Variability of bursting patterns in a neuron model in the presence of noise

Abstract

Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent, and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped windows.

Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells

“…7(c1)]. This is similar to neuronal bursting models perturbed by noise [36]. The variability of the number of spikes in a burst is reflected in a broad peak at low frequency, corresponding to the bursting period and its higher harmonics.…”

“…A zoom of the bifurcation diagram in Fig. 4(b) reveals that each subsequent spike adding is accompanied by chaotic bursting within a narrow parameter window, in a manner similar to neuronal models [30,31,34–36]. Near the terminal point of the spike adding cascade the model generates unpredictably long bursting trains with chaotically alternating numbers of spikes [Fig.…”

The effect of morphology upon electrophysiological responses of retinal ganglion cells: simulation results

“…Also, it was shown that the noise in the dendrites has a large effect on the spike precision (van Rossum et al 2003). Also, the bursting patterns vary substantially in the presence of noise (Channell et al 2009). Our model can be extended to explore underlying mechanisms of these phenomena.…”

Robust design of polyrhythmic neural circuits

“…Phase reduction, for example, is not applicable in the analysis of stability of burster networks that are strongly coupled. Conversely, random perturbations can effectively elucidate the dynamical stability of such systems that otherwise evade standard analysis methods [36]. Such systems also include those near bifurcations and those that are singularly perturbed [37,38].…”