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Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons
Mahmut Ozer, Matjaz Perc, Muhammet Uzuntarla
TL;DR
The paper asks how sodium and potassium channel blockage affects collective spiking regularity across small-world networks and cell sizes. Using stochastic Hodgkin–Huxley neurons, it finds that tuning shortcut fraction and cell size can resonantly enhance regularity, with the pattern depending on channel blockage.
Problem
The paper examines how channel blockage affects collective spiking regularity in small-world networks, extending prior work on single neurons and coupled arrays.
Source: Introduction. – · pp. 1–2Method
The authors model stochastic Hodgkin–Huxley neurons on Newman–Watts networks while varying shortcut fraction, cell size, and unblocked sodium and potassium channel fractions.
Source: Introduction. – · p. 2, Mathematical model and setup. – · p. 2Results
At p ≈0.15, CV is minimized for many channel-blocking conditions, while optimal cell sizes are around S = 2–4 µm²; the resonant p dependence vanishes for xK ≤0.5.
Source: Results and discussion. – · pp. 3–4, Summary. – · p. 6Takeaways & Limitations
Spiking regularity can be resonantly enhanced by tuning network shortcut fraction and intrinsic noise, with the strongest improvement at high xNa and low xK.
Source: Summary. – · p. 6
Abstract
from arXiv · showhide
We investigate the regularity of spontaneous spiking activity on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise and fraction of blocked voltage-gated sodium and potassium ion channels embedded in neuronal membranes. We show that there exists an optimal fraction of shortcut links between physically distant neurons, as well as an optimal intensity of intrinsic noise, which warrant an optimally ordered spontaneous spiking activity. This doubly coherence resonance-like phenomenon depends significantly, and can be controlled via the fraction of closed sodium and potassium ion channels, whereby the impacts can be understood via the analysis of the firing rate function as well as the deterministic system dynamics. Potential biological implications of our findings for information propagation across neural networks are also discussed.
Introduction. –
The introduction connects finite-channel noise to spontaneous neuronal activity and motivates studying channel blockage on small-world networks. The paper extends earlier channel-blocking studies to examine collective spiking regularity across network structure and cell size.
Introduction. –
- Near spike threshold, fluctuations from only a few open channels can trigger transitions between firing and non-firing states.Such transitions have been linked to missing spikes, subthreshold membrane voltage, and spontaneous spikes.Source: Introduction. – · p. 1
- Blocking sodium or potassium channels can either increase or decrease spontaneous-spike regularity in single stochastic Hodgkin–Huxley neurons.In coupled-neuron arrays, channel blockage can also enhance or reduce collective regularity depending on cell size.Source: Introduction. – · pp. 1–2
- Small-world networks combine clustering with long-range links and have been used to study neuronal circuitry and complex activity patterns.They have been proposed as a topology supporting both local and distributed information processing.Source: Introduction. – · p. 2
- This study examines how sodium and potassium channel blockage affects collective spiking regularity across small-world network structure and cell size.The stated aim is to investigate these effects under conditions intended to more closely mimic actual conditions.Source: Introduction. – · p. 2
Mathematical model and setup. –
The study models coupled Hodgkin–Huxley neurons with stochastic channel gating and variable fractions of unblocked sodium and potassium channels. It varies network shortcuts and cell size, then quantifies collective spiking regularity from the mean membrane potential.
Mathematical model and setup. –
- The model uses coupled Hodgkin–Huxley neurons, with membrane voltage shaped by sodium, potassium, leakage, and inter-neuron coupling terms.The leakage conductance is fixed, while sodium and potassium conductances vary dynamically.Source: Mathematical model and setup. – · p. 2
- The factors xNa and xK represent the fractions of sodium and potassium channels that remain unblocked, respectively.They scale the channel conductances and are confined to the unit interval.Source: Mathematical model and setup. – · p. 2
- Finite channel populations are modeled with stochastic gating dynamics, and cell size sets intrinsic noise through the number of sodium and potassium channels.As cell size and channel counts increase, stochastic effects become negligible and the model approaches the deterministic description.Source: Mathematical model and setup. – · p. 2
- The network starts as a ring of N = 60 identical neurons with k = 2 neighbors, then gains M randomly placed, undirected links under the Newman–Watts construction.The shortcut fraction is related to the number of added links by p = 2M/[N(N −1)].Source: Mathematical model and setup. – · pp. 2–3, Figure 1 · p. 3
- Collective regularity is measured by the coefficient of variation of inter-spike intervals in the mean membrane potential.Network spikes are upward crossings of Vavg through 0 mV; lower CV indicates more ordered spike trains, and CV vanishes for a deterministic signal.Source: Mathematical model and setup. – · p. 3
Results and discussion. –
Spiking regularity depends on shortcut density, channel block, intrinsic noise, and coupling: the results identify an optimal network structure and cell-size range, with firing-rate and deterministic-dynamics analyses clarifying the patterns.
Results and discussion. –
- CV has a minimum near p≈0.15 for both channel-block types; for xK≤0.5, the minimum shifts to slightly lower p.The minimum persists across the scaling factors considered for xNa and for xK>0.5.Source: Figure 2 · p. 3, Results and discussion. – · p. 3
- At fixed cell size, fewer working sodium channels reduce regularity, whereas fewer working potassium channels increase it; for xNa>0.9, regularity is high across xK values at p≈0.15.The reported regularity for xNa>0.9 is very high compared with at the same cell size and scaling factors.Source: Results and discussion. – · pp. 3–4
- Fr peaks near p≈0.15 under sodium block; under potassium block, its peak shifts to lower p as xK falls below 0.95, and higher Fr accompanies lower CV.The authors relate this pattern to the refractory period: as firing frequency rises, the mean ISI decreases and CV falls.Source: Figure 3 · p. 4, Results and discussion. – · p. 4
- For xK=0.5 and 0.25, deterministic-network firing rates are 51Hz and 61Hz, respectively; at small p, stochastic-network rates exceed those values, but this advantage vanishes as p→0 or p→1.As p→1, stochastic firing rates approach the deterministic values, and connectivity has negligible impact on firing rate or CV for xK≤0.5.Source: Results and discussion. – · p. 4
- At optimal p, best regularity occurs around S=2–4µm² for all xNa and xK>0.5; for xK≤0.5, increasing S beyond about 2µm² brings little improvement.Regularity in the 2–4µm² range varies more substantially with xNa than with xK.Source: Results and discussion. – · pp. 4–5, Figure 4 · p. 5
- As ε increases, the p yielding minimum CV decreases while the minimum remains unchanged; regularity is very low near p→0 and p→1 regardless of ε.The resonance-like CV pattern across coupling strengths was reported for both xNa=0.95 and xK=0.85.Source: Figure 5 · p. 5, Results and discussion. – · pp. 5–6
Summary. –
Spiking regularity is resonantly enhanced by tuning network shortcut fraction p and cell size S, with the strongest improvement at high xNa and low xK. The resonances depend on channel block and coupling strength, and are supported by firing-rate and deterministic-dynamics analyses.
Summary. –
- Spontaneous spiking regularity is resonantly enhanced by fine-tuning both p and S.The resonant dependence on p persists across coupling strengths, although the minima shift.Source: Summary. – · p. 6
- The regularity improvement is maximal at high xNa and low xK.With potassium blockage xK ≤0.5, the resonant dependence on p vanishes and the first minimum CV occurs at somewhat lower p.Source: Summary. – · p. 6
- Cell sizes S = 2−4µm2 provide an optimal intensity of internal noise for maximal spiking regularity on small-world networks.Source: Summary. – · p. 6
- Firing-rate analysis and deterministic model dynamics corroborate the resonant-like dependencies associated with sodium and potassium channel block.Source: Summary. – · p. 6
- The study suggests synaptic noise may also affect the findings because it can be approximated by non-zero mean Gaussian white noise.Source: Summary. – · p. 6
- The proposed optimal cell sizes may correspond to spatially restricted dendritic or axonal regions called hot spots.The passage also notes these sizes may correspond to spatially restricted regions in dendritic or axonal trees.Source: Summary. – · p. 6