Asynchronous response of coupled pacemaker neurons

We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock spike-to-spike for strong mutual coupling. But the shared input can desynchronize the locked spike-pairs by selectively eliminating the lagging spike or modulating its timing with respect to the leading spike depending on their separation time window. Such loss of synchrony is also found in a large network of sparsely coupled heterogeneous spiking neurons receiving shared input.

💡 Research Summary

In this paper the authors investigate how shared inhibitory synaptic input can disrupt the synchrony of two conductance‑based pacemaker neurons that are otherwise phase‑locked through strong mutual coupling. Each neuron is modeled with Hodgkin‑Huxley type ionic currents (Na⁺, K⁺, leak, etc.) and receives a constant bias current that sets its intrinsic firing frequency. The two cells differ slightly in this intrinsic frequency, mimicking heterogeneity that is common in biological pacemaker populations.

The neurons are coupled either excitatorily (E→E) or inhibitorily (I→I) via a synaptic conductance g_syn with a fixed delay τ_syn. When g_syn exceeds a critical value, the pair settles into a stable 1:1 phase‑locked state: the leading neuron fires first, and the lagging neuron fires after a fixed interval Δt that depends on the coupling strength and delay. In this regime the spike times of the two cells are highly correlated, and the network behaves as a single rhythmic unit.

To probe the robustness of this lock, the authors introduce a third element: a shared inhibitory Poisson train that projects simultaneously onto both neurons. Each inhibitory event produces a transient increase in a conductance g_inh that hyperpolarizes the target cell for a brief window. By varying the mean rate λ of the Poisson process and the amplitude of g_inh, the authors explore a wide range of input conditions.

Two distinct desynchronizing mechanisms emerge. First, if an inhibitory event arrives during the interval between the leading spike and the lagging spike (i.e., before the lagging neuron reaches threshold), it can suppress the lagging spike entirely. This “spike deletion” effectively breaks the pair, leaving only the leading spike to propagate. The probability of deletion rises sharply with both λ and g_inh, and it dominates when the inhibitory conductance is strong. Second, when an inhibitory event arrives close to the expected time of the lagging spike, it does not necessarily abolish the spike but shifts its timing forward or backward. This “phase modulation” widens the distribution of Δt, reducing the pairwise correlation without eliminating spikes. The net effect is a gradual loss of synchrony that can be tuned continuously by the strength and timing of the shared inhibition.

Importantly, these phenomena are observed for both excitatory and inhibitory mutual coupling. In excitatory coupling the leading neuron normally pulls the follower forward, but shared inhibition can counteract this pull. In inhibitory coupling the two cells already tend to fire out of phase; shared inhibition can either amplify or diminish that phase offset, again depending on the timing of the inhibitory events.

To test whether the same principles apply to larger, more realistic circuits, the authors simulate a network of several hundred heterogeneous pacemaker neurons with sparse random connections. The network includes a mixture of excitatory and inhibitory synapses, and each neuron retains a distinct intrinsic frequency. When a shared inhibitory Poisson input is applied to the entire population, the global synchrony index (average pairwise correlation) drops dramatically, and the coefficient of variation of inter‑spike intervals increases. This demonstrates that the desynchronizing impact of shared inhibition scales from a dyad to a population level.

The authors discuss the physiological relevance of their findings. Pacemaker neurons underlie many rhythmic processes such as cardiac pacing, respiratory rhythm generation, and low‑frequency cortical oscillations. In vivo, these cells are exposed to common modulatory signals—e.g., neuromodulators, global inhibitory bursts, or extracellular field effects—that can be modeled as shared inhibitory input. The present work suggests that such common inputs can serve as a flexible control knob, allowing a nervous system to switch between tightly synchronized rhythms (useful for efficient signal transmission) and more desynchronized, flexible patterns (useful for adapting to changing demands or preventing pathological entrainment).

In summary, the paper shows that (1) strong mutual coupling can lock two pacemaker neurons into a precise spike‑to‑spike relationship, (2) a shared inhibitory Poisson drive can break this lock either by deleting the lagging spike or by jittering its timing, (3) these mechanisms persist in large, sparsely connected heterogeneous networks, and (4) the results provide a mechanistic framework for understanding how common inhibitory signals regulate synchrony in physiological rhythm‑generating circuits and may contribute to pathological desynchronization observed in disorders such as arrhythmia or Parkinsonian tremor.