Coregulation of Voltage-Dependent Kinetics of Na⁺ and K⁺ Currents in Electric Organ

Voltage-dependent activation and deactivation kinetics of K⁺ current covary

The delayed rectifying K⁺ current of the Sternopygus electrocyte is similar to that of the eel electrocyte in its general properties: that is, a noninactivating outward current that activates at approximately −40 mV (Shenkel and Sigworth, 1991). This current does not include any Ca²⁺-activated K⁺ currents because it is unaffected by removal of extracellular Ca²⁺ or addition of extracellular Co⁺ or Cd⁺ (Ferrari and Zakon, 1993).

Delayed rectifier K⁺ current was recorded from electrocytes of fish across the range of EOD frequencies of the species. Typical currents from electrocytes of fish with EOD frequencies of 137, 89, and 43 Hz are illustrated in Figure2. Outward currents from the fish with the highest EOD frequency activate more rapidly than those from the fish with a midrange EOD frequency, and these, in turn, activate more rapidly than those from the low EOD frequency fish (Fig. 2).

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Fig. 2.

Delayed rectifying K⁺currents from electrocytes of fish over a range of EOD frequencies. Each fish's EOD frequency is indicated to the right of the currents. The activation time constants for the currents at 25 mV above activation threshold (traces indicated byasterisks) are 4.65 msec (137 Hz), 5.81 (89 Hz), and 8.40 (48 Hz). The illustrated currents are from voltage steps in 10 mV increments with the first trace at 5 mV below activation threshold.

The rising phase, or activation, of a delayed rectifying K⁺ current at each voltage step can be described quantitatively by fitting the current with a power function, namely I_k(t) =I_k,max (1 −e^−t/τ)ⁿ, where I_k(t) is the development of the current with time,I_k,max is the maximum current attained, t is time, and τ is the time constant of activation (Hodgkin and Huxley, 1952). As sometimes occurs with the K⁺ current, the value of nthat gives the best fit varies with membrane potential or cell type (Campbell, 1992; Klemic et al., 1998). The best overall fit with our data were obtained with n = 2, which was the value we used in this study. Although the value of the exponent (2, 3, or 4) changed the value of the time constants, they were all shifted in the same direction, leaving the general conclusions of this study unchanged.

As is true of the delayed rectifying K⁺current in other cells, the rate of activation varied with membrane potential, being faster at more positive voltages (Fig.3A). We plotted the time constant of activation at 25 mV above threshold (threshold is defined as the voltage step with the first indication of an outward current using voltage steps of 5 mV intervals) for the complete sample of cells to determine whether the rate constant of activation varied systematically with EOD frequency (Fig. 3B). We used this value as our standard for comparison because this point is in the linear portion of the current–voltage curve. Rates of activation varied from 4.19 to 10.93 msec and were highly correlated with EOD frequency (−0.83; p < 0.0001; n = 28 cells, each from a different fish).

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Fig. 3.

Activation time constant as a function of voltage and EOD frequency. A, Activation time constant varies with voltage within a cell, becoming faster at more depolarized voltages. Arrows denotes the value taken at 25 mV above activation threshold that was used for comparison across fish.B, Time constant of activation (at 25 mV above activation threshold) varies with EOD frequency.

We examined tail currents to observe whether rates of deactivation also vary with EOD frequency and whether the rates of activation and deactivation of the current from a single cell were correlated. Electrocytes were clamped to 0 mV for 45 msec to activate the delayed rectifying K⁺ current fully and then clamped for 45 msec to voltages ranging from −105 to −30 mV in 5 mV steps. Figure 4Aillustrates tail currents from electrocytes of two fish with EOD frequencies of 42 and 154 Hz. Tail currents were well fit with a single exponential time constant whose value was voltage-dependent (Fig.4B).

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Fig. 4.

Potassium current deactivation kinetics vary with EOD frequency. A, Tail currents were recorded at voltages from −105 to −30 mV in 5 mV steps (see insetof voltage protocol). Traces from −30 to −45 mV are shown. Time constant of decay of the current at −40 mV is 8.47 msec for the fish with an EOD frequency of 42 Hz and 5.66 msec for the fish with an EOD frequency of 154 Hz. B, Deactivation time constant changes with membrane potential. Values at −40 mV are indicated by asterisks.

We used the deactivation time constant at −40 mV as our standard of comparison across cells because this value is positive enough to avoid contamination from any unblocked inward rectifier current. Deactivation time constants (at −40 mV) for the complete sample of cells ranged from 4.80 to 8.77 msec and were highly correlated with EOD frequency (r = −0.90; p < 0.001;n = 15) and the activation time constants of each current (r = 0.84; p < 0.001;n = 15) (Fig. 5).

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Fig. 5.

Potassium current deactivation is correlated with EOD frequency (A) and the activation time constant of the current from the same cell (B).

No other attributes of the K⁺ current were systematically correlated with EOD frequency or K⁺ current activation time constant, including activation voltage (mean, −38.4 mV; SD, 5.96 mV;n = 27) or current magnitude (taken at 25 mV above threshold; mean, 1524 nA; SD, 492 nA).

Voltage-dependent properties of K⁺ and Na⁺ currents recorded in the same cell are correlated

A previous study found that the inactivation kinetics of the electrocyte Na⁺ current vary with EOD frequency (Ferrari et al., 1995). To examine how well correlated the voltage-dependent kinetics of K⁺ and Na⁺ currents are on a cell-by-cell basis, both currents were measured in a subset of cells. This was accomplished by measuring the total current under voltage clamp, measuring K⁺ currents after eliminating the Na⁺ current with 1 μm TTX, and then retrieving the Na⁺ current by digital subtraction of these two traces at each voltage step. The Na⁺ currents measured in this way are identical to those recorded by pharmacological isolation after complete blockade the K⁺ current with tetraethylammonium (Ferrari et al., 1995).

Figure 6 illustrates K⁺ and Na⁺currents from electrocytes of two fish with EOD frequencies at 131 and 55 Hz. The activation of the K⁺ current and the inactivation of the Na⁺ current are more rapid in the electrocyte from the fish with the higher EOD frequency. Currents were sampled from electrocytes of fish across the range of EOD frequencies and their voltage-dependent kinetics were compared. As reported previously, inactivation of the Na⁺ current was faster in individuals with higher EOD frequencies (Ferrari et al., 1995). The inactivation kinetics of the peak Na⁺ current were each also correlated with the activation kinetics of the K⁺ current (r = 0.88;p < 0.0001; n = 17) (Fig.7).

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Fig. 6.

The voltage-dependent kinetics of the K⁺ (left) and Na⁺(right) currents in an electrocyte from a fish with a high EOD frequency (131 Hz) are more rapid than those of an electrocyte from a fish with a low EOD frequency (55 Hz). Traces of K⁺ currents as in Figure 2; Na⁺currents illustrate the peak Na⁺ current for each cell and currents at two other values of membrane potential arbitrarily chosen for each cell. By visual inspection, the activation of the Na⁺ current is also more rapid in fish with a high EOD frequency. However, we did not fit time constants to its activation phase because we could not be certain there was no influence of the capacitative transient caused by charging the membrane on the early part of the current record.

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Fig. 7.

Activation time constant of the K⁺ current versus inactivation time constant of the Na⁺ current for 17 cells in which both currents were measured.

We did not measure the rate of activation of the Na⁺ current because its onset was sometimes obscured by the capacitative artifact of the voltage clamp. However, visual inspection suggests that the activation phase is slower in electrocytes from fish with low EOD frequencies.

Additionally, the magnitudes of the Na⁺(at peak current) and K⁺ currents (at 25 mV above activation threshold) were correlated (r = 0.68; p < 0.002; n = 17) as in a previous study (Ferrari and Zakon, 1993). This likely reflects variation in electrocyte size (Mills et al., 1992) with larger electrocytes possessing more active membrane and, therefore, larger currents. This point is suggested by the correlation between the length of membrane labeled with a sodium channel antibody and the length of the electrocyte (r = 0.52; p < 0.05) (H. Zakon, S. R. Levinson, unpublished observations).

Variation in the voltage-dependent kinetics of delayed rectifying K⁺ currents

The voltage-dependent kinetics of the K⁺ current differ in different cell types, may change in a single cell type during development or under different hormonal conditions, or show regional variations in its expression (Barish, 1986; Harris et al., 1988; Campbell, 1992; Erulker et al., 1994; Goodman and Art 1996; Kros et al., 1998; Nerbonne, 1998). Our observation of systematic graded variations in the voltage-dependent kinetics of a delayed rectifying K⁺current in electrocytes demonstrates the precision with which this current may be controlled. The only observation of comparable precision in the control of the kinetics of this current is in hair cells in which the voltage-dependent kinetics of the current vary with position along the cochlea (Goodman and Art, 1996).

Activation and deactivation kinetics of electrocyte K⁺ current covary, and this is observed in other cell types with spatial or developmental variation in K⁺ current kinetics (Barish, 1986; Goodman and Art, 1996). On one hand, covariation in rates of activation and deactivation of the K⁺ current is supported by kinetic models and mutational analysis of channel function (Monks et al., 1999). On the other hand, these properties need not always covary; K⁺ channels with rapid activation kinetics may have either rapid (Kv3.1) or slow (Kv1.5) rates of deactivation (Grissmer et al., 1994), and rates of activation and deactivation may be uncoupled in a variety of experimental circumstances (Augustine and Bezanilla, 1990; Patton et al., 1997;Jerng et al., 1999). Thus, some active regulation may be required for these parameters to covary so precisely.

The covariation of these two kinetic parameters likely has important functional consequences; the activation phase of the K⁺ current occurs during the falling phase of the EO pulse, whereas deactivation phase occurs during the period between EO pulses. Thus, a fish with a low-frequency EOD must have a K⁺ current that develops slowly to prolong the AP and slow deactivation kinetics to ensure that the K⁺ current contributes to electrocyte hyperpolarization between EOD pulses. A fish with a higher frequency EOD must have a K⁺ current that activates faster to repolarize the AP faster and a deactivation phase that is more rapid so that the K⁺ current is terminated before the next EOD pulse. The voltage-dependent kinetics of the K⁺ current appear to be graded to accommodate the individual variation in EOD frequency and pulse duration in this species.

Covariation in voltage-dependent kinetics of the Na⁺ and K⁺ currents

The most novel finding of this study is that the kinetics of a K⁺ and a Na⁺current are tightly coregulated. There are numerous examples of covariation in the magnitudes of two currents (O'Dowd et al., 1988;Erulker et al., 1994; Desai et al., 1999), and a few cases reporting covariation in the magnitude of one current and the kinetics and/or magnitude of another, such as the calcium current and the calcium-activated K⁺ current in cochlea hair cells (Wu and Fettiplace, 1996). However, this is the first report of covariation of the voltage-dependent kinetics of two ionic currents.

The cellular mechanisms by which this occurs are unknown. Variations in the kinetics of a single current could arise by molecular control, such as differential expression of different channel genes, or splice products or edited mRNAs of a single gene, each of which produces channels with different kinetic properties (Schaller et al., 1992;Gurantz et al., 1996; Patton et al., 1997; Liu and Kaczmarek, 1998;Martina et al., 1998; Nerbonne, 1998; Hanrahan et al., 1999). There is evidence for all of these mechanisms controlling voltage-dependent Na⁺ and K⁺channel variation in the literature, although control by alternative splicing is rare in vertebrates, and RNA editing is only known for invertebrate Na⁺ and K⁺ channel genes.

One might imagine that coregulation of two currents occurs through complementary processes in the expression of both Na⁺ and K⁺channel genes. This scenario is potentially complicated by the fact that Na⁺ channels are a single protein, whereas K⁺ channels are tetramers of smaller subunits (Wei et al., 1990). Additionally, some K⁺ channel subunits (i.e., Kv2.3), although incapable of forming functional channels themselves, influence the activation and deactivation kinetics of the K⁺ channels with which they coassemble (Castellano et al., 1997).

We know that at least two muscle Na⁺channel genes (SKM1 and SKM2) (Lopreato et al., 1999) and a number of K⁺ channels from different families (Kv1, Kv2, Kv3, and Kv4) (P. Few, unpublished observations) are expressed in the electrocytes ofSternopygus. However, we do not yet know their expression patterns in the electrocytes of fish over the range of EOD frequencies.

Regulation of kinetics could also occur by association of the channel with β subunits (Isom et al., 1992; Rettig et al., 1994; Ramanathan et al., 1999). However, the known β subunits that associate with Na⁺ and K⁺channels are of molecularly distinct gene families. Regulation of two different currents via this mechanism, again, requires coordinated expression of different β subunit genes and comparable actions of each β subunit on its particular channel type.

Numerous studies show that phosphorylation by a variety of kinases affects activation or inactivation rates of either Na⁺ or K⁺currents (Augustine and Bezanilla, 1990; Desarmenien and Spitzer, 1991;Numann et al., 1991; Li et al., 1993; Jonas and Kaczmarek, 1996; Roeper et al., 1997). Coordinate control by this mechanism would have the virtue that a single kinase could regulate both channel types. However, because most studies typically focus on the effects of phosphorylation on a single current, it is not known whether kinases can coordinately regulate the kinetics of two currents with the precision that we observe here. To date, only the actions of protein kinase A on the Na⁺ current in theSternopygus electric organ have been studied; activation of protein kinase A increases the magnitude of the electrocyte Na⁺ current but does not affect its voltage-dependent kinetics (McAnelly and Zakon, 1996).

Other possibilities include regulation by variations in the lipid microenvironment of the surrounding membrane (Burnashev et al., 1991;Kang and Leaf, 1996) or the association with the cytoskeleton (Undrovinas et al., 1995), both of which are known to influence the voltage-dependent parameters of the cardiac Na⁺ current. Each of these could conceivably also influence the gating of K⁺ channels and thus account for the coordination between them.

General functional consequences

The coregulation of Na⁺ and K⁺ currents and their role in shaping AP duration is easily observed in the electrocyte in which AP wave shape must be precisely regulated over a fourfold range of duration (3–12 msec) in different individuals and in which the result of these biophysical control mechanisms is evident in recordings from behaving animals. Such coregulation of ionic channels would be much more difficult to observe in the CNS. However, even subtle manifestations of this phenomenon in CNS neurons could have profound implications for a variety of processes. Coregulation of Na⁺and K⁺ channels underlying the action potential in synaptic terminals could strongly influence Ca²⁺ influx and neurotransmitter release (Jackson et al., 1991; Quattrocki et al., 1994; Whim and Kaczmarek, 1998). Similarly, the coregulation of these channels in dendrites could affect the gain and frequency response of the dendritic membrane to subthreshold synaptic events, as well as the characteristics of back-propagated action potentials. Thus, we propose coregulation of channel kinetics as a more general mechanism for regulating action potentials and membrane excitability.