Neuronal model

First Neuron Model McCulloch-Pitts [mccul43]... 

The dynamic behavior of the cyclic enzyme system display catastrophic behavior in response to specific changes in external input. The system can realize a neuronic model capable of storing memory. 

C. Koch and I. Segev, eds.. Methods in Neuronal Modeling. From Synapses to Networks, 2nd ed., MIT Press, Cambridge, MA, 1998. 

F.A. Schanne, J.R. Moskal, R.K. Gupta, Effect of lead on intracellularfree calcium ion concentration in a presynaptic neuronal model 19F-NMR study of NG108-15 cells. Brain Res. 503 (1989) 308-311. 

Vitko I, Chen Y, Arias JM, Shen Y, Wu XR, Perez-Reyes E (2005) Functional characterization and neuronal modeling of the effects of childhood absence epilepsy variants of CACNA1H, a T-type calcium channel. J Neurosci 25 4844-4855. 

Oja E 1982 A simplified neuron model as a principal component analyzer. Journal of Mathematical Biology 15, 267-273. 

In recent years, neuron models have been successfully used they are more stable than traditional climate models. For instance, Pasini et al. (2006) considered an application of the neural network for climate modeling. The study was carried out into the temperature trend on regional and global scales for the last 140 years. It showed that the model based on the neural network reproduces with high accuracy the non-linear effects observed in temperature variations over the northern Atlantic. 

V. Belykh, I. Belykh, and E. Mosekilde Hyperbolic Plykin attractor can exist in neuron models. Int. J. Bifurcation and Chaos 2005,15 3567-3578. 

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. 

In our case, the episode generator is comparably stable, far away from spontaneous episode generation. The subthreshold mechanisms are normally also in a steady state but can be tuned with a disease variable into oscillatory limit cycles with increasing frequency and amplitude. Anyhow, the structure of the equations is the same for the two episodes and the two subthreshold variables and the similarities to the neuronal models immediately become evident from the equations. For a more detailed description see Huber s work [2-4, 7, 25]. 

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. 

As indicated in the introduction we decided to build a computational model of the STN and its surrounding structures. Let us use as a neuron model the leaky integrate and fire (LIF) in which the membrane potential of the neuron is the only variable ... 

Yang CR, Seamans JK, Gorelova N. 1999. Developing a neuronal model for the pathophysiology of schizophrenia based on the nature of electrophysiological actions of dopamine in the prefrontal cortex. Neuropsychopharmacology 21 161-194. 

Vidyasagar TR. 1999. A neuronal model of attentional spotlight Parietal guiding the temporal. Brain Res Brain Res Rev 30 66-76. 

Key words In vitro neuronal models, Specific neuronal and glial endpoints, Regulatory context, Toxicity testing... 

Fig. 4 3D human neuronal model from Lund human mesencephalic (LUHMES) neuronal precursor cells cultured under constant gyratory shaking, at (a) 7 days, (b) 11 days, and (c) 18 days after induction of neuronal differentiation... 

Clearly the solitary neuron model is just an abstraction of much larger circuits in the brain. But such reductionism affords not only a conceptual model for approaching epilepsy but also an experimental model for testing certain hypotheses. The one neuron model appears to be the minimal circuit for cortical forms of epilepsy, but for modelhng subcortical absence epilepsy it appears that a two neuron model is the minimal circuit one excitatory neuron with prominent Ca currents connected to one inhibitory neuron with prominent Ca2+ currents (von Krosigk et al 1993). 

As reviewed here, cannabinoids may lead to opposite effects on the cell sur-vival/death decision. For example, in the case of neural cells, cannabinoids may kill tumour cells and protect their non-transformed counterparts from death (Guzman 2003) (Fig. 1). It is conceivable that different experimental factors may account for this yin-yang action, for example (1) cannabinoid neuroprotection is usually more evident in whole-animal than in cultured-neuron models, which may result from their aforementioned impact on various brain cell types (neurons, astroglia, oligodendroglia, microglia, vascular endothelium) (2) cannabinoids may exert... 

Bodennec J., Pelled D., Riebeling C., Trajkovic S., Futerman A.H., Phosphatidylcholine synthesis is elevated in neuronal models of Gaucher disease due to direct activation of CTP phosphocholine cytidylyltransferase by glucosylceramide, Faseb J 16 (2002) 1814-1816. 

In order to use models of neurons that are biologically plausible, we have first simulated the conductance based models of the PNs and LNs used in Bazhenov et al. [6]. Both neurons were found to be type I neurons and we chose to model them with the theta neuron model [11]. We then fitted the parameters of the theta models so as to match the instantaneous firing frequency vs. applied current curves (see Figure Al). Note however that these instantaneous frequency curves do not take into account a possible frequency adaptation leading to a decrease of the frequency over time. Therefore, the two parameters involved in the adaptation current of the theta models have been fitted independently so that the time responses to applied constant current correspond to the ones obtained with the conductance based model. Figures A2 and A3 clearly indicate a close match between the time responses of the two models. In particular, the frequency adaptation seen in the conductance based model of the LN is similar to the one of the theta model (see Figure A3). The parameters for the fitted theta models are given below. 

W. Gerstner and W.M. Kistler, Spiking neuron models - single neurons, populations, plasticity, Cambridge Univ. Press, (2002). 

The model of globally coupled oscillators is commonly used as a simplest model of neural synchrony. We illustrate this using a computationally efficient neuronal model, proposed by Rulkov [42, 43]. In this model a neuron is described by a 2D map. In spite of its simplicity, this model reproduces most regimes exhibited by the full Hodgkin-Huxley model, but at essentially lower computational costs, thus allowing detailed analysis of the dynamics of large ensembles. The model reads... 

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