Exemple #1
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def degrees_of_freedom(model):
    """
    Return the degrees of freedom, i.e. number of "free variables".

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    Notes:
    ------
    This specifically refers to the dimensionality of the right nullspace
    of the S matrix, as dim(Null(S)) corresponds directly to the number of
    free variables in the system [1]_. The forumla used calculates this using
    the rank-nullity theorem [2]_.

    References:
    -----------
    .. [1] Fukuda, K. & Terlaky, T. Criss-cross methods: A fresh view on
       pivot algorithms. Mathematical Programming 79, 369-395 (1997).

    .. [2] Alama, J. The Rank+Nullity Theorem. Formalized Mathematics 15,
       (2007).

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    return s_matrix.shape[1] - matrix_rank(model)
Exemple #2
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def degrees_of_freedom(model):
    """
    Return the degrees of freedom, i.e., number of "free variables".

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    Notes
    -----
    This specifically refers to the dimensionality of the (right) null space
    of the stoichiometric matrix, as dim(Null(S)) corresponds directly to the
    number of free variables in the system [1]_. The formula used calculates
    this using the rank-nullity theorem [2]_.

    References
    ----------
    .. [1] Fukuda, K. & Terlaky, T. Criss-cross methods: A fresh view on
       pivot algorithms. Mathematical Programming 79, 369-395 (1997).

    .. [2] Alama, J. The Rank+Nullity Theorem. Formalized Mathematics 15,
       (2007).

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    return s_matrix.shape[1] - matrix_rank(model)
Exemple #3
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def absolute_extreme_coefficient_ratio(model):
    """Return the absolute max and absolute non-zero min coefficients."""
    # S-Matrix with absolute values:
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    abs_matrix = np.absolute(s_matrix)

    absolute_max_coef = np.amax(abs_matrix)
    absolute_non_zero_min_coef = abs_matrix[abs_matrix > 0].min()

    return (absolute_max_coef, absolute_non_zero_min_coef)
Exemple #4
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def matrix_rank(model):
    """
    Return the rank of the model's stoichiometric matrix.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    return con_helpers.rank(s_matrix)
Exemple #5
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def absolute_extreme_coefficient_ratio(model):
    """
    Return the maximum and minimum absolute, non-zero coefficients.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    abs_matrix = np.abs(s_matrix)
    return abs_matrix.max(), abs_matrix[abs_matrix > 0].min()
Exemple #6
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def matrix_rank(model):
    """
    Return the rank of the model's stoichiometric matrix.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    return con_helpers.rank(s_matrix)
Exemple #7
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def number_steady_state_flux_solutions(model):
    """
    Return the amount of steady-state flux solutions of this model.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    n_matrix = con_helpers.nullspace(s_matrix)
    return n_matrix.shape[1]
Exemple #8
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def number_independent_conservation_relations(model):
    """
    Return the amount of conserved metabolic pools.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    ln_matrix = con_helpers.nullspace(s_matrix.T)
    return ln_matrix.shape[1]
Exemple #9
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def absolute_extreme_coefficient_ratio(model):
    """
    Return the maximum and minimum absolute, non-zero coefficients.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    abs_matrix = np.abs(s_matrix)
    return abs_matrix.max(), abs_matrix[abs_matrix > 0].min()
Exemple #10
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def number_independent_conservation_relations(model):
    """
    Return the number of conserved metabolite pools.

    This number is given by the left null space of the stoichiometric matrix.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    left_ns = con_helpers.nullspace(s_matrix.T)
    return left_ns.shape[1] if len(left_ns) > 1 else 0
Exemple #11
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def number_independent_conservation_relations(model):
    """
    Return the number of conserved metabolite pools.

    This number is given by the left null space of the stoichiometric matrix.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.

    """
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(
        model.metabolites, model.reactions
    )
    ln_matrix = con_helpers.nullspace(s_matrix.T)
    return ln_matrix.shape[1]
Exemple #12
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def find_inconsistent_min_stoichiometry(model, atol=1e-13):
    """
    Detect inconsistent minimal net stoichiometries.

    Parameters
    ----------
    model : cobra.Model
        The metabolic model under investigation.
    atol : float, optional
        Values below the absolute tolerance are treated as zero. Expected to be
        very small but larger than zero.

    Notes
    -----
    See [1]_ section 3.3 for a complete description of the algorithm.

    References
    ----------
    .. [1] Gevorgyan, A., M. G Poolman, and D. A Fell.
           "Detection of Stoichiometric Inconsistencies in Biomolecular
           Models."
           Bioinformatics 24, no. 19 (2008): 2245.

    """
    if check_stoichiometric_consistency(model):
        return set()
    Model, Constraint, Variable, Objective = con_helpers.get_interface(model)
    unconserved_mets = find_unconserved_metabolites(model)
    LOGGER.info("model has %d unconserved metabolites", len(unconserved_mets))
    internal_rxns = con_helpers.get_internals(model)
    internal_mets = set(met for rxn in internal_rxns
                        for met in rxn.metabolites)
    get_id = attrgetter("id")
    reactions = sorted(internal_rxns, key=get_id)
    metabolites = sorted(internal_mets, key=get_id)
    stoich, met_index, rxn_index = con_helpers.stoichiometry_matrix(
        metabolites, reactions)
    left_ns = con_helpers.nullspace(stoich.T)
    # deal with numerical instabilities
    left_ns[np.abs(left_ns) < atol] = 0.0
    LOGGER.info("nullspace has dimension %d", left_ns.shape[1])
    inc_minimal = set()
    (problem,
     indicators) = con_helpers.create_milp_problem(left_ns, metabolites, Model,
                                                   Variable, Constraint,
                                                   Objective)
    LOGGER.debug(str(problem))
    cuts = list()
    for met in unconserved_mets:
        row = met_index[met]
        if (left_ns[row] == 0.0).all():
            LOGGER.debug("%s: singleton minimal unconservable set", met.id)
            # singleton set!
            inc_minimal.add((met, ))
            continue
        # expect a positive mass for the unconserved metabolite
        problem.variables[met.id].lb = 1e-3
        status = problem.optimize()
        while status == "optimal":
            LOGGER.debug("%s: status %s", met.id, status)
            LOGGER.debug("sum of all primal values: %f",
                         sum(problem.primal_values.values()))
            LOGGER.debug("sum of binary indicators: %f",
                         sum(var.primal for var in indicators))
            solution = [
                model.metabolites.get_by_id(var.name[2:]) for var in indicators
                if var.primal > 0.2
            ]
            LOGGER.debug("%s: set size %d", met.id, len(solution))
            inc_minimal.add(tuple(solution))
            if len(solution) == 1:
                break
            cuts.append(
                con_helpers.add_cut(problem, indicators,
                                    len(solution) - 1, Constraint))
            status = problem.optimize()
        LOGGER.debug("%s: last status %s", met.id, status)
        # reset
        problem.variables[met.id].lb = 0.0
        problem.remove(cuts)
        cuts.clear()
    return inc_minimal
Exemple #13
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def matrix_rank(model):
    """Return the rank of the model's stoichiometric matrix."""
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    return con_helpers.rank(s_matrix)
Exemple #14
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def number_steady_state_flux_solutions(model):
    """Return the amount of steady-state flux solutions of this model."""
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    n_matrix = con_helpers.nullspace_basis(s_matrix)
    return n_matrix.shape[1]
Exemple #15
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def number_independent_conservation_relations(model):
    """Return the amount of conserved metabolic pools."""
    s_matrix, _, _ = con_helpers.stoichiometry_matrix(model.metabolites,
                                                      model.reactions)
    ln_matrix = con_helpers.nullspace_basis(s_matrix.T)
    return ln_matrix.shape[1]