- Author:
- Shelley Fong <sfon036@UoA.auckland.ac.nz>
- Date:
- 2022-06-22 16:16:24+12:00
- Desc:
- Init
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/8ab/rawfile/3bd36f5ad0fa106f9b6a31beb5f428b73d34af5f/parameter_finder/kinetic_parameters_IPR.py
# PLC module, translated from Bhalla and Iyengar 1999
# Return kinetic parameters, constraints, and vector of volumes in each
# compartment (pL) (1 if gating variable, or in element corresponding to
# kappa)
# Based on 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']
fkc = 1e6
smr = 1e-3
# constants used in subunits
a = [400e3, 0.2e3, 400e3, 0.2e3, 20e3] # [=] 1/mM.s
d = [0.13e-3, 1.049e-3, 943.4e-6, 144.5e-6, 82.34e-6] # [=] mM
b = [d[i]*a[i] for i in range(len(a))] # [=] 1/s
k1p = a[3]
k2p = a[4]
k3p = b[3]
k4p = b[4]
k5p = a[1]
k6p = a[4]
k7m = b[1]
k8p = b[4]
k9p = a[2]
k10p = b[0]
k11p = a[2]
k12p = b[0]
k1m = b[3]
k2m = b[4]
k3m = a[3]
k4m = a[4]
k5m = b[1]
k6m = b[4]
k7p = a[1]
k8m = a[4]
k9m = b[2]
k10m = a[0]
k11m = b[2]
k12m = a[0]
# closed loops present, but parameters are adjusted from kinetic model to meet detailed balance
# k7p = k4m*k5p*k6p*k7m/(k4p*k5m*k6m) # error is ~zero when this commented out
# k8m = k4m*k5p*k6p*k8p/(k4p*k5m*k6m)
k4m = k1p*k2p*k3p*k4p/(k1m*k2m*k3m)
k8m = k5p*k6p*k7p*k8p/(k5m*k6m*k7m)
k10m = k9p*k5m*k10p*k1p/(k9m*k5p*k1m)
k12m = k11p*k7p*k12p*k3m/(k11m*k7m*k3p)
# Calculate bond graph constants from kinetic parameters
# Note: units of kappa are fmol/s, units of K are fmol^-1
kf = [
k1p,
k2p,
k3p,
k4p,
k5p,
k6p,
k7p,
k8p,
k9p,
k10p,
k11p,
k12p
]
kr = [
k1m,
k2m,
k3m,
k4m,
k5m,
k6m,
k7m,
k8m,
k9m,
k10m,
k11m,
k12m
]
k_IPR_main = [6,6] # [=] 1/s neglecting c_1 volume adjustment as BG already takes care of this
k_kinetic = [k_IPR_main[0]] + kf + kf + kf + [k_IPR_main[1]] + kr + kr + kr # 3 identical and independent subunits
# CONSTRAINTS
N_cT = []
K_C = []
# volume vector
# W = list(np.append([1] * num_cols, [V['V_myo']] * num_rows))
W = [1] * num_cols + [V['V_myo']] +[V['V_SR']] + [V['V_myo']] + [1]*(num_rows-3)
return (k_kinetic, N_cT, K_C, W)
