Fig 1.
A. (modified from Ref. [5]) Eigenmannia, showing the electric organ (EO) location and the anterior(a)/posterior(p) disposition of its constituent electrocytes, each innervated posteriorly by a (central pacemaker driven) cholinergic electromotor neuron synapse (i.e., electroplaque). Due to the rapidly alternating head-positive/head-negative polarization from the continual EO discharge (EOD), the fish in its aqueous medium approximates an oscillating dipole [6]. B. Plot from Ref. [6], summarizing the unexpected observation (calculated from whole fish O2 consumption data linked to Eigenmannia EOD frequencies) that APs cost more as AP frequency increases. C. Left, an MKZ-simulated AP train (gNamax = 700 μS) driven by pulsatile Iclamp as labeled, and right, one AP with the time scale expanded to make evident the apparent threshold region (~-17 mV) (inset: Vpeak as a function of Istim).
Table 1.
Kinetic constants for the MKZ and Epm models.
MKZ parameters are from Ref [6]. Listed gNamax values are for the 200 Hz case. For Epm, the gNamax values used for other frequencies are discussed in the Section Frequency-dependent cost per AP.
Fig 2.
Graphical comparison of the V-gated conductances of MKZ and Epm.
The plots are generated using parameters in Table 1. Left: equilibrium (i.e., t → ∞) values of the Hodgkin-Huxley parameters. As labeled, gNa and gK are proportional to m3 and n4 respectively, and, h is proportional to the availability (or inactivation status) of the Na conductance. Right: time constants for these processes (see text for more explanation). For tauh (V) curves, the voltage regions dominated by the recovery and the inactivation processes are indicated.
Fig 3.
Sustained step and ramp Iclamp stimulation of Epm.
Standard gNamax (700 μS) is used unless otherwise specified, Istim as labeled, other parameters as in Table 1. See text for further explanation.
Fig 4.
A. The standard pulsatile stimulus shape synclamp (t) used in Epm has 3 segments: a linear rise for 0.05 ms, a plateau for 0.200 ms and an exponential decay to zero (specifically the segments are: synclamp1.0 (t) = t/0.05 (t<0.05); 1 (0.05<t<0.25); and exp[-(t-0.25)/0.1] (t>0.25), t in ms)). Bi. For comparison, a depiction of the fastest cholinergic post-synaptic event we found in the literature for electroplaques, shown at the same time scale as the standard pulsatile stimulus in A. The miniature electroplaque current (mepc) depicted exemplifies a fast subclass of of mepc recorded in relatively intact Torpedo electroplaques [24]. Bii depicts the average time course of mepcs measured from lizard intercostal muscle [25]. The pulsatile stimulus used in Epm is speedier in all respects than these mepcs. Whereas a mepc results from a quantal release event that would be insufficient to stimulate an entire electroplaque, the synclamp stimuli of Epm must provide sufficient “ACh-activated” Ication at the Eigenmannia electroplaque to rapidly depolarize to threshold 50 nF of post-synaptic membrane. Thus, 1:1 triggering (1 electromotor neuron AP: 1 electrocyte AP) is assumed, but how it would be achieved at up to 600 Hz in vivo is not understood.
Fig 5.
Epm-simulated APs stimulated by pulsatile synaptic current.
A. One AP from a 200 Hz AP train (stimulus: synclamp1.0200Hz) with gNamax = 700 μS. B. For gNamax values as labeled, APs from trains with stimulus synclamp1.0200Hz or synclamp1.0600Hz. First column, gNamax = 700 μS; second column, for synclamp1.0600Hz, gNamax is raised to 1126 μS to bring Vpeak to 13 mV. See text for further explanation.
Fig 6.
Cost of Epm APs at different AP frequencies based on Na+-entry.
A. Illustrated are APs firing at 200 Hz and 600 Hz and then failing at 700 Hz which, however, exceeds the biological range of Eigenmannia (700 Hz stimulation elicits APs with irregular amplitudes and timing). For all frequencies the pulsatile stimulus amplitude was synclamp1.0 and gNamax was adjusted to yield Vpeak = 13 mV. To calculate Na+-entry (= the time integral of the three sources of INa seen in Fig 5A) trains of at least 20 APs were used. B. Na+ entry plotted to assess the cost/AP at different frequencies, as labeled and as explained in the text. Starred region beyond 600 Hz signifies that although this is beyond the species range, Epm is still able to produce regular APs at 650 Hz (though not, as seen in B, at 700 Hz). Calculations were done by requiring that Vpeak = 12.86 mV for each frequency but this is referred to throughout the paper as 13 mV. Larger fonts for gNamax values at 200 Hz and 600 Hz emphasize that these represent the extremes of the biological range for Eigenmannia EODs.
Fig 7.
Effect of pulsatile stimulus amplitude.
A. Single APs elicited by the standard pulsatile stimulus (Vm(t) units are arbitrary, with the synclamp1200Hz AP as reference) calculated for synclamp1200Hz or synclamp5200Hz, and V-gated currents (INaT, where T signifies the transient component; persistent INa not shown), IK (delayed rectifier) plus the INa component of current through the AChR channels; gNamax = 700 μS, stimuli at 200 Hz. B. For such APs elicited by pulsatile synaptic stimulation at increasing intensities (from synclamp0.5200Hz to synclamp5.0200Hz), Na+-entry via the stimulus (AChR) channels increases dramatically (red) but total Na+-entry (green) is almost unaffected. The Vpeak is relatively insensitive to stimulus intensity beyond synclamp = 1 (an “all-or-none” AP feature). C. Further testing of pulsatile synclamp intensity, for APs at 200 Hz and 600 Hz with the gNamax values indicated. The dashed black line in C is equivalent to the dashed black line in B (where values are normalized).
Fig 8.
For APs at frequencies ± 10 Hz near 400 Hz, with gNamax at 783 μS, Vpeak differs minimally. This suggests that typical ± 10 Hz JARs in Eigenmannia might require no increased expression of Nav channels.
Fig 9.
Background synaptic stimulation.
Ai. Epm APs for three steady-state (i.e. 0 Hz) levels of AChR activation, synclamp0.030Hz, synclamp0.050Hz, and synclamp0.40Hz fire at 137 Hz, 202 Hz, and 541 Hz respectively (gNamax = 700 μS throughout). Aii. Epm AP frequency as a function of stimulus intensity (conditions as in Ai); squares color-coded for the plots in Ai. Aiii. Red trace at 541 Hz firing (conditions as in Ai) with a second overlaid trace showing APs when gNamax is increased to 1155 μS (this produces APs of Vpeak = 9 mV, i.e., the same as for synclamp0.030Hz with gNamax = 700 μS). Bi. APs elicited by a 200 Hz pulsatile stimulus in the presence of a subthreshold background stimulus (synclamp0.007360Hz). For synclamp0.1200Hz (orange) the output AP frequency is 50 Hz whereas for synclamp0.4200Hz (blue) the target frequency of 200 Hz is attained. Bii. This background stimulus (synclamp0.007360Hz) plus 200 Hz pulsatile stimuli at the amplitudes indicated elicits APs at different frequencies as shown here in a “devil’s staircase” plot.
Table 2.
Na+ entry for various synaptic stimulus regimes∆.