In the present study, we tested the hypothesis that changes in [K+]out induce alterations in fPn. This was achieved by using an in vitro preparation of the Pn and by assessing through extracellular recordings possible effects of changes in [K+]out in the perfusate on this frequency, while maintaining the osmolarity of the medium.

Effects of changes in osmolarity and [Na+]out on Pn oscillation frequency

The initial experiments of the present study showed that an acute increase in osmolarity of the perfusate of the Pn preparation prompted a rapid decrease in oscillation frequency. This result is congruent with the well-established idea that the excitability of the brain is highly sensitive to acute alterations of the extracellular osmolarity (for reviews see Andrew 1991; Schwartzkroin et al. 1998). For example, in rat hippocampal slices reduction in extracellular osmolarity leads to hyperexcitability and enhanced epileptiform bursting, while this effect can be abolished by reversal of the hyposmolar state through mannitol (Andrew et al. 1989; Roper et al. 1992).

Our initial observations underscored the need to compensate for changes in osmolarity whenever [K+]out is altered. However, such compensation cannot be adequately achieved by reduction of the concentration of NaCl in the perfusate, as was done by Dye (1991) because our initial experiments also demonstrated that changes in [Na+]out have a pronounced impact on the oscillation frequency of the Pn. This effect was also seen when changes in NaCl concentration were compensated for by equivalent changes in osmolarity through addition or reduction of choline chloride. While these findings are in line with the notion that sodium currents are involved in the regulation of the pacemaker rhythm (Smith and Zakon 2000), they stress the need for compensation of osmolarity changes without alteration of [Na+]out. Thus, in the subsequent experiments during which we changed [K+]out, this was done by proper adjustment of the choline chloride concentration in the ACSF.

Effects of changes in [K+]out on Pn oscillation frequency

In the current study, we demonstrated that a 10 mM reduction in [K+]out results in an approximately 25 Hz reduction in fEOD over a [K+]out range of 0 to 20 mM (Fig. 4), indicating that the K+-buffering hypothesis can explain at least partially the sexual dimorphic fEOD in A. leptorhynchus. Yet, to achieve the marked average difference in fEOD of approximately 140 Hz between males and females through modulation of buffering, it would be necessary that [K+]out assume values with differences between the sexes that far exceed the normal variability within other vertebrate brain systems, which ranges from approximately 3.5–5 mM. The [K+]out-fPn relation is likely to be mediated by potassium ion channels in the pacemaking neurons and/or the associated astrocytic glia. Involvement of potassium ion channels in controlling fPn in A. leptorhynchus was demonstrated with potassium channel blockers (Smith and Zakon 2000). Identification of the specific types of potassium channels will be facilitated by the results of RNA-sequencing in the central nervous system of A. leptorhynchus, which revealed a total of 74 K+ channel genes (Salisbury et al. 2015).

We hypothesize that in our in vitro experiments the observed effects of [K+]out on fPn were possible because (i) the perfusate reached major portions of the extracellular space and the capillaries of the submerged tissue preparation rapidly; (ii) the volume of the perfusate was so large, and its flow rate was so high, that buffering by astrocytes had a rather minor impact on the regulation of [K+]out. This notion is supported by two observations. First, fPn, which was measured with the baseline perfusate containing 3.5 mM K+, was 93 ± 25 Hz (mean ± standard deviation; n = 8 fish) lower than fEOD measured in intact fish. Second, the [K+]out-fPn function (Fig. 4) showed a linear relation over a wide range of [K+]out, including 0 mM.

Sex-dependent differences in Pn frequency shifts induced by changes in extracellular potassium concentration

Analysis of the shifts in fPn induced by changes in [K+]out, relative to the arbitrarily chosen standard concentration of 3.5 mM, indicated some notable sex-dependent differences in the degree of these shifts at concentrations ≤ 10 mM. Concentration changes from 3.5 mM to 0 mM, 6 mM, and 10 mM resulted in fPn changes that were, on average, larger in males than in females. This finding is consistent with the previous observations that the association of astrocytes with the pacemaker and relay cells within the Pn is markedly higher in females than in males, and that this difference, presumably, results in better buffering of K+ ions in the extracellular space in females (Zupanc et al. 2014).

Although the relative differences between males and females in the fPn shifts induced by alteration of [K+]out are pronounced, ranging from 32 to 104%, they translate to absolute values of less than 1 Hz in each of the 3 experiments. As mentioned in the previous section of the Discussion, in our experiments the buffering by the astrocytes of extracellular K+ ions is, likely, heavily obscured by the large volume of the perfusate and its high flow rate. We, therefore, interpret the small absolute differences in fPn shifts between males and females as a consequence of these experimental conditions. Nevertheless, the existence of sex-dependent differences under acute experimental conditions, and the sizeable degree of these differences in relative terms, are compatible with the notion that in situ similar differences in the buffering capacity of astrocytes translate into differences in [K+]out, thereby ultimately causing (at least partially) the sexual dimorphisms in fPn, and fEOD.

Perspectives

The main result of the present study—fPn correlates positively with [K+]out—is consistent with the hypothesis that differences between males and females in astrocyte-mediated buffering cause differences in [K+]out, which lead to shifts in EK, thereby ultimately establishing the sexual dimorphism in fEOD. For such a mechanism to generate the required male–female-related differential distribution of fEOD within the species-specific range of 650–1,000 Hz, a substantial variability in [K+]out among individual fish is required, from a few millimolar in females to several tens of millimolar in males.

Variations in [K+]out, correlating with different physiological states of an organism, have recently been found in murine models of Alzheimer’s disease, amyotrophic lateral sclerosis, and Huntington’s disease. In each of these disease models, [K+]out was elevated, compared to healthy wild-type mice (Ding et al. 2024). Yet, these differences in [K+]out were < 1 mM. Thus, to further test the hypothesis that [K+]out mediates the sexual dimorphism in fPn (and thereby in fEOD), it will be imperative to determine [K+]out locally in the Pn and to check whether this concentration differs between males and females.

Investigations in a few (non-electric) fish have shown that the range over which [K+]out varies across different species is rather narrow (1.7–3.6 mM; Nilsson et al. 1993; Rice and Nicholson 1988). These values are reminiscent of the resting K+ concentration in the extracellular fluid of the mammalian brain, which is approximately 3 mM (Lux and Neher 1973; Prince et al. 1973; Moody et al. 1974). Nevertheless, given the continuously high-frequency (~ 1 kHz) oscillations of the Pn of A. leptorhynchus throughout the fish’s life, it appears well possible that [K+]out in this nucleus is significantly higher than the concentrations known from the vast majority of other brain systems that fire only intermittently and/or at much lower frequencies. Experiments in leech have indicated that the generation of a single action potential results in an increase in [K+]out of approximately 0.8 mM (Baylor and Nicholls 1969). Although this value is not directly transferable to explain the dynamics of [K+]out fluctuations in the pacemaker nucleus, due to the many morphological and physiological differences between the two systems, it nevertheless provides a first indication of the large amount of K+ that is likely to exit from the firing pacemaking neurons into the extracellular space. This amount of K+ in the extracellular space plays a critical role by providing the substrate for alteration through modulation of the buffering capacity of astrocytes. Such a mechanism would be well suited for regulation of the extracellular potassium dynamics, and thereby for the establishment of the sexual dimorphism in the distribution of the fEOD of individual fish. However, further experiments, including direct measurement of [K+]out in the Pn of males and females, and experimental modulation of the K+ buffering capacity of the astrocytic syncytium in this nucleus, will be necessary for a definite conclusion on this point.