the current carried by Ca²⁺ ions (i_Ca²⁺). From the “one-site” model they derive equations for i_Na⁺_−Mg²⁺ and i_Ca²⁺, copied here with their original numbering, for the reader's convenience:

Noticeably, current reversal potential has been omitted in both equations.

Inserting into Eq. 4 the values of K_DCa2+ derived by fitting, the authors conclude that with an external solution containing 150 mM NaCl plus 100 mM CaCl₂, the inward current is “carried exclusively by Ca²⁺ ions.” This is a central point in the paper, as it is a key prediction of the model and is used to show that the error introduced neglecting current reversal potential in Eqs. 3 and 4 is small.

This statement is not supported by experimental data presented in the paper. With 100 mM CaCl₂ plus 150 mM NaCl in the external solution, the reversal potential of ACh-evoked currents is +18 mV (Elenes et al., 2009). When Ca²⁺ ions completely replace monovalent ions in the external solution (and therefore are the only inward-flowing ions), the reversal potential of the ACh-evoked current (E_ACh) undergoes a hyperpolarizing shift (Bregestovski et al., 1979; Lewis, 1979; Adams et al., 1980; Villarroel and Sakmann, 1996). In particular, with 100 mM CaCl₂ but no monovalent ions in the external solution, E_ACh is −22.3 and −10 mV for fetal and adult mouse AChR, respectively (Villarroel and Sakmann, 1996). The large difference of E_ACh in the presence or absence of extracellular Na⁺ ions indicates that they do contribute measurably to the inward current, even when [Ca²⁺]_o is 100 mM. Should a high [Ca²⁺]_o prevent the flux of Na⁺ ions, the latter would not influence E_ACh any more than other impermeant ions.

Furthermore, to our knowledge, it has never been demonstrated experimentally (for instance, by means of Na⁺-sensitive fluorescent dyes) that Na⁺ ions do not flow through AChR channels if [Ca²⁺]_o is high. Ca²⁺ ions pass through AChR channels, although the unitary channel conductance is reduced in a Ca²⁺-dependent manner (Bregestovski et al., 1979; Lewis, 1979; Decker and Dani, 1990; Grassi and Degasperi, 2000; Elenes et al., 2009) until it reaches a plateau value at [Ca²⁺]_o of ∼40 mM. At high [Ca²⁺]_o, unitary conductance of AChR channels is independent of the presence of monovalent cations, which has been interpreted as suggesting that at high [Ca²⁺]_o, Ca²⁺ ions are the main current carriers (Decker and Dani, 1990).

Below, we show how including the reversal potential for i_Ca²⁺ and i_Na⁺_−Mg²⁺ (E_Ca²⁺ and E_Na⁺_−Mg²⁺, respectively) in Eqs. 3 and 4, and dropping the unsupported assumption that with [Ca²⁺]_o = 100 mM Na⁺ ions do not contribute to inward current, leads to conclusions that are very different from those presented by Elenes et al. (2009), yet compatible with their experimental data.

Eqs. 3 and 4 must be amended as follows:

Under the experimental conditions used by Elenes et al. (2009) ([Na⁺]_o = 150 mM and [Ca²⁺]_o = 100 mM), E_Na⁺_−Mg²⁺ is indeed close to 0 mV, but i_Ca²⁺, being a pure Ca²⁺ current, changes sign at the Ca²⁺ equilibrium potential. E_Ca²⁺ must not be confused with the bi-ionic reversal potential of a current resulting from the steady-state counter-diffusion of extracellular Ca²⁺ and intracellular K⁺ ions (such as that measured by the experiment shown by Elenes et al., 2009 in their Fig. 15), as the current carried by K⁺ ions is included in the term i_Na⁺_−Mg²⁺ in the present model. The slope conductance of i_Ca²⁺ and i_Na⁺_−Mg²⁺ can be calculated from Eqs. 3a and 4a (Fig. 1 A; see figure legend for details). Using numerical values given by Elenes et al. (2009), we find that i_total with a slope conductance of 30.6 pS corresponds to a pure i_Ca²⁺ with a slope conductance of 7 pS. When the I-V curve is shifted to the left (as done by Elenes et al., 2009), the error introduced is much larger for i_total than for i_Ca²⁺ because of their different conductances, thereby causing a marked overestimation of the ratio i_Ca²⁺/i_total.

At variance with the original equations, Eqs. 3a and 4a also describe i_Ca²⁺ and i_Na⁺_−Mg²⁺ as compatible with the experimental observation that, at high [Ca²⁺]_o, single-channel conductance of i_total varies little regardless of whether monovalent cations are added to external solutions (Decker and Dani, 1990) (Fig. 1 B).

In conclusion, neglecting equilibrium potentials in Eqs. 3 and 4 causes overestimation of the fractional Ca²⁺ current. We therefore invite the authors to repeat their fits using Eqs. 3a and 4a, as given here. This might lead to estimates for the fractional Ca²⁺ current in closer agreement with other reports. It might also disclose why the estimates proposed by Elenes et al. (2009) are better for receptors thought to have high fractional Ca²⁺ current than for those with low ones.