Modelling Beta-adrenergic Control of Cardiac Myocyte Contractility in Silico Catherine Lloyd Auckland Bioengineering Institute, The University of Auckland Model Status This CellML version of the Saucerman and McCulloch 2003 model is a translation of Jeff Saucerman's original MATLAB code. It doesn't run in COR due to the presence of differential algebraic equations (DAEs). Use of additional RDF intial condition hints allow this version to run in the head revision of OpenCell using IDA as the solver. Exporting the CellML to MATLAB using OpenCell and then running the MATLAB output also works. It recreates the results of the original published model. Units require further correction and we are continuting to work on this model. Model Structure ABSTRACT: The beta-adrenergic signaling pathway regulates cardiac myocyte contractility through a combination of feedforward and feedback mechanisms. We used systems analysis to investigate how the components and topology of this signaling network permit neurohormonal control of excitation-contraction coupling in the rat ventricular myocyte. A kinetic model integrating beta-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements. Model analysis was used to investigate quantitatively the effects of specific molecular perturbations. 3-Fold overexpression of adenylyl cyclase in the model allowed an 85% higher rate of cyclic AMP synthesis than an equivalent overexpression of beta 1-adrenergic receptor, and manipulating the affinity of Gs alpha for adenylyl cyclase was a more potent regulator of cyclic AMP production. The model predicted that less than 40% of adenylyl cyclase molecules may be stimulated under maximal receptor activation, and an experimental protocol is suggested for validating this prediction. The model also predicted that the endogenous heat-stable protein kinase inhibitor may enhance basal cyclic AMP buffering by 68% and increasing the apparent Hill coefficient of protein kinase A activation from 1.0 to 2.0. Finally, phosphorylation of the L-type calcium channel and phospholamban were found sufficient to predict the dominant changes in myocyte contractility, including a 2.6x increase in systolic calcium (inotropy) and a 28% decrease in calcium half-relaxation time (lusitropy). By performing systems analysis, the consequences of molecular perturbations in the beta-adrenergic signaling network may be understood within the context of integrative cellular physiology. The original paper reference is cited below: Modeling beta-adrenergic control of cardiac myocyte contractility in silico , Jeffrey J. Saucerman, Laurence L. Brunton, Anushka P. Michailova, and Andrew D. McCulloch, 2003, Journal of Biological Chemistry , 48, 47997-48003. PubMed ID: 12972422 cell diagram <imagedata fileref="saucerman_mcculloch_2003.png" /> Schematic diagram of the integrated model components, including the beta-adrenergic network, calcium handling, and the electrophysiology of the rat ventricular myocyte.
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saucerman_brunton_michailova_mcculloch_2003
testout
Charge flow rate
Chemical concentration
Chemical potential
Chemical concentration flow rate
Nernst potential
Cytosol of cardiac myocyte
Junctional sarcoplasmic reticulum of cardiac muscle cell
Sarcoplasmic reticulum of cardiac muscle cell
Sarcolemma of cardiac muscle cell
Extracellular space
cAMP biosynthetic process
junctional sarcoplasmic reticulum membrane
calcium channel complex
potassium channel complex
sodium channel complex
sodium:potassium-exchanging ATPase activity involved in regulation of cardiac muscle cell membrane potential
sodium/calcium exchanger 1
adenylate cyclase
null
A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A computational assignment triggered by an Event
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
The output of an SBML-style Function Definition
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
sodium(1+)
potassium(1+)
calcium(2+)
forskolin
3-isobutyl-1-methylxanthine
ventricular cardiac muscle cell
Beta-1 adrenergic receptor
Background Na+ current flow
CICR release current
Ca2+ ion flux into the rat ventricular myocyte
Ca2+ transfer from JSR to NSR
Ca2+ uptake into the NSR by the SR
Calcium Nernst potential
Background Ca current
Sarcoplasm membrane potential
<eq /> I_CaB <times /> G_CaB <minus /> V_m E_Ca
Concentration of intracellular calcium in the rat ventricular myocyte
Concentration of junctional SR Ca2+ ions
<eq /> t_rel <plus /> trel 2 <sep /> -3 <eq /> ryr_on <minus /> 1 <exp /> <divide /> <minus /> t_rel tau_on <eq /> ryr_off <exp /> <divide /> <minus /> t_rel tau_off <eq /> g_rel <divide /> G_max_rel <plus /> 1 <exp /> <divide /> <plus /> I_Ca_tot 5 0.9 <eq /> I_rel <times /> g_rel ryr_on ryr_off <minus /> Ca_jsr Ca_i
Concentration of Protein phosphatase-1
Concentration of phosphodiesterase
<eq /> b_trpn <divide /> <times /> TRPN_bar Km_TRPN <power /> <plus /> Km_TRPN Ca_i 2 <eq /> b_cmdn <divide /> <times /> CMDN_bar Km_CMDN <power /> <plus /> Km_CMDN Ca_i 2 <eq /> b_indo <divide /> <times /> INDO_bar Km_INDO <power /> <plus /> Km_INDO Ca_i 2 <eq /> B_myo <divide /> 1 <plus /> 1 b_cmdn b_trpn b_trpn b_indo
Sodium nernst potential
Na+ flux across sarcolemma of rat ventricular myocyte
Time
<eq /> am <divide /> <times /> 0.32 <plus /> V_m 47.13 <minus /> 1 <exp /> <times /> <minus /> 0.1 <plus /> V_m 47.13 <eq /> bm <times /> 0.08 <exp /> <divide /> <minus /> V_m 11 <eq /> ah 0 <geq /> V_m <minus /> 40 <times /> 0.135 <exp /> <divide /> <plus /> 80 V_m <minus /> 6.8 <eq /> aj 0 <geq /> V_m <minus /> 40 <divide /> <times /> <minus /> <times /> <minus /> 1.2714 <sep /> 5 <exp /> <times /> 0.2444 V_m <times /> 3.474 <sep /> -5 <exp /> <times /> <minus /> 0.04391 V_m <plus /> V_m 37.78 <plus /> 1 <exp /> <times /> 0.311 <plus /> V_m 79.23 <eq /> bh <divide /> 1 <times /> 0.13 <plus /> 1 <exp /> <divide /> <minus /> <plus /> V_m 10.66 11.1 <geq /> V_m <minus /> 40 <plus /> <times /> 3.56 <exp /> <times /> 0.079 V_m <times /> 3.1 <sep /> 5 <exp /> <times /> 0.35 V_m <eq /> bj <divide /> <times /> 0.3 <exp /> <times /> <minus /> 2.575 <sep /> -7 V_m <plus /> 1 <exp /> <times /> <minus /> 0.1 <plus /> V_m 32 <geq /> V_m <minus /> 40 <divide /> <times /> 0.1212 <exp /> <times /> <minus /> 0.01052 V_m <plus /> 1 <exp /> <times /> <minus /> 0.1378 <plus /> V_m 40.14 <eq /> <diff /> time m <times /> 1 <sep /> 3 <minus /> <times /> am <minus /> 1 m <times /> bm m <eq /> <diff /> time h <times /> 1 <sep /> 3 <minus /> <times /> ah <minus /> 1 h <times /> bh h <eq /> <diff /> time j <times /> 1 <sep /> 3 <minus /> <times /> aj <minus /> 1 j <times /> bj j <eq /> I_Na <times /> G_Na <power /> m 3 h j <minus /> V_m E_Na
Total K+ current
Total membrane Na+ current
Concentration of intracellular potassium in the rat ventricular myocyte.
Concentration of intracellular sodium in the rat ventricular myocyte
<eq /> V_clamp V_test <and /> <gt /> time 59.1 <lt /> time 59.5 V_hold <eq /> I_app 0 <eq /> protocol 0 I_pace <eq /> protocol 1 <divide /> <minus /> V_clamp V_m 0.02 <eq /> <diff /> time Na_i <divide /> <times /> <minus /> 1 <sep /> 3 I_Na_tot A_Cap <times /> V_myo z_Na Frdy <eq /> <diff /> time K_i <divide /> <times /> <minus /> 1 <sep /> 3 I_K_tot A_Cap <times /> V_myo z_K Frdy <eq /> <diff /> time Ca_i <times /> <minus /> B_myo <minus /> <plus /> <divide /> <times /> 1 <sep /> 3 I_Ca_tot A_Cap <times /> V_myo z_Ca Frdy <divide /> <times /> <minus /> I_up I_leak V_nsr V_myo <divide /> <times /> I_rel V_jsr V_myo <eq /> <diff /> time V_m <times /> <minus /> 1 <sep /> 3 <minus /> <plus /> I_Ca_tot I_K_tot I_Na_tot I_app <eq /> <diff /> time trel <minus /> 1 <times /> 1 <sep /> 4 trel <gt /> <times /> <minus /> 1 <sep /> 3 <minus /> <plus /> I_Ca_tot I_K_tot I_Na_tot I_app 30 <sep /> 3 1
<eq /> LCCa <minus /> LCC_tot LCCa_p <eq /> LCCa_PHOSPH <divide /> <times /> epsilon k_pka_lcc PKAC_II LCCa <plus /> Km_pka_lcc <times /> epsilon LCCa <eq /> LCCa_DEPHOSPH <divide /> <times /> epsilon k_pp2a_lcc PP2A_lcc_tot LCCa_p <plus /> Km_pp2a_lcc <times /> epsilon LCCa_p <eq /> LCCb <minus /> LCC_tot LCCb_p <eq /> LCCb_PHOSPH <divide /> <times /> epsilon k_pka_lcc PKAC_II LCCb <plus /> Km_pka_lcc <times /> epsilon LCCb <eq /> LCCb_DEPHOSPH <divide /> <times /> epsilon k_pp1_lcc PP1_lcc_tot LCCb_p <plus /> Km_pp1_lcc <times /> epsilon LCCb_p <eq /> <diff /> time LCCa_p <minus /> LCCa_PHOSPH LCCa_DEPHOSPH <eq /> <diff /> time LCCb_p <minus /> LCCb_PHOSPH LCCb_DEPHOSPH <eq /> frac_LCCa_p <divide /> LCCa_p LCC_tot <eq /> frac_LCCa_po 0.2041 <eq /> frac_LCCb_p <divide /> LCCb_p LCC_tot <eq /> frac_LCCb_po 0.2336
L-Type calcium current
Potassium current through the channel
Total L-type Ca2+ current
<eq /> a_lcc <times /> 400 <exp /> <divide /> <plus /> V_m 2 10 <eq /> b_lcc <times /> 50 <exp /> <divide /> <times /> <minus /> 1 <plus /> V_m 2 13 <eq /> f_lcc <times /> f <plus /> <divide /> <times /> 0.375 frac_LCCa_p frac_LCCa_po 0.625 <eq /> y_lcc_inf <plus /> <divide /> 1 <plus /> 1 <exp /> <divide /> <plus /> V_m 55 7.5 <divide /> 0.1 <plus /> 1 <exp /> <divide /> <plus /> <minus /> V_m 21 6 <eq /> tau_y_lcc <plus /> 0.02 <divide /> 0.3 <plus /> 1 <exp /> <divide /> <plus /> V_m 30 9.5 <eq /> gamma <times /> gamma_o Ca_i <eq /> v_gamma <times /> gamma <plus /> <power /> <minus /> 1 v 4 <times /> 2 v <power /> <minus /> 1 v 3 <times /> 4 <power /> v 2 <power /> <minus /> 1 v 2 <times /> 8 <power /> v 3 <minus /> 1 v <times /> 16 <power /> v 4 <minus /> 1 <divide /> f_lcc g <eq /> v_omega <times /> omega <plus /> <power /> <minus /> 1 w 4 <times /> 0.5 w <power /> <minus /> 1 w 3 <times /> 0.25 <power /> w 2 <power /> <minus /> 1 w 2 <times /> 0.125 <power /> w 3 <minus /> 1 w <times /> 0.0625 <power /> w 4 <eq /> <diff /> time v <minus /> <times /> a_lcc <minus /> 1 v <times /> b_lcc v <eq /> <diff /> time w <minus /> <times /> 2 a_lcc <minus /> 1 w <times /> <divide /> b_lcc 2 w <eq /> <diff /> time x <minus /> <times /> f_lcc <minus /> 1 x <times /> g x <eq /> <diff /> time y <divide /> <minus /> y_lcc_inf y tau_y_lcc <eq /> <diff /> time z <minus /> <times /> v_omega <minus /> 1 z <times /> v_gamma z <eq /> i_bar_Ca <divide /> <times /> p_Ca 4 V_m Frdy FoRT <minus /> <times /> 1 <sep /> -3 <exp /> <times /> 2 V_m FoRT <times /> 0.341 Ca_ext <minus /> <exp /> <times /> 2 V_m FoRT 1 <eq /> i_bar_K <divide /> <times /> p_K V_m Frdy FoRT <minus /> <times /> K_i <exp /> <times /> V_m FoRT K_ext <minus /> <exp /> <times /> V_m FoRT 1 <eq /> f_avail <times /> 0.5 <plus /> <divide /> <times /> 0.4 frac_LCCb_p frac_LCCb_po 0.6 <eq /> I_Ca <times /> i_bar_Ca N_lcc f_avail <power /> v 4 x y z <eq /> I_CaK <times /> <divide /> i_bar_K <plus /> 1 <divide /> I_Ca I_Ca05 N_lcc f_avail <power /> v 4 x y z <eq /> I_Ca_tot <plus /> I_Ca I_CaK
Na+ - Ca2+ current exchanger across sarcolemma
Na+ - K+ pump current across sarcolemma
Background Na+ current
<eq /> I_NaB <times /> G_NaB <minus /> V_m E_Na
<eq /> s4 <times /> <exp /> <times /> eta V_m FoRT <power /> Na_i 3 Ca_ext <eq /> s5 <times /> <exp /> <times /> <minus /> eta 1 V_m FoRT <power /> Na_ext 3 Ca_i <eq /> I_NCX <times /> <divide /> k_NaCa <times /> <plus /> <power /> Km_Na 3 <power /> Na_ext 3 <plus /> Km_Ca Ca_ext <plus /> 1 <times /> k_sat <exp /> <times /> <minus /> eta 1 V_m FoRT <minus /> s4 s5
<eq /> sigma <divide /> <minus /> <exp /> <divide /> Na_ext 67.3 1 7 <eq /> f_NaK <divide /> 1 <plus /> 1 <times /> 0.1245 <exp /> <times /> <minus /> 0.1 V_m FoRT <times /> 0.0365 sigma <exp /> <times /> <minus /> V_m FoRT <eq /> I_NaK <divide /> <times /> <divide /> <times /> I_bar_NaK f_NaK <plus /> 1 <power /> <divide /> Km_Nai Na_i 1.5 K_ext <plus /> K_ext Km_Ko
Potassium nernst potentials
<eq /> FoRT <divide /> <divide /> Frdy R Temp <eq /> E_Na <times /> <divide /> 1 <times /> FoRT z_Na <ln /> <divide /> Na_ext Na_i <eq /> E_K <times /> <divide /> 1 <times /> FoRT z_K <ln /> <divide /> K_ext K_i <eq /> E_Ca <times /> <divide /> 1 <times /> FoRT z_Ca <ln /> <divide /> Ca_ext Ca_i <eq /> E_Cl <minus /> 40
Network SR
Network SR Ca2+ concentration
Transfer flux of Ca2+ from the JSR to the NSR
<eq /> Km_up <divide /> <times /> Km_up0 <plus /> 1 <times /> 2 frac_PLB <plus /> 1 <times /> 2 frac_PLB_o <eq /> I_up <divide /> <times /> I_up_bar <power /> Ca_i 2 <plus /> <power /> Km_up 2 <power /> Ca_i 2 <eq /> I_leak <divide /> <times /> I_up_bar Ca_nsr NSR_bar <eq /> I_tr <divide /> <minus /> Ca_nsr Ca_jsr tau_tr <eq /> B_jsr <divide /> 1 <plus /> 1 <divide /> <times /> CSQN_bar Km_CSQN <power /> <plus /> Km_CSQN Ca_jsr 2 <eq /> <diff /> time Ca_nsr <minus /> <minus /> I_up I_leak <divide /> <times /> I_tr V_jsr V_nsr <eq /> <diff /> time Ca_jsr <times /> B_jsr <minus /> I_tr I_rel <eq /> SR_content <times /> 1 <sep /> 3 <plus /> <divide /> <times /> <plus /> Ca_jsr <divide /> Ca_jsr B_jsr V_jsr V_myo <divide /> <times /> Ca_nsr V_nsr V_myo
Concentration of cyclic AMP
<eq /> PKI <divide /> <times /> PKI_tot Ki_pki <plus /> Ki_pki PKAC_I PKAC_II <eq /> A2RC_I <times /> <divide /> PKAC_I K_d PKAC_I <plus /> 1 <divide /> PKI Ki_pki <eq /> A2R_I <times /> PKAC_I <plus /> 1 <divide /> PKI Ki_pki <eq /> A2RC_II <times /> <divide /> PKAC_II K_d PKAC_II <plus /> 1 <divide /> PKI Ki_pki <eq /> A2R_II <times /> PKAC_II <plus /> 1 <divide /> PKI Ki_pki <eq /> ARC_I <times /> <divide /> K_a cAMP A2RC_I <eq /> ARC_II <times /> <divide /> K_a cAMP A2RC_II <eq /> PKA_temp <plus /> <divide /> <times /> K_a K_b K_d <divide /> <times /> K_a cAMP K_d <divide /> <power /> cAMP 2 K_d <eq /> cAMP <minus /> <minus /> cAMP_tot <plus /> ARC_I <times /> 2 A2RC_I <times /> 2 A2R_I <plus /> ARC_II <times /> 2 A2RC_II <times /> 2 A2R_II <eq /> zed <minus /> <times /> 2 PKAI_tot <power /> cAMP 2 <times /> PKAC_I <plus /> 1 <divide /> PKI Ki_pki <plus /> <times /> PKA_temp PKAC_I <power /> cAMP 2 <eq /> zed1 <minus /> <times /> 2 PKAII_tot <power /> cAMP 2 <times /> PKAC_II <plus /> 1 <divide /> PKI Ki_pki <plus /> <times /> PKA_temp PKAC_II <power /> cAMP 2
Concentration of phospholamban
<eq /> PLB <minus /> PLB_tot PLB_p <eq /> PLB_PHOSPH <divide /> <times /> k_pka_plb PKAC_I PLB <plus /> Km_pka_plb PLB <eq /> PLB_DEPHOSPH <divide /> <times /> k_pp1_plb PP1 PLB_p <plus /> Km_pp1_plb PLB_p <eq /> Inhib1 <minus /> Inhib1_tot Inhib1p_tot <eq /> Inhib1p_PP1 <divide /> <times /> Inhib1p PP1 Ki_inhib1 <eq /> Inhib1_PHOSPH <divide /> <times /> k_pka_i1 PKAC_I Inhib1 <plus /> Km_pka_i1 Inhib1 <eq /> Inhib1_DEPHOSPH <divide /> <times /> Vmax_pp2a_i1 Inhib1p_tot <plus /> Km_pp2a_i1 Inhib1p_tot <eq /> <diff /> time PLB_p <minus /> PLB_PHOSPH PLB_DEPHOSPH <eq /> <diff /> time Inhib1p_tot <minus /> Inhib1_PHOSPH Inhib1_DEPHOSPH <eq /> Inhib1p <minus /> Inhib1p_tot Inhib1p_PP1 <eq /> PP1 <minus /> PP1_tot Inhib1p_PP1 <eq /> frac_PLB_p <divide /> PLB_p PLB_tot <eq /> frac_PLB <divide /> PLB PLB_tot <eq /> frac_PLB_o 0.9613
<eq /> I_pace 10 <and /> <geq /> time 0 <leq /> time 10 <leq /> <minus /> <minus /> time 0 <times /> <floor /> <divide /> <minus /> time 0 1 1 0.003 0
Plateau K+ current
<eq /> Kp <divide /> 1 <plus /> 1 <exp /> <divide /> <minus /> 7.488 V_m 5.98 <eq /> I_Kp <times /> G_Kp Kp <minus /> V_m E_K
Sarcolemmal Ca2+ pump current
<eq /> I_PCa <divide /> <times /> I_bar_PCa Ca_i <plus /> Km_PCa Ca_i
Sodium flux across sarcolemma of rat ventricular myocyte
Subspace steady state current across sarcolemma
<eq /> r_ss_inf <divide /> 1 <plus /> 1 <exp /> <divide /> <plus /> V_m 11.5 <minus /> 11.82 <eq /> tau_r_ss <divide /> 10 <plus /> <times /> 45.16 <exp /> <times /> 0.03577 <plus /> V_m 50 <times /> 98.9 <exp /> <times /> <minus /> 0.1 <plus /> V_m 38 <eq /> s_ss_inf <divide /> 1 <plus /> 1 <exp /> <divide /> <plus /> V_m 87.5 10.3 <eq /> tau_s_ss 2.1 <eq /> <diff /> time r_ss <divide /> <minus /> r_ss_inf r_ss tau_r_ss <eq /> <diff /> time s_ss <divide /> <minus /> s_ss_inf s_ss tau_s_ss <eq /> I_ss <times /> G_ss r_ss s_ss <minus /> V_m E_K
Time independent K+ current across sarcolemma
<eq /> a_Ki <divide /> 1.02 <plus /> 1 <exp /> <times /> 0.2385 <minus /> <minus /> V_m E_K 59.215 <eq /> b_Ki <divide /> <plus /> <times /> 0.49124 <exp /> <times /> 0.08032 <minus /> <plus /> V_m 5.476 E_K <exp /> <times /> 0.06175 <minus /> <minus /> V_m E_K 594.31 <plus /> 1 <exp /> <times /> <minus /> 0.5143 <plus /> <minus /> V_m E_K 4.753 <eq /> Ki_ss <divide /> a_Ki <plus /> a_Ki b_Ki <eq /> I_Ki <times /> G_Ki_bar <root /> <divide /> K_ext 5.4 Ki_ss <minus /> V_m E_K
Time independent K current
Transient Outward K+ current
<eq /> I_Na_tot <plus /> I_Na I_NaB <times /> 3 I_NCX <times /> 3 I_NaK <eq /> I_K_tot <plus /> <minus /> <plus /> I_to I_ss I_Ki I_Kp <times /> 2 I_NaK I_CaK <eq /> I_Ca_tot <minus /> <plus /> I_Ca I_CaB I_PCa <times /> 2 I_NCX
<eq /> r_toss <divide /> 1 <plus /> 1 <exp /> <divide /> <plus /> V_m 10.6 <minus /> 11.42 <eq /> s_toss <divide /> 1 <plus /> 1 <exp /> <divide /> <plus /> V_m 43.5 6.8841 <eq /> tau_r_to <divide /> 1 <plus /> <times /> 45.16 <exp /> <times /> 0.03577 <plus /> V_m 50 <times /> 98.9 <exp /> <times /> <minus /> 0.1 <plus /> V_m 38 <eq /> tau_s_to <plus /> <times /> 0.35 <exp /> <times /> <minus /> 1 <power /> <divide /> <plus /> V_m 70 15 2 0.035 <eq /> tau_ss_to <plus /> <times /> 3.7 <exp /> <times /> <minus /> 1 <power /> <divide /> <plus /> V_m 70 30 2 0.035 <eq /> <diff /> time r_to <divide /> <minus /> r_toss r_to tau_r_to <eq /> <diff /> time s_to <divide /> <minus /> s_toss s_to tau_s_to <eq /> <diff /> time ss_to <divide /> <minus /> s_toss ss_to tau_ss_to <eq /> I_to <times /> G_to r_to <plus /> <times /> 0.886 s_to <times /> 0.114 ss_to <minus /> V_m E_K
Concentration of GTP-bound G_s alpha
Beta1-specific in activation by phosphorylation at S464 by beta-adrenergic receptor kinase.
Beta1-specific in activation by phosphorylation at S301 by beta-adrenergic receptor kinase.
Concentration of beta1-adrenergic signaling in the cardiac myocyte
<eq /> LR <divide /> <times /> L R Kl <eq /> LRG <divide /> <times /> LR Gs Kr <eq /> RG <divide /> <times /> R Gs Kc <eq /> BARK_DESENS <times /> k_bar_kp <plus /> LR LRG <eq /> BARK_RESENS <times /> k_bar_km b1_AR_d <eq /> PKA_DESENS <times /> k_p_kap PKAC_I b1_AR_tot <eq /> PKA_RESENS <times /> k_p_kam b1_AR_p <eq /> G_ACT <times /> k_g_act <plus /> RG LRG <eq /> HYD <times /> k_hyd Gs_agtp_tot <eq /> REASSOC <divide /> <times /> k_reassoc Gs_agdp Gs_bg 1 <eq /> L <minus /> <minus /> L_totmax LR LRG <eq /> R <minus /> <minus /> <minus /> b1_AR_tot LR LRG RG <eq /> Gs <minus /> <minus /> Gs_tot LRG RG <eq /> <diff /> time b1_AR_tot <minus /> <plus /> <minus /> BARK_RESENS BARK_DESENS PKA_RESENS PKA_DESENS <eq /> <diff /> time b1_AR_d <minus /> BARK_DESENS BARK_RESENS <eq /> <diff /> time b1_AR_p <minus /> PKA_DESENS PKA_RESENS <eq /> <diff /> time Gs_agtp_tot <minus /> G_ACT HYD <eq /> <diff /> time Gs_agdp <minus /> HYD <times /> REASSOC 1 <eq /> <diff /> time Gs_bg <minus /> G_ACT <times /> REASSOC 1
Concentration of adenylyl cyclase in the rat ventricular myocyte
Concentration of forskolin on the sarcolemma
Concentration of IBMX (3-isobutyl-1-methylxanthine)
Concentration of nonspecific phosphodiesterase inhibitor IBMX
<eq /> Gsa_GTP_AC <divide /> <times /> Gsa_GTP AC K_gsa <eq /> Fsk_AC <divide /> <times /> Fsk AC K_fsk <eq /> AC_ACT_BASAL <divide /> <times /> k_ac_basal AC ATP <plus /> Km_basal ATP <eq /> AC_ACT_GSA <divide /> <times /> k_ac_gsa Gsa_GTP_AC ATP <plus /> Km_gsa ATP <eq /> AC_ACT_FSK <divide /> <times /> k_ac_fsk Fsk_AC ATP <plus /> Km_fsk ATP <eq /> PDE_ACT <divide /> <times /> k_pde PDE cAMP <plus /> Km_pde cAMP <eq /> PDE_IBMX <divide /> <times /> PDE IBMX Ki_ibmx <eq /> Gsa_GTP <minus /> Gs_agtp_tot Gsa_GTP_AC <eq /> Fsk <minus /> Fsk_tot Fsk_AC <eq /> AC <minus /> AC_tot Gsa_GTP_AC <eq /> PDE <minus /> PDE_tot PDE_IBMX <eq /> IBMX <minus /> IBMX_tot PDE_IBMX <eq /> <diff /> time cAMP_tot <plus /> <minus /> <plus /> AC_ACT_BASAL AC_ACT_GSA PDE_ACT AC_ACT_FSK