Sensitivity to ISO

Sensitivity to ISO#

using ModelingToolkit
using OrdinaryDiffEq, SteadyStateDiffEq, DiffEqCallbacks
using Plots
using LsqFit
using CaMKIIModel
using CaMKIIModel: μM, hil, Hz, hilr, second
Plots.default(lw=1.5)

Setup b1AR system#

@parameters ATP = 5000μM ISO = 0μM
sys = get_bar_sys(ATP, ISO; simplify=true)
\[\begin{split} \begin{align} \frac{\mathrm{d} \mathtt{AC\_GsaGTP}\left( t \right)}{\mathrm{d}t} &= - \mathtt{k\_G\_hyd} \mathtt{AC\_GsaGTP}\left( t \right) - \mathtt{kr\_AC\_Gsa} \mathtt{AC\_GsaGTP}\left( t \right) + \mathtt{kf\_AC\_Gsa} \mathtt{AC}\left( t \right) \mathtt{GsaGTP}\left( t \right) \\ \frac{\mathrm{d} \mathtt{GsaGDP}\left( t \right)}{\mathrm{d}t} &= \mathtt{k\_G\_hyd} \mathtt{AC\_GsaGTP}\left( t \right) + \mathtt{k\_G\_hyd} \mathtt{GsaGTP}\left( t \right) - \mathtt{k\_G\_reassoc} \mathtt{Gsby}\left( t \right) \mathtt{GsaGDP}\left( t \right) \\ \frac{\mathrm{d} \mathtt{GsaGTP}\left( t \right)}{\mathrm{d}t} &= \mathtt{k\_G\_act} \mathtt{RG}\left( t \right) + \mathtt{k\_G\_act} \mathtt{LRG}\left( t \right) - \mathtt{k\_G\_hyd} \mathtt{GsaGTP}\left( t \right) + \mathtt{kr\_AC\_Gsa} \mathtt{AC\_GsaGTP}\left( t \right) - \mathtt{kf\_AC\_Gsa} \mathtt{AC}\left( t \right) \mathtt{GsaGTP}\left( t \right) \\ \frac{\mathrm{d} \mathtt{I1p}\left( t \right)}{\mathrm{d}t} &= \frac{\mathtt{k\_PKA\_I1} \mathtt{PKACI}\left( t \right) \mathtt{I1}\left( t \right)}{\mathtt{Km\_PKA\_I1} + \mathtt{I1}\left( t \right)} + \frac{ - \mathtt{Vmax\_PP2A\_I1} \mathtt{I1p}\left( t \right)}{\mathtt{Km\_PP2A\_I1} + \mathtt{I1p}\left( t \right)} + \mathtt{kr\_PP1\_I1} \mathtt{I1p\_PP1}\left( t \right) - \mathtt{kf\_PP1\_I1} \mathtt{PP1}\left( t \right) \mathtt{I1p}\left( t \right) \\ \frac{\mathrm{d} \mathtt{I1p\_PP1}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kr\_PP1\_I1} \mathtt{I1p\_PP1}\left( t \right) + \mathtt{kf\_PP1\_I1} \mathtt{PP1}\left( t \right) \mathtt{I1p}\left( t \right) \\ \frac{\mathrm{d} \mathtt{KURp}\left( t \right)}{\mathrm{d}t} &= \frac{ - \mathtt{PP1\_KURtot} \mathtt{epsilon} \mathtt{k\_pp1\_KUR} \mathtt{KURp}\left( t \right)}{\mathtt{Km\_pp1\_KUR} + \mathtt{epsilon} \mathtt{KURp}\left( t \right)} + \frac{\mathtt{PKAII\_KURtot} \mathtt{epsilon} \mathtt{k\_pka\_KUR} \mathtt{KURn}\left( t \right) \mathtt{PKACII}\left( t \right)}{\mathtt{PKAIItot} \left( \mathtt{Km\_pka\_KUR} + \mathtt{epsilon} \mathtt{KURn}\left( t \right) \right)} \\ \frac{\mathrm{d} \mathtt{LCCap}\left( t \right)}{\mathrm{d}t} &= \frac{\mathtt{PKACII\_LCCtotBA} \mathtt{epsilon} \mathtt{k\_PKA\_LCC} \mathtt{PKACII}\left( t \right) \mathtt{LCCa}\left( t \right)}{\mathtt{PKAIItot} \left( \mathtt{Km\_PKA\_LCC} + \mathtt{epsilon} \mathtt{LCCa}\left( t \right) \right)} + \frac{ - \mathtt{PP2A\_LCC} \mathtt{epsilon} \mathtt{k\_PP2A\_LCC} \mathtt{LCCap}\left( t \right)}{\mathtt{Km\_PP2A\_LCC} + \mathtt{epsilon} \mathtt{LCCap}\left( t \right)} \\ \frac{\mathrm{d} \mathtt{LCCbp}\left( t \right)}{\mathrm{d}t} &= \frac{\mathtt{PKACII\_LCCtotBA} \mathtt{epsilon} \mathtt{k\_PKA\_LCC} \mathtt{LCCb}\left( t \right) \mathtt{PKACII}\left( t \right)}{\mathtt{PKAIItot} \left( \mathtt{Km\_PKA\_LCC} + \mathtt{epsilon} \mathtt{LCCb}\left( t \right) \right)} + \frac{ - \mathtt{PP1\_LCC} \mathtt{epsilon} \mathtt{k\_PP1\_LCC} \mathtt{LCCbp}\left( t \right)}{\mathtt{Km\_PP1\_LCC} + \mathtt{epsilon} \mathtt{LCCbp}\left( t \right)} \\ \frac{\mathrm{d} \mathtt{LR}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kf\_bARK} \mathtt{LR}\left( t \right) - \mathtt{kr\_LR} \mathtt{LR}\left( t \right) + \mathtt{kr\_LRG} \mathtt{LRG}\left( t \right) + \mathtt{kr\_bARK} \mathtt{b1AR\_S464}\left( t \right) + \mathtt{ISO} \mathtt{kf\_LR} \mathtt{b1AR}\left( t \right) - \mathtt{kf\_LRG} \mathtt{LR}\left( t \right) \mathtt{Gs}\left( t \right) - \mathtt{kf\_PKA} \mathtt{PKACI}\left( t \right) \mathtt{LR}\left( t \right) \\ \frac{\mathrm{d} \mathtt{LRG}\left( t \right)}{\mathrm{d}t} &= - \mathtt{k\_G\_act} \mathtt{LRG}\left( t \right) - \mathtt{kf\_bARK} \mathtt{LRG}\left( t \right) - \mathtt{kr\_LRG} \mathtt{LRG}\left( t \right) + \mathtt{kf\_LRG} \mathtt{LR}\left( t \right) \mathtt{Gs}\left( t \right) - \mathtt{kf\_PKA} \mathtt{PKACI}\left( t \right) \mathtt{LRG}\left( t \right) \\ \frac{\mathrm{d} \mathtt{PDEp}\left( t \right)}{\mathrm{d}t} &= - \mathtt{k\_PP\_PDE} \mathtt{PDEp}\left( t \right) + \mathtt{k\_PKA\_PDE} \mathtt{PDE}\left( t \right) \mathtt{PKACII}\left( t \right) \\ \frac{\mathrm{d} \mathtt{PKACI}\left( t \right)}{\mathrm{d}t} &= \mathtt{kf\_RcAMPcAMP\_C} \mathtt{RCcAMPcAMP\_I}\left( t \right) + \mathtt{kr\_PKA\_PKI} \mathtt{PKACI\_PKI}\left( t \right) - \mathtt{kf\_PKA\_PKI} \mathtt{PKACI}\left( t \right) \mathtt{PKI}\left( t \right) - \mathtt{kr\_RcAMPcAMP\_C} \mathtt{PKACI}\left( t \right) \mathtt{RcAMPcAMP\_I}\left( t \right) \\ \frac{\mathrm{d} \mathtt{PKACII}\left( t \right)}{\mathrm{d}t} &= \mathtt{kf\_RcAMPcAMP\_C} \mathtt{RCcAMPcAMP\_II}\left( t \right) + \mathtt{kr\_PKA\_PKI} \mathtt{PKACII\_PKI}\left( t \right) - \mathtt{kf\_PKA\_PKI} \mathtt{PKI}\left( t \right) \mathtt{PKACII}\left( t \right) - \mathtt{kr\_RcAMPcAMP\_C} \mathtt{PKACII}\left( t \right) \mathtt{RcAMPcAMP\_II}\left( t \right) \\ \frac{\mathrm{d} \mathtt{PKACII\_PKI}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kr\_PKA\_PKI} \mathtt{PKACII\_PKI}\left( t \right) + \mathtt{kf\_PKA\_PKI} \mathtt{PKI}\left( t \right) \mathtt{PKACII}\left( t \right) \\ \frac{\mathrm{d} \mathtt{PKACI\_PKI}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kr\_PKA\_PKI} \mathtt{PKACI\_PKI}\left( t \right) + \mathtt{kf\_PKA\_PKI} \mathtt{PKACI}\left( t \right) \mathtt{PKI}\left( t \right) \\ \frac{\mathrm{d} \mathtt{PLBp}\left( t \right)}{\mathrm{d}t} &= \frac{ - \mathtt{k\_PP1\_PLB} \mathtt{PP1}\left( t \right) \mathtt{PLBp}\left( t \right)}{\mathtt{Km\_PP1\_PLB} + \mathtt{PLBp}\left( t \right)} + \frac{\mathtt{k\_PKA\_PLB} \mathtt{PLB}\left( t \right) \mathtt{PKACI}\left( t \right)}{\mathtt{Km\_PKA\_PLB} + \mathtt{PLB}\left( t \right)} \\ \frac{\mathrm{d} \mathtt{PLMp}\left( t \right)}{\mathrm{d}t} &= \frac{\mathtt{k\_PKA\_PLM} \mathtt{PKACI}\left( t \right) \mathtt{PLM}\left( t \right)}{\mathtt{Km\_PKA\_PLM} + \mathtt{PLM}\left( t \right)} + \frac{ - \mathtt{k\_PP1\_PLM} \mathtt{PP1}\left( t \right) \mathtt{PLMp}\left( t \right)}{\mathtt{Km\_PP1\_PLM} + \mathtt{PLMp}\left( t \right)} \\ \frac{\mathrm{d} \mathtt{RCcAMP\_I}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kr\_RC\_cAMP} \mathtt{RCcAMP\_I}\left( t \right) + \mathtt{kr\_RCcAMP\_cAMP} \mathtt{RCcAMPcAMP\_I}\left( t \right) + \mathtt{kf\_RC\_cAMP} \mathtt{RC\_I}\left( t \right) \mathtt{cAMP}\left( t \right) - \mathtt{kf\_RCcAMP\_cAMP} \mathtt{RCcAMP\_I}\left( t \right) \mathtt{cAMP}\left( t \right) \\ \frac{\mathrm{d} \mathtt{RCcAMP\_II}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kr\_RC\_cAMP} \mathtt{RCcAMP\_II}\left( t \right) + \mathtt{kr\_RCcAMP\_cAMP} \mathtt{RCcAMPcAMP\_II}\left( t \right) + \mathtt{kf\_RC\_cAMP} \mathtt{RC\_II}\left( t \right) \mathtt{cAMP}\left( t \right) - \mathtt{kf\_RCcAMP\_cAMP} \mathtt{RCcAMP\_II}\left( t \right) \mathtt{cAMP}\left( t \right) \\ \frac{\mathrm{d} \mathtt{RCcAMPcAMP\_I}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kf\_RcAMPcAMP\_C} \mathtt{RCcAMPcAMP\_I}\left( t \right) - \mathtt{kr\_RCcAMP\_cAMP} \mathtt{RCcAMPcAMP\_I}\left( t \right) + \mathtt{kf\_RCcAMP\_cAMP} \mathtt{RCcAMP\_I}\left( t \right) \mathtt{cAMP}\left( t \right) + \mathtt{kr\_RcAMPcAMP\_C} \mathtt{PKACI}\left( t \right) \mathtt{RcAMPcAMP\_I}\left( t \right) \\ \frac{\mathrm{d} \mathtt{RCcAMPcAMP\_II}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kf\_RcAMPcAMP\_C} \mathtt{RCcAMPcAMP\_II}\left( t \right) - \mathtt{kr\_RCcAMP\_cAMP} \mathtt{RCcAMPcAMP\_II}\left( t \right) + \mathtt{kf\_RCcAMP\_cAMP} \mathtt{RCcAMP\_II}\left( t \right) \mathtt{cAMP}\left( t \right) + \mathtt{kr\_RcAMPcAMP\_C} \mathtt{PKACII}\left( t \right) \mathtt{RcAMPcAMP\_II}\left( t \right) \\ \frac{\mathrm{d} \mathtt{RG}\left( t \right)}{\mathrm{d}t} &= - \mathtt{k\_G\_act} \mathtt{RG}\left( t \right) - \mathtt{kr\_RG} \mathtt{RG}\left( t \right) + \mathtt{kf\_RG} \mathtt{Gs}\left( t \right) \mathtt{b1AR}\left( t \right) \\ \frac{\mathrm{d} \mathtt{RyRp}\left( t \right)}{\mathrm{d}t} &= \frac{ - \mathtt{PP1\_RyR} \mathtt{epsilon} \mathtt{kcat\_pp1\_RyR} \mathtt{RyRp}\left( t \right)}{\mathtt{Km\_pp1\_RyR} + \mathtt{epsilon} \mathtt{RyRp}\left( t \right)} + \frac{\mathtt{PKAII\_RyRtot} \mathtt{epsilon} \mathtt{kcat\_pka\_RyR} \mathtt{PKACII}\left( t \right) \mathtt{RyRn}\left( t \right)}{\mathtt{PKAIItot} \left( \mathtt{Km\_pka\_RyR} + \mathtt{epsilon} \mathtt{RyRn}\left( t \right) \right)} + \frac{ - \mathtt{PP2A\_RyR} \mathtt{epsilon} \mathtt{kcat\_pp2a\_RyR} \mathtt{RyRp}\left( t \right)}{\mathtt{Km\_pp2a\_RyR} + \mathtt{epsilon} \mathtt{RyRp}\left( t \right)} \\ \frac{\mathrm{d} \mathtt{TnIp}\left( t \right)}{\mathrm{d}t} &= \frac{ - \mathtt{PP2A\_TnI} \mathtt{k\_PP2A\_TnI} \mathtt{TnIp}\left( t \right)}{\mathtt{Km\_PP2A\_TnI} + \mathtt{TnIp}\left( t \right)} + \frac{\mathtt{k\_PKA\_TnI} \mathtt{PKACI}\left( t \right) \mathtt{TnI}\left( t \right)}{\mathtt{Km\_PKA\_TnI} + \mathtt{TnI}\left( t \right)} \\ \frac{\mathrm{d} \mathtt{b1AR\_S301}\left( t \right)}{\mathrm{d}t} &= - \mathtt{kr\_PKA} \mathtt{b1AR\_S301}\left( t \right) + \mathtt{kf\_PKA} \mathtt{PKACI}\left( t \right) \mathtt{LR}\left( t \right) + \mathtt{kf\_PKA} \mathtt{PKACI}\left( t \right) \mathtt{LRG}\left( t \right) + \mathtt{kf\_PKA} \mathtt{PKACI}\left( t \right) \mathtt{b1AR}\left( t \right) \\ \frac{\mathrm{d} \mathtt{b1AR\_S464}\left( t \right)}{\mathrm{d}t} &= \mathtt{kf\_bARK} \mathtt{LR}\left( t \right) + \mathtt{kf\_bARK} \mathtt{LRG}\left( t \right) - \mathtt{kr\_bARK} \mathtt{b1AR\_S464}\left( t \right) \\ \frac{\mathrm{d} \mathtt{cAMP}\left( t \right)}{\mathrm{d}t} &= \frac{\mathtt{ATP} \mathtt{k\_AC\_basal} \mathtt{AC}\left( t \right)}{\mathtt{ATP} + \mathtt{Km\_AC\_basal}} + \frac{\mathtt{ATP} \mathtt{k\_AC\_Gsa} \mathtt{AC\_GsaGTP}\left( t \right)}{\mathtt{ATP} + \mathtt{Km\_AC\_Gsa}} + \frac{\left( - \mathtt{k\_cAMP\_PDE} \mathtt{PDE}\left( t \right) - \mathtt{k\_cAMP\_PDEp} \mathtt{PDEp}\left( t \right) \right) \mathtt{cAMP}\left( t \right)}{\mathtt{Km\_PDE\_cAMP} + \mathtt{cAMP}\left( t \right)} + \mathtt{kr\_RC\_cAMP} \mathtt{RCcAMP\_I}\left( t \right) + \mathtt{kr\_RC\_cAMP} \mathtt{RCcAMP\_II}\left( t \right) + \mathtt{kr\_RCcAMP\_cAMP} \mathtt{RCcAMPcAMP\_II}\left( t \right) + \mathtt{kr\_RCcAMP\_cAMP} \mathtt{RCcAMPcAMP\_I}\left( t \right) - \mathtt{kf\_RC\_cAMP} \mathtt{RC\_II}\left( t \right) \mathtt{cAMP}\left( t \right) - \mathtt{kf\_RC\_cAMP} \mathtt{RC\_I}\left( t \right) \mathtt{cAMP}\left( t \right) - \mathtt{kf\_RCcAMP\_cAMP} \mathtt{RCcAMP\_I}\left( t \right) \mathtt{cAMP}\left( t \right) - \mathtt{kf\_RCcAMP\_cAMP} \mathtt{RCcAMP\_II}\left( t \right) \mathtt{cAMP}\left( t \right) \end{align} \end{split}\]
prob = SteadyStateProblem(sys, [])
alg = DynamicSS(Rodas5P())

SteadyStateDiffEq.DynamicSS{OrdinaryDiffEqRosenbrock.Rodas5P{0, ADTypes.AutoForwardDiff{nothing, Nothing}, Nothing, typeof(OrdinaryDiffEqCore.DEFAULT_PRECS), Val{:forward}(), true, nothing, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!)}, Float64}(OrdinaryDiffEqRosenbrock.Rodas5P{0, ADTypes.AutoForwardDiff{nothing, Nothing}, Nothing, typeof(OrdinaryDiffEqCore.DEFAULT_PRECS), Val{:forward}(), true, nothing, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!)}(nothing, OrdinaryDiffEqCore.DEFAULT_PRECS, OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, ADTypes.AutoForwardDiff()), Inf)

Log scale for ISO concentration

iso = exp10.(range(log10(1e-4μM), log10(1μM), length=1001))

1001-element Vector{Float64}:
 0.0001
 0.00010092528860766844
 0.00010185913880541169
 0.00010280162981264735
 0.00010375284158180127
 0.00010471285480508996
 0.00010568175092136585
 0.0001066596121230258
 0.0001076465213629835
 0.00010864256236170655
 ⋮
 0.9289663867799364
 0.9375620069258802
 0.9462371613657931
 0.954992586021436
 0.9638290236239705
 0.9727472237769651
 0.9817479430199844
 0.9908319448927676
 1.0

prob_func = (prob, i, repeat) -> remake(prob, p=[ISO => iso[i]])
trajectories = length(iso)
sol = solve(prob, alg; abstol=1e-10, reltol=1e-10) ## warmup
sim = solve(EnsembleProblem(prob; prob_func, safetycopy=false), alg; trajectories, abstol=1e-10, reltol=1e-10)

EnsembleSolution Solution of length 1001 with uType:
SciMLBase.NonlinearSolution{Float64, 1, Vector{Float64}, Vector{Float64}, SciMLBase.SteadyStateProblem{Vector{Float64}, true, ModelingToolkit.MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xb378eac9, 0x0fff56a3, 0x3d991826, 0xa2e85ac1, 0x04254701), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x87f371e0, 0x3ecffe55, 0x0dc0593c, 0x2ce0b432, 0x0878ab55), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}}, SteadyStateDiffEq.DynamicSS{OrdinaryDiffEqRosenbrock.Rodas5P{0, ADTypes.AutoForwardDiff{nothing, ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}, Nothing, typeof(OrdinaryDiffEqCore.DEFAULT_PRECS), Val{:forward}(), true, nothing, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!)}, Float64}, SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, ModelingToolkit.MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.ODEFunction{true, true, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xb378eac9, 0x0fff56a3, 0x3d991826, 0xa2e85ac1, 0x04254701), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x87f371e0, 0x3ecffe55, 0x0dc0593c, 0x2ce0b432, 0x0878ab55), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEqRosenbrock.Rodas5P{0, ADTypes.AutoForwardDiff{nothing, ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}, Nothing, typeof(OrdinaryDiffEqCore.DEFAULT_PRECS), Val{:forward}(), true, nothing, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!)}, OrdinaryDiffEqCore.InterpolationData{SciMLBase.ODEFunction{true, true, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xb378eac9, 0x0fff56a3, 0x3d991826, 0xa2e85ac1, 0x04254701), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x87f371e0, 0x3ecffe55, 0x0dc0593c, 0x2ce0b432, 0x0878ab55), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, OrdinaryDiffEqRosenbrock.RosenbrockCache{Vector{Float64}, Vector{Float64}, Float64, Vector{Float64}, Matrix{Float64}, Matrix{Float64}, OrdinaryDiffEqRosenbrock.RodasTableau{Float64, Float64}, SciMLBase.TimeGradientWrapper{true, SciMLBase.ODEFunction{true, true, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xb378eac9, 0x0fff56a3, 0x3d991826, 0xa2e85ac1, 0x04254701), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x87f371e0, 0x3ecffe55, 0x0dc0593c, 0x2ce0b432, 0x0878ab55), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, Vector{Float64}, ModelingToolkit.MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}}, SciMLBase.UJacobianWrapper{true, SciMLBase.ODEFunction{true, true, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xb378eac9, 0x0fff56a3, 0x3d991826, 0xa2e85ac1, 0x04254701), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x87f371e0, 0x3ecffe55, 0x0dc0593c, 0x2ce0b432, 0x0878ab55), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, ModelingToolkit.MTKParameters{Vector{Float64}, StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc36895e5, 0x9ac752fe, 0x3a540328, 0x440216c2, 0xa0ef95bb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x0cc26c10, 0x0af07f66, 0x2e7e0f26, 0x652b5a42, 0xeec751e0), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.System}, Nothing, ModelingToolkit.System, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardNonlinearProblem}, Nothing, Nothing, Nothing, ModelingToolkit.InitializationMetadata{ModelingToolkit.ReconstructInitializeprob{ModelingToolkit.var"#_getter#913"{Tuple{ComposedFunction{ModelingToolkit.PConstructorApplicator{typeof(identity)}, ComposedFunction{Base.Fix1{typeof(reduce), typeof(vcat)}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Tuple{SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}}, Nothing}, SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}, Nothing}}}, Returns{StaticArraysCore.SizedVector{0, Float64, Vector{Float64}}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{Any}}}}, Nothing, ModelingToolkit.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}}, Val{true}}, Nothing}, Float64, ModelingToolkit.MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}}, LinearSolve.LinearCache{Matrix{Float64}, Vector{Float64}, Vector{Float64}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Matrix{Float64}, Vector{Float64}, Vector{Int64}}, Nothing, Nothing}, LinearSolve.InvPreconditioner{LinearAlgebra.Diagonal{Float64, Vector{Float64}}}, LinearAlgebra.Diagonal{Float64, Vector{Float64}}, Float64, Bool, LinearSolve.LinearSolveAdjoint{Missing}}, Tuple{DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgJacobianPrep{Nothing, ForwardDiff.JacobianConfig{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9}}}}, Tuple{}}, DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgJacobianPrep{Nothing, ForwardDiff.JacobianConfig{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9}}}}, Tuple{}}}, Tuple{DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgDerivativePrep{Nothing, ForwardDiff.DerivativeConfig{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, Tuple{}}, DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgDerivativePrep{Nothing, ForwardDiff.DerivativeConfig{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, Tuple{}}}, Float64, OrdinaryDiffEqRosenbrock.Rodas5P{0, ADTypes.AutoForwardDiff{nothing, ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}}, Nothing, typeof(OrdinaryDiffEqCore.DEFAULT_PRECS), Val{:forward}(), true, nothing, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!)}, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!)}, Nothing}, SciMLBase.DEStats, Nothing, Nothing, Nothing, Nothing}, Nothing, Nothing, Nothing}

"""Extract values from ensemble simulations by a symbol"""
extract(sim, k) = map(s -> s[k], sim)
"""Calculate Root Mean Square Error (RMSE)"""
rmse(fit) = sqrt(sum(abs2, fit.resid) / length(fit.resid))

Main.var"##264".rmse

xopts = (xlims=(iso[begin], iso[end]), minorgrid=true, xscale=:log10, xlabel="ISO (μM)",)
plot(iso, extract(sim, sys.cAMP); lab="cAMP", ylabel="Conc. (μM)", legend=:topleft, xopts...)
_images/fa15bcc1057f18f18cb754221efd3e95fefc64f3da652ab8eab75f2d066c998b.png 
plot(iso, extract(sim, sys.PKACI / sys.RItot); lab="PKACI", ylabel="Activation fraction")
plot!(iso, extract(sim, sys.PKACII / sys.RIItot), lab="PKACII")
plot!(iso, extract(sim, sys.PP1 / sys.PP1totBA), lab="PP1", legend=:topleft; xopts...)
_images/2aee8fa4258a3c7f0d9826d66bbb5da801182202f0ac77c55f0e4602fb53b569.png

Fitting active PKACI#

@. model(x, p) = p[1] * x / (x + p[2]) + p[3]
xdata = iso
ydata = extract(sim, sys.PKACI / sys.RItot)
p0 = [0.3, 0.01μM, 0.08]
lb = [0.0, 0.0, 0.0]
pkac1_fit = curve_fit(model, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pkac1_coef = coef(pkac1_fit)

3-element Vector{Float64}:
 0.19937291345634858
 0.013906166994958996
 0.07340270008369426

println("PKACI")
println("Basal activity: ", pkac1_coef[3])
println("Activated activity: ", pkac1_coef[1])
println("Michaelis constant: ", pkac1_coef[2], " μM")
println("RMSE: ", rmse(pkac1_fit))

PKACI
Basal activity: 0.07340270008369426
Activated activity: 0.19937291345634858
Michaelis constant: 0.013906166994958996 μM
RMSE: 0.0003269390156489721

ypred = model.(xdata, Ref(pkac1_coef))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="PKACI", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="PKACI error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/057380052dd4fdc6ed21661536bff363d77b60835b693010b9652f080952e0b5.png

Fitting active PKACII#

xdata = iso
ydata = extract(sim, sys.PKACII / sys.RIItot)
p0 = [0.4, 0.01μM, 0.2]
lb = [0.0, 0.0, 0.0]
pkac2_fit = curve_fit(model, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pkac2_coef = coef(pkac2_fit)

3-element Vector{Float64}:
 0.34437076643315717
 0.010251017453491905
 0.18399251059731786

println("PKACII")
println("Basal activity: ", pkac2_coef[3])
println("Activated activity: ", pkac2_coef[1])
println("Michaelis constant: ", pkac2_coef[2], " μM")
println("RMSE: ", rmse(pkac2_fit))

PKACII
Basal activity: 0.18399251059731786
Activated activity: 0.34437076643315717
Michaelis constant: 0.010251017453491905 μM
RMSE: 0.0002437201626009943

ypred = model.(xdata, Ref(pkac2_coef))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="PKACII", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="PKACII error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/b717cc2f53759a101c77ec622a3844311145752a63d11721003546d4493ac168.png

Least-square fitting of PP1 activity#

@. model_pp1(x, p) = p[1] * p[2] / (x + p[2]) + p[3]
xdata = iso
ydata = extract(sim, sys.PP1 / sys.PP1totBA)
p0 = [0.1, 3e-3μM, 0.8]
lb = [0.0, 0.0, 0.0]
pp1_fit = curve_fit(model_pp1, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pp1_coef = coef(pp1_fit)

3-element Vector{Float64}:
 0.04919195738460954
 0.006361892266077822
 0.8927131246712454

println("PP1")
println("Repressible activity: ", pp1_coef[1])
println("Minimal activity: ", pp1_coef[3])
println("Repressive Michaelis constant: ", pp1_coef[2], " μM")
println("RMSE: ", rmse(pp1_fit))

PP1
Repressible activity: 0.04919195738460954
Minimal activity: 0.8927131246712454
Repressive Michaelis constant: 0.006361892266077822 μM
RMSE: 3.540627041031313e-5

ypred = model_pp1.(xdata, Ref(pp1_coef))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="PP1", legend=:topright; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="PP1 error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/3002d1d2c2114dd204847dec0489f8c8eac36cbc66cb75346588ba030cbf7c26.png

Fitting PLBp#

xdata = iso
ydata = extract(sim, sys.PLBp / sys.PLBtotBA)
plot(xdata, ydata, title="PLBp fraction", lab=false; xopts...)
_images/ecf29e4a5ce04c589caa0ffa0954d4b27f2bb764a704855ff09862bc64755eb4.png

First try: Hill function

@. model_plb(x, p) = p[1] * hil(x, p[2], p[3]) + p[4]
p0 = [0.8, 1e-2μM, 1.0, 0.1]
lb = [0.5, 1e-9μM, 1.0, 0.0]
fit = curve_fit(model_plb, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

4-element Vector{Float64}:
 0.7923203638864403
 0.0059366429478444555
 1.8386683911467603
 0.08301219500235378

println("PLBp")
println("Basal activity: ", pestim[4])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("Hill coefficient: ", pestim[3])
println("RMSE: ", rmse(fit))

PLBp
Basal activity: 0.08301219500235378
Activated activity: 0.7923203638864403
Michaelis constant: 0.0059366429478444555 μM
Hill coefficient: 1.8386683911467603
RMSE: 0.00841923579697079

ypred = model_plb.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="PLBp", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="PLBp error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/4a6ff667cb9a1032ff209eee00cdff5deaf9c4be72168d184fe38b2f5419ac32.png

Fitting PLMp#

xdata = iso
ydata = extract(sim, sys.PLMp / sys.PLMtotBA)
plot(xdata, ydata, title="PLMp fraction", lab=false; xopts...)
_images/bb64534746a6a5ac594d5e9de93631bef9dcc6643a5409260f91faa4a1c757f8.png 
@. model_plm(x, p) = p[1] * hil(x, p[2], p[3]) + p[4]
p0 = [0.8, 1e-2μM, 1.0, 0.1]
lb = [0.5, 1e-9μM, 1.0, 0.0]
fit = curve_fit(model_plm, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

4-element Vector{Float64}:
 0.6617189658028633
 0.008181708897402069
 1.3710343912708827
 0.11772719854676429

println("PLMp")
println("Basal activity: ", pestim[4])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("Hill coefficient: ", pestim[3])
println("RMSE: ", rmse(fit))

PLMp
Basal activity: 0.11772719854676429
Activated activity: 0.6617189658028633
Michaelis constant: 0.008181708897402069 μM
Hill coefficient: 1.3710343912708827
RMSE: 0.0032738872588563687

ypred = model_plm.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="PLMp", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="PLMp error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/91fc3cde5ed265be4d4029c3e7aaea933c0670c27e02daabd54b81e19156e6df.png

Fitting TnIp#

xdata = iso
ydata = extract(sim, sys.TnIp / sys.TnItotBA)
plot(xdata, ydata, title="TnIp fraction", lab=false; xopts...)
_images/1d8e28bb5e4322083dd97d2a1235bb6bc8c8c6a7c2fd8330a96bc350079f8a7d.png 
@. model_tni(x, p) = p[1] * hil(x, p[2], p[3]) + p[4]
p0 = [0.8, 1e-2μM, 1.0, 0.1]
lb = [0.1, 1e-9μM, 1.0, 0.0]
fit = curve_fit(model_tni, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

4-element Vector{Float64}:
 0.7481954808708322
 0.00785633732627897
 1.6973365103955782
 0.0675295812706609

println("TnIp")
println("Basal activity: ", pestim[4])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("Hill coefficient: ", pestim[3])
println("RMSE: ", rmse(fit))

TnIp
Basal activity: 0.0675295812706609
Activated activity: 0.7481954808708322
Michaelis constant: 0.00785633732627897 μM
Hill coefficient: 1.6973365103955782
RMSE: 0.0074371608083827825

ypred = model_tni.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="TnIp", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="TnIp error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/eff3aba3459047e4d78782ed94a5942962fed8b23d9b552519b541eb3f769c26.png

Fitting LCCap#

xdata = iso
ydata = extract(sim, sys.LCCap / sys.LCCtotBA)
plot(xdata, ydata, title="LCCap fraction", lab=false; xopts...)
_images/956d9bbe16169dc4ed80455a5a90105f820bacfb324dd68e2959af2585135956.png 
@. model_lcc(x, p) = p[1] * hil(x, p[2]) + p[3]
p0 = [0.8, 1e-2μM, 0.1]
lb = [0.1, 1e-9μM, 0.0]
fit = curve_fit(model_lcc, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

3-element Vector{Float64}:
 0.23338204841250842
 0.0072633474620138055
 0.22081942519006909

println("LCCap")
println("Basal activity: ", pestim[3])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("RMSE: ", rmse(fit))

LCCap
Basal activity: 0.22081942519006909
Activated activity: 0.23338204841250842
Michaelis constant: 0.0072633474620138055 μM
RMSE: 0.00013473143523738058

ypred = model_lcc.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="LCCap", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="LCCap error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/c76081da74c2e9b678e46fd0b400d9e7a225c55a8ce3429744d9ee3ab4e64ed5.png

Fitting LCCbp#

xdata = iso
ydata = extract(sim, sys.LCCbp / sys.LCCtotBA)
plot(xdata, ydata, title="LCCbp fraction", lab=false; xopts...)
_images/8617bd7dd17be46a809a6dc17abbbeea33ff192bf48be81d5b241d67d7c1c2c9.png 
p0 = [0.8, 1e-2μM, 0.1]
lb = [0.1, 1e-9μM, 0.0]
fit = curve_fit(model_lcc, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

3-element Vector{Float64}:
 0.245589048436944
 0.006961122639504384
 0.2520079480716994

println("LCCbp")
println("Basal activity: ", pestim[3])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("RMSE: ", rmse(fit))

LCCbp
Basal activity: 0.2520079480716994
Activated activity: 0.245589048436944
Michaelis constant: 0.006961122639504384 μM
RMSE: 0.00013806538956776142

ypred = model_lcc.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="LCCbp", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="LCCbp error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/aaa751caac0c95bc96b52795e9fd78c0d7370e0b7eb18c1d7076efbbfc68c36e.png

Fitting KURp#

xdata = iso
ydata = extract(sim, sys.KURp / sys.IKurtotBA)
plot(xdata, ydata, title="LCCbp fraction", lab=false; xopts...)
_images/954aff398611c274d4c22cbd25ad7bafc3455bf89f64ebf64e5cedcbf1b398d4.png 
@. model_kur(x, p) = p[1] * hil(x, p[2]) + p[3]
p0 = [0.8, 1e-2μM, 0.1]
lb = [0.1, 1e-9μM, 0.0]
fit = curve_fit(model_kur, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

3-element Vector{Float64}:
 0.25565728489475253
 0.005578153001052855
 0.43936395497570857

println("KURp")
println("Basal activity: ", pestim[3])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("RMSE: ", rmse(fit))

KURp
Basal activity: 0.43936395497570857
Activated activity: 0.25565728489475253
Michaelis constant: 0.005578153001052855 μM
RMSE: 0.00014849268102349092

ypred = model_lcc.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="KURp", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="KURp error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/6652ff31d90d3fa5eca93863b8f798e706b25e0cf4127cb599da8d79d76b1a14.png

Fitting RyRp#

xdata = iso
ydata = extract(sim, sys.RyR_PKAp)
plot(xdata, ydata, title="RyRp fraction", lab=false; xopts...)
_images/76c5a4672c6410171b7760b2358669a7ef620e50333411a5206d6cd79080120d.png 
@. model(x, p) = p[1] * x / (x + p[2]) + p[3]
p0 = [0.3, 1e-2μM, 0.1]
lb = [0.0, 1e-9μM, 0.0]
fit = curve_fit(model, xdata, ydata, p0; lower=lb, autodiff=:forwarddiff)
pestim = coef(fit)

3-element Vector{Float64}:
 0.23988672456710036
 0.0075098682208393245
 0.20539800480783868

println("RyRp")
println("Basal activity: ", pestim[3])
println("Activated activity: ", pestim[1])
println("Michaelis constant: ", pestim[2], " μM")
println("RMSE: ", rmse(fit))

RyRp
Basal activity: 0.20539800480783868
Activated activity: 0.23988672456710036
Michaelis constant: 0.0075098682208393245 μM
RMSE: 7.687295387195984e-5

ypred = model.(xdata, Ref(pestim))
p1 = plot(xdata, [ydata ypred], lab=["Full model" "Fitted"], line=[:dash :dot], title="RyRp", legend=:topleft; xopts...)
p2 = plot(xdata, (ypred .- ydata) ./ ydata .* 100; title="RyRp error (%)", lab=false, xopts...)
plot(p1, p2, layout=(2, 1), size=(600, 600))
_images/96aed4e80cb5ac45edc892975e3102c7654a723817ff35cfff55eab7bdf61af8.png

This notebook was generated using Literate.jl.

Contents