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{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{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{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{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{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{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{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{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{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) \\ \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{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{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{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{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{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{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{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{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{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)} \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:
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(0xc0a04efd, 0xeef5c310, 0xb93fc60d, 0x147790af, 0x0fe8fb2e), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :__mtk_arg_1, :___mtkparameters___), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xc3447e86, 0x5d76acbd, 0xaca3a21c, 0x0626d68d, 0x613284b2), Nothing}}}}, Nothing}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}}, SteadyStateDiffEq.DynamicSS{OrdinaryDiffEqRosenbrock.Rodas5P{9, ADTypes.AutoForwardDiff{9, Nothing}, 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{}}, 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"""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.

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