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1962_noble.xml

Lloyd Catherine May c.lloyd@auckland.ac.nz The University of Auckland Bioengineering Institute 2001-12-18 Encapsulated the model under an interface component for use when importing the model into a specific experiment or simulation. Nickerson David P 2004-12-21 Changed units and added stimulus current. Nickerson David P 2003-04-05 Changed the model name so the model loads in the database easier. Cuellar Autumn A 2003-04-05 Corrected membrane_voltage_diff_eq. Lloyd Catherine May 2002-02-28 Updated metadata to conform to the 16/01/2002 CellML Metadata 1.0 Specification. Cuellar Autumn A. 2002-01-20 Bioengineering Institute, The University of Auckland. The 1962 Noble Model of Purkinje Fibre Action and Pace-maker Potentials This is the CellML description of Noble's 1962 mathematical model of Purkinje fibre action and pace-maker potentials. The equations formulated by Hodgkin and Huxley (1952) to describe the electrical activity of squid nerve have been modified to describe the action and pace-maker potentials of the Purkinje fibres of the heart. Catherine Lloyd Mammalia 14480151 Noble Denis A Modification of the Hodgkin-Huxley Equations Applicable to Purkinje Fibre Action and Pace-maker Potentials 1962 Journal of Physiology 160 317 352 Here we define a component which encapsulates the entire model and provides the interface to model boundary conditions and outputs. The main component of the model, containing the membrane currents and defining the transmembrane potential. The kinetics of the transmembrane potential. time V I_stim i_Na i_K i_Leak Cm This is a dummy equation that we simply use to make grabbing the value easier. IStimC I_stim The modified sodium current from the 1952 Hodgkin Huxley model. Calculation of the channel conductance. g_Na m 3.0 h g_Na_max Calculation of the channel current. i_Na g_Na_max m 3.0 h 0.14e-2 V E_Na The voltage-dependent activation gate for the sodium channel - the m gate. The opening rate for the m gate. alpha_m 0.1 V 48.0 V 48.0 15.0 1.0 The closing rate for the m gate. beta_m 0.12 V 8.0 V 8.0 5.0 1.0 The kinetics of the m gate. time m alpha_m 1.0 m beta_m m The voltage-dependent inactivation gate for the sodium channel - the h gate. The opening rate for the h gate. alpha_h 0.17 V 90.0 20.0 The closing rate for the h gate. beta_h 1.0 1.0 V 42.0 10.0 The kinetics of the h gate. time h alpha_h 1.0 h beta_h h The modified Hodgkin Huxley 1952 potassium channel. Calculation of the potassium current. The g_K_add conductance term can be used to obtain a quiescent variant of the model by setting its value to 0.001 mS/mm2. i_K g_K1 g_K2 g_K_add V 100.0 The conductance of the first "type" of potassium channels present in this model, using an empirical formaulation. g_K1 1.2e-2 V 90.0 50.0 0.015e-2 V 90.0 60.0 The conductance of the second "type" of potassium channels present in this model, using the Hodgkin Huxley 1952 type kinetics. g_K2 1.2e-2 n 4.0 The voltage-dependent activation gate for the potassium channel - the n gate. The opening rate for the n gate. alpha_n 0.0001 V 50.0 V 50.0 10.0 1.0 The closing rate for the n gate. beta_n 0.002 V 90.0 80.0 The kinetics of the n gate. time n alpha_n 1.0 n beta_n n A non-specific background current attributed in part to chloride ions. Can be turned on by specifying an appropriate value for the conductance (~0.00075 mS/mm2). i_Leak g_L V E_L