### Single-compartment deterministic oscillating cell model?

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**Mon Dec 17, 2018 8:17 pm**Hi, I am trying to implement a published single compartment-model in Neuron or Matlab that is not available on Modeldb:

CLAYTON T. DICKSON, JACOPO MAGISTRETTI, MARK H. SHALINSKY, ERIK FRANSEN, MICHAEL E. HASSELMO, AND ANGEL ALONSO1Properties and Role of Ih in the Pacing of Subthreshold Oscillations in Entorhinal Cortex Layer II Neurons. J. Neurophysiol. 83: 2562–2579, 2000.

I cannot get the model to oscillate using what I presume to be the HH-type equations the authors used (I had to adjust some of the rate equations for sign and magnitude, but the shape appears to be generally correct). The resting potential and input resistance are close to what the authors report in their paper. My main goal in trying to implement the model is to get a general model of deterministic oscillations due to interactions between the persistent sodium current (Na-p) and the HCN-gated current (Ih) that I can modify for my specific purposes rather than trying to implement this exact model. By deterministic I mean a model that does not rely upon on a noise source or a stochastic mechanism to oscillate.

1) Can someone refer me to a model with code available of Na-p/Ih intrinsic oscillations (as opposed to those due to network mechanisms, stochastic ion channel gating, synaptic noise)?

2) Has anyone had any luck implementing the Dickson et al. 2000 model? Here's the relevant equations that I'm using:

For Na-P (note activation is modeled as instantaneous in the Dickson paper):

mInf = 1.0/(1+exp((v- vhalfa)/ka))

hInf = 1.0/(1+exp((v- vhalfh)/kh))

hAlpha = (0.001*(-2.88e-3*v - 4.9e-2))/(1 - exp((v + 4.9e-2/2.88e-3)/4.63))

hBeta = (0.001*(6.94e-3*v + 0.447))/(1 - exp(-(v + 0.447/6.94e-3)/2.63))

hTau = 1/(hAlpha + hBeta)

For Ih:

CLAYTON T. DICKSON, JACOPO MAGISTRETTI, MARK H. SHALINSKY, ERIK FRANSEN, MICHAEL E. HASSELMO, AND ANGEL ALONSO1Properties and Role of Ih in the Pacing of Subthreshold Oscillations in Entorhinal Cortex Layer II Neurons. J. Neurophysiol. 83: 2562–2579, 2000.

I cannot get the model to oscillate using what I presume to be the HH-type equations the authors used (I had to adjust some of the rate equations for sign and magnitude, but the shape appears to be generally correct). The resting potential and input resistance are close to what the authors report in their paper. My main goal in trying to implement the model is to get a general model of deterministic oscillations due to interactions between the persistent sodium current (Na-p) and the HCN-gated current (Ih) that I can modify for my specific purposes rather than trying to implement this exact model. By deterministic I mean a model that does not rely upon on a noise source or a stochastic mechanism to oscillate.

1) Can someone refer me to a model with code available of Na-p/Ih intrinsic oscillations (as opposed to those due to network mechanisms, stochastic ion channel gating, synaptic noise)?

2) Has anyone had any luck implementing the Dickson et al. 2000 model? Here's the relevant equations that I'm using:

For Na-P (note activation is modeled as instantaneous in the Dickson paper):

mInf = 1.0/(1+exp((v- vhalfa)/ka))

hInf = 1.0/(1+exp((v- vhalfh)/kh))

hAlpha = (0.001*(-2.88e-3*v - 4.9e-2))/(1 - exp((v + 4.9e-2/2.88e-3)/4.63))

hBeta = (0.001*(6.94e-3*v + 0.447))/(1 - exp(-(v + 0.447/6.94e-3)/2.63))

hTau = 1/(hAlpha + hBeta)

For Ih: