Sensitiviy analysis - Mitochondrial dynamics

Influence of parameters on the average degree of mitochondrial node

using DifferentialEquations
using OrdinaryDiffEqSDIRK
using SteadyStateDiffEq
using ModelingToolkit
using MitochondrialDynamics
using Tables
using MarkdownTables

Setup the ODE system¶

@time "Build system" @named sys = make_model()
@time "Build problem" prob = SteadyStateProblem(sys, [])

params = parameters(sys)
sol0 = solve(prob, DynamicSS(FBDF()); reltol=1e-8, abstol=1e-8)
# Average degree of mitochondrial node
@unpack degavg = sys
d0 = sol0[degavg]

println("The default average degree of mitochondrial node is: ", d0)

function _calc_sens(k)
    original_value = prob.ps[k]
    _prob = remake(prob, p=[k => original_value * 1.01]) ## Increase 1% of the parameter value
    sol = solve(_prob, DynamicSS(FBDF()); reltol = 1e-8, abstol = 1e-8)
    return (sol[degavg] / d0 - 1) * 100
end

Build system: 0.044025 seconds (93.92 k allocations: 19.642 MiB)
Build problem: 5.888595 seconds (8.29 M allocations: 421.907 MiB, 1.02% gc time, 99.10% compilation time)
The default average degree of mitochondrial node is: 1.563773465956938

_calc_sens (generic function with 1 method)

Sensitivity analysis of the solution at t=300 sec against parameters.

@time sensitivities = Dict(k => _calc_sens(k) for k in params)

 15.522613 seconds (19.16 M allocations: 964.904 MiB, 1.69% gc time, 90.39% compilation time)

Dict{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}, Float64} with 68 entries:
  KnadhLDH    => 0.000669056
  ATPstiochGK => 0.00369046
  V_MTX       => -0.000155114
  KvF1        => -0.40975
  KadpGPD     => -3.75005e-7
  KnaNCLX     => 0.0176436
  KadpF1      => -0.0187778
  kATPCa      => 0.00815121
  V_I         => 0.0449948
  rHL         => -0.154314
  pHleak      => -0.154314
  rETC        => 0.00114121
  F_M         => 4.98543e-8
  kATP        => 0.0383119
  KglcGK      => -0.0585603
  KbETC       => 0.000781999
  kNADHc      => -6.69336e-5
  Σn_c        => -9.86499e-5
  kfiss2      => -0.0573986
  ⋮           => ⋮

println("Relative sensitivity of average degree of mitochondrial node to parameters:")

ks = keys(sensitivities) |> collect
vs = values(sensitivities) |> collect

t = Tables.table([ks vs]; header=["Parameter", "Relative Sensitivity"])
MarkdownTables.markdown_table(t)

Relative sensitivity of average degree of mitochondrial node to parameters:

This notebook was generated using Literate.jl.