# Location: BG_GPCR_M2_reduced @ e831afee2206 / parameter_finder / kinetic_parameters_GPCR_M2_reduced.py

- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-02-18 13:28:26+13:00
- Desc:
- Updating way cellml is written
- Permanent Source URI:
- https://models.cellml.org/workspace/7dd/rawfile/e831afee220663860fb5e91083cf1d4805d59f5f/parameter_finder/kinetic_parameters_GPCR_M2_reduced.py

# 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 = 1e4 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 = 30 # uM Kc KRh = 0.16 # uM Kh KRL = 11 # uM Kl KRr = KRL/(KRc*KRh) kRcp = fastKineticConstant kRcm = kRcp*KRc kRLp = fastKineticConstant kRLm = kRLp*KRL kRrp = fastKineticConstant # find kRLm using detailed balance # kRrm = kRcm*kRhm*kRrp*kRLp/(kRcp*kRhp*kRLm) kRrm = kRrp * KRr kAct1p = 2.5 # 1/s kAct1m = medReverse # 1/s kAct2p = 2.5 # 1/s kAct2m = medReverse # 1/s kHydp = 0.8 # 1/s kHydm = medReverse # 1/s kReassocp = 1.21e3 # 1/uM.s kReassocm = medReverse # 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, kRLp, kAct1p, kAct2p, kHydp, kReassocp, k_interRp, k_interLRp, k_Rswitchm,k_LRswitchm,kRcm, kRrm, kRLm, 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)