def moma(wt_model, mutant_model, objective_sense='maximize', solver=None,
tolerance_optimality=1e-8, tolerance_feasibility=1e-8,
minimize_norm=False, the_problem='return', lp_method=0,
combined_model=None, norm_type='euclidean'):
"""Runs the minimization of metabolic adjustment method described in
Segre et al 2002 PNAS 99(23): 15112-7.
wt_model: A cobra.Model object
mutant_model: A cobra.Model object with different reaction bounds vs wt_model.
To simulate deletions
objective_sense: 'maximize' or 'minimize'
solver: 'gurobi', 'cplex', or 'glpk'. Note: glpk cannot be used with
norm_type 'euclidean'
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
the_problem: None or a problem object for the specific solver that can be
used to hot start the next solution.
lp_method: The method to use for solving the problem. Depends on the solver. See
the cobra.flux_analysis.solvers.py file for more info.
For norm_type == 'euclidean':
the primal simplex works best for the test model (gurobi: lp_method=0, cplex: lp_method=1)
combined_model: an output from moma that represents the combined optimization
to be solved. when this is not none. only assume that bounds have changed
for the mutant or wild-type. This saves 0.2 seconds in stacking matrices.
NOTE: Current function makes too many assumptions about the structures of the models
"""
if solver is None:
if norm_type == "euclidiean":
solver = get_solver_name(qp=True)
else:
solver = get_solver_name() # linear is not even implemented yet
if combined_model is not None or the_problem not in ['return']:
warn("moma currently does not support reusing models or problems. " +\
"continuing without them")
combined_model = None
the_problem = 'return'
if solver.lower() == 'cplex' and lp_method == 0:
#print 'for moma, solver method 0 is very slow for cplex. changing to method 1'
lp_method = 1
if solver.lower() == 'glpk' and norm_type == 'euclidean':
try:
from gurobipy import Model
solver = 'gurobi'
warn("GLPK can't solve quadratic problems like MOMA. Switched solver to %s"%solver)
except:
warn("GLPK can't solve quadratic problems like MOMA. Switching to linear MOMA")
if norm_type == 'euclidean':
#Reusing the basis can get the solver stuck.
reuse_basis = False
if combined_model and combined_model.norm_type != norm_type:
print('Cannot use combined_model.norm_type = %s with user-specified norm type'%(combined_model.norm_type,
norm_type))
print('Defaulting to user-specified norm_type')
combined_model = None
number_of_reactions_in_common = len(set([x.id for x in wt_model.reactions]).intersection([x.id for x in mutant_model.reactions]))
number_of_reactions = len(wt_model.reactions) + len(mutant_model.reactions)
#Get the optimal wt objective value and adjust based on optimality tolerances
wt_model.optimize(solver=solver)
wt_optimal = deepcopy(wt_model.solution.f)
if objective_sense == 'maximize':
wt_optimal = floor(wt_optimal/tolerance_optimality)*tolerance_optimality
else:
wt_optimal = ceil(wt_optimal/tolerance_optimality)*tolerance_optimality
if norm_type == 'linear':
raise Exception('linear MOMA is not currently implmented')
quadratic_component = None
if minimize_norm:
raise Exception('minimize_norm is not currently implemented')
#just worry about the flux distribution and not the objective from the wt
combined_model = mutant_model.copy()
#implement this: combined_model.reactions[:].objective_coefficients = -wt_solution.x_dict
else:
#Construct a problem that attempts to maximize the objective in the WT model while
#solving the quadratic problem. This new problem is constructed to try to find
#a solution for the WT model that lies close to the mutant model. There are
#often multiple equivalent solutions with M matrices and the one returned
#by a simple cobra_model.optimize call may be too far from the mutant.
#This only needs to be adjusted if we update mutant_model._S after deleting reactions
if not combined_model:
#Collect the set of wt reactions contributing to the objective.
objective_reaction_coefficient_dict = dict([(x.id, x.objective_coefficient)
for x in wt_model.reactions
if x.objective_coefficient])
combined_model = construct_difference_model(wt_model, mutant_model, norm_type)
#Add in the virtual objective metabolite to constrain the wt_model to the space where
#the objective was maximal
objective_metabolite = Metabolite('wt_optimal')
objective_metabolite._bound = wt_optimal
if objective_sense == 'maximize':
objective_metabolite._constraint_sense = 'G'
else:
objective_metabolite._constraint_sense = 'L'
#TODO: this couples the wt_model objective reaction to the virtual metabolite
#Currently, assumes a single objective reaction; however, this may be extended
[combined_model.reactions.get_by_id(k).add_metabolites({objective_metabolite: v})
for k, v in objective_reaction_coefficient_dict.items()]
if norm_type == 'euclidean':
#Makes assumptions about the structure of combined model
quadratic_component = s_vstack((lil_matrix((number_of_reactions, number_of_reactions + number_of_reactions_in_common )),
s_hstack((lil_matrix((number_of_reactions_in_common, number_of_reactions)),
eye(number_of_reactions_in_common,number_of_reactions_in_common)))))
elif norm_type == 'linear':
quadratic_component = None
combined_model.norm_type = norm_type
cobra_model = combined_model
the_problem = combined_model.optimize(objective_sense='minimize',
quadratic_component=quadratic_component,
solver=solver,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility,
lp_method=lp_method, reuse_basis=reuse_basis)
if combined_model.solution.status != 'optimal':
warn('optimal moma solution not found: solver status %s'%combined_model.solution.status +\
' returning the problem, the_combined model, and the quadratic component for trouble shooting')
return(the_problem, combined_model, quadratic_component)
solution = combined_model.solution
mutant_dict = {}
#Might be faster to quey based on mutant_model.reactions with the 'mutant_' prefix added
_reaction_list = [x for x in combined_model.reactions if x.id.startswith('mutant_')]
mutant_f = sum([mutant_model.reactions.get_by_id(x.id[len('mutant_'):]).objective_coefficient *
x.x for x in _reaction_list])
mutant_dict['objective_value'] = mutant_f
wild_type_flux_total = sum([abs(solution.x_dict[x.id]) for x in wt_model.reactions])
mutant_flux_total = sum(abs(x.x) for x in _reaction_list)
#Need to use the new solution as there are multiple ways to achieve an optimal solution in
#simulations with M matrices.
mutant_dict['status'] = solution.status
#TODO: Deal with maximize / minimize issues for a reversible model that's been converted to irreversible
mutant_dict['flux_difference'] = flux_difference = sum([(solution.x_dict[x.id[len('mutant_'):]]
- x.x)**2 for x in _reaction_list])
mutant_dict['the_problem'] = the_problem
mutant_dict['combined_model'] = combined_model
del wt_model, mutant_model, quadratic_component, solution
return(mutant_dict)
def moma(wt_model, mutant_model, objective_sense='maximize', solver=None,
tolerance_optimality=1e-8, tolerance_feasibility=1e-8,
minimize_norm=True, norm_flux_dict=None, the_problem='return', lp_method=0,
combined_model=None, norm_type='euclidean'):
"""Runs the minimization of metabolic adjustment method described in
Segre et al 2002 PNAS 99(23): 15112-7.
wt_model: A cobra.Model object
mutant_model: A cobra.Model object with different reaction bounds vs wt_model.
objective_sense: 'maximize' or 'minimize'
solver: 'gurobi', 'cplex', or 'glpk'. Note: glpk cannot be used with norm_type 'euclidean'
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
the_problem: None or a problem object for the specific solver that can be
used to hot start the next solution.
lp_method: The method to use for solving the problem. Depends on the solver. See
the cobra.flux_analysis.solvers.py file for more info.
For norm_type == 'euclidean':
the primal simplex works best for the test model (gurobi: lp_method=0, cplex: lp_method=1)
combined_model: an output from moma that represents the combined optimization to be solved.
"""
if solver is None:
if norm_type == "euclidean":
solver = get_solver_name(qp=True)
else:
solver = get_solver_name() # linear is not even implemented yet
if combined_model is not None or the_problem not in ['return']:
warn("moma currently does not support reusing models or problems. " +\
"continuing without them")
combined_model = None
the_problem = 'return'
if solver.lower() == 'cplex' and lp_method == 0:
#print 'for moma, solver method 0 is very slow for cplex. changing to method 1'
lp_method = 1
if solver.lower() == 'glpk' and norm_type == 'euclidean':
try:
# from gurobipy import Model
solver = 'gurobi'
warn("GLPK can't solve quadratic problems like MOMA. Switched solver to %s"%solver)
except:
warn("GLPK can't solve quadratic problems like MOMA. Switching to linear MOMA")
if norm_type == 'euclidean':
#Reusing the basis can get the solver stuck.
reuse_basis = False
if combined_model and combined_model.norm_type != norm_type:
print('Cannot use combined_model.norm_type = %s with user-specified norm type'%(combined_model.norm_type,
norm_type))
print('Defaulting to user-specified norm_type')
combined_model = None
if norm_type == 'linear':
raise Exception('linear MOMA is not currently implmented')
quadratic_component = None
if minimize_norm:
if norm_flux_dict is None:
optimize_minimum_flux(wt_model, objective_sense='maximize',
tolerance_feasibility=tolerance_feasibility)
norm_flux_dict = wt_model.solution.x_dict
else:
# update the solution of wt model according to norm_flux_dict
wt_model.optimize() # this is just to make sure wt_model.solution and mutant_model.solution refer to different object.
objective_reaction_coefficient_dict = dict([(x.id, x.objective_coefficient)
for x in wt_model.reactions
if x.objective_coefficient])
try:
wt_model.solution.f = sum([norm_flux_dict[k] * v for k, v in
objective_reaction_coefficient_dict.items()])
wt_model.solution.x_dict = norm_flux_dict
except:
print('incorrect norm_flux_dict')
raise
# formulate qMOMA using wt_flux as reference
# make a copy not to change the objective coefficients of original mutant model
mutant_model_moma = mutant_model.copy()
nRxns = len(mutant_model_moma.reactions)
quadratic_component = 2 * eye(nRxns, nRxns)
# linear component
[setattr(x, 'objective_coefficient', -2 * norm_flux_dict[x.id]) for x in mutant_model_moma.reactions]
the_problem = mutant_model_moma.optimize(objective_sense='minimize',
quadratic_component=quadratic_component,
solver=solver,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility,
lp_method=lp_method)
#, reuse_basis=reuse_basis) # this should be commented out when solver is 'cplex'
if mutant_model_moma.solution.status != 'optimal':
warn('optimal moma solution not found: solver status %s'%mutant_model_moma.solution.status +\
' returning the problem, the_combined model, and the quadratic component for trouble shooting')
return(the_problem, mutant_model_moma, quadratic_component)
solution = mutant_model_moma.solution
mutant_dict = {}
mutant_f = sum([mutant_model.reactions.get_by_id(x.id).objective_coefficient * x.x for x in mutant_model_moma.reactions])
mutant_dict['objective_value'] = mutant_f
mutant_dict['status'] = solution.status
#TODO: Deal with maximize / minimize issues for a reversible model that's been converted to irreversible
mutant_dict['flux_difference'] = flux_difference = sum([(norm_flux_dict[r.id] - mutant_model_moma.solution.x_dict[r.id])**2
for r in mutant_model_moma.reactions])
mutant_dict['the_problem'] = the_problem
mutant_dict['mutant_model'] = mutant_model_moma
# update the solution of original mutant model
mutant_model.solution.x_dict = the_problem.x_dict
mutant_model.solution.status = solution.status
mutant_model.solution.f = mutant_f
# del wt_model, mutant_model, quadratic_component, solution
return(mutant_dict)
else:
#Construct a problem that attempts to maximize the objective in the WT model while
#solving the quadratic problem. This new problem is constructed to try to find
#a solution for the WT model that lies close to the mutant model. There are
#often multiple equivalent solutions with M matrices and the one returned
#by a simple cobra_model.optimize call may be too far from the mutant.
#This only needs to be adjusted if we update mutant_model._S after deleting reactions
number_of_reactions_in_common = len(set([x.id for x in wt_model.reactions]).intersection([x.id for x in mutant_model.reactions]))
number_of_reactions = len(wt_model.reactions) + len(mutant_model.reactions)
#Get the optimal wt objective value and adjust based on optimality tolerances
wt_model.optimize(solver=solver)
wt_optimal = deepcopy(wt_model.solution.f)
if objective_sense == 'maximize':
wt_optimal = floor(wt_optimal/tolerance_optimality)*tolerance_optimality
else:
wt_optimal = ceil(wt_optimal/tolerance_optimality)*tolerance_optimality
if not combined_model:
#Collect the set of wt reactions contributing to the objective.
objective_reaction_coefficient_dict = dict([(x.id, x.objective_coefficient)
for x in wt_model.reactions
if x.objective_coefficient])
combined_model = construct_difference_model(wt_model, mutant_model, norm_type)
#Add in the virtual objective metabolite to constrain the wt_model to the space where
#the objective was maximal
objective_metabolite = Metabolite('wt_optimal')
objective_metabolite._bound = wt_optimal
if objective_sense == 'maximize':
objective_metabolite._constraint_sense = 'G'
else:
objective_metabolite._constraint_sense = 'L'
#TODO: this couples the wt_model objective reaction to the virtual metabolite
#Currently, assumes a single objective reaction; however, this may be extended
[combined_model.reactions.get_by_id(k).add_metabolites({objective_metabolite: v})
for k, v in objective_reaction_coefficient_dict.items()]
if norm_type == 'euclidean':
#Makes assumptions about the structure of combined model
quadratic_component = s_vstack((lil_matrix((number_of_reactions, number_of_reactions + number_of_reactions_in_common )),
s_hstack((lil_matrix((number_of_reactions_in_common, number_of_reactions)),
eye(number_of_reactions_in_common,number_of_reactions_in_common)))))
elif norm_type == 'linear':
quadratic_component = None
combined_model.norm_type = norm_type
cobra_model = combined_model
the_problem = combined_model.optimize(objective_sense='minimize',
quadratic_component=quadratic_component,
solver=solver,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility,
lp_method=lp_method) #, reuse_basis=reuse_basis) # this should be commented out when solver is 'cplex'
if combined_model.solution.status != 'optimal':
warn('optimal moma solution not found: solver status %s'%combined_model.solution.status +\
' returning the problem, the_combined model, and the quadratic component for trouble shooting')
return(the_problem, combined_model, quadratic_component)
solution = combined_model.solution
mutant_dict = {}
#Might be faster to quey based on mutant_model.reactions with the 'mutant_' prefix added
_reaction_list = [x for x in combined_model.reactions if x.id.startswith('mutant_')]
mutant_f = sum([mutant_model.reactions.get_by_id(x.id[len('mutant_'):]).objective_coefficient *
x.x for x in _reaction_list])
mutant_dict['objective_value'] = mutant_f
wild_type_flux_total = sum([abs(solution.x_dict[x.id]) for x in wt_model.reactions])
mutant_flux_total = sum(abs(x.x) for x in _reaction_list)
#Need to use the new solution as there are multiple ways to achieve an optimal solution in
#simulations with M matrices.
mutant_dict['status'] = solution.status
#TODO: Deal with maximize / minimize issues for a reversible model that's been converted to irreversible
mutant_dict['flux_difference'] = flux_difference = sum([(solution.x_dict[x.id[len('mutant_'):]]
- x.x)**2 for x in _reaction_list])
mutant_dict['the_problem'] = the_problem
mutant_dict['combined_model'] = combined_model
del wt_model, mutant_model, quadratic_component, solution
return(mutant_dict)
def moma(wt_model, mutant_model, objective_sense='maximize', solver='gurobi',
tolerance_optimality=1e-8, tolerance_feasibility=1e-8,
minimize_norm=False, the_problem='return', lp_method=0,
combined_model=None, norm_type='euclidean', print_time=False):
"""Runs the minimization of metabolic adjustment method described in
Segre et al 2002 PNAS 99(23): 15112-7.
wt_model: A cobra.Model object
mutant_model: A cobra.Model object with different reaction bounds vs wt_model.
To simulate deletions
objective_sense: 'maximize' or 'minimize'
solver: 'gurobi', 'cplex', or 'glpk'. Note: glpk cannot be used with
norm_type 'euclidean'
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
the_problem: None or a problem object for the specific solver that can be
used to hot start the next solution.
lp_method: The method to use for solving the problem. Depends on the solver. See
the cobra.flux_analysis.solvers.py file for more info.
For norm_type == 'euclidean':
the primal simplex works best for the test model (gurobi: lp_method=0, cplex: lp_method=1)
combined_model: an output from moma that represents the combined optimization
to be solved. when this is not none. only assume that bounds have changed
for the mutant or wild-type. This saves 0.2 seconds in stacking matrices.
"""
warn('MOMA is currently non-functional. check back later')
if solver.lower() == 'cplex' and lp_method == 0:
#print 'for moma, solver method 0 is very slow for cplex. changing to method 1'
lp_method = 1
if solver.lower() == 'glpk' and norm_type == 'euclidean':
print "GLPK can't solve quadratic problems like MOMA. Switching to linear MOMA"
if norm_type == 'euclidean':
#Reusing the basis can get the solver stuck.
reuse_basis = False
if combined_model and combined_model.norm_type != norm_type:
print 'Cannot use combined_model.norm_type = %s with user-specified norm type'%(combined_model.norm_type,
norm_type)
print 'Defaulting to user-specified norm_type'
combined_model = None
#Add a prefix in front of the mutant_model metabolites and reactions to prevent
#name collisions in DictList
for the_dict_list in [mutant_model.metabolites,
mutant_model.reactions]:
[setattr(x, 'id', 'mutant_%s'%x.id)
for x in the_dict_list]
the_dict_list._generate_index() #Update the DictList.dicts
wt_model.optimize(solver=solver)
wt_solution = deepcopy(wt_model.solution)
if objective_sense == 'maximize':
wt_optimal = floor(wt_solution.f/tolerance_optimality)*tolerance_optimality
else:
wt_optimal = ceil(wt_solution.f/tolerance_optimality)*tolerance_optimality
if norm_type == 'euclidean':
quadratic_component = eye(wt_solution.x.shape[0],wt_solution.x.shape[0])
elif norm_type == 'linear':
raise Exception('linear MOMA is not currently implmented')
quadratic_component = None
if minimize_norm:
raise Exception('minimize_norm is not currently implemented')
#just worry about the flux distribution and not the objective from the wt
combined_model = mutant_model.copy()
#implement this: combined_model.reactions[:].objective_coefficients = -wt_solution.x_dict
else:
#Construct a problem that attempts to maximize the objective in the WT model while
#solving the quadratic problem. This new problem is constructed to try to find
#a solution for the WT model that lies close to the mutant model. There are
#often multiple equivalent solutions with M matrices and the one returned
#by a simple cobra_model.optimize call may be too far from the mutant.
#This only needs to be adjusted if we update mutant_model._S after deleting reactions
if print_time:
start_time = time()
number_of_reactions = len(mutant_model.reactions)
if norm_type == 'euclidean':
reaction_coefficient = 1
elif norm_type == 'linear':
reaction_coefficient = 2
if not combined_model:
#Collect the set of wt reactions contributing to the objective.
objective_reaction_coefficient_dict = dict([(x.id, x.objective_coefficient)
for x in wt_model.reactions
if x.objective_coefficient])
#This does a deepcopy of both models which might result in a huge overhead.
#Update cobra.core.Model to improve performance.
combined_model = wt_model + mutant_model
if print_time:
print 'add time %f'%(time()-start_time)
[setattr(x, 'objective_coefficient', 0.)
for x in combined_model.reactions]
#Add in the difference reactions. The mutant reactions and metabolites are already added.
#This must be a list to maintain the correct order when adding the difference_metabolites
difference_reactions = [Reaction('difference_%i'%i)
for i in range(reaction_coefficient*number_of_reactions)]
[setattr(x, 'lower_bound', -1000)
for x in difference_reactions]
combined_model.add_reactions(difference_reactions)
index_to_reaction = combined_model.reactions
id_to_reaction = combined_model.reactions._object_dict
#This is slow
#Add in difference metabolites
difference_metabolite_dict = dict([(i, Metabolite('difference_%i'%i))
for i in xrange(number_of_reactions)])
combined_model.add_metabolites(difference_metabolite_dict.values())
for i, tmp_metabolite in difference_metabolite_dict.iteritems():
if norm_type == 'linear':
tmp_metabolite._constraint_sense = 'G'
index_to_reaction[i].add_metabolites({tmp_metabolite: -1.},
add_to_container_model=False)
index_to_reaction[i+number_of_reactions].add_metabolites({tmp_metabolite: 1.}, add_to_container_model=False)
index_to_reaction[i+2*number_of_reactions].add_metabolites({tmp_metabolite: 1.}, add_to_container_model=False)
#Add in the virtual objective metabolite
objective_metabolite = Metabolite('wt_optimal')
objective_metabolite._bound = wt_optimal
if objective_sense == 'maximize':
objective_metabolite._constraint_sense = 'G'
else:
objective_metabolite._constraint_sense = 'L'
#TODO: this couples the wt_model objective reaction to the virtual metabolite
#Currently, assumes a single objective reaction; however, this may be extended
[id_to_reaction[k].add_metabolites({objective_metabolite: v})
for k, v in objective_reaction_coefficient_dict.items()]
if print_time:
print 'Took %f seconds to construct combined model'%(time()-start_time)
start_time = time()
if norm_type == 'euclidean':
quadratic_component = s_vstack((lil_matrix((2*number_of_reactions, 3*number_of_reactions)),
s_hstack((lil_matrix((number_of_reactions, 2*number_of_reactions)),
quadratic_component))))
elif norm_type == 'linear':
quadratic_component = None
combined_model.norm_type = norm_type
cobra_model = combined_model
if print_time:
print 'Took %f seconds to update combined model'%(time()-start_time)
start_time = time()
the_result = combined_model.optimize(objective_sense='minimize',
quadratic_component=quadratic_component,
solver=solver,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility,
lp_method=lp_method, reuse_basis=reuse_basis)
the_problem = the_result
the_solution = combined_model.solution
if print_time:
print 'Took %f seconds to solve problem'%(time()-start_time)
start_time = time()
mutant_dict = {}
x_vector = the_solution.x
if hasattr(x_vector, 'flatten'):
x_vector = x_vector.flatten()
mutant_dict['x'] = mutant_fluxes = array(x_vector[1*number_of_reactions:2*number_of_reactions])
#Need to use the new solution as there are multiple ways to achieve an optimal solution in
#simulations with M matrices.
wt_model.solution.x = array(x_vector[:number_of_reactions])
mutant_dict['objective_value'] = mutant_f = float(matrix(mutant_fluxes)*matrix([x.objective_coefficient
for x in mutant_model.reactions]).T)
mutant_dict['status'] = the_solution.status
mutant_dict['flux_difference'] = flux_difference = sum((wt_model.solution.x - mutant_fluxes)**2)
mutant_dict['the_problem'] = the_problem
mutant_dict['combined_model'] = combined_model
if print_time:
print 'Took %f seconds to assemble solution'%(time()-start_time)
del wt_model, mutant_model, quadratic_component, the_solution
return(mutant_dict)