### Weird "trap" function in Bazhenov 2002 model

Posted:

**Wed Oct 03, 2018 11:27 am**I am trying to code the Bazhenov 2002 sleep model in NEURON (ModelDB link: https://senselab.med.yale.edu/ModelDB/s ... odel=28189), and I have run across a very strange "trap" function for the fast sodium current in the cortical pyramidal cells. The details of this current are found in the appendix of Timofeev 2000 ("Origin of Slow Cortical Oscillations in Deafferented Cortical Slabs") and Table 2 of Chen 2012 ("Interneuron-mediated inhibition synchronizes neuronal activity during slow oscillation"). There, the alpha function associated with the "m" gating variable is:

alpha(v) = 0.182*(v+25.0)/(1.0 - exp(-(v+25.0)/9.0) ) if |v-10|/35 > 10^{-6}

alpha(v) = 1.638 if |v-10|/35 < 10^{-6}

I understand that trap functions are employed numerically to prevent dividing by zero. However, there is no possibility of dividing by 0 at v=10. Furthermore, this curve is equal to approximately 6.503 at v=10, so setting it to 1.638 makes the function discontinuous.

The authors provide no explanation for this, and they have not responded to my inquiries over email.

Has anyone seen anything like this before? I am baffled...

alpha(v) = 0.182*(v+25.0)/(1.0 - exp(-(v+25.0)/9.0) ) if |v-10|/35 > 10^{-6}

alpha(v) = 1.638 if |v-10|/35 < 10^{-6}

I understand that trap functions are employed numerically to prevent dividing by zero. However, there is no possibility of dividing by 0 at v=10. Furthermore, this curve is equal to approximately 6.503 at v=10, so setting it to 1.638 makes the function discontinuous.

The authors provide no explanation for this, and they have not responded to my inquiries over email.

Has anyone seen anything like this before? I am baffled...