GongBetaAdrenergicSignaling

A Julia package providing a ModelingToolkit.jl implementation of the Gong et al. (2020) beta-adrenergic signaling model for cardiac myocytes.

Features

• 57 state variables: G-protein signaling, cAMP dynamics, PKA activation, PDE phosphorylation, PP1 inhibition, and substrate phosphorylation
• 167 parameters: Automatically computed from structural parameters
• Isoproterenol stimulation: Simply set iso_conc and all 167 parameters automatically update
• Phosphorylation observables: Built-in observables for effective fractions of 8 cardiac ion channels/proteins
• ModelingToolkit integration: Symbolic model construction with automatic code generation

Basic Usage

using GongBetaAdrenergicSignaling
using OrdinaryDiffEq

# Create model with baseline (no isoproterenol)
@mtkcompile sys = GongBetaAdrenergic()

# Create ODE problem with default initial conditions
prob = ODEProblem(sys, [], (0.0, 1000.0))

# Solve with stiff solver
sol = solve(prob, Rodas5P())

Isoproterenol Stimulation

The key feature of this model is the ability to simulate beta-adrenergic stimulation by simply changing the iso_conc parameter. All 167 model parameters automatically recalculate based on the isoproterenol concentration:

# Simulate with 1.0 μM isoproterenol
@mtkcompile sys = GongBetaAdrenergic(iso_conc=1.0)
prob = ODEProblem(sys, [], (0.0, 1000.0))
sol = solve(prob, Rodas5P())

# Try different concentrations
for iso in [0.0, 0.01, 0.1, 1.0]
    @mtkcompile sys = GongBetaAdrenergic(iso_conc=iso)
    prob = ODEProblem(sys, [], (0.0, 5000.0))
    sol = solve(prob, Rodas5P())
    # Analyze dose-response...
end

You can also adjust the cell geometry via radiusmultiplier:

@mtkcompile sys = GongBetaAdrenergic(iso_conc=1.0, radiusmultiplier=1.2)

Phosphorylation Fraction Observables

The model automatically computes effective phosphorylation fractions for 8 cardiac substrates as observables. These are available directly from the solution:

using GongBetaAdrenergicSignaling
using OrdinaryDiffEq

# Solve the model
@mtkcompile sys = GongBetaAdrenergic(iso_conc=1.0)
prob = ODEProblem(sys, [], (0.0, 5000.0))
sol = solve(prob, Rodas5P())

# Access phosphorylation fractions (available at all time points)
fICaL_PKA = sol[sys.fICaL_PKA]   # L-type calcium channel
fIKs_PKA = sol[sys.fIKs_PKA]     # Slow delayed rectifier K+ channel
fPLB_PKA = sol[sys.fPLB_PKA]     # Phospholamban (SERCA regulation)
fTnI_PKA = sol[sys.fTnI_PKA]     # Troponin I (myofilament Ca2+ sensitivity)
fINa_PKA = sol[sys.fINa_PKA]     # Sodium channel
fINaK_PKA = sol[sys.fINaK_PKA]   # Na+/K+ pump
fRyR_PKA = sol[sys.fRyR_PKA]     # Ryanodine receptor (Ca2+ release)
fIKur_PKA = sol[sys.fIKur_PKA]   # Ultra-rapid delayed rectifier K+ channel
fMyBPC_PKA = sol[sys.fMyBPC_PKA] # Myosin binding protein C

# Extract final values
final_fICaL = sol[sys.fICaL_PKA][end]

These observables are computed automatically during the solve and represent the effective fraction of each substrate that is phosphorylated by PKA.

Accessing Parameters

This package uses ModelingToolkit v11, which reorders parameters during structural simplification. Always use symbolic access to retrieve parameter values:

# Correct: symbolic parameter access
c1_value = prob.ps[sys.c1]   # iso_conc
c50_value = prob.ps[sys.c50]

# Wrong: positional indexing (unreliable)
# c1_value = prob.p[1][1]  # DO NOT USE

Reference

Gong, J.Q.X., Susilo, M.E., Sher, A., Musante, C.J., & Sobie, E.A. (2020). Quantitative analysis of variability in an integrated model of human ventricular electrophysiology and β-adrenergic signaling. Journal of Molecular and Cellular Cardiology, 143, 96-106. DOI: https://doi.org/10.1016/j.yjmcc.2020.04.009