CHMC

Public functions

MarkovWeightedEFMs.CHMC.Standard.steady_state_efm_distribution — Function

steady_state_efm_distribution(#
    S::Matrix{<:Integer},
    v::Vector{<:Real},
    I::Int64 = 1;
    solver = nothing,
    issparse::Bool = false
)

Enumerate the EFMs from stoichiometry matrix S and compute the steady state probabilities of each EFM according to the discrete-time, cycle-history Markov chain.

S is a fully-connected, unimolecular, m by n stoichiometry matrix with m metabolites and n reactions.

v is the n-length steady state flux vector associated with S.

I is the initial starting state for rooting the cycle-history Markov chain. The choice of initial starting state does not affect the steady state EFM probabilities. The default is 1 and must be a whole number between 1:m.

solver is the type used for eigenvector calculations. Default is nothing and LinearSolve will pick the best solver. Consult LinearSolve.jl for specifying other solvers.

issparse is true will use a sparse transition probability for the CHMC to save memory.

Example

julia> S = [#
 -1  0  0  0  0  0  0  0  0  0  1
  1 -1  1 -1  0  0  0  0  0  0  0
  0  1 -1  0 -1  1  0  0  0  0  0
  0  0  0  1  0  0 -1  0  0  0  0
  0  0  0  0  1 -1  1 -1  1 -1  0
  0  0  0  0  0  0  0  0  0  1 -1
  0  0  0  0  0  0  0  1 -1  0  0
];
julia> v = [3, 2, 1, 2, 3, 2, 2, 1, 1, 3, 3];
julia> res = steady_state_efm_distribution(S, v);
julia> res.e # EFM state sequences
6-element Vector{Vector{Int64}}:
 [3, 2, 3]
 [3, 2, 4, 5, 3]
 [3, 5, 3]
 [6, 1, 2, 4, 5, 6]
 [7, 5, 7]
 [6, 1, 2, 3, 5, 6]

julia> res.p # EFM probabilities
6-element Vector{Float64}:
 0.10638297872340426
 0.0425531914893617
 0.25531914893617025
 0.1914893617021277
 0.14893617021276595
 0.25531914893617025

julia> res.w # EFM weights
6-element Vector{Float64}:
 0.7142857142857142
 0.2857142857142857
 1.7142857142857144
 1.2857142857142858
 0.9999999999999999
 1.7142857142857144

source

MarkovWeightedEFMs.CHMC.Standard.steady_state_efm_distribution — Function

steady_state_efm_distribution(#
    T::Union{Matrix{<:Real}, SparseMatrixCSC{Float64, Int64}},
    I::Int64 = 1;
    solver = nothing,
    verbose::Bool = true
)

Enumerate the EFMs from (right) transition probability matrix T whose rows sum to one, and compute the steady state probabilities of each EFM according to the discrete-time, cycle-history Markov chain.

T is the discrete-time transition probability matrix with probabilities proportional to the outgoing fluxes.

solver is the type used for eigenvector calculations. Default is nothing and LinearSolve will pick the best solver. Consult LinearSolve.jl for specifying other solvers.

Example

julia> T = [#
  0.0  1.0   0.0       0.0  0.0   0.0  0.0
  0.0  0.0   0.5       0.5  0.0   0.0  0.0
  0.0  0.25  0.0       0.0  0.75  0.0  0.0
  0.0  0.0   0.0       0.0  1.0   0.0  0.0
  0.0  0.0   0.333333  0.0  0.0   0.5  0.166667
  1.0  0.0   0.0       0.0  0.0   0.0  0.0
  0.0  0.0   0.0       0.0  1.0   0.0  0.0
];
julia> res = steady_state_efm_distribution(T);
julia> res.e # EFM state sequences
6-element Vector{Vector{Int64}}:
 [3, 2, 3]
 [3, 2, 4, 5, 3]
 [3, 5, 3]
 [6, 1, 2, 3, 5, 6]
 [7, 5, 7]
 [6, 1, 2, 4, 5, 6]

julia> res.p # EFM probabilities
6-element Vector{Float64}:
 0.13723110896294213
 0.035797649943428565
 0.26989203316869914
 0.20302350628312624
 0.13926980198123254
 0.2147858996605714

source

MarkovWeightedEFMs.CHMC.Standard.stoichiometry_to_transition_matrix — Function

stoichiometry_to_transition_matrix(S::Matrix{<:Integer}, v::Vector{<:Real})

Convert stoichiometry matrix S with vector of steady state fluxes to a right stochastic transition probability matrix with rows summing to one.

S is the m by n stoichiometry matrix with m metabolites and n reactions.

v is the steady state flux vector with length n.

Examples

julia> S = [#
  -1  0  0  0  0  0  0  0  0  0  1
   1 -1  1 -1  0  0  0  0  0  0  0
   0  1 -1  0 -1  1  0  0  0  0  0
   0  0  0  1  0  0 -1  0  0  0  0
   0  0  0  0  1 -1  1 -1 -1  1  0
   0  0  0  0  0  0  0  1  0  0 -1
   0  0  0  0  0  0  0  0  1 -1  0
]
julia> v = [2, 2, 2, 2, 2, 2, 2, 2, 4]
julia> stoich_to_transition(S, v)
7x7 Matrix{Float64}:
 0.0  1.0   0.0       0.0  0.0   0.0  0.0
 0.0  0.0   0.5       0.5  0.0   0.0  0.0
 0.0  0.25  0.0       0.0  0.75  0.0  0.0
 0.0  0.0   0.0       0.0  1.0   0.0  0.0
 0.0  0.0   0.333333  0.0  0.0   0.5 0.166667
 1.0  0.0   0.0       0.0  0.0   0.0  0.0
 0.0  0.0   0.0       0.0  1.0   0.0  0.0

source

MarkovWeightedEFMs.CHMC.Standard.reshape_efm_matrix — Function

reshape_efm_matrix(ϕ::Matrix{Int64}, S::Matrix{<:Real})

Convert a matrix of EFMs ϕ to a nested vector of EFMs from a stoichiometry matrix S. Stoichiometry matrix may only contain unimolecular reactions.

ϕ is the n by k EFM matrix with n reactions (rows) and k EFMs (cols).

S is the m by n stoichiometry matrix with m metabolites (rows) and n reactions (cols).

Examples

julia> ϕ = [#
  1  1  0  0  0  0
  1  0  1  0  0  0
  0  0  1  0  0  1
  0  1  0  0  0  1
  1  0  0  1  0  0
  0  0  0  1  0  1
  0  1  0  0  0  1
  1  1  0  0  0  0
  0  0  0  0  1  0
  0  0  0  0  1  0
  1  1  0  0  0  0
]
julia> S = [#
  -1  0  0  0  0  0  0  0  0  0  1
   1 -1  1 -1  0  0  0  0  0  0  0
   0  1 -1  0 -1  1  0  0  0  0  0
   0  0  0  1  0  0 -1  0  0  0  0
   0  0  0  0  1 -1  1 -1 -1  1  0
   0  0  0  0  0  0  0  1  0  0 -1
   0  0  0  0  0  0  0  0  1 -1  0
]
julia> efm_vector = reshape_efm_matrix(ϕ, S)
6-element Vector{Vector{Int64}}:
 [1, 2, 3, 5, 6, 1]
 [1, 2, 4, 5, 6, 1]
 [2, 3, 2]
 [3, 5, 3]
 [5, 7, 5]
 [3, 2, 4, 5, 3]

source

MarkovWeightedEFMs.CHMC.Standard.reshape_efm_vector — Function

reshape_efm_vector(ϕ::Vector{Vector{Int64}}, S::Matrix{<:Real})

Convert nested vector of EFM indices ϕ with length k to an n by k matrix of EFMs based on m by n stoichiometry matrix S. Stoichiometry matrix may only contain unimolecular reactions.

ϕ is the nested vector of EFMs with length k and elements corresponding to EFM metabolite indices in S.

S is the m by n stoichiometry matrix with m metabolites (rows) and n reactions (cols).

Examples

julia> ϕ = [#
  [1, 2, 3, 5, 6, 1],
  [1, 2, 4, 5, 6, 1],
  [2, 3, 2], [3, 5, 3], [5, 7, 5], [2, 4, 5, 3, 2]
]
julia> S = [#
  -1  0  0  0  0  0  0  0  0  0  1
   1 -1  1 -1  0  0  0  0  0  0  0
   0  1 -1  0 -1  1  0  0  0  0  0
   0  0  0  1  0  0 -1  0  0  0  0
   0  0  0  0  1 -1  1 -1 -1  1  0
   0  0  0  0  0  0  0  1  0  0 -1
   0  0  0  0  0  0  0  0  1 -1  0
]
julia> efm_matrix = reshape_efm_vector(ϕ, S)
11x6 Matrix{Int64}:
 1  1  0  0  0  0
 1  0  1  0  0  0
 0  0  1  0  0  1
 0  1  0  0  0  1
 1  0  0  1  0  0
 0  0  0  1  0  1
 0  1  0  0  0  1
 1  1  0  0  0  0
 0  0  0  0  1  0
 0  0  0  0  1  0
 1  1  0  0  0  0

source

Index

MarkovWeightedEFMs.CHMC.Standard.reshape_efm_matrix
MarkovWeightedEFMs.CHMC.Standard.reshape_efm_vector
MarkovWeightedEFMs.CHMC.Standard.steady_state_efm_distribution
MarkovWeightedEFMs.CHMC.Standard.steady_state_efm_distribution
MarkovWeightedEFMs.CHMC.Standard.stoichiometry_to_transition_matrix