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1975_mcallister_noble_tsien.xml

Lloyd Catherine May c.lloyd@auckland.ac.nz The University of Auckland The Bioengineering Research Group 2001-09-27 Changed some units and added a stimulus current. Nickerson David P 2003-10-13 Changed the model name so the model loads in the database easier. Cuellar Autumn A 2003-04-05 Added more metadata. Lloyd Catherine May 2002-07-19 Corrected units 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 Altered parent-child relationships as x1 and x2 were made to be gates of the plateau potassium currents. Lloyd Catherine May 2002-01-03 Changed equations after checking with the mathml validator. Lloyd Catherine May 2001-12-10 Made changes to some of the metadata, bringing them up to date with the most recent working draft (26th September) of the Metadata Specification. Lloyd Catherine May 2001-10-24 Removed document type definition as this is declared as optional according to the W3C recommendation. Lloyd Catherine May 2001-10-19 The University of Auckland, Bioengineering Research Group The McAllister-Noble-Tsien Model of Cardiac Action Potentials in Purkinje fibres, 1975 This is the CellML description of McAllister, Noble and Tsien's mathematical model of cardiac action potentials of Purkinje fibres. It describes transmembrane ionic currents in terms of Hodgkin-Huxley type equations. It is a significant development of the Noble (1962) model as more currents are added based on new experimental data. Catherine Lloyd Purkinje Fibre 1185607 McAllister R E Noble Denis Tsien R W Reconstruction of the electrical activity of cardiac purkinje fibres 1975-09 Journal of Physiology 251 1 59 The main component of the model, containing the definition of the model's action potential. The kinetics of the transmembrane potential, defined as the sum of the trans-sarcolemmal currents and an applied stimulus current. time V I_stim i_Na i_si i_K2 i_x1 i_x2 i_qr i_K1 i_Na_b i_Cl_b C This is a dummy equation that we simply use to make grabbing the value in CMISS much easier. IStimC I_stim The fast sodium current, primarily responsible for the upstroke of the action potential. Calculation of the fast sodium current. i_Na g_Na m 3.0 h V E_Na The voltage-dependent activation gate for the fast sodium channel - the m gate. The opening rate of the m gate. alpha_m V 47.0 1.0 V 47.0 10.0 The closing rate of the m gate. beta_m 40.0 V 72.0 17.86 The kinetics of the m gate. time m alpha_m 1.0 m beta_m m The voltage-dependent inactivation gate for the fast sodium channel - the h gate. The opening rate of the h gate. alpha_h 0.0085 V 71.0 5.435 The closing rate of the h gate. beta_h 2.5 V 10.0 12.2 1.0 The kinetics of the h gate. time h alpha_h 1.0 h beta_h h The secondary (or sometimes slow) inward current activates much more slowly than the sodium current and it is responsible for holding up the plateau after the initial activation and for controlling the duration of the action potential. At the time of this model, it was assumed that the flux of both Na and Ca ions through the cell membrane was responsible for this current. This channel has an activation gate d and an inactivation gate f. It was observed in earlier experiments that a portion of this current would not completely inactivate. This is represented by the second term in the secondary current equation which has an activation variable d1, but no deactivation variable. Calculation of the second inward current. i_si g_si d f V E_si g_si_ d1 V E_si The voltage-dependent activation gate for the secondary inward current - the d gate. The opening rate of the d gate. alpha_d V 40.0 500.0 1.0 V 40.0 10.0 The closing rate of the d gate. beta_d 0.02 V 40.0 11.26 The kinetics of the d gate. time d alpha_d 1.0 d beta_d d The voltage-dependent inactivation gate for the secondary inward current - the f gate. The opening rate of the f gate. alpha_f 0.000987 V 60.0 25.0 The closing rate of the f gate. beta_f 0.02 V 26.0 11.5 1.0 The kinetics of the f gate. time f alpha_f 1.0 f beta_f f The activation variable for the slow component of the secondard inward current - the d1 gate (corresponds to the d' variable in the MNT paper. Calculation of the activation variable d1. d1 1.0 1.0 V 40.0 6.667 A potassium current activated over the "pace-maker" range of potentials. Provides the pacemaker function of the model. Calculation of the pacemaker current. i_K2 I_K2 s The maximal pacemaker current. I_K2 0.028 V E_K 25.0 1.0 V 60.0 12.5 V 60.0 25.0 The voltage-dependent gating variable for the pacemaker current - the s gate. The opening rate of the s gate. alpha_s 0.001 V E_s 1.0 V E_s 5.0 The closing rate of the s gate. beta_s 0.00005 V E_s 15.0 The kinetics of the s gate. time s alpha_s 1.0 s beta_s s The equations for the plateau potassium currents (x1 and x2) are based on experiments performed by Noble and Tsien (1969) which showed that additional potassium currents were activated in the plateau range of potentials. They appear to play an essential role in membrane repolarisation. Calculation of the first plateau potassium current. i_x1 x1 I_x1 Calculation of the maximal first plateau potassium current. I_x1 0.012 V 95.0 25.0 1.0 V 45.0 25.0 The voltage-dependent gating variable for the first plateau potassium current - the x1 gate. The opening rate of the x1 gate. alpha_x1 5e-4 V 50.0 12.1 1.0 V 50.0 17.5 The closing rate of the x1 gate. beta_x1 0.0013 V 20.0 16.67 1.0 V 20.0 20.0 The kinetics of the x1 gate. time x1 alpha_x1 1.0 x1 beta_x1 x1 The second of the plateau potassium currents. Calculation of the second plateau potassium current. i_x2 x2 I_x2 The linear maximal second plateau potassium current. I_x2 0.25 0.00385 V The gating variable for the second plateau potassium current - the x2 gate. The opening rate for the x2 gate. alpha_x2 0.000127 1.0 1.0 V 19.0 5.0 The closing rate for the x2 gate. beta_x2 0.0003 V 20.0 16.67 1.0 V 20.0 25.0 The kinetics of the x2 gate. time x2 alpha_x2 1.0 x2 beta_x2 x2 The transient chloride current (i_qr) is responsible for the rapid repolarisation from the peak of the depolarisation spike of the action potential, to the start of the plateau. The current has 2 gating variables, q and r. Calculation of the transient chloride current. i_qr g_qr q r V E_Cl The voltage-dependent activation gate for the transient chloride channel - the q gate. The opening rate for the q gate. alpha_q 0.008 V 1.0 V 10.0 The closing rate for the q gate. beta_q 0.08 V 11.26 The kinetics of the q gate. time q alpha_q 1.0 q beta_q q The voltage-dependent inactivation gate for the transient chloride current - the r gate. The opening rate for the r gate. alpha_r 0.00018 V 80 25.0 The closing rate for the r gate. beta_r 0.02 V 26 11.5 1.0 The kinetics of the r gate. time r alpha_r 1.0 r beta_r r The time-independent (background) current carried by potassium ions. Calculation of the time-independent potassium current. i_K1 I_K2 2.8 0.002 V E_K1 1.0 V E_K1 25.0 The sodium background current is a time-independent diffusion of Na ions down their electrochemical gradient, through the cell surface membrane into the cytosol. Calculation of the sodium background current. i_Na_b g_Nab V E_Na The chloride background current contributes to maintaining the plateau and helps to determine the action potential duration. Calculation of the background chloride current. i_Cl_b g_Clb V E_Cl