Modelling the Membrane Behaviour of LDT Neurons
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model contains partial differentials and as such can not currently be solved by existing CellML tools.
Model Structure
The laterodorsal tegmental nucleus (LDT) is located at the junction of the pons and the midbrain - regions of the brain. The neurons from this area are thought to play an essential role in the generation of the electroencephalographic (EEG)-desyncronised states of waking and rapid eye movement (REM) sleep. The neurons are heterogeneous, displaying different firing rates in waking, slow-wave (SW), and REM sleep. Different membrane properties, cell morphology and synaptic input signals are thought to underlie this firing heterogeneity.
In order to evaluate the relative importance of these factors, Surkis et al. analysed the cable properties of the principal LDT neurons. (the complete original paper reference is cited below). Data from these experiments were then used to produce a biologically realistic mathematical model of these cells. Their study involved developing two cell models, one in which the membrane was assumed to be passive, and one in which it was assumed that voltage-dependent conductances were contributing to cell behaviour. They found that only the active membrane model could adequately describe the behaviour of the LDT cells, and it is this model which is described below.
Recovery of Cable Properties Through Active and Passive Modeling of Subthreshold Membrane Responses From Laterodorsal Tegmental Neurons, A. Surkis, C.S. Peskin, D. Tranchina, and C.S. Leonard, 1998,
Journal of Neurophysiology
, 80, 2593-2607. (Full text and PDF versions of the article are available for Journal Members on the Journal of Neurophysiology website.) PubMed ID: 9819266
cell schematic for the model
Schematic diagram of the voltage-dependent conductances across the plasma membrane of a LDT neuron. IA
represents a transient subthreshold K+ current. IH
is a cation current that has a depolarising influence and it is activated on hyperpolarisation of the cell.
$\frac{\partial^{1}v}{\partial \mathrm{time}}=\frac{\frac{a}{2.0\mathrm{Ri}}(\mathrm{v\_x2}+\mathrm{v\_x}\frac{2.0}{a}\mathrm{a\_x})(1.0+\mathrm{a\_x}^{2.0})^{0.5}-\mathrm{Gm}(v-\mathrm{Em})+\mathrm{Gsh}(v-\mathrm{Esh})+\mathrm{i\_H}+\mathrm{i\_A}}{\mathrm{Cm}}\frac{\partial^{1}v}{\partial x}=\mathrm{v\_x}\frac{d a}{d x}=\mathrm{a\_x}\frac{\partial^{2.0}v}{\partial x^{2.0}}=\mathrm{v\_x2}$
$\mathrm{i\_H}=\mathrm{GH}\mathrm{mH}(v-\mathrm{EH})$
$\mathrm{mH\_infinity}=\frac{1.0}{1.0+e^{\frac{v+75.0}{5.5}}}\mathrm{tau\_mH}=\frac{1.0}{e^{-14.06-0.86v}+e^{-1.87+0.070v}}$
$\mathrm{i\_A}=\mathrm{GA}\mathrm{mA}\mathrm{hA}(v-\mathrm{EA})$
$\mathrm{mA\_infinity}=\frac{1.0}{1.0+e^{\frac{v+39.0}{-5.6}}}$
$\mathrm{hA\_infinity}=\frac{1.0}{1.0+e^{\frac{v+57.0}{4.8}}}$
mitochondria
energy transfer
neuron
cardiac myocyte
electrophysiology
cable properties
metabolism
keyword
The University of Auckland, Bioengineering Institute
2003-09-09
Catherine
Lloyd
May
A
Surkis
Changed units of Gm in membrane component from microS_per_cm2.
Surkis et al's 1998 mathematical model of the cable properties of
laterodorsal tegmental neurons.
laterodorsal tegmental neurons
Recovery of Cable Properties Through Active and Passive Modeling of Subthreshold Membrane Responses From Laterodorsal Tegmental Neurons
80
2593
2607
C
Peskin
S
D
Tranchina
Autumn
Cuellar
A
c.lloyd@auckland.ac.nz
2002-12-05T00:00:00+00:00
The University of Auckland
The Bioengineering Institute
9819266
Journal of Neurophysiology
This is the CellML description of Surkis et al's 1998 mathematical model of the cable properties of laterodorsal tegmental neurons.
1998-11
Catherine Lloyd
C
Leonard
S