def find_unconserved_metabolites(model):
"""
Detect unconserved metabolites.
Parameters
----------
model : cobra.Model
The metabolic model under investigation.
Notes
-----
See [1]_ section 3.2 for a complete description of the algorithm.
.. [1] Gevorgyan, A., M. G Poolman, and D. A Fell.
"Detection of Stoichiometric Inconsistencies in Biomolecular Models."
Bioinformatics 24, no. 19 (2008): 2245.
"""
Model, Constraint, Variable, Objective = con_helpers.get_interface(model)
stoich_trans = Model()
internal_rxns = con_helpers.get_internals(model)
metabolites = set(met for rxn in internal_rxns for met in rxn.metabolites)
# The binary variables k[i] in the paper.
k_vars = list()
for met in metabolites:
# The element m[i] of the mass vector.
m_var = Variable(met.id)
k_var = Variable("k_{}".format(met.id), type="binary")
k_vars.append(k_var)
stoich_trans.add([m_var, k_var])
# This constraint is equivalent to 0 <= k[i] <= m[i].
stoich_trans.add(
Constraint(k_var - m_var, ub=0, name="switch_{}".format(met.id)))
stoich_trans.update()
con_helpers.add_reaction_constraints(stoich_trans, internal_rxns,
Constraint)
# The objective is to maximize the binary indicators k[i], subject to the
# above inequality constraints.
stoich_trans.objective = Objective(1)
stoich_trans.objective.set_linear_coefficients({var: 1. for var in k_vars})
stoich_trans.objective.direction = "max"
status = stoich_trans.optimize()
if status == "optimal":
# TODO: See if that could be a Boolean test `bool(var.primal)`.
return set([
model.metabolites.get_by_id(var.name[2:]) for var in k_vars
if var.primal < 0.8
])
else:
raise RuntimeError(
"Could not compute list of unconserved metabolites."
" Solver status is '{}'"
" (only optimal or infeasible expected).".format(status))
def check_stoichiometric_consistency(model):
"""
Verify the consistency of the model stoichiometry.
Parameters
----------
model : cobra.Model
The metabolic model under investigation.
Notes
-----
See [1]_ section 3.1 for a complete description of the algorithm.
.. [1] Gevorgyan, A., M. G Poolman, and D. A Fell.
"Detection of Stoichiometric Inconsistencies in Biomolecular Models."
Bioinformatics 24, no. 19 (2008): 2245.
"""
Model, Constraint, Variable, Objective = con_helpers.get_interface(model)
# The transpose of the stoichiometric matrix N.T in the paper.
stoich_trans = Model()
internal_rxns = con_helpers.get_internals(model)
metabolites = set(met for rxn in internal_rxns for met in rxn.metabolites)
LOGGER.info("model '%s' has %d internal reactions", model.id,
len(internal_rxns))
LOGGER.info("model '%s' has %d internal metabolites", model.id,
len(metabolites))
for metabolite in metabolites:
stoich_trans.add(Variable(metabolite.id, lb=1))
stoich_trans.update()
con_helpers.add_reaction_constraints(stoich_trans, internal_rxns,
Constraint)
# The objective is to minimize the metabolite mass vector.
stoich_trans.objective = Objective(1)
stoich_trans.objective.set_linear_coefficients(
{var: 1.
for var in stoich_trans.variables})
stoich_trans.objective.direction = "min"
status = stoich_trans.optimize()
if status == "optimal":
return True
elif status == "infeasible":
return False
else:
raise RuntimeError(
"Could not determine stoichiometric consistencty."
" Solver status is '{}'"
" (only optimal or infeasible expected).".format(status))
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