Sensitivity to ISO

Contents

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{array}{r} \begin{aligned} \frac{d LR (t)}{d t} & = - kf_bARK LR (t) - kr_LR LR (t) + kr_LRG LRG (t) + kr_bARK b 1 AR_S 464 (t) + ISO kf_LR b 1 AR (t) - kf_LRG LR (t) Gs (t) - kf_PKA PKACI (t) LR (t) \\ \frac{d LRG (t)}{d t} & = - k_G_act LRG (t) - kf_bARK LRG (t) - kr_LRG LRG (t) + kf_LRG LR (t) Gs (t) - kf_PKA PKACI (t) LRG (t) \\ \frac{d RG (t)}{d t} & = - k_G_act RG (t) - kr_RG RG (t) + kf_RG Gs (t) b 1 AR (t) \\ \frac{d GsaGTP (t)}{d t} & = k_G_act RG (t) + k_G_act LRG (t) - k_G_hyd GsaGTP (t) + kr_AC_Gsa AC_GsaGTP (t) - kf_AC_Gsa AC (t) GsaGTP (t) \\ \frac{d GsaGDP (t)}{d t} & = k_G_hyd AC_GsaGTP (t) + k_G_hyd GsaGTP (t) - k_G_reassoc Gsby (t) GsaGDP (t) \\ \frac{d b 1 AR_S 464 (t)}{d t} & = kf_bARK LR (t) + kf_bARK LRG (t) - kr_bARK b 1 AR_S 464 (t) \\ \frac{d b 1 AR_S 301 (t)}{d t} & = - kr_PKA b 1 AR_S 301 (t) + kf_PKA PKACI (t) LR (t) + kf_PKA PKACI (t) LRG (t) + kf_PKA PKACI (t) b 1 AR (t) \\ \frac{d AC_GsaGTP (t)}{d t} & = - k_G_hyd AC_GsaGTP (t) - kr_AC_Gsa AC_GsaGTP (t) + kf_AC_Gsa AC (t) GsaGTP (t) \\ \frac{d PDEp (t)}{d t} & = - k_PP_PDE PDEp (t) + k_PKA_PDE PDE (t) PKACII (t) \\ \frac{d cAMP (t)}{d t} & = \frac{ATP k_AC_basal AC (t)}{ATP + Km_AC_basal} + \frac{ATP k_AC_Gsa AC_GsaGTP (t)}{ATP + Km_AC_Gsa} + \frac{(- k_cAMP_PDE PDE (t) - k_cAMP_PDEp PDEp (t)) cAMP (t)}{Km_PDE_cAMP + cAMP (t)} + kr_RC_cAMP RCcAMP_I (t) + kr_RC_cAMP RCcAMP_II (t) + kr_RCcAMP_cAMP RCcAMPcAMP_II (t) + kr_RCcAMP_cAMP RCcAMPcAMP_I (t) - kf_RC_cAMP RC_II (t) cAMP (t) - kf_RC_cAMP RC_I (t) cAMP (t) - kf_RCcAMP_cAMP RCcAMP_I (t) cAMP (t) - kf_RCcAMP_cAMP RCcAMP_II (t) cAMP (t) \\ \frac{d RCcAMP_I (t)}{d t} & = - kr_RC_cAMP RCcAMP_I (t) + kr_RCcAMP_cAMP RCcAMPcAMP_I (t) + kf_RC_cAMP RC_I (t) cAMP (t) - kf_RCcAMP_cAMP RCcAMP_I (t) cAMP (t) \\ \frac{d RCcAMP_II (t)}{d t} & = - kr_RC_cAMP RCcAMP_II (t) + kr_RCcAMP_cAMP RCcAMPcAMP_II (t) + kf_RC_cAMP RC_II (t) cAMP (t) - kf_RCcAMP_cAMP RCcAMP_II (t) cAMP (t) \\ \frac{d RCcAMPcAMP_I (t)}{d t} & = - kf_RcAMPcAMP_C RCcAMPcAMP_I (t) - kr_RCcAMP_cAMP RCcAMPcAMP_I (t) + kf_RCcAMP_cAMP RCcAMP_I (t) cAMP (t) + kr_RcAMPcAMP_C PKACI (t) RcAMPcAMP_I (t) \\ \frac{d RCcAMPcAMP_II (t)}{d t} & = - kf_RcAMPcAMP_C RCcAMPcAMP_II (t) - kr_RCcAMP_cAMP RCcAMPcAMP_II (t) + kf_RCcAMP_cAMP RCcAMP_II (t) cAMP (t) + kr_RcAMPcAMP_C PKACII (t) RcAMPcAMP_II (t) \\ \frac{d PKACI (t)}{d t} & = kf_RcAMPcAMP_C RCcAMPcAMP_I (t) + kr_PKA_PKI PKACI_PKI (t) - kf_PKA_PKI PKACI (t) PKI (t) - kr_RcAMPcAMP_C PKACI (t) RcAMPcAMP_I (t) \\ \frac{d PKACII (t)}{d t} & = kf_RcAMPcAMP_C RCcAMPcAMP_II (t) + kr_PKA_PKI PKACII_PKI (t) - kf_PKA_PKI PKI (t) PKACII (t) - kr_RcAMPcAMP_C PKACII (t) RcAMPcAMP_II (t) \\ \frac{d PKACI_PKI (t)}{d t} & = - kr_PKA_PKI PKACI_PKI (t) + kf_PKA_PKI PKACI (t) PKI (t) \\ \frac{d PKACII_PKI (t)}{d t} & = - kr_PKA_PKI PKACII_PKI (t) + kf_PKA_PKI PKI (t) PKACII (t) \\ \frac{d I 1 p (t)}{d t} & = \frac{k_PKA_I 1 PKACI (t) I 1 (t)}{Km_PKA_I 1 + I 1 (t)} + \frac{- Vmax_PP 2 A_I 1 I 1 p (t)}{Km_PP 2 A_I 1 + I 1 p (t)} + kr_PP 1_I 1 I 1 p_PP 1 (t) - kf_PP 1_I 1 PP 1 (t) I 1 p (t) \\ \frac{d I 1 p_PP 1 (t)}{d t} & = - kr_PP 1_I 1 I 1 p_PP 1 (t) + kf_PP 1_I 1 PP 1 (t) I 1 p (t) \\ \frac{d PLBp (t)}{d t} & = \frac{- k_PP 1_PLB PP 1 (t) PLBp (t)}{Km_PP 1_PLB + PLBp (t)} + \frac{k_PKA_PLB PLB (t) PKACI (t)}{Km_PKA_PLB + PLB (t)} \\ \frac{d PLMp (t)}{d t} & = \frac{k_PKA_PLM PKACI (t) PLM (t)}{Km_PKA_PLM + PLM (t)} + \frac{- k_PP 1_PLM PP 1 (t) PLMp (t)}{Km_PP 1_PLM + PLMp (t)} \\ \frac{d TnIp (t)}{d t} & = \frac{- PP 2 A_TnI k_PP 2 A_TnI TnIp (t)}{Km_PP 2 A_TnI + TnIp (t)} + \frac{k_PKA_TnI PKACI (t) TnI (t)}{Km_PKA_TnI + TnI (t)} \\ \frac{d LCCap (t)}{d t} & = \frac{PKACII_LCCtotBA epsilon k_PKA_LCC PKACII (t) LCCa (t)}{PKAIItot (Km_PKA_LCC + epsilon LCCa (t))} + \frac{- PP 2 A_LCC epsilon k_PP 2 A_LCC LCCap (t)}{Km_PP 2 A_LCC + epsilon LCCap (t)} \\ \frac{d LCCbp (t)}{d t} & = \frac{PKACII_LCCtotBA epsilon k_PKA_LCC LCCb (t) PKACII (t)}{PKAIItot (Km_PKA_LCC + epsilon LCCb (t))} + \frac{- PP 1_LCC epsilon k_PP 1_LCC LCCbp (t)}{Km_PP 1_LCC + epsilon LCCbp (t)} \\ \frac{d KURp (t)}{d t} & = \frac{- PP 1_KURtot epsilon k_pp 1_KUR KURp (t)}{Km_pp 1_KUR + epsilon KURp (t)} + \frac{PKAII_KURtot epsilon k_pka_KUR KURn (t) PKACII (t)}{PKAIItot (Km_pka_KUR + epsilon KURn (t))} \\ \frac{d RyRp (t)}{d t} & = \frac{- PP 1_RyR epsilon kcat_pp 1_RyR RyRp (t)}{Km_pp 1_RyR + epsilon RyRp (t)} + \frac{PKAII_RyRtot epsilon kcat_pka_RyR PKACII (t) RyRn (t)}{PKAIItot (Km_pka_RyR + epsilon RyRn (t))} + \frac{- PP 2 A_RyR epsilon kcat_pp 2 a_RyR RyRp (t)}{Km_pp 2 a_RyR + epsilon RyRp (t)} \end{aligned} \end{array}

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:
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ModelingToolkit.var"#_RGF_ModTag", (0xc4a79f81, 0x3bfb94bc, 0x0caf0fc6, 0xf3d7cfd9, 0x1d1ba7a7), Nothing}}}}, Nothing}, Nothing}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.ODESystem}, Nothing, ModelingToolkit.ODESystem, 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", (0x62d8d8e6, 0xec7beb7a, 0x30fd358e, 0x2cd436f7, 0x399ab3a0), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xad558e4f, 0xac675493, 0xbc4ef49e, 0x8ed0ca13, 0x7523eefd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, ModelingToolkit.InitializationSystemMetadata}, ModelingToolkit.UpdateInitializeprob{SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{SymbolicIndexingInterface.AbstractGetIndexer}}, SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xf8f6d8eb, 0xffe98840, 0x4d9dee9c, 0x4f0bea77, 0xf43dc2a0), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc4a79f81, 0x3bfb94bc, 0x0caf0fc6, 0xf3d7cfd9, 0x1d1ba7a7), Nothing}}}}, Nothing}, Nothing}, Vector{Float64}, ModelingToolkit.MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}}, SciMLBase.UJacobianWrapper{true, SciMLBase.ODEFunction{true, true, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, ModelingToolkit.GeneratedFunctionWrapper{(2, 3, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x384dc3e7, 0x21bd2a3d, 0x65382ed1, 0x926dec3d, 0xe6bbdbcb), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___, :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x17f8a9fb, 0x555e1650, 0x76f00842, 0x44879fde, 0x937abf67), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.ODESystem}, Nothing, ModelingToolkit.ODESystem, 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", (0x62d8d8e6, 0xec7beb7a, 0x30fd358e, 0x2cd436f7, 0x399ab3a0), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xad558e4f, 0xac675493, 0xbc4ef49e, 0x8ed0ca13, 0x7523eefd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, ModelingToolkit.InitializationSystemMetadata}, ModelingToolkit.UpdateInitializeprob{SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{SymbolicIndexingInterface.AbstractGetIndexer}}, SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xf8f6d8eb, 0xffe98840, 0x4d9dee9c, 0x4f0bea77, 0xf43dc2a0), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc4a79f81, 0x3bfb94bc, 0x0caf0fc6, 0xf3d7cfd9, 0x1d1ba7a7), Nothing}}}}, Nothing}, Nothing}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.ODESystem}, Nothing, ModelingToolkit.ODESystem, 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", (0x62d8d8e6, 0xec7beb7a, 0x30fd358e, 0x2cd436f7, 0x399ab3a0), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xad558e4f, 0xac675493, 0xbc4ef49e, 0x8ed0ca13, 0x7523eefd), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkit.ObservedFunctionCache{ModelingToolkit.NonlinearSystem}, Nothing, ModelingToolkit.NonlinearSystem, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, ModelingToolkit.InitializationSystemMetadata}, ModelingToolkit.UpdateInitializeprob{SymbolicIndexingInterface.MultipleGetters{SymbolicIndexingInterface.ContinuousTimeseries, Vector{SymbolicIndexingInterface.AbstractGetIndexer}}, SymbolicIndexingInterface.MultipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingToolkit.ParameterIndex{SciMLStructures.Tunable, Int64}}, SymbolicUtils.BasicSymbolic{Real}}}}}, ComposedFunction{typeof(identity), SymbolicIndexingInterface.TimeIndependentObservedFunction{ModelingToolkit.GeneratedFunctionWrapper{(2, 2, true), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, 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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}}, SparseDiffTools.ForwardColorJacCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 9}}, Vector{Float64}, Vector{Vector{NTuple{9, Float64}}}, UnitRange{Int64}, Nothing}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Float64, OrdinaryDiffEqRosenbrock.Rodas5P{9, ADTypes.AutoForwardDiff{9, Nothing}, 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"##230".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/38835116e61bb2a6706788700897cfeec799bec6e9815469e8f3a5c958e68cf7.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/5ebcb684a650fda49d38cf35825248459492219d04d882540a8d02575e44eaed.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}:
 0.19937293764079625
 0.01390617687954668
 0.07340271607767374

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: 0.07340271607767374
Activated activity: 0.19937293764079625
Michaelis constant: 0.01390617687954668 μM
RMSE: 0.000326933550132299

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/d2a4721b3d42cdd732f9710f98173be1a2033c37eacb30c1ceba1f9d219e162c.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}:
 0.3443707798304218
 0.010251025301118936
 0.18399255075380827

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: 0.18399255075380827
Activated activity: 0.3443707798304218
Michaelis constant: 0.010251025301118936 μM
RMSE: 0.00024371222189781725

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/ae13374c676f8e9be2e9897f8ea56c61c86d59308529a8e2a753315b823211fc.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}:
 0.049191952461111785
 0.006361898234866831
 0.892713119276668

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: 0.049191952461111785
Minimal activity: 0.892713119276668
Repressive Michaelis constant: 0.006361898234866831 μM
RMSE: 3.5405233556999936e-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/07c40cf088d1cdf26930454918832092d8f0f763049ef1ffdf2a684be94ad942.png

Fitting PLBp#

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

_images/d0cc79998b17d7e4e1e9db1e01a051a762a14c17feeeae61aa4e2fbf09b605a2.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}:
 0.7923203662040967
 0.005936643968064003
 1.838668097371868
 0.08301221919922296

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: 0.08301221919922296
Activated activity: 0.7923203662040967
Michaelis constant: 0.005936643968064003 μM
Hill coefficient: 1.838668097371868
RMSE: 0.008419222006247033

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/8bed967b649c0a56e7085abe8ce371ff7e3197661123e4598b3090e0d0ba2a2c.png

Fitting PLMp#

xdata = iso
ydata = extract(sim, sys.PLMp / sys.PLMtotBA)
plot(xdata, ydata, title="PLMp fraction", lab=false; xopts...)

_images/9e49db74b301ec10ad0f938b20a70bbeb55aa6587c40b59c464ef314a322e76b.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}:
 0.661718959957796
 0.008181712259423272
 1.3710344582362946
 0.1177272479802758

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: 0.1177272479802758
Activated activity: 0.661718959957796
Michaelis constant: 0.008181712259423272 μM
Hill coefficient: 1.3710344582362946
RMSE: 0.0032738668487186902

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/e8a96b84d308db9b2272a6a65e9bb2b5d3ab85080813872025c1c0cecda3bab2.png

Fitting TnIp#

xdata = iso
ydata = extract(sim, sys.TnIp / sys.TnItotBA)
plot(xdata, ydata, title="TnIp fraction", lab=false; xopts...)

_images/ee22be8988624d6b615c036ec9ffde79a7b7592ef060f8fca9acca506205cc2c.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}:
 0.7481955048227596
 0.007856339604983276
 1.6973362451230387
 0.06752960258346302

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: 0.06752960258346302
Activated activity: 0.7481955048227596
Michaelis constant: 0.007856339604983276 μM
Hill coefficient: 1.6973362451230387
RMSE: 0.007437139678750001

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/5884385bf1c0676451d36ea9010d19612495fc321dfe128c403ebcb62969e807.png

Fitting LCCap#

xdata = iso
ydata = extract(sim, sys.LCCap / sys.LCCtotBA)
plot(xdata, ydata, title="LCCap fraction", lab=false; xopts...)

_images/0a4ab67e6032d64d4fe3dc4420096ad056bbb2c6219ee295da1abc4215b2f027.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}:
 0.23338203470462332
 0.007263353843108377
 0.2208194668956709

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: 0.2208194668956709
Activated activity: 0.23338203470462332
Michaelis constant: 0.007263353843108377 μM
RMSE: 0.00013472586289951688

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/b438b39cc0de94a067bbc495e7fa8a703c11b8e8132fc83deb154aa60c407407.png

Fitting LCCbp#

xdata = iso
ydata = extract(sim, sys.LCCbp / sys.LCCtotBA)
plot(xdata, ydata, title="LCCbp fraction", lab=false; xopts...)

_images/c3589d79b4c910fbdbc8da2ac7eaf0d12e1e00ba302b88e73053b7850ecc5aca.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}:
 0.2455890307864609
 0.006961128884553168
 0.2520079943281469

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: 0.2520079943281469
Activated activity: 0.2455890307864609
Michaelis constant: 0.006961128884553168 μM
RMSE: 0.00013805944672658452

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/dc64749764cd0a4830de5d536957d079f58830acf9559f3c7bc80bf391fecac1.png

Fitting KURp#

xdata = iso
ydata = extract(sim, sys.KURp / sys.IKurtotBA)
plot(xdata, ydata, title="LCCbp fraction", lab=false; xopts...)

_images/bce4e5f36ac5c09bc27823bc6e5fd686ff6c054df2621271c9450168e2f1c671.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}:
 0.25565724721886424
 0.005578158691641229
 0.43936401862491953

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: 0.43936401862491953
Activated activity: 0.25565724721886424
Michaelis constant: 0.005578158691641229 μM
RMSE: 0.0001484852469948616

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/4b2798ab598a4a150dab5d92be013c26dc5d693f9aabe2dea3cd16fc7e7186d9.png

Fitting RyRp#

xdata = iso
ydata = extract(sim, sys.RyR_PKAp)
plot(xdata, ydata, title="RyRp fraction", lab=false; xopts...)

_images/22604c511601362de5a7072728b84a736b0e6b68268cd1959326445aa60b667f.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}:
 0.23988671301945835
 0.0075098746671775985
 0.20539804560868438

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: 0.20539804560868438
Activated activity: 0.23988671301945835
Michaelis constant: 0.0075098746671775985 μM
RMSE: 7.686883892119039e-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/136a54bea33025e4a7a5161bb790ef13679669fb03c67bb006699b8ab649edb4.png

This notebook was generated using Literate.jl.