Published: 28-12-2019| Version 1 | DOI: 10.17632/72pv9sfxkw.1
Shimon Marom


Excitability – a threshold governed transient in trans-membrane voltage – is a fundamental physiological process that controls the function of the heart, endocrine, muscles and neuronal tissues. The 1950's Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin-Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. Ori et al (bioRxiv 10.1101/766154, 2019), experimentally examined functional relations in the Hodgkin-Huxley parameter space, by assembling excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. Their analysis is based on a theoretically derived phase diagram (Ori et al, PNAS 201808552, 10.1073/pnas.1808552115, 2018), where the phenomenon of excitability is reduced to two dimensions (S and K) defined as combinations of the Hodgkin-Huxley model parameters. The set contains HDF5 dynamic clamp data files of Kv1.3 injected Xenopus oocytes, described in Ori et al (2019). In each data file, the n-th trace is stored in "/Trialn/Synchronous Data/Channel Data", containing lists of 4 numbers: {scaled voltage, scaled current, maximal sodium conductance, \alpha-m}. Traces of voltage responses may be extracted from the first column; the S–K phase diagram coordinates are determined by the second two columns (fixed throughout a trace), given the measured maximal Kv1.3 conductance (gKmax, mS/µF) below: file 170208_K1_random, gKmax =0.65 file 170208_K2_random, gKmax =0.55 file 170208_K3_random, gKmax =0.64 file 170208_K4_random, gKmax =0.52 file 170223_K1_random, gKmax =0.74 file 170608_K1_random, gKmax =0.61 file 180308_K1_random, gKmax =1.54 file 180517_K1_random, gKmax =1.04 file 180530_K3_random, gKmax =1.30 Example Mathematica (Wolfram Research, Inc.) script to extract trace number 220 from file "170208_random_K3.h5", calculate S–K coordinates and plot the voltage response: filename = "170208_random_K3.h5" trial = 220 trialNumber = "/Trial" <> ToString[trial] <> "/Synchronous Data/Channel Data" spike = Import[filename, trialNumber]; s = spike[[ 1, 3]]/( spike[[ 1, 3]] + gKmax) k = 2/(3 + spike[[ 1, 4]]) ListLinePlot[spike[[All, 1]]/10]