Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons

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.

💡 Research Summary

This paper investigates how the regularity of spontaneous spiking activity can be controlled in a biologically realistic neuronal network composed of Hodgkin‑Huxley (HH) neurons arranged on a Newman‑Watts small‑world topology. The authors introduce two key sources of variability: intrinsic channel noise, which arises from the stochastic opening and closing of a finite number of voltage‑gated sodium (Na⁺) and potassium (K⁺) channels, and the deliberate blocking (partial inactivation) of these channels, parameterized by the fractions ρ_Na and ρ_K. By systematically varying the shortcut‑link probability p (which determines the density of long‑range connections), the noise intensity D (controlled through the total number of channels per neuron), and the blocking fractions, the study maps out the conditions under which the network exhibits the most regular (lowest coefficient of variation, CV) spontaneous spiking.

Methodologically, each HH neuron is modeled with stochastic gating variables whose transition rates are scaled by the effective number of channels N. Reducing N increases the amplitude of intrinsic noise, allowing the authors to explore a continuum from deterministic dynamics (N → ∞) to highly noisy regimes. The Newman‑Watts construction starts from a one‑dimensional lattice and adds random shortcuts with probability p; this yields a small‑world network that preserves local connectivity while introducing long‑range shortcuts. The blocking of Na⁺ channels raises the activation threshold, whereas K⁺ channel blocking slows repolarization, each altering the firing rate (FR) and inter‑spike interval (ISI) statistics in distinct ways.

Simulation results reveal a double‑coherence‑resonance phenomenon. First, for a given noise level, there exists an optimal shortcut probability p* at which the CV of the ISI distribution reaches a minimum. This reflects the classic small‑world effect: a moderate number of long‑range links enhances synchrony without causing the network to become overly rigid. Second, for a fixed p, the CV also displays a minimum at an intermediate noise intensity D*, confirming the well‑known coherence resonance observed in single stochastic HH neurons. Crucially, the positions and depths of these minima are strongly modulated by the channel‑blocking fractions. Increasing ρ_Na reduces the overall firing rate and, paradoxically, can lower the CV because spikes become rarer and more evenly spaced. In contrast, raising ρ_K tends to increase the CV by prolonging action‑potential duration and promoting burst‑like activity. When both fractions are varied simultaneously, the system can be tuned to a regime where the optimal p* and D* coincide, yielding the most ordered spontaneous spiking.

To interpret these findings, the authors perform a deterministic bifurcation analysis of the HH equations with effective conductances scaled by (1‑ρ_Na) and (1‑ρ_K). They show that Na⁺ channel reduction stabilizes the resting fixed point, suppressing oscillations, while K⁺ channel reduction destabilizes the fixed point and can generate a stable limit cycle. The stochastic system, therefore, operates near a noise‑induced transition between a quiescent state and a self‑sustained oscillatory state. In this “edge‑of‑chaos” region, modest noise efficiently triggers spikes that are subsequently regularized by the network’s small‑world connectivity.

The discussion connects these theoretical insights to physiological and pharmacological contexts. Partial Na⁺ channel block mimics the action of local anesthetics, whereas K⁺ channel block resembles the effect of certain antiepileptic drugs. Both interventions can shift neuronal excitability and, according to the model, either improve or degrade the temporal precision of spontaneous firing depending on the underlying network architecture and intrinsic noise level. The authors suggest that the brain may exploit a similar balance: a modest amount of structural randomness (shortcuts) combined with physiological levels of channel noise to maintain reliable spontaneous activity, which is essential for background information processing and the readiness of neural circuits.

In conclusion, the study demonstrates that three intertwined factors—network topology (p), intrinsic channel noise (D), and selective ion‑channel blocking (ρ_Na, ρ_K)—jointly determine the regularity of spontaneous spiking in small‑world neuronal networks. The identification of a double‑coherence‑resonance regime provides a mechanistic framework for understanding how pharmacological modulation of ion channels could be used to fine‑tune neural synchrony and information propagation. Future work is proposed to extend the model to higher‑dimensional realistic brain connectomes, incorporate synaptic plasticity, and explore the impact of external stimuli on the identified optimal regimes.