Analogue modulation of back-propagating action potentials enables dendritic hybrid signalling

We report that back-propagating action potentials (bAPs) are not simply digital feedback signals in dendrites but also carry analogue information about the overall state of neurons. Analogue information about the somatic membrane potential within a physiological range (from −78 to −64 mV) is retained by bAPs of dentate gyrus granule cells as different repolarization speeds in proximal dendrites and as different peak amplitudes in distal regions. These location-dependent waveform changes are reflected by local calcium influx, leading to proximal enhancement and distal attenuation during somatic hyperpolarization. The functional link between these retention and readout mechanisms of the analogue content of bAPs critically depends on high-voltage-activated, inactivating calcium channels. The hybrid bAP and calcium mechanisms report the phase of physiological somatic voltage fluctuations and modulate long-term synaptic plasticity in distal dendrites. Thus, bAPs are hybrid signals that relay somatic analogue information, which is detected by the dendrites in a location-dependent manner.

(a) The propagation of steady-state voltage signals from the small Rs controlling pipette was reliably followed in the monitoring pipette (left panel), whereas, the voltage signal is distorted when the higher Rs pipettes are used for current injections (right panel). Therefore, high access pipettes were not used for current injection (hence the name, monitoring pipette). Each dot represents individual cells. The data points indicated by red dots derived from those recordings (i.e. same traces), from which data was collected for Fig. 1. (b) Comparison of the peak amplitudes and half-widths of the same APs at the low Rs controlling pipettes and monitoring pipettes with various Rs values in dual somatic recordings. (c) Comparison of the changes of the same APs detected at the monitoring and controlling pipettes during long trains. This analysis exploited the known broadening and amplitude reduction of the GC APs during long trains. Thus, this approach allowed for the comparison of sensitivity of recordings to subtle changes of AP shapes, which were similar to those changes that have been the subject of our study. The obtained data were grouped according to the Rs of the monitoring pipettes. Two representative recordings are shown on the left. On the graphs, each dot represents the change of individual APs relative to a reference AP in the same traces at the controlling pipettes (x-axis) and at the monitoring pipettes (y-axis). The reference AP was chosen from the middle portion of the trains. Adjusted R 2 is shown for each graph together with slope of the linear fits on the data. This analysis indicates that up to 200 MΩ the majority of the values fell close to the ideal (100% slope); thus, our recording conditions were sensitive enough to detect the small changes of the bAP shapes. Rationale: We replicated previous observations concerning asymmetric voltage propagation from soma to dendrites and dendrites to soma in GCs 1,2 . The morphological and biophysical properties of GC dendrites enable more effective voltage propagation in the soma to dendrite direction and this was an important prerequisite for the effective modulation of dendritic processes by somatic membrane potential changes.
Traces on top are average somatic (black) and dendritic (cyan, recorded at 173 µm from the soma) voltage responses evoked by local dendritic (left) or somatic (right) current injection (-20 pA, 600 ms). Graph shows the relative attenuation of steady-state voltage responses of individual recording pairs (n=28 dual recordings). Red circles indicate the example recording. Figure 3. Location-dependency of the bAP-evoked dendritic calcium signals in GCs measured by scanning confocal microscopy and spinning disc confocal imaging.

Supplementary
Rationale: Conventional scanning confocal imaging allows for the spatially precise measurements of individual dendritic spots, whereas, the spinning disc method provides better throughput and simultaneous imaging of large dendritic region. Here we tested whether the results of the two approaches give comparable results compared to each other and compared to previous findings 1 .  and -58.9 ± 0.3 mV, respectively) membrane potentials. Notice the lack of change in the baseline calcium signal (raw traces are shown in arbitrary units) in these membrane potential ranges, which suggests that calcium currents were not activated significantly at these membrane potentials and that the differences of the imaged calcium signals were not due to changes of the baseline signal. (b) Quantification of the membrane potential dependence of bAP-evoked calcium signals. The signal amplitudes were normalized relative to calcium signal amplitudes evoked at resting membrane potential (black symbol) in each cells (gray curves show data from the individual cells).

Supplementary Figure 6. Analog modulation of dendritic calcium signals by GIRK-mediated proximal dendritic hyperpolarization.
Rationale: Throughout the manuscript we employed somatic current injection to evoke membrane potential changes. To test whether more physiological effectors have similar effects on bAP-evoked calcium signals as somatic current injections we employed the mGluR2 activation. Dendritic mGluR2 receptors are localized in the proximal dendritic region of GCs and evoke GIRK-channel-mediated hyperpolarization 3 . First, to exclude the possibility that mGluR2 and its G-protein cascade directly modulate dendritic calcium signaling in GCs in addition to activating this potassium conductance, we tested the effect of the mGluR2 agonist DCG IV in the presence of the GIRK channel blocker tertiapin-Q (0.5 µM). In these experiments, in which the hyperpolarization was specifically eliminated (somatic resting membrane potential in the presence of tertiapin-Q only: -72.9 ± 0.6 mV, and in tertiapin-Q and DCG IV: -73.3 ± 0.6 mV), mGluR2 activation was not able to elicit changes in the measured calcium signals (45-90 μm: -1.6 ± 6.2%, p=0.8, n=9 locations; 97-160 μm: -0.7 ± 6.1%, p=0.9, n=9) indicating that any effect of mGluR2 activation on calcium influx could be attributed to the GIRK-mediated hyperpolarization. As with somatic hyperpolarization, mGluR2 activation by DCG IV application alone (which hyperpolarized the somatic resting membrane potential from -71.0 ± 0.6 mV to -74.9 ± 0.5 mV) bidirectionally modulated the dendritic bAP-evoked calcium signals. Rationale: We employed a model configuration that provided testable hypotheses based on the available calcium currents in GCs. For this, we isolated native calcium currents in nucleated patches from GCs and constrained HVA current models from GCs 4 to the measured parameters. We used two current models, which included a conventional, non-inactivating HVA calcium current (HN, based on the properties of an N-type channel) and an inactivating HVA conductance (HI, R-type). We conducted three simulation sets using these two currents individually and as a composite current (HN:HI composite), which consisted of both HVAs in a one-to-one ratio (maximal conductance). Note that LVA (T-type) calcium currents were likely to be arbitrary overrepresented in nucleated recording configuration (e.g. refs 5-7 ). Rationale: For the mechanisms underlying the proximal enhancement by hyperpolarization-induced bAP narrowing it was crucial that these bAPs maximally activate the available channel population. To test how close is the calcium channel opening to the maximal by the different bAPs we artificially extended them with constant voltage steps (at +40 mV for proximal bAPs and at 0 mV for distal bAPs). If the bAP waveforms do not activate nearly all calcium channels, extending the bAP voltage command was expected to increase the calcium influx. Note that currents were measured at the descending phases of the modified bAP waveforms (tail currents); thus, the driving force was identical in each protocol.
(a) The extension the proximal bAP waveform (recorded at 24 µm) with steady voltage at their peaks (+40 mV for proximal bAP) did not increase significantly the amount of activated calcium currents in nucleated patches indicating that the bAP waveform alone already activated the majority of the available channels.
Traces show the average of all raw currents (i.e. without normalization, n=12 patches, recorded in the presence of NNC55-0396, TTX and 4-AP) elicited by a bAP voltage command extended by 5, 3.75, 2, 0.75 or 0 ms. (b) The graph shows the area of modified proximal (light blue, n = 12 patches) and distal (green, n = 9 patches) bAP-evoked calcium currents relative to that of native bAP (0 ms) in the same nucleated patches. In contrast to the proximal bAP waveform, extension the distal bAP waveform (0 mV, collected at 106 µm) did increase calcium currents indicating that smaller bAPs activate only a fraction of the available calcium channels and, consequently, small changes in their peak amplitude can effectively change the calcium influx. Asterisks mark significant differences (t-tests).

Supplementary Figure 9. Native potassium currents in GCs, which has been employed in the dynamic clamp experiments to narrow APs.
Rationale: The experiment on Fig. 4a was designed to investigate the isolated contributions of repolarization changes to the membrane potential-dependence of bAP-evoked calcium signals. Thus, the influences of AP-shape can be investigated in isolation from the actual membrane potential changes, which can alter other factors such as the differential availability of voltage-gated channels. For this aim, we looked for a tool, which can be employed in dynamic clamp experiments to mimic the narrowing of APs. We characterized the parameters of an inactivating potassium current in GCs, which were used as a template for the conductance fed by the computer in the conductance clamp experiments. Note that presence of these currents did not demonstrate that they were responsible for the membrane potential dependent changes of the bAP shape (see also Supplementary Fig. 10). We have employed them only to mimic the bAP shape changes. Rationale: The simulations predicted (Fig. 4b) a crucial role for the inactivation of the HVA channels.
Here we tested whether low (i.e. physiological) voltage is effective to elicit this inactivation. For this aim we investigated calcium influx in a similar scenario as in Fig. 4b except the preceding membrane potentials, which were set to -60 mV for both the depolarized and hyperpolarized voltage commands.
Thus, only the AP shape remained different between the two commands. We predicted that if the inactivation of HVA currents play important roles, in contrast to the observation with -80 mV preceding membrane potentials, the narrower AP shapes should not result in larger calcium influx when the different AP waveforms were preceded with physiological depolarizations. We addressed this question both with HI:HN simulations and with nucleated patch recordings of native currents.
The upper trace shows the modified voltage commands (blue: originally hyperpolarized, red: originally depolarized) with a 4 sec long preceding step at -60 mV. Currents were simulated by standard activation and inactivation kinetics. And calcium current were elicited in standard nucleated patch recording conditions (n=8 cells) by the same voltage commands. The lower graph shows the summary data (bar), individual recordings (blue symbols) and the simulated results (X) of the differences between calcium influx elicited by the "hyperpolarized" waveform relative to the currents during "depolarized" waveform. Rationale: The development of the effect of somatic hyperpolarization on dendritic calcium signals is important for determining the temporal domains, in which hybrid signaling is available (see Fig. 6).

Supplementary
Because of the proposed important role of the inactivation of the HVA currents in the membrane potential-dependent calcium influx we hypothesized similar time courses for the dependence of calcium signal enhancement on the length of the hyperpolarization and for the recovery time course from inactivation of the HVA currents. Here we measured and compared these two parameters.  the analysis whereas red traces show currents profiles which failed to satisfy our criteria for realistic calcium currents. Specifically, traces were excluded if a double peak current rose with a first peak as large as the one-third of the second peak or too small currents were evoked (i.e. the peak current was five times smaller than the baseline).