Effects of isoproterenol

using ModelingToolkit
using OrdinaryDiffEq, SteadyStateDiffEq, DiffEqCallbacks
using Plots
using CSV
using DataFrames
using Dates
using CaMKIIModel
using CaMKIIModel: second, μM
Plots.default(lw=1.5)

Setup model

sys = build_neonatal_ecc_sys(simplify=true, reduce_iso=true, reduce_camk=true)
tend = 205second
prob = ODEProblem(sys, [], tend)
stimstart = 30second
stimend = 120second
alg = KenCarp47()
KenCarp47(; linsolve = nothing, nlsolve = OrdinaryDiffEqNonlinearSolve.NLNewton{Rational{Int64}, Rational{Int64}, Rational{Int64}, Nothing}(1//100, 10, 1//5, 1//5, false, true, nothing), precs = DEFAULT_PRECS, smooth_est = true, extrapolant = linear, controller = PI, autodiff = ADTypes.AutoForwardDiff(),)

Without isoproterenol

@unpack Istim = sys
callback = build_stim_callbacks(Istim, stimend; period=1second, starttime=stimstart)
@time sol = solve(prob, alg; callback)
 11.687643 seconds (23.21 M allocations: 1.027 GiB, 2.29% gc time, 94.29% compilation time)
retcode: Success
Interpolation: 3rd order Hermite
t: 4019-element Vector{Float64}:
      0.0
      0.019333123284849377
      0.09098129546758026
      0.20735582943983927
      0.4561191027686269
      1.047256292840616
      2.0342667657223767
      3.4517766411484665
      6.733792423912831
     12.45011708102324
      ⋮
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 182484.5491752562
 189877.08679998867
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 205000.0
u: 4019-element Vector{Vector{Float64}}:
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 ⋮
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 [151392.54030147012, 13401.008541992669, -70.04507621661438, 0.13440549845720723, 0.13440579999971797, 0.13440610224650276, 0.1344064052707838, 0.13440670914874442, 0.1344070139596785, 0.13440731978615258  …  0.0011846226574291994, 0.0016131220978756928, 0.00249699961657388, 0.0015971504154408847, 0.9997277178091893, 0.9997257276831517, 0.0064527963308284725, 782.4907193099504, 782.1660479180341, 0.0018438340894160747]
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i = (sys.t / 1000, sys.vm)
plot(sol, idxs=i, tspan=(100second, 101second), title="Action potential", xlabel="Time (s)")

plot(sol, idxs=(sys.t / 1000, [sys.Cai_sub_SR, sys.Cai_sub_SL, sys.Cai_mean]), tspan=(100second, 101second), title="Calcium transient", xlabel="Time (s)", ylabel="Conc. (μM)", label=["Ca (SR)" "Ca (SL)" "Ca (avg)"])

plot(sol, idxs=(sys.t / 1000, sys.CaMKAct * 100), title="Active CaMKII", label=false, ylabel="Active fraction (%)", xlabel="Time (s)")

0.1uM isoproterenol

prob2 = remake(prob, p=[sys.ISO => 0.1μM])
sol2 = solve(prob2, alg; callback)
retcode: Success
Interpolation: 3rd order Hermite
t: 4135-element Vector{Float64}:
      0.0
      0.0193322110715843
      0.09097534627605619
      0.20734339686524522
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      3.5324261824253536
      6.954473747659774
     12.881140201769878
      ⋮
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 173545.3761460094
 180014.30394160934
 187606.5812407107
 193771.36169472226
 202258.5546944703
 205000.0
u: 4135-element Vector{Vector{Float64}}:
 [150952.75035000002, 13838.37602, -68.79268, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113, 0.12113  …  0.26081, 0.00977, 0.00188, 0.09243, 0.22156, 0.966, 0.00702, 830.0, 830.0, 0.0026]
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 ⋮
 [150956.61871478386, 13826.31418975028, -70.54110277542554, 0.12651778225662627, 0.1265179719634086, 0.12651815629260185, 0.12651833517326516, 0.12651850853159446, 0.126518676290776, 0.12651883837083117  …  0.001096779480919929, 0.0015547183343295227, 0.002406631510789332, 0.001486983192435375, 0.9996909553239539, 0.9997535701805131, 0.006238780040898278, 922.9710753731903, 921.4606991592178, 0.007238228951503681]
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 [151115.8594846801, 13667.306651210176, -70.2446752057367, 0.12444604318124854, 0.12444621639919698, 0.1244463851034755, 0.12444654923727193, 0.12444670874148314, 0.12444686355459839, 0.12444701361257504  …  0.001148235406541825, 0.001589357861889739, 0.002460240844312338, 0.0015517256493605726, 0.9997395313805426, 0.9997373118314562, 0.00636581348321611, 923.6146819743166, 922.1876724310209, 0.006833930884910477]
 [151163.4086607211, 13619.827718546245, -70.1537573095305, 0.12384349404614278, 0.1238436620508058, 0.12384382578983744, 0.12384398521039737, 0.1238441402575143, 0.12384429087397714, 0.12384443700021946  …  0.0011644922680011747, 0.0016001339858349936, 0.002476918751158997, 0.0015721281378495758, 0.9997344347951802, 0.9997321134613276, 0.006405289011439834, 923.7784770865676, 922.3755365432836, 0.006717471837720127]
 [151200.82606815622, 13582.46575825801, -70.08139556479705, 0.12337470083626634, 0.12337486479282901, 0.12337502467203963, 0.12337518042404486, 0.12337533199698099, 0.12337547933687133, 0.12337562238751705  …  0.0011775993452930135, 0.0016087623854668719, 0.0024902725270956193, 0.001588556182038846, 0.9997302316254195, 0.9997279021129987, 0.006436881287735708, 923.898120635241, 922.5138490527871, 0.006627221043370219]
 [151250.65169013935, 13532.714172153257, -69.98390525504435, 0.12275782332043159, 0.12275798179936408, 0.12275813644906478, 0.12275828722356844, 0.12275843407505577, 0.12275857695375876, 0.12275871580786023  …  0.00119549511241225, 0.001620457708052584, 0.0025083728236204718, 0.0016109545458571817, 0.9997244452962329, 0.9997221251109562, 0.006479679154506328, 924.044929864383, 922.6851457938438, 0.006508950781371656]
 [151266.3392015109, 13517.050030513288, -69.95293244202225, 0.12256532743108159, 0.1225654840866105, 0.12256563698855474, 0.12256578609216744, 0.12256593135089533, 0.12256607271628671, 0.12256621013789329  …  0.00120123515027418, 0.0016241917933589064, 0.0025141525378619177, 0.0016181361677016673, 0.9997225815274644, 0.9997202622044831, 0.006493340266788657, 924.0881165067813, 922.7359559042427, 0.006472154406639179]
plot(sol2, idxs=(sys.t / 1000, sys.vm), tspan=(100second, 101second), title="Action potential", xlabel="Time (s)")

plot(sol2, idxs=(sys.t / 1000, [sys.Cai_sub_SR, sys.Cai_sub_SL, sys.Cai_mean]), tspan=(100second, 101second), title="Calcium transcient", xlabel="Time (s)", ylabel="Conc. (μM)", label=["Ca (SR)" "Ca (SL)" "Ca (avg)"])

plot(sol2, idxs=(sys.t / 1000, sys.CaMKAct * 100), title="Active CaMKII", label=false, ylabel="Active fraction (%)", xlabel="Time (s)")

Comparison

i = (sys.t / 1000, sys.Cai_mean)
tspan = (100second, 101second)
plot(sol, idxs=i, title="Calcium transcient", lab="ISO (-)"; tspan)
plot!(sol2, idxs=i, lab="ISO (0.1uM)", xlabel="Time (s)", ylabel="Concentration (μM)"; tspan)

savefig("iso-caT.pdf")
"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/iso-caT.pdf"

Maximal and minimal calcium concentrations in calcium transients.

ca_ctl = sol(tspan[1]:1:tspan[2], idxs=sys.Cai_mean)
println(extrema(ca_ctl))
(0.23504352227637887, 0.5781129853775092)
ca_iso = sol2(tspan[1]:1:tspan[2], idxs=sys.Cai_mean)
println(extrema(ca_iso))
(0.19033626963164474, 0.7110939356316769)
i = (sys.t / 1000, sys.CaMKAct * 100)
plot(sol, idxs=i, title="Active CaMKII", lab="ISO (-)")
plot!(sol2, idxs=i, lab="ISO (0.1uM)", ylabel="Active fraction (%)", xlabel="Time (s)")

savefig("iso-camkact.pdf")
"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/iso-camkact.pdf"
i = (sys.t / 1000, sys.vm)
tspan = (100second, 101second)
plot(sol, idxs=i, title="Action potential", lab="ISO (-)"; tspan)
plot!(sol2, idxs=i, lab="ISO (0.1uM)", xlabel="Time (ms)", ylabel="Voltage (mV)"; tspan)

Experimental data

chemicaldf = CSV.read(joinpath(@__DIR__, "data/CaMKAR-chemical.csv"), DataFrame)
ts = Dates.value.(chemicaldf[!, "Time"]) ./ 10^9
ctl = chemicaldf[!, "Ctrl Mean"]
ctl_error = chemicaldf[!, "Ctrl SD"] ./ sqrt.(chemicaldf[!, "Ctrl N"])
42-element Vector{Float64}:
 0.02305850621757014
 0.023225557529411765
 0.023536003837902393
 0.022995786588235295
 0.023056161133316953
 0.02236794743822152
 0.02448575734900888
 0.02631837493460871
 0.029628792824062226
 0.0306227531696316
 ⋮
 0.02665056333747046
 0.02525893438851731
 0.024749347823716496
 0.024158682609370527
 0.023572491294117648
 0.0240760416039372
 0.023230166
 0.023759599761907887
 0.02369791084482974
iso = chemicaldf[!, "isoproterenol 100nM Mean"]
iso_error = chemicaldf[!, "isoproterenol 100nM SD"] ./ sqrt.(chemicaldf[!, "isoproterenol 100nM N"])
42-element Vector{Float64}:
 0.01906411500114547
 0.019397124616823788
 0.019533446274478245
 0.019307032321568045
 0.0188119595
 0.019208707594448062
 0.020659484720981783
 0.022823236115241556
 0.02568418993766601
 0.02954342161034184
 ⋮
 0.022059148111952916
 0.020698453917127702
 0.020674867906488113
 0.019922601239830914
 0.019312468873824668
 0.019367967435545023
 0.018689615199686285
 0.01921783399052236
 0.01872515441384824
plot(ts, ctl, yerr=ctl_error, lab="Control", color=:blue, markerstrokecolor=:blue)
plot!(ts, iso, yerr=iso_error, lab="ISO 100nM", color=:red, markerstrokecolor=:red)
plot!(xlabel="Time (sec.)", ylabel="CaMKII activity (A.U.)")

savefig("iso-exp.pdf")
"/home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/iso-exp.pdf"

Runtime information

using InteractiveUtils
InteractiveUtils.versioninfo()
Julia Version 1.12.3
Commit 966d0af0fdf (2025-12-15 11:20 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × Intel(R) Core(TM) i7-8700 CPU @ 3.20GHz
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, skylake)
  GC: Built with stock GC
Threads: 2 default, 1 interactive, 2 GC (on 12 virtual cores)
Environment:
  JULIA_CI = true
  JULIA_CONDAPKG_OFFLINE = true
  LD_LIBRARY_PATH = /home/github/actions-runner-1/_work/_tool/Python/3.14.2/x64/lib
  JULIA_NUM_THREADS = 2
  JULIA_PROJECT = /home/github/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/Project.toml
  JULIA_DEPOT_PATH = /home/github/.julia:/home/github/actions-runner-1/_work/_tool/julia/1.12.3/x64/local/share/julia:/home/github/actions-runner-1/_work/_tool/julia/1.12.3/x64/share/julia
  JULIA_CONDAPKG_BACKEND = Null
  JULIA_LOAD_PATH = @:@v#.#:@stdlib
using Pkg
Pkg.status()
Project CaMKIIModel v0.7.0
Status `~/actions-runner-1/_work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/Project.toml`
  [336ed68f] CSV v0.10.15
  [a93c6f00] DataFrames v1.8.1
  [459566f4] DiffEqCallbacks v4.11.0
  [f6369f11] ForwardDiff v1.3.1
  [682c06a0] JSON v1.3.0
  [23fbe1c1] Latexify v0.16.10
  [98b081ad] Literate v2.21.0
  [2fda8390] LsqFit v0.15.1
⌅ [961ee093] ModelingToolkit v10.31.2
  [77ba4419] NaNMath v1.1.3
  [1dea7af3] OrdinaryDiffEq v6.105.0
  [91a5bcdd] Plots v1.41.3
  [9672c7b4] SteadyStateDiffEq v2.8.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

This notebook was generated using Literate.jl.

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