Single Cell Burster: Hodkin Huxley Model with Persistent Sodium Current and Calcium Current
The following is meant only to provide a guide of the various equations of the models and to familiarize the reader with the parameters that can be set in the python notebooks. For more information on the model, please consult the salient papers (links provided below).
The membrane potential of the model with a persistent sodium current is given by:
where the current terms are given by:
INa and IK are the currents typically found in the Hodgkin-Huxley formulation, while INaP is a persistent sodium current added in (ref to Butera Paper). Itonic-e is the tonic drive and Iapp is the applied current. The gating variables used in current definitions, m, n, h, and p are determined by the following general equations, where x is a standing for the specific gating variable:
The membrane potential of the soma in the is modeled by the equation:
INa, IK, and INaP are the same as in the version with the persistent sodium current above and the gating variables are described by the same generalized set of equations.
The membrane potential of the dendrite is modeled by the equation:
where ICaN, activated by Ca2+, is given by:
ICaN is a function of [Ca]i, the concentration of free Ca in the cytosol, which changes in time according to the differential equation:
which in turn depends on JER,IN and JER,OUT, the flux of Ca into and out of the ER. JER,IN and JER,OUT are given by the following equations:
JER,IN is dependent on two non-constant terms, [Ca]i itself, and l, the IP3 channel gating variable given by:
The code in the Somatic Burster and Dendritic Burster notebooks was modified from a python script supplied by Dr. Natalia Toporikova.