Maternal Diabetes Increases Small Conductance Ca²⁺-Activated K⁺ (SK) Currents That Alter Action Potential Properties and Excitability of Cardiac Motoneurons in the Nucleus Ambiguus

Abstract

Parasympathetic cardiac motoneurons (PCMNs) in the nucleus ambiguus (NA) play a key role in regulating cardiac functions. In this study, we examined the effects of maternal diabetes on excitability, action potential (AP) properties, and small conductance Ca²⁺-activated K⁺ (SK) currents of PCMNs. Neonatal mice from diabetic (OVE26 female, NMDM) and normal (FVB female, control) mothers that had been mated with nondiabetic fathers (FVB male) were used. Tracer XRITC was injected into the pericardial sac at P7-9 to retrogradely label PCMNs. Two days later, XRITC-labeled PCMNs were identified in brain stem slices. The responses of spike frequency, AP repolarization (half-width) and afterhyperpolarization (AHP) of PCMNs to current injections were studied using whole cell current clamp. Outward and afterhyperpolarization currents (I_AHP) in response to voltage steps were measured using whole cell voltage clamp. In examining the effects of maternal diabetes on excitability and AP properties, we found that in NMDM spike frequency decreased, the half-width and AHP peak amplitude increased, and the peak amplitude of outward transient currents and I_AHP increased compared with those measured in control. In examining the effects of maternal diabetes on SK channels, we found that after blockage of SK channels with a specific SK channel blocker apamin, maternal diabetes significantly increased apamin-sensitive outward transient currents and I_AHP, and suppressed AHP amplitude in NMDM more than those in control. Further, apamin application increased the firing rate to current injections and completely abolished the difference of the firing rate between control and NMDM. We suggest that the augmented SK-mediated currents may contribute to the increased AHP amplitude and the attenuated excitability of PCMNs in NMDM.

INTRODUCTION

Human infants from diabetic mothers have an increased risk of developing malformations of the CNS (Ramos-Arroyo et al. 1992). Maternal diabetes decreases proliferation and increases apoptosis of neuroepithelial cells in the developing spinal cords of embryos from streptozotocin (STZ)-induced diabetic (type 1) mouse mothers (Gao and Gao 2007). Fetal hyperglycemia exposure may promote neural malformation via oxidative stress (Hockett et al. 2004). Normalization of maternal metabolism during critical perinatal development prevents neural malformation in offspring from diabetic rat mothers (Harder et al. 2003). In the autonomic nervous system, maternal diabetes impairs sympathetic and parasympathetic development in offspring (Fiorentini et al. 2005; Young and Morrison 1998). Recently Wichi et al. (2005) found that maternal diabetes impairs baroreflex control of heart rate (HR) in offspring of STZ-induced diabetic mothers. Because attenuation of baroreflex sensitivity is associated with many cardiovascular diseases including sudden death (La Rovere et al. 2008), it is critically important to study the effects of maternal diabetes on the neural components within the baroreflex circuitry.

Parasympathetic cardiac motoneurons (PCMNs) in the brain stem regulate cardiac output (Loewy and Spyer 1990; Neff et al. 2003). Previously we demonstrated that the PCMNs in the nucleus ambiguus (NA) project strongly to cardiac ganglia and that the NA has a key role in baroreflex control of HR (Cheng and Polwey 2000; Cheng et al. 2004a,b). In contrast, the dorsal motor nucleus of the vagus does not significantly contribute to baroreflex control of HR (Cheng et al. 2002). Thus far, no studies have been conducted to examine whether maternal diabetes alters excitability and action potential (AP) properties of NA PCMNs in the neonates from diabetic mothers.

In many neurons of the CNS, influx of calcium (Ca²⁺) during APs activates potassium (K⁺) channels. Activation of these channels generates currents that contribute to AP repolarization and the afterhyperpolarization (AHP) that follows them (Lancaster and Pennefather 1987; Sah and McLachlan 1992; Storm 1987). There are three major types of Ca²⁺-activated K⁺ channels: 1) large conductance (BK) voltage-sensitive channels that are potently blocked by the scorpion venom toxin charybdotoxin (ChTX) and selectively blocked by paxilline (Sanchez and McManus 1996; Strøbaek et al. 1996); 2) intermediate conductance (IK) channels that are potently blocked by ChTX and the antifungal imidazole compound clotrimazole (CTL) (Ishii et al. 1997; Logsdon et al. 1997); and 3) small conductance (SK) voltage-insensitive channels that are selectively blocked by the bee toxin apamin (Castle et al. 1989). BK currents mainly contribute to AP repolarization and the fast AHP (fAHP, a few milliseconds) (Faber and Sah 2007) that immediately follows it (Lancaster and Adams 1986; Lancaster and Nicoll 1987; Sah and McLachlan 1992; Storm 1987), whereas activation of SK currents largely generates medium AHP (mAHP; tens to several hundreds milliseconds), which significantly mediates firing frequency and patterns (Sah 1996). IK channels play a role in maintaining rapid Ca²⁺ entry in many cells types including myenteric neurons (Fanger et al. 2001; Tharp and Bowles 2009; Vogalis et al. 2002), but IK channels have not been reported in central neurons.

Our goal was to study the cellular mechanisms for the maternal diabetes-induced alteration of PCMN excitability. Because activation of BK and SK channels negatively regulate action potentials, we explored the contribution of BK and SK channels to the firing rate of PCMNs and the effect of maternal diabetes on BK and SK channels. According to our preliminary data, maternal diabetes attenuates excitability of PCMNs. However, blockade of BK channels with ChTX or paxilline decreased spike firing frequency in response to current injections in both control and NMDM (Lin et al. 2010a). In contrast, blockade of SK channels with apamin increased the firing rate in response to current injections and largely abolished the difference in the firing rate of PCMNs between control and NMDM (Lin et al. 2010b). Therefore we focused only on SK channels in the present study.

SK channels are expressed in many central neurons and their function in regulating neuronal excitability has been well established (Pedarzani and Stocker 2008; Stocker 2004). The activity of SK channels causes an increased interspike interval and a prolonged AHP during which the return to the resting membrane potential reflects the decay of intracellular Ca²⁺ levels. Blockade of SK channels with apamin increases excitability and enhancement of SK channels with enhancer 1-ethyl-2-benzimidazolinone (1-EBIO) decreases excitability (Stocker 2004). Depending on the neuronal subtype and its associated ion channels, the SK channels may contribute to regulation of burst firing (Cingolani et al. 2002; Hallworth et al. 2003; Womack and Khodakhah 2003), spike frequency adaptation (Bond et al. 1999; Vergara et al. 1998), spike patterning (Cloues and Sather 2003; Wolfart et al. 2001), and long-term potentiation (Faber et al. 2005; Ngo-Anh et al. 2005; Stackman et al. 2002) as well as the final termination of action potentials (Constanti and Sim 1987; Lancaster and Adams 1986; Schwindt et al. 1988; Storm 1990). Recently, we found that SK channels regulate the firing properties and excitability of parasympathetic cardiac motoneurons in the NA (Lin et al. 2010c).

In this study, we investigated the effects of maternal diabetes on the excitability and AP properties of PCMNs in neonatal mice. Because SK channels contribute to the intrinsic firing properties and regulation of excitability in other central neurons (Faber and Sah 2002; Sah and McLachlan 1992; Storm 1987) as well as the NA cardiac motoneurons (Lin et al. 2010c). We also examined the effect of maternal diabetes on the SK channels and the contribution of SK currents to maternal diabetes-induced changes of AP properties and excitability. We found that maternal diabetes attenuated excitability, altered AP properties, and increased SK currents that likely contribute to the increased AHP amplitude and attenuated excitability of PCMNs.

METHODS

Animal models

Neonatal mice from wild-type FVB (female) and OVE26 diabetic females (1.5–2 mo) that had been mated with wild-type FVB males (2–3 mo) were used. Female mice were separated into individual cages after they became pregnant. OVE26 mice develop type 1 diabetes due to specific overexpression of the calmodulin transgene in pancreatic beta cells (Epstein et al. 1989, 1992). OVE26 mice are a particularly valuable model of diabetes because 1) no toxic chemicals are needed to induce the disease, 2) all OVE26 mice have sustained hyperglycemia >500 mg/dl from 30 days of age and can survive well over a year without insulin administration, and 3) neonates show normal blood glucose levels before 15 days of age. Two main groups (groups 1 and 2) of neonatal mice were used. Group 1: neonates from FVB mothers that were fed by their own natural mothers (control/natural, or control for simplicity). Group 2: neonatal mice from OVE26 diabetic mothers (NMDM) were fed by their own natural diabetic mothers (NMDM/natural; or NMDM for simplicity). In this group, neonates from diabetic mothers may be either transgenic (half of the pups) or nontransgenic (half of the pups). In addition to groups 1 and 2, groups 3 and 4 were added as references to study whether the calmodulin transgene or quality of milk of diabetic mothers had any effects on body weight, blood glucose level, cell excitability, and outward currents in their offspring at the time (P9–11) of experiments. In groups 3 and 4, all neonates from OVE26 mothers were fed by normal FVB mothers (surrogate) immediately after birth. At the time of experiments (P9–11), transgenic and nontransgenic neonates could be easily distinguished by examining the size of their eyes under the light microscope [eye size is reduced by overexpression of the GR19 gene in OVE26 mice (Epstein et al. 1989)]. Transgenic and nontransgenic neonates were labeled as transgenic/surrogate (group 3) and nontransgenic/surrogate (group 4), respectively. The neonates in groups 3 and 4 were different neonates from those mice used in NMDM. Body weight, blood glucose level, and membrane properties of the neurons in these four groups are listed in Tables 1 and 2. Animals had free access to food and water, and no insulin therapy was given. All procedures were approved by the University of Central Florida Animal Care and Use Committee and followed the guidelines of National Institutes of Health. Efforts were made to reduce the number of animals used.

Table 1.

Basic values in control, NMDM, transgenic, and non-transgenic mice

Group	Body Weight, g	Blood glucose, mg/dl
Control	4.1 ± 0.2	141.0 ± 11.0
NMDM	3.7 ± 0.2	131.9 ± 10.2
Surrogate mother
transgenic mice	4.3 ± 0.3#	177.9 ± 21.6#
non-transgenic mice	4.8 ± 0.3*	197.3 ± 11.9*

Body weights and blood glucose levels of control, neonatal mice from diabetic mothers (NMDM), transgenic/surrogate and nontransgenic/surrogate n = 7/group. There was no difference between NMDM and control groups. Values are means ± SE.

^*P < 0.05: compared to the control group.

^#P < 0.05: compared to the NMDM group.

Table 2.

Passive membrane properties and action potentials of parasympathetic cardiac neurons of control and NMDM

Group	Vm, mV	Rin, MΩ	Cm, pF	AP Threshold, mV	AP Amplitude, mV
Control	−70.3 ± 1.1 (17)	246.6 ± 19.0 (15)	60.8 ± 2.8 (15)	−40.8 ± 1.2 (10)	85.5 ± 2.0 (15)
NMDM	−71.4 ± 1.6 (17)	222.1 ± 10.8 (15)	61.6 ± 1.4 (15)	−43.2 ± 1.6 (10)	85.5 ± 1.5 (15)

Passive membrane properties of parasympathetic cardiac motoneurons (PCMNs) of the nucleus ambiguus (NA) in control and NMDM. No significances were found between control and NMDM. Values in parenthesis indicate the number of cells recorded. V_m, resting membrane potential; R_in, input resistance; C_m, membrane capacitance.

Fluorescent labeling of NA PCMNs and medullary slice preparation

Neonatal mice (postnatal days P7–9) were anesthetized with 3% isoflurane (Abbott Laboratories, North Chicago, IL) and cooled to ∼4°C to decrease heart rate. After a right thoracotomy was performed, the retrograde fluorescent tracer X-rhodamine-5 (and 6)-isothiocyanate (XRITC, 2%, 4–8 μl, Molecular Probes, Eugene, OR) was injected into the pericardial sac at the base of the heart. After a 48 h recovery period, neonatal mice were deeply anesthetized with 4% isoflurane. The hindbrains were rapidly removed. The brain stem including PCMNs were sliced into coronal sections (250 μm) using a vibrating blade microslicer (DTK-1000, Kyoto, Japan) and maintained in an interface chamber superfused with artificial cerebral spinal fluid (ACSF) containing (mM): 126 NaCl, 2.5 KCl, 2 CaCl₂, 26 NaHCO₃, 1.25 NaH₂PO₄, 2 MgSO₄, and 10 dextrose, equilibrated with 95% O₂-5% CO₂, and pH adjusted to 7.4. Slices were transferred to a recording chamber maintained at room temperature (22–25°C).

Whole cell current clamp recording

Brain stem slices were viewed with infrared illumination, differential interference optics (Zeiss, Göttingen, Germany) and a near infrared-sensitive camera (AxioCom MRm, Göttingen, Germany). PCNMs in the NA were identified by the presence of the fluorescent tracer in superimposed fluorescent and infrared images (Fig. 1). Whole cell current clamp recordings were made from fluorescently labeled NA neurons. Within the recording chamber, slices were held in position using a nylon net stretched over a flattened U-shaped platinum wire and were continuously superfused at room temperature with oxygenated ACSF. When cadmium (Cd²⁺) was used to block voltage-gated Ca²⁺ channels, NaHPO₄ was removed from the ACSF to prevent cadmium from precipitating out of solution. Patch electrodes used for rupture patch recordings were fabricated from borosilicate glass (1.5 mm OD; World Precision Instruments, Sarasota, FL) with a Flaming Brown horizontal puller (P-97, Sutter Instruments, Novato, CA). Electrodes were heat-polished to a final tip resistance of 3–5 MΩ and filled with a pipette solution containing (in mM) 120 potassium-gluconate, 20 KCl, 2 MgCl₂, 10 HEPES, 0.1 EGTA, 2 ATP, and 0.25 GTP, with pH adjusted to 7.3 with KOH. Signals were recorded using a MultiClamp 700B patch-clamp amplifier (Axon Instruments, Foster City, CA). Responses were low-pass filtered at 3 kHz and digitized at 50 kHz with a 16 bit data acquisition system (Digidata 1322A, Axon Instruments).

Fig. 1.

Patch-clamp recording of tracer XRITC-labeled parasympathetic cardiac motoneurons (PCMNs) in the nucleus ambiguus (NA) in brain stem slices. A: fluorescent imaging of PCMNs. ↓, the recorded PCMN in B. B: DIC imaging of single PCMNs for recording. ↓, a recorded PCMN. C: the merged image of A and B. Scale bar: 40 μm.

APs were recorded by applying a 0.5 ms depolarizing current pulse of sufficient intensity (1–2 nA) to generate a single AP. To standardize AP recordings, neurons were depolarized to a holding potential of –60 mV by DC application through the recording electrode. AP was recorded within minutes after good recording conditions were established. Spike half-width was measured as the spike width at the half-maximal voltage using Clampfit 9.2 software (Axon Instruments). AHP amplitudes were measured at 10 and 50 ms. To investigate the firing frequency of neurons, 10 current injection steps (1,000 ms each) were applied from 0 to 200 pA in 20 pA increments. The mean spike frequency was calculated as the average of the inverse of all interspike intervals in response to 1 s constant current pulse. Input resistance (R_in) was determined from a linear regression in the linear range (generally ±10 mV from resting potential) of the voltage-current relationship established by plotting the steady-state voltage changes in response to a series of de- and hyperpolarizing current injections. To determine the membrane potential threshold, AP trains were evoked by a 1.5 s, 0.2 pA /ms ramp current from a holding potential of −60 mV in control ACSF and the threshold was measured at the beginning of the first AP.

Data acquisition was performed using the ClampEx program in the pClamp 9 software package. Before seals were made on cells, offset potentials were nulled. Recordings were accepted when resting membrane potentials measured immediately after membrane rupture were more negative to −60 mV, the AP amplitude was ≥70 mV from threshold to the peak.

Whole cell voltage clamp recording

PCMNs of the NA were again identified in brain stem slices by the presence of fluorescent tracer. Whole cell voltage clamp recordings were made from neurons in the NA. To record calcium (Ca²⁺)-activated potassium (K⁺) currents, cells were superfused with an oxygenated HEPES solution containing (in mM) 140 NaCl, 3 KCl, 2 CaCl₂, 1 MgCl₂, 10 HEPES, 0.0005 TTX, 1 4-aminopyridine (4-AP), 0.005 glybenclamide, and 10 glucose, pH adjusted to 7.4 with NaOH. TTX, 4-AP, and glybenclamide were included routinely in the K⁺ recording solution unless otherwise indicated. 4-AP (1 mM) was used to reduce voltage-gated K⁺ currents and unmask Ca²⁺ dependence of K⁺ currents. A low concentration of 4-AP was chosen to minimize possible nonspecific blockade on other K⁺ currents. Experiments were conducted at room temperature (22–25°C). Electrodes were heat-polished to a final tip resistance of 2–4 MΩ and filled with pipette solution containing (in mM) 110 K-gluconate, 10 KCl, 5 NaCl, 2 MgCl₂, 10 HEPES, 0.5 EGTA, 1 ATP, 0.2 GTP, and 0.1 leupeptin, with pH adjusted to 7.3 with KOH. Capacitance subtraction was used in all recordings. Membrane potential measurements were not corrected for the liquid junction potential (∼15 mV) and the series resistances were in the range of 10–20 MΩ.

Outward currents were evoked by a series of depolarizing steps from −70 to +40 mV in +10 mV increments, using 250 ms for transient current measurement or 800 ms for persistent current measurement. The peak for the transient outward current and steady-state current at 780 ms for the persistent current were measured. Current-voltage (I-V) relationships were then plotted^. The mean peak values of outward currents were plotted against membrane potential and was fitted by the Boltzmann equation (Spray et al. 1981). To study the afterhyperpolarization current (I_AHP), outward currents were evoked by a 100 ms pulse from a −70 mV holding potential to +10 mV followed by a 1.5 s pulse of −50 mV. The peak amplitude of I_AHP was measured as the peak current after the onset of the −50 mV pulse.

Drugs and chemicals

All the channel blockers used in the present study were purchased from Sigma-Aldrich (St. Louis, MO). Blockers were applied by directly adding them to the superfusate from stock solutions.

Data analysis

Data were presented as means ± SE. Body weight, blood glucose levels, membrane properties, spike half-width, AHP, outward currents, I_AHP, and decay time constants between two groups were compared using Student's t-test. Spike frequency-current intensity curves, current-voltage curves and AHP-time relationships between groups were compared using two-way ANOVA with repeated measures followed by a Tukey-Kramer post hoc test. P < 0.05 was considered as significant.

RESULTS

General conditions

The body weights and blood glucose levels of the four different groups were measured on the experimental day (Table 1). The blood was sampled from the tail of nonfasting neonates, and blood glucose levels were measured using a blood glucose monitoring system (Nova Biomedical, Waltham, MA). Compared with control group, body weights and blood glucose levels in NMDM and transgenic/surrogate were not significantly different. Body weights and blood glucose levels in surrogate mother groups were significantly higher than in those in the corresponding groups with natural mothers (control and NMDM; P < 0.05). As shown in Zheng et al. (2004), the blood glucose levels of FVB control mice were <200 mg/dl. Therefore we consider that the animals used in the present experiments were all within the normal blood glucose range. Along with the data in Figs. 2, C and D, and 5E, we conclude that the small difference of body weight (range: 3.7–4.8 g) or variation of blood glucose levels (131.9–197.3 mg/dl) among groups did not affect spike frequency and outward currents.

Fig. 2.

Maternal diabetes reduced the excitability of PCMNs in response to current injections. A, 1 and 2: representative PCMN spikes in response to current injections at 40 and 80 pA in a control animal. B, 1 and 2: representative PCMN spikes in response to current injections at 40 and 80 pA in a neonatal mouse with diabetic mother (NMDM). C: mean spike frequency was markedly reduced in NMDM compared with that in control animal (†P < 0.05). D: mean spike frequencies in response to current injections (40–140 pA) were comparable in NMDM (with nontransgenic and transgenic neonates from their own diabetic mothers), nontransgenic neonates fed by surrogate nondiabetic mothers, and transgenic neonates fed by surrogate nondiabetic mothers.

Fig. 5.

Maternal diabetes increased the transient outward current in PCMNs. A: control. The outward currents were evoked by the voltage steps from −70 to +40 mV for 250 ms in 10 mV steps every 5 s to show the transient currents. B: NMDM. The outward currents were evoked by voltage steps using the same protocol as in A. C: control. Outward currents evoked by voltage steps from −70 to +30 mV for 800 ms in 10 mV steps every 5 s to show the persistent currents. D: NMDM. Outward currents evoked by voltage steps using the same protocol as in C. E: the transient outward currents in NMDM significantly increased compared with control (as shown in inset E′, †P < 0.05), but the transient outward currents were similar in NMDM, nontransgenic neonates/surrogate mothers and transgenic neonates/surrogate mothers (as shown in E. P > 0.05). F: the persistent outward currents were not significantly different among the four different groups. V_m: membrane potential. The symbols for different mouse groups are shown at the bottom right of the figure.

Membrane properties

Table 2 lists the membrane properties of PCMNs of control and NMDM groups. The average resting membrane potentials, input resistances, thresholds, and mean amplitudes of APs did not significantly differ between these two groups.

Maternal diabetes reduced spike frequency of PCMNs in response to current injections

In the present study, 126 cells from 38 control mice and 159 cells from 28 NMDM mice were analyzed. All recorded neurons were strongly labeled by the tracer XRITC. Figure 1 shows XRITC labeled PCMNs (Fig. 1A) and one of these labeled neurons was recorded using an electrode pipette (B). Current-induced trains of APs in both groups are shown in Fig. 2, A, 1 and 2, and B, 1 and 2. Trains of APs were evoked using 1 s depolarizing current steps of varying amplitudes (40–140 pA). Spike frequency or firing rate increased as a function of current intensity but was significantly decreased by maternal diabetes (Fig. 2C, P < 0.05). Spike frequencies in response to current injections in transgenic and nontransgenic neonates from surrogate mothers were compared with that in NMDM, and no significant differences were found between these three groups (Fig. 2D, P > 0.05). Thus calmodulin transgene or milk did not significantly alter the excitability of PCMNs. Therefore we only compared the data obtained from control (group 1) and NMDM (group 2) using current clamp in the rest of our experiments.

Maternal diabetes increased the spike half-width and AHP

Under physiological conditions, spike broadening has been shown to be frequency dependent in a number of different neurons (Aldrich et al. 1979; Ma and Koester 1996; Quattrocki et al. 1994; Shao et al. 1999). As shown in Fig. 3, A′, inset, the spike widths of the first spike selected from the 4, 7, and 10 Hz AP trains in PCMNs induced by different current intensities of 1,000 ms were different. To standardize AP recordings, the membrane potential was held at −60 mV (below the threshold), and the AP was evoked by a 0.5-ms depolarizing current injection with an intensity that only generated a single spike (Fig. 3, A and B). Compared with control, maternal diabetes significantly increased the spike half-width from 1.20 ± 0.07 to 1.51 ± 0.06 ms (Fig. 3, A and C; P < 0.05). In addition to AP half-width, AHP amplitudes of these neurons were measured. Compared with control, AHP amplitudes at 10 ms and 50 ms were all significantly greater in NMDM, respectively (Fig. 3, B and D; P < 0.05).

Fig. 3.

Maternal diabetes broadened the spike half-width and increased the amplitude of afterhyperpolarization (AHP) of action potentials (AP) in PCMNs. A and C: maternal diabetes significantly broadened the spike half-width (*P < 0.01). Inset A′: the 1st spikes in the AP trains of 4, 7, and 10 Hz that were evoked by adjusting current intensity. The higher the frequency of spike trains, the wider the 1st spike. B and D: maternal diabetes significantly increased the amplitude of AHP at 10 and 50 ms from the onset of AP (†P < 0.05).

Transient and persistent outward currents of PCMNs

The extracellular recording solution contained a mixture of channel blockers: TTX, 0.5 μM, for Na⁺ current; 4-AP, 1 mM, for transient voltage-gated K⁺ current; and glybenclamide, 5 μM, for ATP-sensitive K⁺ current. These agents were added routinely to the recording perfusate unless otherwise stated. To record apamin-sensitive currents, tetraethylammonium (TEA, 1 mM) was also added to suppress voltage-dependent K⁺ currents.

Figure 4A shows the in- and outward currents in a PCMN, evoked by a depolarizing pulse of +10 mV from a holding potential of −70 mV before application of any channel blockers. The inward currents were blocked by TTX. Figure 4B shows a family of outward currents evoked by 250 ms steps from a holding potential of −70 mV to +40 mV in 10 mV increments after application of TTX. Each outward current was composed of a rapidly activating transient component that reached the peak within several ms and then rapidly inactivated, followed by a persistent component (delayed rectifier-type K⁺-like current). The expanded traces in Fig. 4B′ were from corresponding current traces in B to show individual traces more clearly. Figure 4C includes a family of outward currents from a representative PCMN evoked by 800 ms steps from a holding potential of −70 to +30 mV in 10 mV increments after application of TTX at a compressed time scale to show the persistent currents.

Fig. 4.

Outward currents in PCMNs. A: a current trace was evoked by a voltage step without TTX to show an inward current and an outward current. B: superimposed outward current traces in response to voltage steps (10 mV, 250 ms, every 5 s) from a holding potential of −70 to +40 mV in a bath solution containing 0.5 μM TTX, 1 mM 4-aminopyridine (4-AP), and 5 μM glybenclamide. The inward current was completely blocked. B′: 6 expanded current traces taken from B showing the transient outward current at depolarizing voltages from −50 to 0 mV. C: currents were elicited by depolarizing voltage steps (−70 to +30 mV) from a holding potential of −70 mV (10 mV, 800 ms, 5 s) at a compressed time window to show persistent currents.

Maternal diabetes increased transient outward currents of PCMNs

In Fig. 5, A and B, depolarizing voltage steps of +10 mV from the holding potential of −70 to +40 mV induced a family of outward K⁺ current traces, including transient currents followed by persistent current traces in both control and NMDM. Compared with control, maternal diabetes significantly increased the peaks of the transient currents in NMDM as shown in the inset (Fig. 5E′) of Fig. 5E. In Fig. 5E, the peaks of the transient currents were almost identical in NMDM, transgenic neonates and nontransgenic neonates from surrogate mothers. Thus calmodulin transgene or milk did not significantly alter the transient outward currents of PCMNs. Therefore we did not differentiate the transgenic and nontransgenic neonates in NMDM in the following experiments. Figure 5, C and D, shows the outward currents in a compressed time scale for measurement of persistent currents. There were no significant differences between the four groups (Fig. 5F). Therefore we did not further examine persistent currents.

Maternal diabetes increased SK transient outward currents

Because maternal diabetes increased transient outward K⁺ currents, we further examined the effect of maternal diabetes on SK transient currents and SK channel-mediated AP repolarization. To obtain the SK currents, outward currents were first evoked by voltage steps of +10 mV from −70 to +40 mV before apamin application (Fig. 6A, 1 and 2). Following administration of 100 nM apamin (a specific SK channel blocker), the outward currents were evoked again (Fig. 6B, 1 and 2). By subtracting outward currents evoked after apamin application from those before apamin application (Fig. 6, A1 and B1, and A2 and B2), apamin-sensitive currents were obtained (C, 1 and 2). The current-voltage curves are shown in Fig. 6D. Maternal diabetes significantly increased the apamin-sensitive transient currents (P < 0.05, Fig. 6D).

Fig. 6.

Maternal diabetes increased the small conductance Ca²⁺-activated K⁺ (SK) transient outward currents in PCMNs: effect of the SK channel blocker apamin. Membrane potential was held at −70 mV and stepped from −70 to +40 mV for 250 ms with 10 mV steps every 5 s as shown in the bottom of the traces. A1–C1: control. Outward currents evoked by voltage steps before (A1) and after (B1) application of apamin. C1: apamin-sensitive current (subtraction of A1 and B1). A2–C2: NMDM. Outward currents evoked by voltage steps before (A2) and after (B2) application of apamin. C2: apamin-sensitive currents (subtraction of A2 and B2). Insets in B1 and B2: the black trace (before apamin) and gray trace (after apamin washout) showing that a well-known irreversible effect after apamin blockade (Wolfart et al. 2001). D: apamin-sensitive transient outward currents were significantly increased in NMDM compared with control (†P < 0.05).

Effect of SK channels on the repolarization half-width of AP was determined by application of apamin. Using current clamp recording, a single AP was first evoked as above. As shown in Fig. 7, A and B, application of apamin significantly increased the spike half-width in both control (before: 1.19 ± 0.07 ms; after: 1.37 ± 0.05 ms; *P < 0.05) and NMDM groups (before: 1.50 ± 0.06 ms; after: 1.68 ± 0.04 ms; *P < 0.05). Under this experimental condition (i.e., 0.5 ms depolarizing current), the increase of spike half-width after application of apamin was comparable between the two groups (control: 13.6 ± 4.1% vs. NMDM: 10.6 ± 4.0%). Under a different experimental condition that used a longer depolarizing current (250 ms; Fig. 7, C and D), application of apamin also significantly increased the spike half-width in both control (before: 1.91 ± 0.1 ms and apamin: 2.16 ± 0.1 ms, *P < 0.05) and NMDM groups (before: 2.85 ± 0.2 ms, after: 3.62 ± 0.2 ms; **P < 0.01). In addition, apamin significantly broadened the spike half-width in NMDM (21.3 ± 0.2%) more than that in control (11.6 ± 0.1%) (n = 8/group, P < 0.05).

Fig. 7.

Apamin application increased spike half-width: effects of 0.5 ms (A and B) and 250 ms (C and D) current injections. A: representative AP traces evoked by a 0.5 ms depolarization current in control and NMDM before (- - -) and after apamin (—) application. B: apamin significantly increased spike half-width in both control and NMDM, (*P < 0.05). The increase of spike half-width after application of apamin was comparable in control and NMDM. C: representative AP traces evoked by a 250 ms depolarization current in control and NMDM before (- - -) and after apamin (—) application. D: apamin significantly increased spike half-width in both control and NMDM (P < 0.05). Apamin significantly broadened the spike half-width in NMDM more than that in control (P < 0.05).

Maternal diabetes increased apamin-sensitive I_AHP and augmented the contribution of SK channels to AHP

To determine whether maternal diabetes altered the contribution of SK channels to I_AHP and AHP, we blocked SK channels with apamin in control and NMDM (Fig. 8, A and B). Apamin application reduced the peak amplitudes of I_AHP in the control (Fig. 8A) and NMDM groups (B). The peak amplitudes of I_AHP were measured and compared between control and NMDM. The top (dark) traces in Fig. 8, A and B, are representative recordings of I_AHP in control and NMDM before apamin was administered. The peak amplitudes of I_AHP were significantly increased in NMDM (314.3 ± 47.1 pA) compared with control (186.6 ± 47.0 pA, P < 0.05). Thus maternal diabetes significantly increased I_AHP.

Fig. 8.

Maternal diabetes increased apamin afterhyperpolarization (AHP) currents (I_AHP) and augmented the contribution of SK channels to AHP. I_AHP current was evoked by a depolarizing voltage pulse of +10 mV (100 ms) from holding potential −70 mV followed by a returning −50 mV step. The peak of I_AHP was measured. A (control) and B (NMDM). The black trace is the I_AHP before apamin, and the gray trace is the I_AHP after apamin. A′ (control) and B′ (NMDM). The apamin-sensitive I_AHP was obtained by subtracting the current after apamin from the current before apamin. The decay of apamin I_AHP was fitted by a single exponential equation (red line). C: maternal diabetes significantly increased apamin-sensitive I_AHP (*P < 0.05) but did not change the decay time constant. D and E: representative AHP waveforms of control (D) and NMDM (E) PCMNs before and after apamin. F: apamin significantly reduced AHP in both groups (†P < 0.05). In addition, maternal diabetes induced a significant greater reduction of AHP compared with control (*P < 0.05).

Apamin-sensitive I_AHP was obtained by subtracting I_AHP after apamin application from the I_AHP before apamin (Fig. 8, A′ and B′). Compared with control, the peak amplitude of apamin-sensitive I_AHP in NMDM was significantly increased (Fig. 8C, *P < 0.05). The decay time constant of the apamin-sensitive I_AHP, as fitted by a single exponential equation, was comparable in control and NMDM (Fig. 8C).

Using current clamp recording, an AP was first evoked by a 0.5-ms depolarizing current of sufficient intensity to generate a single spike. As shown in Fig. 8, D–F, application of apamin significantly decreased the spike AHP in both control and NMDM groups (†P < 0.05). Noticeably, application of apamin induced a significantly greater reduction of spike AHP in NMDM (from −12.5 ± 0.9 to −7.5 ± 0.5 mV at 10 ms and from −12.3 ± 1.0 to −2.0 ± 0.4 mV at 50 ms) than that in control (from −9.9 ± 0.8 to −7.4 ± 0.6 mV at 10 ms and from −5.5 ± 1.1 to −2.4 ± 0.4 mV at 50 ms; †P < 0.05). After blockade of SK channels with apamin, the AHP amplitudes at 10 ms (NMDM: −7.5 ± 0.5 mV; control: −7.4 ± 0.6 mV) and at 50 ms (NMDM: −2.0 ± 0.4 mV; control: −2.4 ± 0.4 mV) were not significantly different.

Because SK channels are Ca²⁺-dependent, we examined whether blockade of Ca²⁺ may yield a similar effect on I_AHP and AHP as seen in apamin application. Therefore we blocked Ca²⁺ influx using the general Ca²⁺ channel blocker Cd²⁺ in control and NMDM. To evoke I_AHP, a 100 ms pulse of +10 mV from a holding potential of −70 mV was given and immediately followed by a 1.5 s −50 mV pulse. The peak amplitudes of I_AHP were measured and compared between control and NMDM. The top (dark) traces in Figs. 9, A and B, are representative recordings of I_AHP in control and NMDM before Cd²⁺ was administered. As shown in Fig. 8, A and B, maternal diabetes again significantly increased I_AHP. Cd²⁺ bath application reduced the amplitude of I_AHP in both control (Fig. 9A) and NMDM groups (B). Cd²⁺–sensitive I_AHP was obtained by the difference of the I_AHP before and after application of Cd²⁺ (Fig. 9A', 9B'). Similar to apamin application, the peak amplitude of Cd²⁺-sensitive I_AHP was significantly increased in NMDM (Fig. 9C, *P < 0.05). The decay time constant of Cd²⁺-sensitive I_AHP, as fitted by a single exponential equation, was comparable in control and NMDM (Fig. 9C).

Fig. 9.

Dependency of maternal diabetes-induced increase of AHP currents (I_AHP) and AHP on Ca²⁺influx in PCMNs. The I_AHP current and AHP were evoked and measured as in Fig. 8. In addition, AHP was evoked by a current injection of sufficient intensity to generate a single AP. The peak of AHP was measured at 10 and 50 ms. A: (control) and B (NMDM). The black trace is the I_AHP before Cd²⁺, and the gray trace is the I_AHP after Cd²⁺ application. A′ (control) and B′ (NMDM). The Cd²⁺–sensitive I_AHP was obtained by subtracting the current after Cd²⁺ from the current before Cd²⁺ application. The decay of Cd²⁺–sensitive I_AHP was fitted by a single exponential equation (red line). C: maternal diabetes significantly increased Cd²⁺–sensitive I_AHP (*P < 0.05) but did not increase decay time constant. D and E: representative AHP waveforms of control (D) and NMDM (E) PCMNs before and after Cd²⁺ application. F: Cd²⁺ significantly reduced AHP in both groups (†P < 0.05). After application of Cd²⁺, the AHP amplitude at 10 and 50 ms in NMDM was comparable to control, indicating that blockade of Ca²⁺influx completely abolished maternal diabetes-induced increase of AHP. In addition, maternal diabetes induced a significant greater reduction of AHP compared with control (*P < 0.05).

Using current clamp recording, an AP was first evoked by a 0.5-ms depolarizing current of an intensity which was sufficient to generate a single spike. As shown in Fig. 9, D–F, maternal diabetes significantly increased the spike AHP in NMDM before Cd²⁺ application at 10 and 50 ms (†P < 0.05; also see Fig. 3, B–D). Cd²⁺ significantly decreased the spike AHP in both control and NMDM groups (†P < 0.05). Noticeably, consistent with apamin examination, application of Cd²⁺ induced a significantly greater reduction of spike AHP in NMDM (from −12.3 ± 0.9 to −6.7 ± 1.1 mV at 10 ms and from −11.9 ± 1.1 to −3.1 ± 0.9 mV at 50 ms) than that in control (from −10.0 ± 0.7 to −7.2 ± 0.5 mV at 10 ms and from −5.7 ± 1.0 to −2.7 ± 0.5 mV at 50 ms; P < 0.05; Fig. 9F). After blockade of Ca²⁺ influx, the AHP amplitude was not significantly different between the two groups.

Apamin increased spike frequency and abolished the difference of spike frequency of PCMNs in response to current injections between control and NMDM

AP trains were evoked by 1 s depolarizing current steps of varying intensities (40–140 pA). Current (100 pA)-induced AP trains before and after apamin application are shown in Fig. 10, A, 1 and 2 (control group) and B, 1 and 2 (NMDM group). Consistent with Fig. 2C, maternal diabetes significantly decreased spike frequency in NMDM compared with control (Fig. 10C, black and red lines). As shown in Fig. 10C, spike frequency increased as a function of current intensity in both control and NMDM. To test the effect of SK channels on excitability, we first blocked SK channels with apamin. Apamin significantly increased spike frequency (†P < 0.05) and largely abolished the spike frequency difference between the two groups (i.e., spike frequency after apamin was not significantly different between control and NMDM).

Fig. 10.

Apamin application abolished the difference in spike frequencies of PCMNs in response to current injections between control and NMDM. A, 1 and 2: control; B, 1 and 2: NMDM. Representative traces of AP trains evoked by 1 s-depolarizing current (100 pA) injection during control aCSF and after apamin application in control and NMDM. C_. Before apamin, spike frequency was significantly different in control and NMDM (†P < 0.05), which is consistent with Fig. 2C. After apamin application, spike frequency significantly increased in both groups (†P < 0.05), with a significant greater increase in NMDM compared with control (*P < 0.05). There was no difference of spike frequencies between control and NMDM, indicating the difference of spike frequencies between control and NMDM completely diminished.

Again because SK channels are Ca²⁺-dependent, we examined whether blockade of Ca²⁺ may yield a similar effect on spike frequency to that seen in apamin application. Therefore we blocked Ca²⁺ influx using Cd²⁺ in control and NMDM. Similar to apamin, Cd²⁺ application significantly increased spike frequency in both control (Fig. 11, A, 1 and 2, and C) and NMDM (B, 1 and 2, and C). Cd²⁺ application diminished the difference of spike frequency between the two groups (i.e., spike frequency after Cd²⁺ was not significantly different between control and NMDM; Fig. 11C).

Fig. 11.

Effect of blockade of Ca²⁺ influx on spike frequency of PCMNs in control and NMDM. Cd²⁺ application abolished the difference in spike frequency of PCMNs in response to current injections between control and NMDM. A, 1 and 2: control; B, 1 and 2: NMDM. Representative traces of AP trains evoked by 1 s depolarizing current (100 pA) injection during control Artificial cerebrospinal fluid and after Cd²⁺ application in control and NMDM. C_. Before Cd²⁺, spike frequencies were significantly different between control and NMDM (†P < 0.05) which is consistent with Fig. 10C. After Cd²⁺ application, spike frequency significantly increased in both groups (†P < 0.05), with a significant greater increase in NMDM compared with control (*P < 0.05). There was no difference of spike frequencies between control and NMDM, confirming that the difference of spike frequencies between control and NMDM was Ca²⁺-dependent.

DISCUSSION

We have demonstrated that maternal diabetes significantly reduced the spike frequency, broadened AP repolarization (increased AP repolarization half-width), and increased AHP amplitude of NA PCMNs in NMDM. These results indicate that maternal diabetes decreases PCMN excitability, possibly due to increased AP broadening and increased AHP. Because SK channels mediate spike AHP and excitability (Stocker 2004), we hypothesized that maternal diabetes alters SK currents. Indeed our data indicated that maternal diabetes increased SK-mediated currents that may contribute to the increased AHP in NMDM. Blockade of SK channels with apamin substantially increased excitability and largely abolished maternal diabetes-induced reduction of spike frequency in NMDM. Therefore we suggest that the increased SK currents contribute to the reduced excitability of PCMNs in NMDM.

Identity of NA cardiac motoneurons

In the present study, we injected tracer XRITC into the pericardial sac at the base of atria at P7–9. After 2 days, cardiac motoneurons in the NA were brightly labeled by XRITC as shown in Fig. 1. One concern is that the NA is a large nucleus that projects to parasympathetic ganglia in the heart as well as other organs near the heart (Bieger and Hopkins 1987). The external formation of NA is the major source projecting to the heart in adult animals (Bieger and Hopkins 1987). However, the external formation could not be clearly identified at the age of P9–11. Therefore whether tracer injection only labeled cardiac motoneurons in the NA was a concern. To minimize the leakage of tracer to other organs, we injected a small amount of tracer (4–8 μl) into the pericardial sac. Using this injection volume at the base of the atria but outside the pericardial sac in preliminary studies, we occasionally found some weakly labeled neurons randomly distributed in the NA region. Thus we only recorded brightly labeled neurons in the NA in the experiment. In such a way, we could optimally avoid noncardiac neurons in the NA that might have been weakly labeled due to leakage of tracer to other organs.

Fast, medium, and slow AHP of PCMNs

In many neurons, AHP has multiple components, including fast, medium, and slow components (fAHP, mAHP, and sAHP). The fAHP that follows a single AP lasts a few to ten ms (Sah 1996; Storm 1989). The mAHP and sAHP have much longer durations (mAHP: from tens to several hundred ms; sAHP: from several hundred ms to seconds) (Faber and Sah 2002; Sah and Faber 2002). The mAHP largely contributes to spike frequency and the sAHP mainly contributes to spike train adaption (Faber and Sah 2002). Unlike other neurons (Saar and Barkai 2003; Saar et al. 2001), we did not differentiate the different types of AHPs because there were not clear boundaries between fAHP, mAHP, and sAHP traces in PCMNs as seen in some other central neurons (Li and Bennett 2007; Stocker et al. 1999). Instead, we measured AHP at 10 and 50 ms in neurons in a solution which did not contain any channel blockers. Approximately 10 ms is in the fast or early medium duration range of AHP, and 50 ms is in the range of medium AHP. Because AHP almost returned to the resting membrane potentials at 100 ms for single spikes in control (Fig. 3B), PCMNs may not have a significant sAHP.

Maternal diabetes reduced excitability, broadened AP repolarization and increased AHP

Because the NA is one of the critical components in regulating cardiac function, we examined excitability and AP properties of PCMNs. Maternal diabetes did not change the passive membrane properties and threshold but significantly reduced the spike frequency in response to current injections, broadened spike, and increased AHP amplitude. Because broadened spike and increased AHP slow the AP recovery, they together may contribute to reduced excitability of PCMNs in NMDM.

Maternal diabetes increased the contribution of SK channels to AHP

In the brain, SK channels are widely expressed in many regions including hippocampal neurons, lateral amygdala neurons, the dorsal motor nucleus and nucleus ambiguus (Faber and Sah 2002; Pedarzani et al. 2000; Sailer et al. 2004; Stocker 2004; Stocker and Pedarzani 2000). Consistent with these studies, we have shown that NA PCMNs do have SK channels in this study and Lin et al. (2010c). Previously, it has been reported that SK channels contribute more to mAHP without significant contribution to AP repolarization in other central neurons (Faber and Sah 2002; Stocker 2004). In our study, we demonstrated that SK channels contribute significantly to AP repolarization because apamin blockade of SK channels induces a significant increase in spike half-width of PCMNs in both control and NMDM. Further, we found maternal diabetes increased SK transient outward currents, which may contribute to augmented transient outward currents in NMDM.

One concern may be that apamin may alter the AP depolarizing input resistance (R_input). We have calculated the R_input, which was defined as the ratio of membrane potential change (ΔV_m) relative to membrane potential baseline and current injection increase (ΔI) at the beginning of the first AP in a ramp test. During apamin application, R_input decreased in NMDM, whereas it increased in control as compared with that before apamin application (data not shown here). According to Ohm's law (outward currents = ΔV_m /R_input), for the same ΔV_m, the outward currents increased during apamin application because apamin decreased R_input in NMDM compared with that without apamin. Thus the actual value of apamin-sensitive currents obtained from subtraction of the currents before and after apamin application should be smaller than what we have shown here in NMDM. In contrast, because apamin application increased R_input in control compared with that without apamin, the actual value of the apamin-sensitive currents obtained from subtraction of the currents before and after apamin application should be larger than what we have shown here in control. Therefore the conclusion that maternal diabetes increases the apamin-sensitive currents as shown in Fig. 6 should be a conservative estimate and correct. At this time, we cannot explain why apamin application increases R_input in control but decreases it in NMDM.

Because transient outward currents may contribute to repolarization (Giese et al. 1998; Ma and Koester 1996; Wilson et al. 2002), we had initially postulated that maternal diabetes might have decreased SK transient outward currents as an explanation for why maternal diabetes induced an increase of spike half-width. Opposite to our assumption, our data showed that maternal diabetes actually increased the SK transient outward currents. If transient outward currents were indeed to contribute to repolarization, then we would expect that the increased SK transient outward currents were associated with a larger percentage increase of spike half-width in NMDM than in control. However, our data in Fig. 7, A and B, show that the percentage increase of spike half-width in NMDM and control were comparable under the experimental conditions to evoke single APs using the depolarizing current of 0.5 ms. However, using a longer depolarizing current (250 ms) to evoke single APs, we found that maternal diabetes significantly increased the percentage of spike broadening in NMDM more than that in control (Fig. 7, C and D). Therefore the increased SK outward currents in NMDM might have a significant effect on AP repolarization. Nevertheless the increased SK channel outward currents could not explain the overall AP broadening in NMDM. Although the increased SK outward currents could not explain the overall AP broadening, they may contribute to the increased AHP in NMDM because transient outward currents were reported to contribute to AHP (Giese et al. 1998; Wilson et al. 2002).

Because SK channel-mediated I_AHP contributes to AHP in many central neurons (Lancaster and Adams 1986; Lancaster and Nicoll 1987; Sah 1996; Sah and McLachlan 1992; Stocker et al. 1999; Stocker 2004), we then examined the effect of maternal diabetes on SK channel-mediated I_AHP and the effect of blockade of SK channels on AHP in control and NMDM. We found that maternal diabetes increased SK channel-mediated I_AHP and augmented AHP at 10 ms (fAHP) and 50 ms (mAHP). Thus we suggest that maternal diabetes increases SK channel I_AHP, and this may in turn contribute to the increased AHP in NMDM. Very importantly, blockade of SK channels with apamin completely abolished the maternal diabetes-induced increase of AHP at 10 ms (fAHP) and 50 ms (mAHP), strongly suggesting that SK channels play a major role in maternal diabetes-induced increase of AHP. In our study, we also used the Ca²⁺-channel antagonist Cd²⁺ to block Ca²⁺ influx. Similar to apamin application, Cd²⁺ application increased Cd²⁺-sensitive I_AHP and completely diminished the difference of AHP at 10 ms (fAHP) and 50 ms (mAHP) to current injections between control and NMDM, This confirms that Ca²⁺-activated K⁺ channels (most likely SK channels) play a major role in maternal diabetes-induced increase in AHP of PCMNs. As to whether other Ca²⁺-activated K⁺ channels (BK) contribute to maternal diabetes-induced changes in AHP should be investigated (Lin et al. 2010a).

In this study we used two different methods to examine the effect of maternal diabetes on SK currents (transient currents and I_AHP). We found that both SK transient currents and I_AHP increased in NMDM, which may contribute to maternal diabetes-increased AHP.

Maternal diabetes-induced reduction of excitability in PCMNs attributes to increased SK currents

It has been well established that blockade of SK channels reduces AHP and increases firing frequency in other central neurons and that increasing SK currents with channel enhancers increases AHP and reduces firing frequency (Stocker 2004). Consistent with this report, we found that apamin application substantially increased spike firing frequency in both control and NMDM in the present study. Very importantly, apamin application completely abolished the difference of spike frequency responses to current injections between control and NMDM, strongly suggesting that SK channels play a major role in maternal diabetes-induced decrease in excitability of PCMNs. In our study, we also used the Ca²⁺-channel antagonist Cd²⁺ to block the Ca²⁺ influx. Similar to apamin application, Cd²⁺ application also completely eliminated the difference of spike frequency response to current injections between control and NMDM, confirming that Ca²⁺-activated K⁺ channels (most likely SK channels) play a major role in maternal diabetes-induced decrease in excitability of PCMNs. As to whether other Ca²⁺-activated K⁺ channels contribute to maternal diabetes-induced changes in excitability should be investigated (Lin et al. 2010a).

Summary

In this study, we found that maternal diabetes significantly reduced spike frequency, broadened the AP, and increased the AHP amplitude of NA PCMNs in NMDM. In addition, we demonstrated that maternal diabetes increased SK channel-mediated currents, which may likely contribute to the increased AHP in NMDM. Blockade of SK channels with apamin almost completely diminished the maternal diabetes-induced difference in AHP and excitability between control and NMDM. Therefore we conclude that augmented SK currents may play an important role in maternal diabetes-induced reduction of excitability of PCMNs in NMDM.

GRANTS

This work was supported by NIH Grants HL-79636 and AG-021020.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).