- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-11-11 15:45:21+13:00
- Desc:
- update with i/o
- Permanent Source URI:
- https://models.cellml.org/workspace/705/rawfile/e0331caa0df31df9490100e9a1461ed37246375a/parameter_finder/grand_kinetic_parameters.py
# Kinetic rate constants for composite model of FCU-AC
# they must be computed together because of the presence of new potential closed loops
# order: {'cAMP','LRGbinding_B1AR','LRGbinding_M2','GsProtein','GiProtein'}
# 27Oct21 distregarding recharge of GDP to GTP. Adding intermediate compound between GDP off and GTP on in GEF action
import numpy as np
def grand_kinetic_parameters(M, include_type2_reactions, dims, V, noLRG):
num_cols = dims['num_cols']
num_rows = dims['num_rows']
# shared large/small constants
# bigNum = 1e6
fastKineticConstant = 1e6
# smallReverse = 1e0
# cAMP
K1_m = 1.03e3 # uM
k1cat = 0.2 # 1/s
K2_m = 3.15e+2 # uM
k2cat = 8.5 # 1/s
K3_m = 8.60e+2 # uM
k3cat = 1e-16 # 1/s
K4_m = 1.30 # uM
k4cat = 5 # 1/s
K5_m = 30 # uM
K6_m = 0.4 # uM
K7_m = 44 # uM
KGiAC_m = 10 # made up value # uM
# initialise arrays
vkap = np.zeros(4)
vkam = np.zeros(4)
vkbp = np.zeros(4)
vkbm = np.zeros(4)
vkm2 = np.zeros(4)
vkp2 = np.zeros(4)
vK_m = [K1_m,K2_m,K3_m,K4_m,K5_m,K6_m,K7_m,KGiAC_m]
vkcat = [k1cat,k2cat,k3cat,k4cat]
kap_mult = [0.93, 0.1, 1, 1,0.1] # finding rates from literature?
# include the Gi reaction to remove it from the system in inhibited
# form
iks = range(4)
for i in range(4):
vkap[i] = kap_mult[i]*fastKineticConstant
vkam[i] = vkap[i]*vK_m[iks[i]] - vkcat[i]
vkbp[i] = vkcat[i]
vkbm[i] = (vkap[i]*vkbp[i])/vkam[i]
iks = range(4,8)
for i in range(4):
vkm2[i] = fastKineticConstant
vkp2[i] = vkm2[i]/vK_m[iks[i]]
# B1AR composite: LRG_B1AR + GsProtein
bigNum = 1e6
fastKineticConstant = bigNum
Ksig1 = 33 # uM Kc
Ksig2 = 0.285 # uM Kl
Ksig3 = 0.062 # uM Kr
ksig1p = fastKineticConstant
ksig1m = ksig1p*Ksig1
ksig2p = fastKineticConstant
ksig2m = ksig2p*Ksig2
ksig3p = fastKineticConstant
ksig3m = ksig3p*Ksig3
ksig4p = fastKineticConstant
# find ksig4m using detailed balance
ksig4m = ksig1m*ksig2m*ksig3p*ksig4p/(ksig1p*ksig2p*ksig3m)
bigNum = 1e3
fastKineticConstant = bigNum
smallReverse = fastKineticConstant/(pow(bigNum,2))
k_Doff1p = fastKineticConstant
k_Doff1m = smallReverse
k_Ton1p = fastKineticConstant
k_Ton1m = smallReverse
k_Doff2p = fastKineticConstant
k_Doff2m = smallReverse
k_Ton2p = fastKineticConstant
k_Ton2m = smallReverse
kAct1p = 16 # 1/s
kAct1m = smallReverse # 1/s
kAct2p = 16 # 1/s
kAct2m = smallReverse # 1/s
kHydp = 0.8 # 1/s
kHydm = smallReverse # 1/s
kReassocp = 1.21e3 # 1/uM.s
kReassocm = kReassocp/fastKineticConstant # 1/s
# phosphorylation of GDP by NDPK (nucleoside diphosphate kinase) - omitting MM enzyme
kPiPhosp = fastKineticConstant
kPiPhosm = smallReverse
# Loop1: find kact1m using detailed balance
# kAct1m = (kAct1p*ksig1p)/ksig1m
# Loop2: find kact1m using detailed balance
# kAct2m = (kAct2p*ksig3p)/ksig3m
kAct2m = kAct1m * kAct2p / kAct1p
# Big Loop: find ksig3p or kact2m using detailed balance
# *** unnecessary ***
# ksig3m = kAct1p*ksig2m*ksig3p*ksig4p/(kAct1m*ksig2p*ksig4m)
# CLOSED LOOP involving G - aGTP - aGDP - G
# use detailed balance to find kReasocm with either Act (as they have
# same equilibrium constant
if True:
kReassocm = kAct1p*kHydp*kReassocp/(kAct1m*kHydm)
# M2 composite: LRG_M2 + GiProtein
bigNum = 1e6
fastKineticConstant = bigNum
K_M2sig1 = 30 # uM Kc
K_M2sig2 = 0.16 # uM Kh
K_M2sig4 = 11 # uM Kl
k_M2sig1p = fastKineticConstant
k_M2sig1m = k_M2sig1p*K_M2sig1
k_M2sig2p = fastKineticConstant
k_M2sig2m = k_M2sig2p*K_M2sig2
k_M2sig4p = fastKineticConstant
k_M2sig4m = k_M2sig4p*K_M2sig4
k_M2sig3p = fastKineticConstant
k_M2sig3m = k_M2sig1m*k_M2sig2m*k_M2sig3p*k_M2sig4p/(k_M2sig1p*k_M2sig2p*k_M2sig4m) # interim?
bigNum = 1e3
fastKineticConstant = bigNum
smallReverse = fastKineticConstant/(pow(bigNum,2))
k_M2Doff1p = fastKineticConstant
k_M2Doff1m = smallReverse
k_M2Ton1p = fastKineticConstant
k_M2Ton1m = smallReverse
k_M2Doff2p = fastKineticConstant
k_M2Doff2m = smallReverse
k_M2Ton2p = fastKineticConstant
k_M2Ton2m = smallReverse
k_M2Act1p = 2.5 # 1/s
k_M2Act1m = smallReverse # 1/s
k_M2Act2p = 0.05 # 1/s
k_M2Act2m = smallReverse # 1/s
k_M2Hydp = 0.8 # 1/s
k_M2Hydm = smallReverse # 1/s
k_M2Reassocp = 1.21e3 # 1/uM.s
k_M2Reassocm = k_M2Reassocp/fastKineticConstant # 1/s
# Loop1: find kact1m using detailed balance
# k_M2Act1m = (k_M2Act1p*k_M2sig1p)/k_M2sig1m
# Loop2: find kact1m using detailed balance
# k_M2Act2m = (k_M2Act2p*k_M2sig3p)/k_M2sig3m
k_M2Act2m = k_M2Act1m * k_M2Act2p / k_M2Act1p
# Big Loop: find k_M2sig3p or kact2m using detailed balance
# *** unnecessary ***
# k_M2sig3m = k_M2Act1p*k_M2sig2m*k_M2sig3p*k_M2sig4p/(k_M2Act1m*k_M2sig2p*k_M2sig4m)
# CLOSED LOOP involving G - aGTP - aGDP - G
# use detailed balance to find kReasocm with either Act (as they have
# same equilibrium constant
if True:
k_M2Reassocm = k_M2Act1p*k_M2Hydp*k_M2Reassocp/(k_M2Act1m*k_M2Hydm)
# TOTAL
# order: {'cAMP','LRGbinding_B1AR','LRGbinding_M2','GsProtein','GiProtein'}
# forwaard first, then reverse!
k_kinetic = [vkap[0], vkbp[0], #cAMP
vkap[1], vkbp[1],
vkap[2], vkbp[2],
vkap[3], vkbp[3],
# list(vkp2[:4]), # vkp2[:4]' transpose?
vkp2[0], vkp2[1],vkp2[2], vkp2[3],
ksig1p, ksig2p, ksig3p, ksig4p, #LRG B1AR
k_M2sig1p, k_M2sig2p, k_M2sig3p, k_M2sig4p,# LRG_M2
k_Doff1p, k_Ton1p, kAct1p, k_Doff2p, k_Ton2p, kAct2p, kHydp, kReassocp, # kPiPhosp,#GsProtein
k_M2Doff1p, k_M2Ton1p, kAct1p, k_M2Doff2p, k_M2Ton2p, k_M2Act2p, k_M2Hydp, k_M2Reassocp, #GiProtein
vkam[0], vkbm[0],
vkam[1], vkbm[1],
vkam[2], vkbm[2],
vkam[3], vkbm[3],
# vkm2[:4], # transpose?(1:4)'
vkm2[0], vkm2[1],vkm2[2], vkm2[3],
ksig1m, ksig2m, ksig3m, ksig4m,
k_M2sig1m, k_M2sig2m, k_M2sig3m, k_M2sig4m,
k_Doff1m, k_Ton1m, kAct1m, k_Doff2m, k_Ton2m, kAct2m, kHydm, kReassocm, #kPiPhosm,
k_M2Doff1m, k_M2Ton1m, kAct1m, k_M2Doff2m, k_M2Ton2m, k_M2Act2m, k_M2Hydm, k_M2Reassocm
]
if noLRG:
k_kinetic = [vkap[0], vkbp[0], #cAMP
vkap[1], vkbp[1],
vkap[2], vkbp[2],
vkap[3], vkbp[3],
vkp2[0], vkp2[1], vkp2[2], vkp2[3],
kPhosRGp, kPhosLRGp, kAct1p, kAct2p, kHydp, kReassocp, #GsProtein
k_M2PhosRGp, k_M2PhosLRGp, k_M2Act1p, k_M2Act2p, k_M2Hydp, k_M2Reassocp, #GiProtein
vkam[0], vkbm[0],
vkam[1], vkbm[1],
vkam[2], vkbm[2],
vkam[3], vkbm[3],
vkm2[0], vkm2[1], vkm2[2], vkm2[3],
kPhosRGm, kPhosLRGm, kAct1m, kAct2m, kHydm, kReassocm,
k_M2PhosRGm, k_M2PhosLRGm, k_M2Act1m, k_M2Act2m, k_M2Hydm, k_M2Reassocm,
]
if False: # Gs and LRG_B1 only
k_kinetic = [ksig1p, ksig2p, ksig3p, ksig4p, #LRG B1AR
kAct1p, kAct2p, kHydp, kReassocp, #GsProtein
ksig1m, ksig2m, ksig3m, ksig4m,
kAct1m, kAct2m, kHydm, kReassocm,
]
if False:
k_kinetic = [k_M2sig1p, k_M2sig2p, k_M2sig3p, k_M2sig4p,# LRG_M2
k_M2Act1p, k_M2Act2p, k_M2Hydp, k_M2Reassocp, #GiProtein
k_M2sig1m, k_M2sig2m, k_M2sig3m, k_M2sig4m,
k_M2Act1m, k_M2Act2m, k_M2Hydm, k_M2Reassocm,
]
# CONSTRAINTS
N_cT = []
if False:
N_cT = np.zeros([1,size(M,2)])
# substrate B1ARp is in eqlm with product B1ARtot
N_cT[0][num_cols] = 1
N_cT[0][num_cols + 1] = -1
K_C = np.ones([1,len(N_cT)])
# volume vector
W = [np.ones([num_cols,1]), V['V_myo']*np.ones([num_rows,1])]
return ([k_kinetic, N_cT, K_C, W])
