The generic geometry of steady state varieties

File descriptions

• A Julia file functions.jl that contains functions for testing whether a network admits positive nondegenerate steady states when modeled with (generalized) mass action kinetics.
  
  
• Two notebooks with examples:
  • IDH.ipynb for the isocitrate dehydrogenase network in Example 4.1 of the paper.
  •  167.ipynb for the network BIOMD0000000167 from ODEbase discussed in Example 4.11 of the paper.
    
    
• Files from the database results presented in the paper:
  • investigated_models.csv with all consistent networks in ODEbase (as of November 2, 2023) with at least one reaction with integer stoichiometric coefficients. The networks that do not satisfy this are listed in excluded_networks.csv.
  • nondegenerate_networks.csv with all networks from investigated_models.csv that admit a positive nondegenerate steady state.
  • degenerate_networks.csv with all networks from investigated_models.csv that have a positive steady states, but all of them are degenerate.
  • generic_local_acr.csv with all networks from investigated_models.csv that satisfy the following criteria:
    • admits nondegenerate positive steady states
    • is not of full rank (after removing nonparticipating species)
    • has generic local ACR in at least one speceis.

Dependencies

Julia example

include("functions.jl");

rn = @reaction_network begin

k1, X1 + X2 --> X3

k2, X3 --> X1 + X2

k3, X3 --> X1 + X4

k4, X3 + X4 --> X5

k5, X5 --> X3 + X4

k6, X5 --> X2 + X3

end;

julia> is_consistent(rn)

true

julia> has_nondegenerate_steady_state(rn, use_conservation_laws=true)

true

 

julia> generic_local_acr(rn, 1)

false

 

julia> generic_local_acr(rn, 4)

true

julia> local_acr_polynomial(rn, 4)

k[4]*k[6]*x[4] - k[3]*k[5] - k[3]*k[6]

N = matrix(QQ, netstoichmat(rn))

B = matrix(ZZ, substoichmat(rn))

L = matrix(QQ, conservationlaws(rn))

 

has_nondegenerate_zero(N, B, L)

generic_local_acr(N, B, 1)

generic_local_acr(N, B, 4)

local_acr_polynomial(N, B, 4)