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)
 10.291383 seconds (23.47 M allocations: 1.231 GiB, 4.14% gc time, 91.80% 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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 168819.53333337096
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 182484.55452456992
 189877.09234962234
 197904.13271346927
 205000.0
u: 4019-element Vector{Vector{Float64}}:
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 ⋮
 [151183.0300539171, 13610.02245300075, -70.43523764740401, 0.13696768055827266, 0.13696770541453013, 0.13696772581563565, 0.13696774168076362, 0.13696775292580518, 0.13696775946320075, 0.1369677612017623  …  0.0011149985785722724, 0.001567008773646594, 0.002425643258995569, 0.0015098981196588529, 0.9995947867979871, 0.999747869519957, 0.0062838568216599, 784.9060277549053, 784.5419852203329, 0.002043321971582329]
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 [151392.54033053597, 13401.008513010966, -70.04507616188909, 0.13440549809439598, 0.13440579963690186, 0.13440610188368185, 0.13440640490795813, 0.13440670878591354, 0.13440701359684315, 0.1344073194233121  …  0.0011846226674978554, 0.001613122104436531, 0.0024969996267265597, 0.001597150427996013, 0.9997277178059533, 0.9997257276799157, 0.0064527963548380775, 782.4907188080006, 782.1660474217084, 0.0018438340587762746]
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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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      1.0549952720719484
      2.0687580593126724
      3.5324261824253536
      6.954473747659774
     12.881140201769878
      ⋮
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 161577.99373485308
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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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 ⋮
 [150956.6187147592, 13826.314189776862, -70.54110277547377, 0.12651778225698412, 0.12651797196376646, 0.12651815629295968, 0.12651833517362307, 0.12651850853195237, 0.1265186762911339, 0.1265188383711891  …  0.0010967794809075475, 0.0015547183343237651, 0.0024066315107807144, 0.0014869831924248325, 0.9996909553239575, 0.9997535701805159, 0.006238780040877805, 922.971075373069, 921.4606991590817, 0.007238228951575744]
 [150993.3250348188, 13789.661340753633, -70.47384314763443, 0.12603297147267323, 0.12603315749211752, 0.12603333833678584, 0.1260335139390861, 0.1260336842286991, 0.12603384913243948, 0.12603400857410785  …  0.0011082167393088522, 0.0015625100254287247, 0.002418693176625084, 0.0015014376432098348, 0.9997360968472492, 0.9997499718312494, 0.006267381163349558, 923.1323809169393, 921.6415965711435, 0.007143086075388378]
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 [151074.03077395892, 13709.07379239066, -70.3237244461183, 0.12498223734955859, 0.1249824149500789, 0.12498258781596323, 0.12498275588682323, 0.12498291909983734, 0.12498307738962662, 0.12498323068812273  …  0.0011343095994690384, 0.0015800472776391747, 0.0024458303181922594, 0.0015341954465510688, 0.9997434153103265, 0.9997417491177489, 0.006331688104796494, 923.4597999739248, 922.0113036830816, 0.006937996984118315]
 [151115.85948465823, 13667.306651234054, -70.24467520578284, 0.12444604318154842, 0.12444621639949686, 0.12444638510377543, 0.12444654923757184, 0.12444670874178305, 0.12444686355489831, 0.124447013612875  …  0.0011482354065336258, 0.0015893578618842773, 0.0024602408443038922, 0.0015517256493502826, 0.9997395313805453, 0.9997373118314591, 0.006365813483196116, 923.6146819742337, 922.1876724309261, 0.006833930884968582]
 [151163.40866070002, 13619.827718569324, -70.15375730957557, 0.12384349404642822, 0.12384366205109126, 0.12384382579012292, 0.12384398521068285, 0.12384414025779981, 0.12384429087426266, 0.12384443700050499  …  0.0011644922679930215, 0.0016001339858296311, 0.0024769187511507066, 0.0015721281378393182, 0.9997344347951828, 0.9997321134613302, 0.006405289011420214, 923.7784770864921, 922.3755365431966, 0.006717471837774962]
 [151200.82606813576, 13582.46575828045, -70.0813955648416, 0.12337470083653851, 0.12337486479310114, 0.12337502467231169, 0.12337518042431692, 0.12337533199725298, 0.12337547933714323, 0.1233756223877889  …  0.001177599345285002, 0.001608762385461543, 0.002490272527087365, 0.0015885561820287806, 0.9997302316254224, 0.9997279021130013, 0.006436881287716186, 923.8981206351701, 922.5138490527056, 0.006627221043422825]
 [151250.65169011973, 13532.71417217486, -69.98390525508839, 0.12275782332068579, 0.12275798179961825, 0.12275813644931892, 0.12275828722382258, 0.12275843407530986, 0.12275857695401286, 0.12275871580811433  …  0.0011954951124043243, 0.0016204577080472665, 0.002508372823612225, 0.0016109545458471704, 0.9997244452962354, 0.9997221251109589, 0.006479679154486839, 924.0449298643186, 922.6851457937693, 0.006508950781421128]
 [151266.33920149156, 13517.050030534614, -69.95293244206611, 0.1225653274313242, 0.1225654840868531, 0.1225656369887973, 0.12256578609240996, 0.12256593135113784, 0.1225660727165292, 0.12256621013813575  …  0.0012012351502659548, 0.0016241917933535663, 0.0025141525378536873, 0.00161813616769132, 0.9997225815274668, 0.999720262204486, 0.006493340266769187, 924.088116506726, 922.735955904178, 0.006472154406684705]
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/runner/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))
(0.23504352227636677, 0.5781129853775007)
ca_iso = sol2(tspan[1]:1:tspan[2], idxs=sys.Cai_mean)
println(extrema(ca_iso))
(0.1903362696321693, 0.7110939356326587)
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/runner/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/runner/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/docs/iso-exp.pdf"

Runtime information

using InteractiveUtils
InteractiveUtils.versioninfo()
Julia Version 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 4 default, 1 interactive, 4 GC (on 4 virtual cores)
Environment:
  JULIA_CPU_TARGET = generic;icelake-server,clone_all;znver3,clone_all
  JULIA_CONDAPKG_OFFLINE = true
  JULIA_CONDAPKG_BACKEND = Null
  JULIA_CI = true
  LD_LIBRARY_PATH = /opt/hostedtoolcache/Python/3.14.2/x64/lib
  JULIA_NUM_THREADS = auto
using Pkg
Pkg.status()
Project CaMKIIModel v0.7.0
Status `~/work/camkii-cardiomyocyte-model/camkii-cardiomyocyte-model/Project.toml`
  [336ed68f] CSV v0.10.15
  [a93c6f00] DataFrames v1.8.1
  [459566f4] DiffEqCallbacks v4.12.0
  [f6369f11] ForwardDiff v1.3.1
  [682c06a0] JSON v1.4.0
  [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 v6.106.0
  [91a5bcdd] Plots v1.41.4
  [2913bbd2] StatsBase v0.34.10
  [9672c7b4] SteadyStateDiffEq v2.9.0
  [ea8e919c] SHA v0.7.0
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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