Single effective neuron: dendritic coupling effects and stochastic resonance

Abstract

Abstract. We consider a model of a neuron coupled with a surrounding dendritic network subject to Langevin noise and a weak periodic modulation. Through an adiabatic elimination procedure, the single-neuron dynamics are extracted from the coupled stochastic differential equations describing the network of dendrodendritic interactions. Our approach yields a "reduced neuron" model whose dynamics may correspond to neurophysiologically realistic behavior for certain ranges of soma and bath parameters. Cooperative effects (e.g., stochastic resonance) arising from the interplay between the noise and modulation are discussed in detail.

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

“…Such noise-based information maximization is consistent with Linsker's principle of information maximization in neural networks [49], [50]. These findings support the implicit SR conjecture that biological neurons have evolved to computationally exploit their noisy environments [11], [18], [19], [23], [48], [58], [64], [69]. Further support is that these adaptive SR effects still hold for other sigmoidal and nonsigmoidal (Gaussian) neurons as Fig.…”

Towards Simplicity: Noise and Cooperation in the Perfect Integrator

“…It seems reasonable then, that there should exist a form of self-regulatory mechanism such that the internal parameters -12 -of the system (these parameters control, for instance, the height Uo of the potential barrier) can be adjusted in response to the stimulus and noise characteristics. In our previous work [8,9], in fact, we have been lead, in a simple way to the concept of a noisedependent firing threshold. This is important because, for given stimulus and noise, one obtains well-defined histograms for only a small range of U 0 .…”

“…The physics literature is replete with theories and examples of SR with good reviews available in forthcoming articles by Moss [52] and Jung [36] as well as the proceedings of a recent NATO workshop on the subject [53]. From a biological perspective, the recent work on SR in globally coupled arrays of nonlinear switching elements [8,35,54] is particularly significant.…”

“…Such Inter-Spike-Interval Histograms (ISIHs) are ubiquitous in the neurophysiological literature and, as we shall see below, can be simply and elegantly explained by simple models of neurons as bistable dynamic switching devices subject to noise. The results have lead a few bold individuals to speculate on the possible beneficial role of noise (in particular, cooperative stochastic processes such as described in the preceeding paragraph) in the processing of sensory neural information [7][8][9][10][11][44][45][46][47][48]. Other researchers have speculated [40,61,62] that the experimentally observable background noise may be a natural phenomenon rather than a laboratory curiosity.…”

“…11,12) consisted of modelling the sensory neuron as a noisy bistable (describable by a dynamics predicated on a "soft" potential) switching element. Such a model has been derived [8][9][10] from a fully coupled model of a cell body interacting (at the axon hillock), via a weak nonlinear coupling, with a dendritic "bath", the dendrites being represented as quasi-linear elements which, in general, would also be capable of "firing". Of course, the idea of bistability in this context is not new; it dates back to the seminal work of Landahl, McCullough and Pitts [41] -3 -who considered the neuron as a discrete (i.e.…”