SM_EmEx2_data

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 Archive.zip 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]兴奋性（Excitability）——一种受阈值调控的跨膜电压瞬态过程——是控制心脏、内分泌系统、肌肉及神经组织功能的基础生理过程。1950年代，霍奇金与赫胥黎（Hodgkin and Huxley）提出的显式公式为理解兴奋性提供了数学框架，该框架将兴奋性归因于电压门控钠通道（voltage-gated sodium channel）与电压门控钾通道（voltage-gated potassium channel）的特性。相较于兴奋性表现得更为稳健的生物系统，霍奇金-赫胥黎模型对蛋白质密度与动力学的参数变化更为敏感。Ori等人（bioRxiv 10.1101/766154, 2019）通过在爪蟾卵母细胞（Xenopus oocytes）中表达电压门控钾离子通道Kv1.3并结合动态钳（dynamic clamp）技术组装可兴奋性膜，实验探究了霍奇金-赫胥黎参数空间内的功能关系。其分析基于理论推导得到的相图（Ori et al, PNAS 201808552, 10.1073/pnas.1808552115, 2018），该相图将兴奋性现象简化为以S和K为表征的二维空间，S与K由霍奇金-赫胥黎模型参数组合定义。 Archive.zip压缩包包含Ori等人2019年研究中提及的、注入Kv1.3的爪蟾卵母细胞的HDF5格式（HDF5）动态钳数据文件。每个数据文件中，第n条轨迹存储于路径"/Trialn/Synchronous Data/Channel Data"下，包含4个数值的列表：{缩放电压、缩放电流、最大钠电导（maximal sodium conductance）、α-m}。电压响应轨迹可从第一列提取；S-K相图坐标由后两列确定（同一条轨迹内数值固定不变），前提已知如下测量得到的最大Kv1.3电导（gKmax, mS/µF）： 170208_K1_random，gKmax=0.65 170208_K2_random，gKmax=0.55 170208_K3_random，gKmax=0.64 170208_K4_random，gKmax=0.52 170223_K1_random，gKmax=0.74 170608_K1_random，gKmax=0.61 180308_K1_random，gKmax=1.54 180517_K1_random，gKmax=1.04 180530_K3_random，gKmax=1.30 以下为示例Mathematica（Wolfram Research, Inc.，沃尔夫勒姆研究公司）脚本，用于从文件"170208_random_K3.h5"中提取第220条轨迹、计算S-K坐标并绘制电压响应： 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]