Robust design of polyrhythmic neural circuits

Abstract

Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.

Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network

“…It is attributed to the occurrence of a stable invariant curve in the proximity of a heteroclinic cycle composed of several saddles representing phase thresholds. In some cases the explicit equations of the phase shift may be introduced so that with a blend of analytical and continuation techniques one can describe the dynamics of such oscillatory networks [1,3]. However, for most of the plausible CPGs the explicit equations for 38002-p1 the phase lags do not exist.…”

Linking dynamics of the inhibitory network to the input structure

“…It is worth noting that similar networks of inhibitory neurons have been extensively studied before, especially in the context of locomotion and CPG dynamics (Golubitsky et al 1998; Collins and bifurcation 1992; Nowotny and Rabinovich 2007; Belykh and Shilnikov 2008; Schwabedal et al 2014; Wojcik et al 2014). In general, networks of identical neurons display coexisting oscillatory rhythms, which are characterized by distinct phase-locking patterns between individual neurons.…”

“…Inhibitory networks have been extensively studied theoretically in the context of rhythmogenesis (Ermentrout 1992; Wang and Rinzel 1992; Golomb et al 1994; Van Vreeswijk et al 1994; Terman et al 1998; Lewis and Rinzel 2003; Belykh and Shilnikov 2008; Schwabedal et al 2014; Wojcik et al 2014) and pattern formation (Ermentrout and Kopell 1994; Rinzel et al 1998; Golomb and Ermentrout 2001; Pinto and Ermentrout 2001) for different network configurations and intrinsic cell properties. The novelty of our study is linking properties of the external stimuli to the inhibitory network dynamics.…”

Dynamic Behavior of Artificial Hodgkin–Huxley Neuron Model Subject to Additive Noise

“…Also, different kinds of noise have distinct influences on some characters of an H-H neuron. Note that the recent work [26]- [28] studies the impact of noise on an H-H neuron model through numerical simulations due to its high dimensionality making any theoretical analysis extremely difficult if not impossible.…”