- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-12-20 15:30:51+13:00
- Desc:
- Updating AND gate
- Permanent Source URI:
- http://models.cellml.org/workspace/7e8/rawfile/976458953ae2c012058c6b595b9665b5c0ed94f9/parameter_finder/kinetic_parameters_KrToy.py
# Kraeutler Reduced Hill Toy module
# Return kinetic parameters, constraints, and vector of volumes in each compartment (pL)
# 8 reactions - 4 MM schemes of 2 reactions each
# Re_AC1
# Re_AC2
# Re_EC1
# Re_EC2
# Re_BD1
# Re_BD2
# Re_AND_E1
# Re_AND_E2
# assume an OR gate is the same as a 1 node
# assume reactions follow classical Hill equation for (1) A*+B <-> complex
# then complex instantaneously breaks into (2) complex -> A* + B*
# the derivations for Km using Kraeutler parameters apply to reaction (1)
import numpy as np
def kinetic_parameters(M, dims, V):
# Set the kinetic rate constants
num_cols = dims['num_cols']
num_rows = dims['num_rows']
num_rx = 5
K_Kraeut = 1.37695668165159
E0 = [1]*num_rx # normalised enzyme concentrations
Ymax = [1]*num_rx # A,B,C,D,E
W = 1
tau = 1
EC50 = 0.5
n = 1.4
beta = (pow(EC50,n) - 1)/(2*pow(EC50,n) - 1)
K1_m = K_Kraeut #AC units?
K2_m = K_Kraeut #EC units?
K3_m = K_Kraeut #BD units?
K4_m = K_Kraeut #AND_CE units?
K5_m = K_Kraeut #AND_DE units?
Vmax = [0]*num_rx
Vmax[0] = W*beta*Ymax[2]/tau
Vmax[1] = W*beta*Ymax[2]/tau
Vmax[2] = W*beta*Ymax[3]/tau
Vmax[3] = W*beta*Ymax[4]/tau # AND gate with same Ymax as E (for E1)
Vmax[4] = W*beta*Ymax[4]/tau #W*beta*YmaxE/tau # AND gate
vkcat = []
for iv, v in enumerate(Vmax):
vkcat.append(v/E0[iv]) # NOT fastKineticConstant as it is NOT transient
# initialise arrays
vkap = np.zeros(num_rx)
vkam = np.zeros(num_rx)
vkbp = np.zeros(num_rx)
vkbm = np.zeros(num_rx)
vK_m = [K1_m,K2_m,K3_m,K4_m, K5_m]
fastKineticConstant = 1e6 # 1/s
smallReverse = 1
for i in range(num_rx):
vkap[i] = fastKineticConstant
vkam[i] = vkap[i]*vK_m[i] - vkcat[i]
vkbp[i] = vkcat[i]
vkbm[i] = (vkap[i]*vkbp[i])/vkam[i]
# Calculate bond graph constants from kinetic parameters
# Note: units of kappa are fmol/s, units of K are fmol^-1
# k_kinetic = [vkap[0], vkbp[0],
# vkap[1], vkbp[1],
# vkap[2], vkbp[2],
# vkap[3], vkbp[3],
# vkam[0], vkbm[0],
# vkam[1], vkbm[1],
# vkam[2], vkbm[2],
# vkam[3], vkbm[3],
# ]
k_kinetic = list(np.column_stack((vkap, vkbp)).flatten()) + list(np.column_stack((vkam, vkbm)).flatten())
# CONSTRAINTS
N_cT = []
K_C = []
# volume vector
W = list(np.append([1] * num_cols, [V['V_myo']] * num_rows))
return (k_kinetic, N_cT, K_C, W)
