Quantitative interactions between the A-type K+ current and inositol trisphosphate receptors regulate intraneuronal Ca2+ waves and synaptic plasticity

Abstract

The A-type potassium current has been implicated in the regulation of several physiological processes. Here, we explore a role for the A-type potassium current in regulating the release of calcium through inositol trisphosphate receptors (InsP3R) that reside on the endoplasmic reticulum (ER) of hippocampal pyramidal neurons. To do this, we constructed morphologically realistic, conductance-based models equipped with kinetic schemes that govern several calcium signalling modules and pathways, and constrained the distributions and properties of constitutive components by experimental measurements from these neurons. Employing these models, we establish a bell-shaped dependence of calcium release through InsP3Rs on the density of A-type potassium channels, during the propagation of an intraneuronal calcium wave initiated through established protocols. Exploring the sensitivities of calcium wave initiation and propagation to several underlying parameters, we found that ER calcium release critically depends on dendritic diameter and that wave initiation occurred at branch points as a consequence of a high surface area to volume ratio of oblique dendrites. Furthermore, analogous to the role of A-type potassium channels in regulating spike latency, we found that an increase in the density of A-type potassium channels led to increases in the latency and the temporal spread of a propagating calcium wave. Next, we incorporated kinetic models for the metabotropic glutamate receptor (mGluR) signalling components and a calcium-controlled plasticity rule into our model and demonstrate that the presence of mGluRs induced a leftward shift in a Bienenstock-Cooper-Munro-like synaptic plasticity profile. Finally, we show that the A-type potassium current could regulate the relative contribution of ER calcium to synaptic plasticity induced either through 900 pulses of various stimulus frequencies or through theta burst stimulation. Our results establish a novel form of interaction between active dendrites and the ER membrane, uncovering a powerful mechanism that could regulate biophysical/biochemical signal integration and steer the spatiotemporal spread of signalling microdomains through changes in dendritic excitability.

Figure 1. Dependence of calcium transients evoked by a backpropagating action potential on the A-type K⁺ channel density

A, morphology of the simplified three-cylinder model neuron used in the study. B, voltage traces recorded at the midpoint of the oblique dendrite in response to a bAP at different A­-conductance densities. C, [Ca²⁺]_c traces in response to the bAPs shown in B. D, peak [Ca²⁺]_c, in response to a bAP, plotted as a function of A-conductance density obtained from the experiments depicted in B–C. E, open probability of InsP₃R (P_o) plotted as a function of [Ca²⁺]_c.

Figure 2. Sensitivity analyses of critical parameters that regulated calcium waves in a three-cylinder model neuron

A, [Ca²⁺]_c traces as a function of time for selected locations on the three-cylinder model when calcium waves were initiated by pairing 10 bAPs separated by 30 ms ISI with elevated [InsP₃]_c. B–C, shape plots of the model neuron depicting peak [Ca²⁺]_c (B) and the time at which this peak occurred (C) along the neuronal topograph for the experiment depicted in A. D, area under the curve (AUC) for the flux of Ca²⁺ through InsP₃R (J_InsP3R), measured at different oblique dendritic locations, plotted as a function of the diameter of the oblique dendrite. E–G, as A–C, but simulations were performed with oblique diameter set at 3 μm. H, as A, but simulations were performed with uniform InsP₃R density throughout the neuron. Location codes for E and H are the same as in A.

Figure 3. A-type K⁺ channels regulated calcium release from ER stores during calcium waves in a three-cylinder neuronal model

A, effect of the A-type conductance in the oblique dendrite on [Ca²⁺]_c during a Ca²⁺ wave. [Ca²⁺]_c traces were recorded at a distance of 8 μm from the branch point with different densities of the A conductance in the oblique dendrite. B–E, area under the curve (AUC) for the [Ca²⁺]_c transients depicted in A (B), full width at half maximum, FWHM (C) and latency-to-peak for these [Ca²⁺]_c transients (D) and AUC for the flux of Ca²⁺ through InsP₃ receptors, (E), in achieving these transients, plotted as functions of A-conductance density, . Plots are shown for different densities of the L-type Ca²⁺ channel, . F and G, time-dependent [Ca²⁺]_c changes (F) and the amplitude (G) of Ca²⁺ wave, computed in the presence of mobile buffers at different affinities (K_mob) to Ca²⁺ binding. Ca²⁺ wave was initiated with 100 μm mobile buffer with the same protocol as in A. H, AUC for plotted as functions of A-conductance density, , when the Ca²⁺ wave was initiated in the presence of 100 μm mobile buffer and with different values of K_mob.

Figure 4. Calcium waves in a morphologically realistic neuronal model

A, [Ca²⁺]_c transients in response to a single backpropagating action potential at various locations in a proximal oblique (Oblique 2 in G), in the absence of A-type K⁺ channels. B, gradient in A-conductance required for normalizing [Ca²⁺]_c transients across various locations in the oblique dendrite under consideration. C, as A, but in the presence of A-type K⁺ channels with a gradient shown in B. D, peak [Ca²⁺]_c at different locations in the oblique 2 in the absence and in the presence of A-type K⁺ channels, quantified from experiments depicted in A and C, respectively. E, [Ca²⁺]_c trace with baseline [InsP₃]_c (= 0.16 μm) at various locations in response to a train of 10 bAPs, separated regularly by 30 ms intervals. F, as E, but with elevated [InsP₃]_c (= 2.25 μm) to model bath application of group I mGluR agonists. Note differences in the peak [Ca²⁺]_c with respect to E. For E and F, distances for trunk locations are radial distances from the soma. For locations on oblique dendrites, distances are path distances from their respective branch points on the trunk. G, shape plot of the model neuron showing peak [Ca²⁺]_c along the neuronal topograph during the Ca²⁺ wave shown in F. Note that [Ca²⁺]_c in basal dendrites is not shown, owing to lack of experimental data on basal dendrites in CA1 pyramidal neurons. H, kymographs showing time-dependent changes in the [Ca²⁺]_c in response to a train of 10 bAPs, separated regularly by 30 ms intervals, under baseline (left) and elevated (right) InsP₃ levels, derived from experiments depicted in E and F, respectively. The ordinate represents the path distance along the somato-dendritic axis (apical dendrites only) and the abscissa represents time. Numbers on the kymograph represent the highest peak value of [Ca²⁺]_c measured across different locations on the somato-dendritic axis. I, as H, but the kymograph shows [Ca²⁺]_c only for the first 500 ms. Note that the scales (presented to the right of each subpanel) are different for the left and the right subpanels. White dashed lines in H and I represent the border between the soma (below the line) and the apical trunk.

Figure 5. In a morphologically realistic model, A-type K⁺ channels altered the amplitude, width and latency of Ca²⁺ waves through regulation of both intrinsic excitability and release of Ca²⁺ from the stores

A and B, [Ca²⁺]_c traces plotted for various A-type K⁺ channel densities (), at representative trunk (A) and proximal oblique (B) locations. C and D, area under the curve (AUC) for total [Ca²⁺]_c plotted as a function of , at representative trunk (C) and proximal oblique (D) locations. E and F, AUC for the Ca²⁺ flux through InsP₃ receptors () plotted as a function of , at representative trunk (E) and proximal oblique (F) locations. G and H, temporal aspects of the Ca²⁺ wave quantified as the wave's full-width at half-maximum (FWHM) and latency to peak, and plotted as functions of , at representative trunk (A) and proximal oblique (B) locations. Trunk: location on the apical trunk 77 μm (radial distance) from the soma; Oblique: location on Oblique 1 (Fig. 4G) 17 μm (path distance) away from the branch point on the trunk. For A–H represents the value of A-type K⁺ channel densities at the soma while the individual compartments had local according to eqn (3) along the neuronal topograph.

Figure 6. Increase in mGluR density induced a saturating leftward shift to a BCM-like synaptic plasticity profile

A, projection of the three-dimensional neuronal reconstruction depicting the location of the synapse where all plasticity experiments were performed. The circle in the middle of Oblique 2 (arrow), located at 148.5 μm away from the trunk branch point represents the synaptic location. B, functional form of the plasticity-regulating function, (eqn (43)), plotted for various concentrations of [Ca²⁺]_c. C–F, evolution of local [InsP₃]_c (C), local [Ca²⁺]_c (D), local Ca²⁺ flux through InsP₃ receptors, (E), and normalized synaptic weight, w (F), when a synapse was stimulated by 900 presynaptic action potentials at 10 Hz, shown for cases where the synapse contained only mGluRs or only NMDARs or both mGluRs and NMDARs. Note that the trace obtained in the presence of only mGluRs and the trace obtained in the presence of both mGluRs and NMDARs are overlapping in C. Insets in C and E show the same plots in C and E, expanded over the first 1 and 5 s of the induction protocol, respectively. G, synaptic plasticity profile across various induction frequencies (900 pulses), shown for various densities of mGluRs in the synaptic compartment.

Figure 7. Interplay between the InsP₃Rs and the A-type K⁺ channels in regulating the modification threshold in a BCM-like synaptic plasticity model

A and B, synaptic plasticity profile across various induction frequencies (900 pulses), shown for various densities of the A-type K⁺ channel () in the synaptic compartment, in the presence (A, density = 1.2 a.u.) and the absence (B) of mGluR. C, percentage change in θ due to mGluR, calculated as 100 × (θ_mGluR – θ_nomGluR)/θ_nomGluR (obtained from experiments shown in A and B), plotted as a function of . The different plots correspond to simulations performed with different values for the NAR, to assess the relative contribution of NMDAR and mGluR to plasticity. D, area under the curve (AUC) of through the 900 pulses protocol plotted as a function of at various induction frequencies employed, for saturating mGluR density (= 1.2 × 10⁻³ a.u.) at 1.5 NAR. AMPAR densities remained the same across these simulations.

Figure 8. Interplay between the InsP₃Rs and the A-type K⁺ channels in regulating synaptic plasticity induced through TBS

A, protocol employed for induction of synaptic plasticity through TBS. Ten bursts are shown, with each burst made of five stimuli separated by 10 ms, and interburst interval set at 200 ms. Synaptic location was the same as depicted in Fig. 6A. B–E, evolution of local [InsP₃]_c (B), local [Ca²⁺]_c (C), local Ca²⁺ flux through InsP₃ receptors, (D), and normalized synaptic weight, w (E), when a synapse was stimulated by TBS, shown for cases where the synapse contained only mGluRs or only NMDARs or both mGluRs and NMDARs. Note that the trace obtained in the presence of only mGluRs and the trace obtained in the presence of both mGluRs and NMDARs are overlapping in B. Insets in B and D show the same plots in B and D, expanded over the first 1 and 5 s of the induction protocol, respectively. F, steady state change in synaptic weight after TBS, shown for various densities of mGluRs in the synaptic compartment. G, Steady-state change in synaptic weight after TBS, plotted as a function of the A-type K⁺ conductance density () for different values of NMDAR:AMPAR ratio (NAR), in the presence and absence of mGluRs. H, percentage change in synaptic weight due to mGluR, calculated as 100 × (Δ%w_mGluR – Δ%w_nomGluR)/Δ%w_nomGluR (obtained from experiments shown in G), plotted as a function of . The different plots correspond to simulations performed with different values for the NAR, to assess the relative contribution of NMDAR and mGluR to plasticity. I, area under the curve (AUC) of through the TBS protocol plotted as a function of , for various values of NAR at saturating concentration of mGluR (= 1.1 × 10⁻³ a.u.). AMPAR densities remained the same across these simulations.