A simplified model of NMDA oscillations in lamprey locomotor neurons (Huss et al. 2008)

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Using experiments in conjunction with this simplified model, we sought to understand the basic mechanisms behind NMDA-induced oscillations in lamprey locomotor neurons, specifically (a) how the oscillation frequency depends on NMDA concentration and why, and (b) what the minimal number of components for generating NMDA oscillations is (in vitro and in the model).
1 . Huss M, Wang D, Trané C, Wikström M, Hellgren Kotaleski J (2008) An experimentally constrained computational model of NMDA oscillations in lamprey CPG neurons. J Comput Neurosci 25:108-21 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Spinal cord lumbar motor neuron alpha ACh cell; Spinal lamprey neuron;
Channel(s): I K; I K,Ca;
Gap Junctions:
Receptor(s): NMDA;
Simulation Environment: XPP;
Model Concept(s): Simplified Models;
Search NeuronDB for information about:  Spinal cord lumbar motor neuron alpha ACh cell; NMDA; I K; I K,Ca;
# A simplified model of NMDA oscillations in lamprey locomotor network neurons
# Mikael Huss 070315

# Components: NMDA, KCa, Kv, leak, Cav, KCa channels
# KCa gets activated by both NMDA-Ca and Cav.

# Voltage equation (the factor 1000 is to get the time in seconds)

dv/dt= 1000 * (p(v)*gnmda*(enmda-v) + gkca*act_kca(C)*(ek-v) + gk*act_k(v)*(ek-v) + gleak*(eleak-v) + gcav*act_cav(v)*(eca-v) + ibias)

dc/dt= inmda*p(v)*gnmda*(enmda-v) + icav*gcav*act_cav(v)*(eca-v) - C/tau

param gnmda=0.005, gkca=20, gk=8, gcav=0.005, gleak=0.001
param tc=0.02, tau=1, inmda=0.2, icav=0.3, ibias=0
param enmda=0, eleak=-70,   ek=-80, eca=150, 
param vmhalf=-60, vkhalf=-1, vcahalf=-45
param sm=.3, sk=-7, sca=-5

# Magnesium block equation

# Kv current (assumed to be a combination of delayed rectifier and A-current)
act_k(v) = 1/(1+exp((v-vkhalf)/sk))

# Assume that we have a calcium component with half-activation at -45 mV
# (Corresponding to the component which "starts to activate between
# -60 and -50 mV"; El Manira and Bussieres 1997)
act_cav(v) = 1/(1+exp((v-vcahalf)/sca))

aux act=act_kca(C)

init v=-70
param v(0)=-70

@ METH=cvode, ATOLER=1e-6, TOLER=1e-6, DT=0.02
@ TOTAL=30, XP=t, YP=v, MAXSTOR=500000, BOUND=50000, BELL=0
@ XLO=0, XHI=30, YLO=-80, YHI=0
@ ntst=400, nmax=20000, dsmin=1e-15, dsmax=.1, ds=1e-4
@ epsl=1e-7, epsu=1e-7, epss=1e-5
@ parmin=0, parmax=0.8
@ autoxmin=0, autoxmax=0.8, autoymin=-80, autoymax=0, autovar=v