- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-03-02 13:58:36+13:00
- Desc:
- Rename
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/826/rawfile/6255536a7de70332ee7d2de72126d6a1a076e1db/parameter_finder/kinetic_parameters_Na_channel.py
# fast Na module
# Return kinetic parameters, constraints, and vector of volumes in each
# compartment (pL) (1 if gating variable, or in element corresponding to
# kappa)
# Translated from Pan 2018 cardiac AP
import numpy as np
def kinetic_parameters(M, include_type2_reactions, dims, V):
# Set the kinetic rate constants
num_cols = dims['num_cols']
num_rows = dims['num_rows']
# load gate transition parameters
params_m = [12.516449859118975, 0.4954094890610479, 0.0799997602584941, -2.4283951182982153]
params_h = [3.353932648035526E-7, -4.189185289647097, 0.7999028222966151, 1.2995102414503217]
params_j = [1.3078733519642442E-7, -4.038149019814894,0.42275822436453375, 1.428087934426136]
alpha_m0_bg = params_m[0]*1e3 # unit s^-1
beta_m0_bg = params_m[2]*1e3 # unit s^-1
alpha_h0_bg = params_h[0]*1e3 # unit s^-1
beta_h0_bg = params_h[2]*1e3 # unit s^-1
alpha_j0_bg = params_j[0]*1e3 # unit s^-1
beta_j0_bg = params_j[2]*1e3 # unit s^-1
# constants are stored in V
F = V['F']
R = V['R']
T = V['T']
N_A = V['N_A']
A_cap = V['A_cap']
cNao = V['cNao']
cNai = V['cNai']
G_Na = 16*A_cap # Unit mA/V
E_Na = R*T/F*np.log(cNao/cNai)
E_Na_norm = F*E_Na/(R*T)
G_GHK = 2*G_Na*(1-np.exp(E_Na_norm))/(cNai - cNao*np.exp(E_Na_norm))*R*T/F # Unit mA/mM
P_Na = G_GHK/F * 1e12 # Unit pL/s . G_GHK [=] Amp/(mol/s)
x_Na_channel = 122720/N_A*1e15 # unit fmol
# Calculate bond graph constants from kinetic parameters
# Note: units of kappa are fmol/s, units of K are fmol^-1
kf_Na = [P_Na/x_Na_channel, # R_GHK
3*alpha_m0_bg, # Rm000
3*alpha_m0_bg, # Rm001
3*alpha_m0_bg, # Rm010
3*alpha_m0_bg, # Rm011
2*alpha_m0_bg, # Rm100
2*alpha_m0_bg, # Rm101
2*alpha_m0_bg, # Rm110
2*alpha_m0_bg, # Rm111
alpha_m0_bg, # Rm200
alpha_m0_bg, # Rm201
alpha_m0_bg, # Rm210
alpha_m0_bg, # Rm211
alpha_h0_bg, # Rh000
alpha_h0_bg, # Rh001
alpha_h0_bg, # Rh100
alpha_h0_bg, # Rh101
alpha_h0_bg, # Rh200
alpha_h0_bg, # Rh201
alpha_h0_bg, # Rh300
alpha_h0_bg, # Rh301
alpha_j0_bg, # Rj000
alpha_j0_bg, # Rj010
alpha_j0_bg, # Rj100
alpha_j0_bg, # Rj110
alpha_j0_bg, # Rj200
alpha_j0_bg, # Rj210
alpha_j0_bg, # Rj300
alpha_j0_bg] # Rj310
kr_Na = [P_Na/x_Na_channel, # R_GHK
beta_m0_bg, # Rm000
beta_m0_bg, # Rm001
beta_m0_bg, # Rm010
beta_m0_bg, # Rm011
2*beta_m0_bg, # Rm100
2*beta_m0_bg, # Rm101
2*beta_m0_bg, # Rm110
2*beta_m0_bg, # Rm111
3*beta_m0_bg, # Rm202
3*beta_m0_bg, # Rm201
3*beta_m0_bg, # Rm210
3*beta_m0_bg, # Rm211
beta_h0_bg, # Rh000
beta_h0_bg, # Rh001
beta_h0_bg, # Rh100
beta_h0_bg, # Rh101
beta_h0_bg, # Rh200
beta_h0_bg, # Rh201
beta_h0_bg, # Rh300
beta_h0_bg, # Rh301
beta_j0_bg, # Rj000
beta_j0_bg, # Rj010
beta_j0_bg, # Rj100
beta_j0_bg, # Rj110
beta_j0_bg, # Rj200
beta_j0_bg, # Rj210
beta_j0_bg, # Rj300
beta_j0_bg] # Rj310
k_kinetic = kf_Na + kr_Na
# CONSTRAINTS
N_cT = []
K_C = []
# volume vector
# W = list(np.append([1] * num_cols, [V['V_myo']] * num_rows))
W = list(np.append([1] * num_cols, [V['V_myo']] * 2)) + list([1] * (num_rows-2))
return (k_kinetic, N_cT, K_C, W)
