Models that contain the Modeling Application : Mathematica (Home Page)

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    Models   Description
1.  CA1 pyramidal neuron: depolarization block (Bianchi et al. 2012)
NEURON files from the paper: On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons by D.Bianchi, A. Marasco, A.Limongiello, C.Marchetti, H.Marie,B.Tirozzi, M.Migliore (2012). J Comput. Neurosci. In press. DOI: 10.1007/s10827-012-0383-y. Experimental findings shown that under sustained input current of increasing strength neurons eventually stop firing, entering a depolarization block. We analyze the spiking dynamics of CA1 pyramidal neuron models using the same set of ionic currents on both an accurate morphological reconstruction and on its reduction to a single-compartment. The results show the specic ion channel properties and kinetics that are needed to reproduce the experimental findings, and how their interplay can drastically modulate the neuronal dynamics and the input current range leading to depolarization block.
2.  Circadian clock model based on protein sequestration (simple version) (Kim & Forger 2012)
"… To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. …"
3.  Circadian clock model in mammals (detailed version) (Kim & Forger 2012)
"… To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. …"
4.  Circadian clock model in mammals (PK/PD model) (Kim & Forger 2013)
A systems pharmacology model of the mammalian circadian clock including PF-670462 (CK1d/e inhibitor).
5.  Minimal model of interictal and ictal discharges “Epileptor-2” (Chizhov et al 2018)
"Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. ..."
6.  Synchronized oscillations of clock gene expression in the choroid plexus (Myung et al 2018)
Our model simulates synchronized rhythms in the clock gene expression found in the choroid plexus. These synchronized oscillations, primarily mediated by gap junctions, showed interesting relationships between their amplitude, oscillation frequency, and coupling strength (gap junction density) in our experimental data. The model is based on coupled Poincaré oscillators and replicates this phenomenon via a non-zero "twist" in each cell.
7.  Thalamic neuron, zebra finch DLM: Integration of pallidal and cortical inputs (Goldberg et al. 2012)
This is a single-compartment model of a zebra finch thalamic relay neuron from nucleus DLM. It is used to explore the interaction between cortex-like glutamatergic input and pallidum-like GABAergic input as they control the spiking output of these neurons.

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