Potential Mechanisms and Functions of Intermittent Neural Synchronization

Abstract

Neural synchronization is believed to play an important role in different brain functions. Synchrony in cortical and subcortical circuits is frequently variable in time and not perfect. Few long intervals of desynchronized dynamics may be functionally different from many short desynchronized intervals although the average synchrony may be the same. Recent analysis of imperfect synchrony in different neural systems reported one common feature: neural oscillations may go out of synchrony frequently, but primarily for a short time interval. This study explores potential mechanisms and functional advantages of this short desynchronizations dynamics using computational neuroscience techniques. We show that short desynchronizations are exhibited in coupled neurons if their delayed rectifier potassium current has relatively large values of the voltage-dependent activation time-constant. The delayed activation of potassium current is associated with generation of quickly-rising action potential. This "spikiness" is a very general property of neurons. This may explain why very different neural systems exhibit short desynchronization dynamics. We also show how the distribution of desynchronization durations may be independent of the synchronization strength. Finally, we show that short desynchronization dynamics requires weaker synaptic input to reach a pre-set synchrony level. Thus, this dynamics allows for efficient regulation of synchrony and may promote efficient formation of synchronous neural assemblies.

Keywords: delayed-rectifier potassium current; intermittency; neural assemblies; neural oscillations; neural synchrony.

Figure 1

Numerical simulation of a voltage of an isolated neuron (Equations 1–5). Examples of spiking activity (ε = 0.001) (A) and quasi-sinusoidal activity (ε = 0.5) (B).

Figure 2

Diagram of a minimal network of excitatory coupled neurons. We use ε₁ ≠ ε₂ (i.e., neurons have different firing rates) and the coupling strength g_syn is not very strong.

Figure 3

The effect of ε₁ when ε₂ = 1.2ε₁. (A) Mode value of the durations of desynchronization events (black line with black dots) and the corresponding probability to observe the mode value (gray line). The high (close to one) value of probability at mode indicates that the desynchronizations of corresponding duration are strongly prevalent. (B) Synchronization strength index γ. (C) The mean frequency of activities of both neurons. Since ε₂ = 1.2ε₁, neuron 2 has slightly higher frequency than the mean frequency while the neuron 1 has slightly lower frequency than the mean frequency.

Figure 4

The effect of β when ε₁ = ε and ε₂ = 1.2ε. (A) Mode value of the durations of desynchronization events (black line with black dots) and the corresponding probability to observe the mode value (gray line). (B) Synchronization strength index γ. (C) The mean frequency of activities of both neurons.

Figure 5

The effect of v_w1 when ε₁ = ε and ε₂ = 1.2ε. (A) Mode value of the durations of desynchronization events (black line with black dots) and the corresponding probability to observe the mode value (gray line). (B) Synchronization strength index γ. (C) The mean frequency of activities of both neurons.

Figure 6

Changing synchronization durations independently from synchrony strength and firing rate. (A) Mode value of the durations of desynchronization events (black line with black dots) and the corresponding probability to observe the mode value (gray line). (B) Synchronization strength index γ. (C) The mean frequency of activities of both neurons.

Figure 7

Diagram of a minimal network of excitatory coupled neurons receiving common synaptic input. Neurons 1 and 2 have different firing rates. They are mutually coupled through excitatory synapses and receive synaptic input from neuron 3.

Figure 8

The synchrony difference γ^(1C) − γ^(4C) is plotted for different strength of synaptic input g_syn1, normalized synchrony difference ($\frac{{\gamma }^{(1C)}-{\gamma }^{(4C)}}{{\gamma }^{(4C)}}$) is presented at the inserts (γ^(1C) and γ^(4C) represent the synchrony index γ for “cycle 1” (short desynchronizations) and “cycle 4” (long desynchronizations) networks, respectively). Subplots (A–D) are for different values of the firing rate of incoming signal, corresponding to ${\epsilon }_3=\left\{0.5{\epsilon }_1,\frac{{\epsilon }_1+{\epsilon }_2}{2},1.5{\epsilon }_1,2{\epsilon }_1\right\}$ respectively.

Figure 9

Threshold value of synaptic strength g_syn1 to reach synchornized dynamics without desynchronization events for different values of ε₃. Black squares represent the critical value of g_syn1 for short desynchronization (“cycle 1”) network and the gray circles represent the critical value of g_syn1 for long desynchronization (“cycle 4”) network.