ES_SAMPLE_STEADY_STATE - Sample feasible stationary state for a network
[c0, c, u, v, Keq, mu, K, Kma, zeta, A] = es_sample_steady_state_state(N, W, ind_ext, es_constraints, es_options)
Sample thermodynamically consistent steady states, including concentrations,
fluxes, and thermodynamic quantities. Enzyme levels are freely sampled.
Inputs (with nm: # metabolites; nr: # reactions)
N - Stoichiometric matrix (nm x nr)
W - Allosteric regulation matrix (nr x nm)
ind_ext - indices of external metabolites
es_constraints, es_options: - explained below (also see 'es_default_options')
Outputs (with nm: # metabolites; nr: # reactions)
c0 - Vector of chemical equilibrium concentrations (optional)
c - Vector of concentrations
u - Vector of enzyme levels
J - Flux vector
Keq - Vector of equilibrium constants
mu - Vector of chemical potentials
K - Kernel matrix
Kma - Vector of mass-action ratios
zeta - zeta vector computed from reaction affinities
A - Vector of reaction affinities (thermodynamic driving forces)
Sampling methods used:
Fluxes:
If a flux vector is predefined in es_constraints.v_fix (no missing values),
this flux vector is directly used. Otherwise, a method to determine the
fluxes must be given in 'es_options.sampling_method':
'accept_flux': use values given in es_constraints.v_mean
'sample_and_discard': sample flux values from the distribution defined by
es_constraints.v_mean, es_constraints.v_std, and es_constraints.v_sign
and omit unfeasible cycles
'convex_optimisation': sample fluxes based on convex FBA from the distribution defined by
es_constraints.v_mean, es_constraints.v_std, and es_constraints.dmu_fix
and omit unfeasible cycles
'v and mu', sample flux values using sample_feasible_v.m
'v from data': sample flux values from the distribution defined by
es_constraints.v_mean, es_constraints.v_std, and es_constraints.v_sign
Concentrations:
Concentrations given in log_c_fix will be directly used. The remaining
concentrations are randomly sampled based on log_c_mean and log_c_std.
Chemical potentials
The method chosen to determine concentrations and flux depends on the
information provided in the "[..]_fix" fields of es_constraints:
mu_fix, dmu_fix, Keq_fix, mu0_fix.
Fields in 'es_constraints' and 'es_options' relevant to this function:
es_options.seed - Random seed used
es_options.sampling_methods - Alternative sampling procedures
'v from data'
'v and mu'
'c0 and c'
'sample_and_discard'
'convex_optimisation'
es_constraints.v_fix - Predefined fluxes (vector, NaNs are ignored)
es_constraints.v_min - Lower flux bounds (vector, NaNs are ignored)
es_constraints.v_max - Upper flux bounds (vector, NaNs are ignored)
es_constraints.v_sign - Flux signs (vector, NaNs are ignored)
es_constraints.log_u_mean - Mean enzyme level (for sampling)
es_constraints.log_u_std - Std dev for enzyme levels (for sampling)
es_constraints.log_c_mean - Mean metabolite concentration (for sampling)
es_constraints.log_c_std - Std dev for metabolite concentrations (for sampling)
Additional fields required, depending on 'es_options.sampling_method':
'v from data' es_constraints.v_mean
es_constraints.v_std
'v and mu' es_constraints.mu_fix
'c0 and c' es_constraints.log_c0
es_constraints.log_c0_std
'sample_and_discard' es_options.cycle_correction
'convex_optimisation' es_constraints.dmu_fix
es_options.cycle_correction
For some methods, additionally required:
es_options.ind_ignore reactions to be ignored in thermodynamic loops
(only needed for flux correction by loop substraction)
(only needed for flux correction by convex FBA)