Oscillation subthreshold

To simulate the disease episodes and subthreshold oscillations we again refer to our neuronal modeling approaches (Fig. 7.2b). The algorithms have been implemented with a simple but physiologically plausible approach, i.e. with two nonlinear feedback loops, one positive and one negative. Depending on the parameter setting, such a system can attain stable dynamics but also can develop oscillations. 

The feedback variables go with first order time delays r i towards their final values flioo- The variables of the subthreshold oscillations activate much slower than those for episode generation. In both subsystems, the positive feedback is faster than the negative feedback ... 

Fig. 7.3 Deterministic (a) and noisy (b) computer simulations of the time course of affective disorders showing the intervals between successive disease episodes (interval duration) as a function of a disease variable S and examples of episode generation from different disease states (figure modified after [2]). In deterministic simulations (a), there is a progression from steady state (S = 18) to subthreshold oscillations (S = 22) with immediate onset of periodic event generation at a certain value of S (slightly below S = 60). With further increase of S, the intervals between successive episodes are continuously...

In deterministic simulations, these subthreshold oscillations may cover only a narrow regime. However, with the addition of noise a broad regime of functionally most interesting patterns can develop exactly in and around the area of subthreshold oscillations. Noise can introduce a random mixture of subthreshold oscillations... 

Bulsara, A., and Gammeitoni, L Tuning in to noise. Phys. Today 1996,1996 39-45. Longtin, A., and Hinzer, K. Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors. Neural Comput 1996,8 215-255. Mosekilde, E., Sosnovtseva, O.V., Postnov, D., Braun, H.A., and Huber, M.T. Noise-activated and noise-induced rhythms in neural systems. Nonlin Stud 2004,11 449-467. 

Huber, M.T., and Braun, H.A. Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation. Phys. Rev. E 2006 73 04129. 

Gutfreund, Y., Yarom, Y., and Segev, I. Subthreshold oscillations and resonant frequency in guinea-pig cortical neurons physiology and modelling. J Physiol 1995, 483(3) 621-640. 

Lampl, I., and Yarom, Y. Subthreshold oscillations of the membrane potential a functional synchronizing and timing device./ Neurophysiol 1993, 70 2181-2186. 

Klink, R., and Alonso, A. Ionic mechanisms for the subthreshold oscillations and differential electroresponsiveness of medial entorhinal cortex layer 11 neurons./ Neurophysiol 1993, 70 144-157. 

Fig. 1.22. Period doubling and Hopf bifurcations. Top enlarged part at low coupling strength K and noise intensity Tioc Bottom Global view of selected bifurcations. AH Andronov-Hopf bifurcation In, onset of regime with n subthreshold oscillations between two spikes h onset of non-intermittent spiking). Parameters e = 0.01, a = 1.05. [41]...

M. Zaks, X. Sailer, L. Schimansky-Geier, and A. Neiman. Noise induced complexity From subthreshold oscillations to spiking in coupled excitable systems. CHAOS, 15 026117, 2005. 

Amir, R., M. Michaelis, and M. Devor (2002). Burst discharge in primary sensory neurons triggered by subthreshold oscillations, maintained by depolarizing afterpotentials. /. Neurosci. 22, 1187-1198. 

---