Calcium regulation of HCN channels supports persistent activity in a multiscale model of neocortex

Abstract

Neuronal persistent activity has been primarily assessed in terms of electrical mechanisms, without attention to the complex array of molecular events that also control cell excitability. We developed a multiscale neocortical model proceeding from the molecular to the network level to assess the contributions of calcium (Ca(2+)) regulation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels in providing additional and complementary support of continuing activation in the network. The network contained 776 compartmental neurons arranged in the cortical layers, connected using synapses containing AMPA/NMDA/GABAA/GABAB receptors. Metabotropic glutamate receptors (mGluR) produced inositol triphosphate (IP3) which caused the release of Ca(2+) from endoplasmic reticulum (ER) stores, with reuptake by sarco/ER Ca(2+)-ATP-ase pumps (SERCA), and influence on HCN channels. Stimulus-induced depolarization led to Ca(2+) influx via NMDA and voltage-gated Ca(2+) channels (VGCCs). After a delay, mGluR activation led to ER Ca(2+) release via IP3 receptors. These factors increased HCN channel conductance and produced firing lasting for ∼1min. The model displayed inter-scale synergies among synaptic weights, excitation/inhibition balance, firing rates, membrane depolarization, Ca(2+) levels, regulation of HCN channels, and induction of persistent activity. The interaction between inhibition and Ca(2+) at the HCN channel nexus determined a limited range of inhibition strengths for which intracellular Ca(2+) could prepare population-specific persistent activity. Interactions between metabotropic and ionotropic inputs to the neuron demonstrated how multiple pathways could contribute in a complementary manner to persistent activity. Such redundancy and complementarity via multiple pathways is a critical feature of biological systems. Mediation of activation at different time scales, and through different pathways, would be expected to protect against disruption, in this case providing stability for persistent activity.

Keywords: I(h); computer simulation; hyperpolarization-activated cyclic nucleotide-gated (HCN) channel; multiscale modeling; neocortex; persistent activity.

Figure 1. Model schematics

(A) Schematic of neocortical network architecture. Red rectangles represent populations of 5-compartment excitatory cells (largest rectangle represents soma, 3 apical-dendrite compartments point upward, basal dendrite compartment points downward); green circles represent fast-spiking interneurons; blue ellipses represent low-threshold firing interneurons. Lines (with arrows) indicate connections between the populations. E cells synapse with AMPAR/NMDARs; I cells synapse with GABA_AR / GABA_BRs. Filled circles represent GABA_AR / GABA_BRs. Open circles and rectangles represent AMPAR/NMDARs. (B) Schematic of chemical signaling in pyramidal cells showing fluxes (black arrows) and second- (and third- etc) messenger modulation (red back-beginning arrows). We distinguish membrane-associated ionotropic and metabotropic receptors and ion channels involved in reaction schemes in red (in reality, it is likely that almost every membrane-bound protein is modulated). External events are represented by yellow lightning bolts – there is no extracellular diffusion; the only extracellular reaction is glutamate binding, unbinding and degradation on mGluR1 after an event. Ca²⁺ is shown redundantly in blue – note that there is only one Ca²⁺ pool for extracellular, 1 pool for cytoplasmic, and 1 pool for ER. (PLC: phospholipase C, DAg: diacyl-glycerol, cAMP: cyclic adenosine monophosphate; PIP₂: phosphatidylinositol 4,5-bisphosphate).

Figure 2. Simulation of a single neuron with high (blue; 1 μm) and low (red; 300 μm) spatial resolution shows similar calcium concentrations

Calcium concentration is displayed as a function of position along the apical dendrite at four different times in the simulation (time from top to bottom). Excitatory stimulus at 10 s admits Ca²⁺ into the cytosol.

Figure 3. Pyramidal cell HCN channel activation

(a) Steady-state HCN channel activation as a function of Ca²⁺ and V_memb. Vertical lines are levels by color in (b). (b) Ih_m voltage-dependence shifts right- and upward with increasing Ca²⁺. red: baseline at 100 nM; green: 2 μM; blue: 12 μM. Maximum steady-state activation is 2 because the second open state has twice the conductance of the first open state. At resting Ca²⁺ maximum steady state activation is 1.

Figure 4. Isolated L5 pyramidal neuron model demonstrates persistent increase in firing after stimulation to AMPAR/NMDAR/mGLUR via a – h sequence of coupled electrical-molecular-electrical activations

(soma levels in blue; apical dendrite levels in red, except in a) (a) Synaptic currents in apical dendrite (blue: GABA_AR; red: AMPAR; green: NMDAR) (b) produces cytosolic calcium concentration increase due to calcium influx via VGCC and NMDAR, (c) while also increasing IP₃ via mGluR-activated cascade, (d) which together with Ca²⁺ activates IP₃R causing efflux of ER Ca²⁺. (e) cAMP is augmented by higher Ca²⁺ (f) persistently increasing normalized HCN conductance (g_h) (g) persistently increasing I_h. (soma values out of range due to lower HCN density) (h) resulting in high rate of firing.

Figure 5. Network persistent activity after stimulating 50% of E-cells

(a) Raster plot of spike times (red: PYR, blue: LTS, green: FS cells) (b) Multiunit activity (MUA; thick: 100 ms bin; thin: 10 ms bin) for stimulated E neurons (light-blue), non-stimulated E neurons (purple), interneurons (gray). (Stimulation added to background activation between black lines: 180× weight 500 Hz Poisson process.)

Figure 6. Stimulation produces both Ca²⁺ influx and release from intracellular stores

Stimulated E5 cell averages (light-blue) vs. non-stimulated E5 cell averages (purple). (a) Transient cytosolic Ca²⁺ rise. (b) ER calcium depletion (non-stim value out of range). (c) Buffered Ca²⁺ increases in stimulated. Decrease in non-stimulated due to reduced influx with hyperpolarization. (d) cAMP. (e) Normalized HCN conductance (g_h).

Figure 7. Targeted stimulation of individual layers produces localized persistent activity

Activation duration of L5 cell with L5 input ~30-40 s, considerably less than the ~60 s activation duration seen in isolated L5 cell. (Layer simulation locations indicated at top of each column. Layer activity by color: E2 – red; E5 – green; E6 – black; inhibitory LTS cells in L5 – gray; within-layer non-stimulated cells – purple; stimulated cells all layers – light-blue in right column.) (a): Baseline network shows no interlaminar excitatory spread for any single layer stimulation. Layer 2/3 stimulation produces spread to L5 inhibitory cells producing reduction in firing in L5. (b): Augmented excitatory connectivity within the network (no change in strength of stimulation or background drive) produces increased durations (except paradoxical decrease with L5 stimulation) and spread of excitation from L2/3 to L5. With all-layer stimulation (right column) some spread of excitation to non-stimulated cells is also seen (purple line). (MUAs with 1000 ms bins; 75 neurons stimulated in each layer. Vertical dotted lines at times where rates drop < 10 Hz.)

Figure 8. Longer-duration weak stimulation produces firing-rate distinctions

Stimuli were 0.1× baseline strength used in other figures. (a) MUAs in response to 1 s stimulus. (b) MUAs in response to 20 s stimulus. (c) FRD in response to 1–20 s stimulus durations (red dots from (a), (b)) (50% E cells all layers; MUAs with 1000 ms bins of stimulated: light-blue; non-stimulated: purple)

Figure 9. Network ensemble dynamics show distinct states at baseline and during expression of persistent activity

(a) Persistent activity lasts >60 s after each identical AMPAR/NMDAR/mGLUR stimulation. Vertical lines represent the stimulus times (60, 185 s; same population of 50% of E neurons across layers). MUA created with 1 s bins. Purple (light-blue) represent stimulated (non-stimulated) E neurons; gray MUA of interneurons. (b) Firing-rate vectors (1 s intervals) transition at onset/offset of persistent activity. Color at time= x, neuron= y represents the firing rate of neuron y during the 1 s interval at time x. Neurons arranged in layers from top (L2/3) to bottom (L6). (c) Pairwise Pearson correlations between all firing rate vectors from (b). Color at times t₁ = x, t₂ = y indicates Pearson correlation between firing-rate vectors at those times.

Figure 10. Modulating E→I (15 levels) and I→E (8 levels) synaptic weights shapes firing rates and intracellular molecular activations

(a) Interneuron and (b) excitatory neuron firing rates after stimulation. (c) Peak cytosolic calcium (mM) in stimulated excitatory cells. (d) cAMP and (e) g_h of stimulated E cells. (f) Stimulated to non-stimulated g_h ratio. (g) FRD (firing-rate distinction). (h) FRD as a function of network inhibition estimated by E→ I×I→ E (16 s simulations; color indicates average ratio of g_h in stimulated P1 vs non-stimulated P2 populations).

Figure 11. Persistent activity can be induced via either AMPAR/NMDAR (external stores) or mGLUR (internal store) activation

AMPAR/NMDAR and mGLUR stimulus strength were each varied independently from 0-3× baseline (n = 31), while holding the other stimulus strength constant at 1× baseline. (a) Average cytosolic calcium in the 5 s after stimulus as a function of stimulus strength of AMPAR/NMDAR (circles) and mGLUR (triangles). (b) Ratio of stimulated to non-stimulated population firing rates (FRD) as a function of stimulus strength of AMPAR/NMDAR (circles) and mGLUR (triangles).

Figure 12. Firing-rate distinction depends on both external (VGCC) and internal (ER) calcium stores, determined respectively by voltage-gated calcium channels (VGCC) density and ER [Ca²⁺]

(a) N = 336 21 s simulations were run varying the density of VGCCs (x-axis) from 0–0.015 nS/cm² (n = 16 levels), and the concentration of calcium in the ER (y-axis) from 0–2.8 mM (n = 21 levels). (b–d) Differences in MUA (light blue: stimulated; purple: non-stimulated; bin size 100 ms) and FRD; examples taken from four corners of (a). (b) High internal stores (upper left of Fig. 12): Absence of VGCCs (0.0) with high ER calcium concentration (2.8 mM) allows for high FRD (26.48); (c) High internal and external stores (upper right of Fig. 12): High density of VGCCs (0.015 nS/cm²) with high ER calcium (2.8 mM) produces moderate FRD (4.48); (d) No Ca²⁺ stores (lower left of Fig. 12): Absence of VGCCs with zero initial ER calcium produces low FRD (0.97); (e) High external stores (lower right of Fig. 12): High density of VGCCs (0.015 nS/cm²) with zero initial ER calcium produces moderate FRD (2.35).

Figure 13. Slowing calcium extrusion pump allows retention of Ca²⁺ and increases firing-rate distinction (FRD)

(a) Average calcium concentration (left y-axis) averaged over 5 s post-stimulus. for stimulated (light-blue) and non-stimulated (purple) populations. Black points (right y-axis) show ratio. (b) Firing-rate distinction (FRD) as a function of pump speed. (n = 40)

Figure 14. Ca²⁺ buffering alters free Ca²⁺ availability for modulation of I_h

Forward rate (FRate) of binding (x-axis) and buffer concentration (y-axis) varied. (a) Cytosolic calcium transient in response to stimulus. (b) HCN activation (g_h) in response to stimulus. (c) Firing-rate distinction: average ratio of firing rate of stimulated population to non-stimulated population during 5 s interval after stimulus. (n = 16 × 16)