diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 8bc9659..24df2d5 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-17T11:23:25","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-10-24T17:24:45","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/1-parametric-models/index.html b/dev/1-parametric-models/index.html index eaf54e8..b0e359f 100644 --- a/dev/1-parametric-models/index.html +++ b/dev/1-parametric-models/index.html @@ -96,4 +96,4 @@ ) m_noparams.fluxes -pqv17 = ParameterLinearValue([1, 2], [2, 1]) * ParameterLinearValue([2], [1]) #src
ParameterQuadraticValue([(1, 2), (2, 2)], Symbolics.Num[2, 1])

This page was generated using Literate.jl.

+pqv17 = ParameterLinearValue([1, 2], [2, 1]) * ParameterLinearValue([2], [1]) #src
ParameterQuadraticValue([(1, 2), (2, 2)], Symbolics.Num[2, 1])

This page was generated using Literate.jl.

diff --git a/dev/2-differentiate-enzyme-model/9e6d67a3.png b/dev/2-differentiate-enzyme-model/9e6d67a3.png new file mode 100644 index 0000000..4fbe4cc Binary files /dev/null and b/dev/2-differentiate-enzyme-model/9e6d67a3.png differ diff --git a/dev/2-differentiate-enzyme-model/9ef4204a.png b/dev/2-differentiate-enzyme-model/9ef4204a.png deleted file mode 100644 index 6a81654..0000000 Binary files a/dev/2-differentiate-enzyme-model/9ef4204a.png and /dev/null differ diff --git a/dev/2-differentiate-enzyme-model/index.html b/dev/2-differentiate-enzyme-model/index.html index 621f1eb..f8d173e 100644 --- a/dev/2-differentiate-enzyme-model/index.html +++ b/dev/2-differentiate-enzyme-model/index.html @@ -84,37 +84,37 @@ 0.0 0.0 0.0 - 4.683067303671569e-15 + 4.685845906545776e-15 ⋮ - 33.896840167762875 - 33.896840167762875 - 38.66807286990511 - 38.66807286990512 - 39.540588031206 - 64.66664492084865 - 64.6666449229127 - 101.8389646492298 - 101.83896465025363

And also many inactive gene products.

sort(abs.(collect(values(ec_solution.gene_product_amounts))))
124-element Vector{Float64}:
- 8.133074170808445e-17
- 8.133074170808445e-17
- 8.133074170808445e-17
- 9.844822698843576e-13
- 1.0444415257704228e-12
- 1.0444415257704228e-12
- 1.0976073657890304e-12
- 1.2566970863762915e-12
- 1.2948270597782135e-12
- 2.8068931592616887e-12
+  33.89684016777724
+  33.89684016777725
+  38.668072869856005
+  38.668072869856005
+  39.54058803115938
+  64.6666449207555
+  64.66664492281971
+ 101.83896464908304
+ 101.83896465010721

And also many inactive gene products.

sort(abs.(collect(values(ec_solution.gene_product_amounts))))
124-element Vector{Float64}:
+ 8.141678306020198e-17
+ 8.141678306020198e-17
+ 8.141678306020198e-17
+ 9.846484300151926e-13
+ 1.0446152588779501e-12
+ 1.0446152588779501e-12
+ 1.097789630627885e-12
+ 1.256902936168616e-12
+ 1.295043723786085e-12
+ 2.807358103195605e-12
  ⋮
- 0.022586033326176952
- 0.022586033355666647
- 0.022586033355666647
- 0.043486538614138044
- 0.0731266615462505
- 0.11726698379387614
- 0.11726698379387614
- 0.12079853655928265
- 0.16335511688946439

With theory, you can show that this introduces flux variability into the solution, making it non-unique, and consequently non-differentiable. To fix this, one need to prune the model, to include only the active reactions and genes. This can be differentiated uniquely. Below we build a pruned kinetic model, by removing all the reactions, metabolites, and genes that are not active.

flux_zero_tol = 1e-6 # these bounds make a real difference!
+ 0.022586033326179002
+ 0.022586033355673742
+ 0.022586033355673742
+ 0.04348653861416314
+ 0.0731266615462882
+ 0.11726698379336735
+ 0.11726698379336735
+ 0.12079853655910855
+ 0.16335511688953944

With theory, you can show that this introduces flux variability into the solution, making it non-unique, and consequently non-differentiable. To fix this, one need to prune the model, to include only the active reactions and genes. This can be differentiated uniquely. Below we build a pruned kinetic model, by removing all the reactions, metabolites, and genes that are not active.

flux_zero_tol = 1e-6 # these bounds make a real difference!
 gene_zero_tol = 1e-6
 
 pruned_reaction_isozymes =
@@ -136,7 +136,7 @@
     objective = pkm.objective.value,
     optimizer = Tulip.Optimizer,
     modifications = [COBREXA.set_optimizer_attribute("IPM_IterationsLimit", 10_000)],
-)
(ConstraintTrees.Tree{Float64}(#= 13 elements =#), [-24.48518948743512, 0.8097342831464754, 0.809734283146501, -24.485189487435118, 8.390000123357188, 0.7505183827480902, -33.20099699220754, 0.8097342831464603, 64.66664537982415, 32.77406461018067  …  0.12079853743661077, 0.005121188382153131, 0.001794785939945985, 0.0010337710784086224, 0.006415206370879354, 0.012263467164832134, 0.010287481239660628, 0.16335511657978555, 0.013360591188965832, 0.014402466503867678], [-0.0003637144327685966, 0.0023267928989637904, 0.0027824213277213715, 0.0, -0.0, -0.0, 0.0, 0.0020147427688167272, 0.0031140358258388286, 0.0010366917501896445  …  0.0009223262087884611, 0.0015352729933074153, 0.0011032142645875927, 0.0007344061982411755, 0.00018361382110090329, 0.0003637144339895737, 0.0021927537387151923, 0.0033911130687809678, 0.00016788735882470866, 0.0014758867713620281], [-2.564658119729536e-15, -2.7306079277658628e-12, -2.6481203081180955e-12, -2.5642560243722185e-15, -0.012533077620649393, -2.234043390535473e-13, -2.7228655729691482e-15, -2.7856597500505597e-12, -1.3087610993912766e-14, -1.959613940103968e-14  …  0.0, 0.0, 0.0, 0.0, -2.4276814704457444e-15, 0.0, -2.7922289252135926e-15, -2.7582801951485097e-15, -2.4039439034840108e-15, -0.017113418119369186])

Notice, the solution is exactly the same as before, except that all the inactive elements are gone.

ec_solution2
ConstraintTrees.Tree{Float64} with 13 elements:
+)
(ConstraintTrees.Tree{Float64}(#= 13 elements =#), [-24.485189487436223, 0.8097342831463148, 0.8097342831463405, -24.485189487436223, 8.390000123367471, 0.7505183827479407, -33.20099699220691, 0.8097342831462997, 64.66664537982322, 32.774064610180126  …  0.04348653850566591, 0.11726698687786197, 0.0019854019751287073, 0.0014080768108310727, 0.0011775007316609776, 0.014402466503864812, 0.013360591188965609, 0.16335511657978186, 0.010287481239658582, 0.012263467164832686], [-0.00036371443276863767, 0.0023267928989590273, 0.0027824213277173244, 0.0, -0.0, -0.0, 0.0, 0.002014742768812649, 0.00311403582583868, 0.0010366917501896827  …  0.0009223262087880106, 0.001535272993307315, 0.0011032142645869476, 0.0007344061982399577, 0.00018361382110082322, 0.0003637144339892305, 0.002192753738711806, 0.0033911130687834675, 0.00016788735882493586, 0.001475886771361535], [-2.5648632097074113e-15, -2.7307996883186784e-12, -2.6483061786531687e-12, -2.564461081706223e-15, -0.012533077620651405, -2.2341675272995034e-13, -2.7230834434230338e-15, -2.7858554439304114e-12, -1.308862742116795e-14, -1.9597639098730116e-14  …  0.0, 0.0, 0.0, 0.0, -2.427875472008117e-15, 0.0, -2.7924524204713963e-15, -2.7585009434656825e-15, -2.40413598659176e-15, -0.017113418119365467])

Notice, the solution is exactly the same as before, except that all the inactive elements are gone.

ec_solution2
ConstraintTrees.Tree{Float64} with 13 elements:
   :coupling                     => ConstraintTrees.Tree{Float64}(#= 0 elements =#)
   :directional_flux_balance     => ConstraintTrees.Tree{Float64}(#= 48 elements =#)
   :flux_stoichiometry           => ConstraintTrees.Tree{Float64}(#= 52 elements =#)
@@ -150,46 +150,46 @@
   :isozyme_forward_amounts      => ConstraintTrees.Tree{Float64}(#= 26 elements =#)
   :isozyme_reverse_amounts      => ConstraintTrees.Tree{Float64}(#= 5 elements =#)
   :objective                    => 0.750518

no zero fluxes

sort(abs.(collect(values(ec_solution2.fluxes))))
48-element Vector{Float64}:
-   0.19190755046859567
-   0.7505183827480902
-   0.8097342831464603
-   0.8097342831464754
-   0.809734283146501
-   0.8097342831465368
-   1.7395389988938417
-   2.010476135065905
-   2.0104761350659057
-   2.1506854776024715
+   0.19190755046855745
+   0.7505183827479407
+   0.8097342831462997
+   0.8097342831463148
+   0.8097342831463405
+   0.8097342831463762
+   1.739538998893496
+   2.010476135065505
+   2.010476135065506
+   2.150685477602044
    ⋮
-  33.8968401107718
-  33.896840110771805
-  38.668073099496674
-  38.668073099496674
-  39.54058824536094
-  64.66664537982413
-  64.66664537982415
- 101.83896538885982
- 101.83896538885982

no zero genes

sort(abs.(collect(values(ec_solution2.gene_product_amounts))))
47-element Vector{Float64}:
- 0.0005876895265928773
- 0.0005934281743690526
- 0.0008428927106182057
- 0.0019854019751291015
- 0.0025855775424925634
- 0.0028285570183546075
- 0.003032537389839215
- 0.0032794216561368985
- 0.0036093078339007735
- 0.004477678876501842
+  33.89684011077103
+  33.89684011077104
+  38.66807309949494
+  38.66807309949494
+  39.54058824535901
+  64.66664537982322
+  64.66664537982322
+ 101.83896538885946
+ 101.83896538885948

no zero genes

sort(abs.(collect(values(ec_solution2.gene_product_amounts))))
47-element Vector{Float64}:
+ 0.0005876895265927602
+ 0.000593428174368933
+ 0.0008428927106180381
+ 0.0019854019751287073
+ 0.0025855775424920503
+ 0.002828557018354045
+ 0.0030325373898386107
+ 0.003279421656136242
+ 0.003609307833900057
+ 0.004477678876501782
  ⋮
- 0.022586033324646485
- 0.022586033324646485
- 0.022586033324646485
- 0.04348653850566663
- 0.0731266613828739
- 0.11726698687786366
- 0.11726698687786366
- 0.12079853743661077
- 0.16335511657978555

prune the kcats, leaving only those that are actually used

pruned_kcats = [
+ 0.022586033324645538
+ 0.022586033324645538
+ 0.022586033324645538
+ 0.04348653850566591
+ 0.07312666138287223
+ 0.11726698687786197
+ 0.11726698687786197
+ 0.12079853743661037
+ 0.16335511657978186

prune the kcats, leaving only those that are actually used

pruned_kcats = [
     begin
         x = first(values(v))
         isnothing(x.kcat_forward) ? x.kcat_reverse : x.kcat_forward
@@ -207,7 +207,7 @@
     parameter_values,
     parameters;
     scale = true, # unitless sensitivities
-)
([0.944774284282412 -0.0 … -0.0 -0.0; 1.140106525775455 0.0 … 0.0 0.0; … ; 0.9941756806741956 -0.0 … -0.0 -0.0; 1.1401065257748115 -0.0 … -0.0 -0.0], Tuple{Symbol, Symbol, Vararg{Symbol}}[(:fluxes, :ACKr), (:fluxes, :ACONTa), (:fluxes, :ACONTb), (:fluxes, :ACt2r), (:fluxes, :ATPM), (:fluxes, :BIOMASS_Ecoli_core_w_GAM), (:fluxes, :CO2t), (:fluxes, :CS), (:fluxes, :CYTBD), (:fluxes, :ENO)  …  (:isozyme_forward_amounts, :SUCCt2_2, :isozyme_1), (:isozyme_forward_amounts, :TALA, :isozyme_1), (:isozyme_forward_amounts, :TKT1, :isozyme_2), (:isozyme_forward_amounts, :TKT2, :isozyme_2), (:isozyme_forward_amounts, :TPI, :isozyme_1), (:isozyme_reverse_amounts, :ACKr, :isozyme_1), (:isozyme_reverse_amounts, :GLUDy, :isozyme_1), (:isozyme_reverse_amounts, :PGK, :isozyme_1), (:isozyme_reverse_amounts, :PGM, :isozyme_3), (:isozyme_reverse_amounts, :RPI, :isozyme_2)])

look at glycolysis and oxidative phosphorylation only

subset_ids = [
+)
([0.9447742842823873 -0.0 … -0.0 -0.0; 1.1401065257754806 0.0 … 0.0 0.0; … ; 1.140106525774991 0.0 … 0.0 0.0; 0.9447742842823852 0.0 … 0.0 0.0], Tuple{Symbol, Symbol, Vararg{Symbol}}[(:fluxes, :ACKr), (:fluxes, :ACONTa), (:fluxes, :ACONTb), (:fluxes, :ACt2r), (:fluxes, :ATPM), (:fluxes, :BIOMASS_Ecoli_core_w_GAM), (:fluxes, :CO2t), (:fluxes, :CS), (:fluxes, :CYTBD), (:fluxes, :ENO)  …  (:isozyme_forward_amounts, :ENO, :isozyme_1), (:isozyme_forward_amounts, :CYTBD, :isozyme_2), (:isozyme_forward_amounts, :CS, :isozyme_1), (:isozyme_forward_amounts, :ACONTb, :isozyme_1), (:isozyme_forward_amounts, :ACONTa, :isozyme_1), (:isozyme_reverse_amounts, :RPI, :isozyme_2), (:isozyme_reverse_amounts, :PGM, :isozyme_3), (:isozyme_reverse_amounts, :PGK, :isozyme_1), (:isozyme_reverse_amounts, :GLUDy, :isozyme_1), (:isozyme_reverse_amounts, :ACKr, :isozyme_1)])

look at glycolysis and oxidative phosphorylation only

subset_ids = [
     r["id"] for r in model.reactions[indexin(string.(keys(pkm.fluxes)), rids)] if
     r["subsystem"] in ["Glycolysis/Gluconeogenesis", "Oxidative Phosphorylation"]
 ]
@@ -222,17 +222,17 @@
 param_ids = parameters[param_idxs]

\[ \begin{equation} \left[ \begin{array}{c} -PGK \\ -PDH \\ -PGM \\ -CYTBD \\ -FBA \\ -GAPD \\ -NADH16 \\ -PFK \\ -PGI \\ -TPI \\ -ENO \\ +\mathtt{PGK} \\ +\mathtt{PDH} \\ +\mathtt{PGM} \\ +\mathtt{CYTBD} \\ +\mathtt{FBA} \\ +\mathtt{GAPD} \\ +\mathtt{NADH16} \\ +\mathtt{PFK} \\ +\mathtt{PGI} \\ +\mathtt{TPI} \\ +\mathtt{ENO} \\ \end{array} \right] \end{equation} @@ -260,4 +260,4 @@ ), ) Colorbar(f[1, 2], hm) -fExample block output

This page was generated using Literate.jl.

+fExample block output

This page was generated using Literate.jl.

diff --git a/dev/3-parameter-estimation/98c59523.png b/dev/3-parameter-estimation/98c59523.png deleted file mode 100644 index 4f80929..0000000 Binary files a/dev/3-parameter-estimation/98c59523.png and /dev/null differ diff --git a/dev/3-parameter-estimation/ffa91456.png b/dev/3-parameter-estimation/ffa91456.png new file mode 100644 index 0000000..4dc17e5 Binary files /dev/null and b/dev/3-parameter-estimation/ffa91456.png differ diff --git a/dev/3-parameter-estimation/index.html b/dev/3-parameter-estimation/index.html index 719ba45..20ea03f 100644 --- a/dev/3-parameter-estimation/index.html +++ b/dev/3-parameter-estimation/index.html @@ -129,10 +129,10 @@ estimated_parameters[r4] -= η * dL_dkcats[2] end -lines(losses; axis = (xlabel = "Iterations", ylabel = "L2 loss"))Example block output
estimated_parameters
Dict{Symbolics.Num, Float64} with 3 entries:
-  r3                 => 2.05711
+lines(losses; axis = (xlabel = "Iterations", ylabel = "L2 loss"))
Example block output
estimated_parameters
Dict{Symbolics.Num, Float64} with 3 entries:
+  r3                 => 6.88387
   capacitylimitation => 50.0
-  r4                 => 3.00787
true_parameter_values
Dict{Symbolics.Num, Float64} with 3 entries:
+  r4                 => 0.993201
true_parameter_values
Dict{Symbolics.Num, Float64} with 3 entries:
   r3                 => 2.0
   capacitylimitation => 50.0
-  r4                 => 3.0

This page was generated using Literate.jl.

+ r4 => 3.0

This page was generated using Literate.jl.

diff --git a/dev/index.html b/dev/index.html index 65e0dfb..a631e83 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -README · DifferentiableMetabolism.jl
GitHub
+README · DifferentiableMetabolism.jl
GitHub
diff --git a/dev/reference/index.html b/dev/reference/index.html index 4efc2c6..116e86a 100644 --- a/dev/reference/index.html +++ b/dev/reference/index.html @@ -1,23 +1,23 @@ -Reference · DifferentiableMetabolism.jl
GitHub

Reference

Parameters

ParameterLinearValue

DifferentiableMetabolism.ParameterLinearValue — Type
struct ParameterLinearValue <: ConstraintTrees.Value

An extension of ConstraintTrees.LinearValue where the weights are parameters.

ParameterLinearValues can be combined additively and multiplied by real-number constants.

Multiplying two ParameterLinearValues yields a quadratic form (in a ParameterQuadraticValue).

Fields

  • idxs::Vector{Int64}

  • weights::Vector{Symbolics.Num}

source

ParameterQuadraticValue

DifferentiableMetabolism.ParameterQuadraticValue — Type
struct ParameterQuadraticValue <: ConstraintTrees.Value

An extension of ConstraintTrees.QuadraticValue where the weights are parameters.

Behaves similarly to ConstraintTrees.QuadraticValue. Thus, the cleanest way to construct a ParameterQuadraticValue is to multiply two ParameterLinearValues.

Fields

  • idxs::Vector{Tuple{Int64, Int64}}

  • weights::Vector{Symbolics.Num}

source

ParameterBound

DifferentiableMetabolism.ParameterBetween — Type
mutable struct ParameterBetween <: ConstraintTrees.Bound

Representation of an "interval" bound where the lower and upper bound values are parameters. Since Symbolics.Num is a subtype of Real, the bounds could also be any real number, but they are converted by the constructors to Symbolics.Nums.

Fields

  • lower::Symbolics.Num

  • upper::Symbolics.Num

source
DifferentiableMetabolism.ParameterEqualTo — Type
mutable struct ParameterEqualTo <: ConstraintTrees.Bound

Representation of an "equality" bound, where the bound value is a parameter. Since Symbolics.Num is a subtype of Real, the bound could also be any real number, but it is converted by the constructor to a Symbolics.Num.

Fields

  • equal_to::Symbolics.Num
source

ParameterIsozyme

DifferentiableMetabolism.ParameterIsozyme — Type
mutable struct ParameterIsozyme

A parameterized isozyme struct which includes parameters in the kcat_forward, and the kcat_backward. If the reaction does not have a turnover number,nothing can be used.

Fields

  • gene_product_stoichiometry::Dict{String, Float64}

  • kcat_forward::Union{Nothing, Symbolics.Num}

  • kcat_reverse::Union{Nothing, Symbolics.Num}

source

Parameterized models

Kinetic models

DifferentiableMetabolism.build_kinetic_model — Method
build_kinetic_model(
+Reference · DifferentiableMetabolism.jl
GitHub
Reference
Parameters
ParameterLinearValue
DifferentiableMetabolism.ParameterLinearValue — Type
struct ParameterLinearValue <: ConstraintTrees.Value
An extension of ConstraintTrees.LinearValue where the weights are parameters.
ParameterLinearValues can be combined additively and multiplied by real-number constants.
Multiplying two ParameterLinearValues yields a quadratic form (in a ParameterQuadraticValue).
Fields
  • idxs::Vector{Int64}
  • weights::Vector{Symbolics.Num}
source
ParameterQuadraticValue
DifferentiableMetabolism.ParameterQuadraticValue — Type
struct ParameterQuadraticValue <: ConstraintTrees.Value
An extension of ConstraintTrees.QuadraticValue where the weights are parameters.
Behaves similarly to ConstraintTrees.QuadraticValue. Thus, the cleanest way to construct a ParameterQuadraticValue is to multiply two ParameterLinearValues.
Fields
  • idxs::Vector{Tuple{Int64, Int64}}
  • weights::Vector{Symbolics.Num}
source
ParameterBound
DifferentiableMetabolism.ParameterBetween — Type
mutable struct ParameterBetween <: ConstraintTrees.Bound
Representation of an "interval" bound where the lower and upper bound values are parameters. Since Symbolics.Num is a subtype of Real, the bounds could also be any real number, but they are converted by the constructors to Symbolics.Nums. 
Fields
  • lower::Symbolics.Num
  • upper::Symbolics.Num
source
DifferentiableMetabolism.ParameterEqualTo — Type
mutable struct ParameterEqualTo <: ConstraintTrees.Bound
Representation of an "equality" bound, where the bound value is a parameter. Since Symbolics.Num is a subtype of Real, the bound could also be any real number, but it is converted by the constructor to a Symbolics.Num.
Fields
  • equal_to::Symbolics.Num
source
ParameterIsozyme
DifferentiableMetabolism.ParameterIsozyme — Type
mutable struct ParameterIsozyme
A parameterized isozyme struct which includes parameters in the kcat_forward, and the kcat_backward. If the reaction does not have a turnover number,nothing can be used. 
Fields
  • gene_product_stoichiometry::Dict{String, Float64}
  • kcat_forward::Union{Nothing, Symbolics.Num}
  • kcat_reverse::Union{Nothing, Symbolics.Num}
source
Parameterized models
Kinetic models
DifferentiableMetabolism.build_kinetic_model — Method
build_kinetic_model(
     model::AbstractFBCModels.AbstractFBCModel;
     reaction_isozymes,
     gene_product_molar_masses,
     capacity
 )
-
Essentially an enzyme constrained metabolic model, but the kcat can be a arbitrary symbolic function.
source
Solving models
Solving models
DifferentiableMetabolism.optimization_model_with_parameters — Method
optimization_model_with_parameters(
     m::ConstraintTrees.Tree{ConstraintTrees.Constraint},
     parameters::Dict{Symbolics.Num, Float64};
     objective,
     optimizer,
     sense
 )
-
Construct a JuMP model by substituting parameters into the model, m. Set the objective and the optimizer, as well as the sense similar to COBREXA.optimization_model.
Converts all inequality constraints to the form A * x ≤ b.
source
DifferentiableMetabolism.optimized_constraints_with_parameters — Method
optimized_constraints_with_parameters(
+
Construct a JuMP model by substituting parameters into the model, m. Set the objective and the optimizer, as well as the sense similar to COBREXA.optimization_model.
Converts all inequality constraints to the form A * x ≤ b.
source
DifferentiableMetabolism.optimized_constraints_with_parameters — Method
optimized_constraints_with_parameters(
     m::ConstraintTrees.Tree{ConstraintTrees.Constraint},
     parameters::Dict{Symbolics.Num, Float64};
     modifications,
@@ -25,23 +25,23 @@
     optimizer,
     sense
 )
-
Solve a model, m, by forwarding arguments to optimization_model_with_parameters. 
Optionally, set optimizer attributes with modifications. If the model does not solve successfully return nothing. Otherwise, return a tuple of the solution tree, and vectors containing the values of the primal variables, the equality constraint dual variables. 
These duals are ordered according to the constraint output of calling equality_constraints and inequality_constraints respectively.
source
Pruning models
DifferentiableMetabolism.prune_gene_product_molar_masses — Method
prune_gene_product_molar_masses(
+
Solve a model, m, by forwarding arguments to optimization_model_with_parameters. 
Optionally, set optimizer attributes with modifications. If the model does not solve successfully return nothing. Otherwise, return a tuple of the solution tree, and vectors containing the values of the primal variables, the equality constraint dual variables. 
These duals are ordered according to the constraint output of calling equality_constraints and inequality_constraints respectively.
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Pruning models
DifferentiableMetabolism.prune_model — Method
prune_model(
     model,
     ec_solution,
     flux_zero_tol,
     gene_zero_tol
 ) -> AbstractFBCModels.CanonicalModel.Model
-
Prune away reactions, metabolites, and genes from a model using ec_solution, which is the result of an enzyme constrained kinetic simulation. Fluxes and gene product concentrations smaller than flux_zero_tol, gene_zero_tol are removed. Metabolites that do not take part in the remaining reactions are also removed.
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DifferentiableMetabolism.prune_reaction_isozymes — Method
prune_reaction_isozymes(
+
Prune away reactions, metabolites, and genes from a model using ec_solution, which is the result of an enzyme constrained kinetic simulation. Fluxes and gene product concentrations smaller than flux_zero_tol, gene_zero_tol are removed. Metabolites that do not take part in the remaining reactions are also removed.
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Differentiation
Differentiation
DifferentiableMetabolism.differentiate — Method
differentiate(
     m::ConstraintTrees.Tree{ConstraintTrees.Constraint},
     objective::ConstraintTrees.Value,
     x_vals::Vector{Float64},
@@ -51,29 +51,29 @@
     parameters::Vector{Symbolics.Num};
     scale
 ) -> Tuple{Any, Any}
-
Differentiate a model m with respect to parameters which take on values parameter_values in the optimal solution with respect to the objective. The primal variables x_vals, and the dual variable values eq_dual_vals and ineq_dual_vals need to be supplied. 
Internally, primal variables with value abs(x) ≤ primal_zero_tol are removed from the computation, and their sensitivities are not calculated.  
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Internals
Constraint tree extensions
Optimization problem builders
DifferentiableMetabolism.equality_constraints — Method
equality_constraints(
+
Differentiate a model m with respect to parameters which take on values parameter_values in the optimal solution with respect to the objective. The primal variables x_vals, and the dual variable values eq_dual_vals and ineq_dual_vals need to be supplied. 
Internally, primal variables with value abs(x) ≤ primal_zero_tol are removed from the computation, and their sensitivities are not calculated.  
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Internals
Constraint tree extensions
Optimization problem builders
DifferentiableMetabolism.equality_constraints — Method
equality_constraints(
     m::ConstraintTrees.Tree{ConstraintTrees.Constraint}
 ) -> Vector{Tuple{Union{ConstraintTrees.LinearValue, ParameterLinearValue}, Symbolics.Num}}
-
Return all the equality constraints of m as a tuple ({Parameter}LinearValue, value) representing {P}LV == value for each entry.
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DifferentiableMetabolism.inequality_constraints — Method
inequality_constraints(
     m::ConstraintTrees.Tree{ConstraintTrees.Constraint}
 ) -> Vector
-
Return all the inequality constraints of m as a tuple of bounds converted to the form ({Parameter}LinearValue, upper) representing {P}LV ≤ upper for each entry. 
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Symbolics extensions

+

Return all the inequality constraints of m as a tuple of bounds converted to the form ({Parameter}LinearValue, upper) representing {P}LV ≤ upper for each entry.

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Symbolics extensions