# Merged GPCR module, which is a combination of GsProtein and LRGbinding_B1AR.
# following Saucerman and Iancu: act1 and act2 with LR
# and LRG as substrates (G is already bound, so there is only one substrate
# to each act reaction)
# Gs is associated with B1AR proteins
# return (k_kinetic, N_cT, K_C, W) kinetic parameters, constraints, and vector of volumes in each
# compartment (pL) (1 if gating variable, or in element corresponding to
# kappa)
# 14Oct21: adding phosphate binding reaction to RG and LRG as separate
# reactions. Only RG_Pi and LRG_Pi proceed to Act reactions.
# 23nov21 removed RG + L -> LRG (sig2)
# 24nov21: merged Gs and GPCR binding
# 24nov21: adding receptor internalisation after aGTP has dissociated from the RG/LRG complex
import numpy as np
def kinetic_parameters(M, include_type2_reactions, dims, V):
# Set the kinetic rate constants.
# original model had reactions that omitted enzymes as substrates e.g. BARK
# convert unit from 1/s to 1/uM.s by dividing by conc of enzyme
# all reactions were irreversible, made reversible by letting kr ~= 0
num_cols = dims['num_cols']
num_rows = dims['num_rows']
bigNum = 1e6
fastKineticConstant = bigNum
smallReverse = 1/bigNum
medReverse = np.sqrt(smallReverse)
k_Rswitchp = fastKineticConstant
k_Rswitchm = k_Rswitchp*0.01 # assume that only 1% of receptors are constitutionally active
k_LRswitchp = fastKineticConstant
k_LRswitchm = smallReverse
KRc = 33 # uM Kc
KRL = 0.285 # uM Kl
KRr = 0.062 # uM Kr
kRcp = fastKineticConstant
kRcm = kRcp*KRc
kRrp = fastKineticConstant
kRrm = kRrp*KRr
# kRLp = fastKineticConstant
# kRLm = kRLp*KRL
kRL_actRp = fastKineticConstant
kRL_actRm = kRL_actRp*KRL
mult = 4e1
kAct1p = 16*mult # 1/s
kAct1m = smallReverse # 1/s
kAct2p = 16*mult # 1/s
kAct2m = smallReverse # 1/s
kHydp = 0.8/mult # 1/s
kHydm = smallReverse # 1/s
kReassocp = 1.21e3 # 1/uM.s
kReassocm = smallReverse # 1/s
# RECEPTOR INTERNALISATION
k_interRp = fastKineticConstant
k_interRm = smallReverse
k_interLRp = fastKineticConstant
k_interLRm = smallReverse
# ensure that the closed loop formed by Act1 & Act2 obey detailed balance
# CLOSED LOOP involving G - aGTP - aGDP - G
# use detailed balance to find kReasocm with either Act (as they have
# same equilibrium constant
if False:
kAct2m = kAct1m * kAct2p / kAct1p
kReassocm = kRcp*kAct1p*kHydp*kReassocp/(kRcm*kAct1m*kHydm)
k_kinetic = [
k_Rswitchp,k_LRswitchp,kRcp, kRrp, kRL_actRp, kAct1p, kAct2p, kHydp, kReassocp, k_interRp, k_interLRp,
k_Rswitchm,k_LRswitchm,kRcm, kRrm, kRL_actRm, kAct1m, kAct2m, kHydm, kReassocm, k_interRm, k_interLRm
]
# CONSTRAINTS
N_cT = []
K_C = []
# [a-GTP] + [a-GDP] = [beta.gamma] **SMALL_ERROR**
if False:
N_cT = np.zeros(len(M[0]))
N_cT[num_cols + 6] = 1 # beta_gamma
N_cT[num_cols + 5] = -1 # a_GTP
N_cT[num_cols + 7] = -1 # a_GDP
K_C = [1]
# volume vector
W = list(np.append([1] * num_cols, [V['V_myo']] * num_rows))
return (k_kinetic, [N_cT], K_C, W)