AlgebraicJulia
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AlgebraicPetri.jl
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Added enzyme reaction example to documentation (#28) 

* Added enzyme reaction example to documentation

* Added solver algorithm

* Moved from OrdinaryDiffEq to DifferentialEquations to test
pull/30/head
Micah Halter 5 months ago
committed by GitHub
parent
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commit
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6 changed files with 275 additions and 15 deletions
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  1. 1
      docs/Project.toml
  2. 1
      docs/make.jl
  3. 5
      examples/enzymes/Project.toml
  4. 264
      examples/enzymes/enzyme_reactions.jl
  5. 11
      src/AlgebraicPetri.jl
  6. 8
      src/Epidemiology.jl

1
docs/Project.toml
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@ -1,6 +1,7 @@
[deps]
AlgebraicPetri = "4f99eebe-17bf-4e98-b6a1-2c4f205a959b"
Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"

1
docs/make.jl
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@ -42,6 +42,7 @@ makedocs(
"examples/predation/lotka-volterra.md",
"examples/covid/epidemiology.md",
"examples/covid/coexist/coexist.md",
"examples/enzymes/enzyme_reactions.md",
],
"Library Reference" => "api.md",
]

5
examples/enzymes/Project.toml
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@ -0,0 +1,5 @@
[deps]
AlgebraicPetri = "4f99eebe-17bf-4e98-b6a1-2c4f205a959b"
Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"

264
examples/enzymes/enzyme_reactions.jl
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@ -0,0 +1,264 @@
# # [Cathepsin Enzyme Reactions](@id enzyme_example)
#
#md # [![](https://img.shields.io/badge/show-nbviewer-579ACA.svg)](@__NBVIEWER_ROOT_URL__/examples/enzymes/enzyme_reactions.ipynb)
using AlgebraicPetri
using Catlab.Programs
using Catlab.Graphics
using Catlab.WiringDiagrams
using Catlab.CategoricalAlgebra
using DifferentialEquations
using Plots
display_uwd(ex) = to_graphviz(ex, box_labels=:name, junction_labels=:variable, edge_attrs=Dict(:len=>".75"));
ode(x, t) = ODEProblem(vectorfield(x), concentrations(x), t, rates(x));
# ## Define objects and initial conditions
ob(x) = codom(Open([first(x)], LabelledReactionNet{Number,Int}(x), [first(x)])).ob;
K = :K=>33000;
S = :S=>33000;
L = :L=>33000;
Kinact = :Kinact=>0;
Sinact = :Sinact=>0;
Linact = :Linact=>0;
E = :E=>700000;
G = :G=>1300000;
# ## Helper functions for generating primitive Petri net operations
inact(in,on::Number) = begin
inact = Symbol(first(in), :inact)
Open(LabelledReactionNet{Number,Int}(unique((in, inact=>0)), ((Symbol(:inact_,first(in)),on),first(in)=>inact)))
end;
bind(in1, in2, on::Number, off::Number) = begin
out = Symbol(first(in1),first(in2))
Open(LabelledReactionNet{Number,Int}(unique((in1, in2,out=>0)), ((Symbol(:bind_,first(in1),first(in2)),on),(first(in1),first(in2))=>out),
((Symbol(:unbind_,out),off),out=>(first(in1),first(in2)))))
end;
unbind(in::Symbol, out1, out2, on::Number) =
Open(LabelledReactionNet{Number,Int}(unique((in=>0, out1,out2)), ((Symbol(:unbind_,in),on),in=>(first(out1),first(out2)))));
deg(prod1,prod2,on::Number) = begin
prod2str = String(first(prod2))
out = Symbol(endswith(prod2str, "inact") ? first(prod2str) : prod2str, :deg)
unbind(Symbol(first(prod1),first(prod2)), prod1, out=>0, on)
end;
# ## Cathepsin *X* reacting with itself
catX = @relation (X, Xinact, Xdeg) where (X, Xinact, Xdeg, XX, XXinact) begin
inactX(X, Xinact)
bindXX(X, XX)
degXX(XX, X, Xdeg)
bindXXinact(X, Xinact, XXinact)
degXXinact(XXinact, X, Xdeg)
end
display_uwd(catX)
# ## Cathepsin *X* reacting with Substrate *Y*
catXsubY = @relation (X, Xinact, Xdeg, Y, Ydeg) where (X, Xinact, Xdeg, Y, XY, Ydeg) begin
bindXY(X, Y, XY)
degXY(XY, X, Ydeg)
end
display_uwd(catXsubY)
# ## Cathepsin *X* reacting with Cathepsin *Y*
catXY = @relation (X, Xinact, Xdeg, Y, Yinact, Ydeg) where (X, Xinact, Xdeg, Y, Yinact, Ydeg, XY, XYinact) begin
bindXY(X, Y, XY)
degXY(XY, X, Ydeg)
bindXYinact(X, Yinact, XYinact)
degXYinact(XYinact, X, Ydeg)
end
display_uwd(catXY)
# ## Define all enzyme reactions
rxns = Dict(
:K => [inact(K, 7.494e-10)
bind(K, K, 7.814e-4, 3.867e-3)
deg(K, K, 2.265e-1)
bind(K, Kinact, 7.814e-4, 3.867e-3)
deg(K, Kinact, 2.265e-1)],
:S => [inact(S, 7.494e-10)
bind(S, S, 7.814e-4, 3.867e-3)
deg(S, S, 2.265e-1)
bind(S, Sinact, 7.814e-4, 3.867e-3)
deg(S, Sinact, 2.265e-1)],
:L => [inact(L, 7.494e-10)
bind(L, L, 7.814e-4, 3.867e-3)
deg(L, L, 2.265e-1)
bind(L, Linact, 7.814e-4, 3.867e-3)
deg(L, Linact, 2.265e-1)],
:KE => [bind(K, E, 9.668e-6, 1e-2)
deg(K, E, 1.728e0)],
:KG => [bind(K, G, 2.764e-6, 8.78e-1)
deg(K, G, 1.502)],
:SE => [bind(S, E, 4.197e-7, 1.06e-3)
deg(S, E, 1.384e4)],
:SG => [bind(S, G, 5.152e-8, 3.894e-3)
deg(S, G, 8.755e-1)],
:LE => [bind(L, E, 1.977e-8, 1e-2)
deg(L, E, 1.066e2)],
:LG => [bind(L, G, 3.394e-8, 2.365e1)
deg(L, G, 4.352)],
:KS => [bind(K, S, 8.822e-4, 4.114e5)
deg(K, S, 9e-10)
bind(K, Sinact, 8.822e-4, 4.114e5)
deg(K, Sinact, 9e-10)],
:KL => [bind(K, L, 1.756e-4, 3.729e4)
deg(K, L, 6.505e6)
bind(K, Linact, 1.756e-4, 3.729e4)
deg(K, Linact, 6.505e6)],
:SK => [bind(S, K, 8.822e-4, 4.114e5)
deg(S, K, 9e-10)
bind(S, Kinact, 8.822e-4, 4.114e5)
deg(S, Kinact, 9e-10)],
:SL => [bind(S, L, 1e-3, 5e2)
deg(S, L, 1e-7)
bind(S, Linact, 1e-3, 5e2)
deg(S, Linact, 1e-7)],
:LK => [bind(L, K, 1e-3, 4.118e3)
deg(L, K, 3.234e1)
bind(L, Kinact, 1e-3, 4.118e3)
deg(L, Kinact, 3.234e1)],
:LS => [bind(L, S, 1.056e-12, 5e2)
deg(L, S, 5e-1)
bind(L, Sinact, 1.056e-12, 5e2)
deg(L, Sinact, 5e-1)]
)
# ## Helper functions to generate oapply calls
cat(cat) = begin
out = oapply(catX, Dict([:inactX, :bindXX, :degXX, :bindXXinact, :degXXinact] .=> rxns[first(cat)]))
bundle_legs(out, [[1,2,3]])
end
cat_sub(cat1, sub) = begin
catsym = first(cat1)
subsym = first(sub)
catsub = Symbol(catsym, subsym)
out = oapply(catXsubY, Dict([:bindXY, :degXY] .=> rxns[catsub]), Dict(
:X=>ob(cat1),
:Xinact=>ob(Symbol(catsym,:inact)=>0),
:Xdeg=>ob(Symbol(catsym,:deg)=>0),
:Y=>ob(sub),
:XY=>ob(Symbol(catsym,subsym)=>0),
:Ydeg=>ob(Symbol(subsym,:deg)=>0)))
bundle_legs(out, [[1,2,3], [4,5]])
end
cat_cat(cat1, cat2) = begin
cat1sym = first(cat1)
cat2sym = first(cat2)
catcat = Symbol(cat1sym, cat2sym)
out = oapply(catXY, Dict([:bindXY, :degXY, :bindXYinact, :degXYinact] .=> rxns[catcat]), Dict(
:X=>ob(cat1),
:Xinact=>ob(Symbol(cat1sym,:inact)=>0),
:Xdeg=>ob(Symbol(cat1sym,:deg)=>0),
:Y=>ob(cat2),
:Yinact=>ob(Symbol(cat2sym,:inact)=>0),
:Ydeg=>ob(Symbol(cat2sym,:deg)=>0),
:XY=>ob(catcat=>0),
:XYinact=>ob(Symbol(catcat,:inact)=>0)))
bundle_legs(out, [[1,2,3], [4,5,6]])
end
functor(x) = oapply(x, Dict(
:catK=>cat(K),
:catS=>cat(S),
:catL=>cat(L),
:catKcatS=>cat_cat(K,S),
:catKcatL=>cat_cat(K,L),
:catScatK=>cat_cat(S,K),
:catScatL=>cat_cat(S,L),
:catLcatK=>cat_cat(L,K),
:catLcatS=>cat_cat(L,S),
:catKsubE=>cat_sub(K,E),
:catSsubE=>cat_sub(S,E),
:catLsubE=>cat_sub(L,E),
:catKsubG=>cat_sub(K,G),
:catSsubG=>cat_sub(S,G),
:catLsubG=>cat_sub(L,G)));
# # Defining Models
# ## CatK, CatS, Elastin
KSE = @relation (K, S, E) begin
catK(K)
catS(S)
catKcatS(K, S)
catScatK(S, K)
catKsubE(K, E)
catSsubE(S, E)
end
KSE_petri = apex(functor(KSE))
ode_prob = ode(KSE_petri, (0.0, 120.0))
sol = solve(ode_prob)
plot(sol)
#-
plot(sol, lw = 2, ylims = (0, 15000), xlims = (0, 30))
# ## CatK, CatS, CatL, Elastin
KSLE = @relation (K, S, L, E) begin
catK(K)
catS(S)
catL(L)
catKcatS(K, S)
catKcatL(K, L)
catScatK(S, K)
catScatL(S, L)
catLcatK(L, K)
catLcatS(L, S)
catKsubE(K, E)
catSsubE(S, E)
catLsubE(L, E)
end
KSLE_petri = apex(functor(KSLE))
ode_prob = ode(KSLE_petri, (0.0,120.0))
sol = solve(ode_prob)
plot(sol, lw = 1, size = (1066, 600))
#-
plot(sol, ylims = (0, 20000), xlims = (0, 30), lw = 2, size = (1066, 600))
# ## CatK, CatS, CatL, Elastin, Gelatin
KSLEG = @relation (K, S, L, E, G) begin
catK(K)
catS(S)
catL(L)
catKcatS(K, S)
catKcatL(K, L)
catScatK(S, K)
catScatL(S, L)
catLcatK(L, K)
catLcatS(L, S)
catKsubE(K, E)
catSsubE(S, E)
catLsubE(L, E)
catKsubG(K, G)
catSsubG(S, G)
catLsubG(L, G)
end
KSLEG_petri = apex(functor(KSLEG))
ode_prob = ode(KSLEG_petri, (0.0,120.0))
sol = solve(ode_prob)
plot(sol, lw = 1, size = (1066, 600))
#-
plot(sol, ylims = (0, 30000), xlims = (0, 50), lw = 2, size = (1066, 600))

11
src/AlgebraicPetri.jl
View File

@ -125,23 +125,16 @@ valueat(f::Function, u, t) = try f(u,t) catch e f(t) end
vectorfield(pn::AbstractPetriNet) = begin
tm = TransitionMatrices(pn)
dt_T = tm.output - tm.input
dt = tm.output - tm.input
log_rates = zeros(nt(pn))
f(du,u,p,t) = begin
u_m = [u[sname(pn, i)] for i in 1:ns(pn)]
p_m = [p[tname(pn, i)] for i in 1:nt(pn)]
# FIX ME: log transform approach to calculating vector fields
# log_rates = log.(map(i->valueat(i,u,t), p_m)) .+ tm.input * log.(u_m)
# new_du = dt_T * exp.(log_rates)
# for s in 1:ns(pn)
# du[sname(pn, s)] = new_du[s]
# end
for i in 1:nt(pn)
log_rates[i] = valueat(p_m[i],u,t) * prod(u_m[j] ^ tm.input[i,j] for j in 1:ns(pn))
end
for j in 1:ns(pn)
du[sname(pn, j)] = sum(log_rates[i] * dt_T[i,j] for i in 1:nt(pn))
du[sname(pn, j)] = sum(log_rates[i] * dt[i,j] for i in 1:nt(pn))
end
return du
end

8
src/Epidemiology.jl
View File

@ -9,7 +9,7 @@ using Catlab.CategoricalAlgebra.FinSets
export oapply_epi, infection, exposure, illness, recovery, death
spontaneous_petri(x::Symbol, y::Symbol, z::Symbol) = Open(LabelledPetriNet(unique([x,y]), z=>(x, y)))
exposure_petri(x::Symbol, y::Symbol, z::Symbol, transition::Symbol) =
exposure_petri(x::Symbol, y::Symbol, z::Symbol, transition::Symbol) =
Open(LabelledPetriNet(unique([x,y,z]), transition=>((x,y)=>(z,y))))
infection = exposure_petri(:S, :I, :I, :inf)
@ -22,10 +22,6 @@ epi_dict = Dict(:infection=>infection, :exposure=>exposure, :illness=>illness, :
""" oapply_epi
"""
oapply_epi(ex) = oapply(ex, epi_dict)
oapply_epi(ex, args...) = oapply(ex, epi_dict, args...)
end
# sir = LabelledReactionNet{Number, Int}((:S=>990, :I=>10, :R=>0), (:inf, .3/1000)=>((:S, :I)=>(:I,:I)), (:rec, .2)=>(:I=>:R))
# siir = LabelledReactionNet{Number, Int}((:S=>990, :I=>10, :A=>0, :R=>0), (:inf_i, .3/1000)=>((:S, :I)=>(:I,:I)), (:inf_a, .0003)=>((:S,:A)=>(:I,:A)), (:asym_i, .0003)=>((:S,:I)=>(:I,:A)), (:asym_a, .0003)=>((:S,:A)=>(:A,:A)),(:rec_i, .2)=>(:I=>:R),(:rec_a, .2)=>(:A=>:R))
# seair = LabelledReactionNet{Number, Int}((:S=>990, :E=>0, :I=>10, :A=>0, :R=>0), (:exp_i, .3/1000)=>((:S, :I)=>(:I,:E)), (:exp_a, .3/1000)=>((:S, :A)=>(:A, :E)), (:inf, .0003)=>(:E=>:I), (:asym, .0003)=>(:E=>:A), (:rec_a, .2)=>(:A=>:R), (:rec_i, .2)=>(:I=>:R))
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