Stochastic and coherence resonance in feed-forward-loop neuronal network motifs

The relationships between noise and complex dynamic behaviors of neuronal ensembles are key questions in computational neuroscience, particularly in understanding some basic signal transmission mechanisms of the brain. Here we systemically investigate both the stochastic resonance (SR) and coherence resonance (CR) in the triple-neuron feed-forward-loop (FFL) network motifs by computational modeling. We use the Izhikevich neuron model as well as the chemical coupling to build the FFL motifs, and consider all possible motif types. The simulation results demonstrate that these motifs can exploit noise to enrich its dynamic performance. With a proper choice of noise intensities, both the SR and CR can be exhibited in many types of the FFLs. On the other hand, our results also indicate that the coupling strength serves as a control parameter, which has great impacts on the stochastic dynamics of the FFL motifs. Additionally, biological implications of presented results in the field of neuroscience are outlined.

Figure 1

Connection patterns: (a) the FFL neuronal network motif: neuron 1 drives neuron 2, and both jointly drive neuron 3; (b) simple drive of neuron 3 by neurons 1 and 2 as a comparison of the FFL.

Figure 2

(Color online) Voltage responses of the Izhikevich neuron to the external current $I$: (a) regular spiking (RS) neuron and (b) fast spiking (FS) neuron.

Figure 3

(Color online) An example of the stochastic oscillation in the T1-FFL, with $D=3$ and $g=0.5$. (a) The time series of $v_3$ as well as the periodic forcing signal of neuron 1 with frequency $f_s=10\text{Hz}$ (for better viewing, the amplitude of the signal is ten times higher than that in the model), and (b) the corresponding power spectrum density graph.

Figure 4

(Color online) The SNR versus the noise intensity for different FFL and simple drive types, with the periodic signal frequency $f_s=10\text{Hz}$. (a) FFL $\left(g=0.15\right)$, (b) FFL $\left(g=0.3\right)$, (c) simple drive $\left(g=0.15\right)$, and (d) simple drive $\left(g=0.3\right)$.

Figure 5

(Color online) Time series of neurons 1 and 3 for different coupling strengths. (a) T1-FFL $\left(g=0.15\right)$, (b) T1-FFL $\left(g=0.3\right)$, (c) T1-FFL $\left(g=0.5\right)$, (d) T2-FFL $\left(g=0.5\right)$, and (e) T1-FFL $\left(g=0.8\right)$. $D=1.08$ and $f_s=10\text{Hz}$ in all cases.

Figure 6

(Color online) The maximum of SNR as a function of the coupling strength for both the T1-FFL and T2-FFL motifs.

Figure 7

(Color online) The output SNR versus the frequency of the input signal for different noise intensities. Noise intensities (a) $D=0.35$, (b) $D=1.5$, and (c) $D=5$. $g=0.5$ in all cases.

Figure 8

(Color online) CR in the FFLs and single Izhikevich neuron model. [(a)–(h)] The coherence factor $R$ versus the noise intensity for different coupling strengths. (a) T1-FFL, (b) T2-FFL, (c) T3-FFL, (d) T4-FFL, (e) T5-FFL, (f) T6-FFL, (g) T7-FFL, and (h) T8-FFL. Coupling strengths $g=0.1$ (circle: “○”), $g=0.3$ (square: “◻”), $g=0.5$ (asterisk: “$\ast$”), and $g=0.75$ (triangle-down: “▽”). (i) The coherence factor $R$ versus the noise intensity for single Izhikevich neuron model. Excitatory neuron (diamond: “◇”) and inhibitory neuron (star: “$\star$”).