# -*- coding: utf-8 -*-
"""Provides functions to remove thermodynamically infeasible loops."""
from __future__ import absolute_import
import numpy
from six import iteritems
from optlang.symbolics import Zero
from cobra.core import Metabolite, Reaction, get_solution
from cobra.util import create_stoichiometric_matrix, nullspace
from cobra.manipulation.modify import convert_to_irreversible
[docs]def add_loopless(model, zero_cutoff=1e-12):
"""Modify a model so all feasible flux distributions are loopless.
In most cases you probably want to use the much faster `loopless_solution`.
May be used in cases where you want to add complex constraints and
objecives (for instance quadratic objectives) to the model afterwards
or use an approximation of Gibbs free energy directions in you model.
Adds variables and constraints to a model which will disallow flux
distributions with loops. The used formulation is described in [1]_.
This function *will* modify your model.
Parameters
----------
model : cobra.Model
The model to which to add the constraints.
zero_cutoff : positive float, optional
Cutoff used for null space. Coefficients with an absolute value smaller
than `zero_cutoff` are considered to be zero.
Returns
-------
Nothing
References
----------
.. [1] Elimination of thermodynamically infeasible loops in steady-state
metabolic models. Schellenberger J, Lewis NE, Palsson BO. Biophys J.
2011 Feb 2;100(3):544-53. doi: 10.1016/j.bpj.2010.12.3707. Erratum
in: Biophys J. 2011 Mar 2;100(5):1381.
"""
internal = [i for i, r in enumerate(model.reactions) if not r.boundary]
s_int = create_stoichiometric_matrix(model)[:, numpy.array(internal)]
n_int = nullspace(s_int).T
max_bound = max(max(abs(b) for b in r.bounds) for r in model.reactions)
prob = model.problem
# Add indicator variables and new constraints
to_add = []
for i in internal:
rxn = model.reactions[i]
# indicator variable a_i
indicator = prob.Variable("indicator_" + rxn.id, type="binary")
# -M*(1 - a_i) <= v_i <= M*a_i
on_off_constraint = prob.Constraint(
rxn.flux_expression - max_bound * indicator,
lb=-max_bound, ub=0, name="on_off_" + rxn.id)
# -(max_bound + 1) * a_i + 1 <= G_i <= -(max_bound + 1) * a_i + 1000
delta_g = prob.Variable("delta_g_" + rxn.id)
delta_g_range = prob.Constraint(
delta_g + (max_bound + 1) * indicator,
lb=1, ub=max_bound, name="delta_g_range_" + rxn.id)
to_add.extend([indicator, on_off_constraint, delta_g, delta_g_range])
model.add_cons_vars(to_add)
# Add nullspace constraints for G_i
for i, row in enumerate(n_int):
name = "nullspace_constraint_" + str(i)
nullspace_constraint = prob.Constraint(Zero, lb=0, ub=0, name=name)
model.add_cons_vars([nullspace_constraint])
coefs = {model.variables[
"delta_g_" + model.reactions[ridx].id]: row[i]
for i, ridx in enumerate(internal) if
abs(row[i]) > zero_cutoff}
model.constraints[name].set_linear_coefficients(coefs)
[docs]def _add_cycle_free(model, fluxes):
"""Add constraints for CycleFreeFlux."""
model.objective = model.solver.interface.Objective(
Zero, direction="min", sloppy=True)
objective_vars = []
for rxn in model.reactions:
flux = fluxes[rxn.id]
if rxn.boundary:
rxn.bounds = (flux, flux)
continue
if flux >= 0:
rxn.bounds = max(0, rxn.lower_bound), max(flux, rxn.upper_bound)
objective_vars.append(rxn.forward_variable)
else:
rxn.bounds = min(flux, rxn.lower_bound), min(0, rxn.upper_bound)
objective_vars.append(rxn.reverse_variable)
model.objective.set_linear_coefficients({v: 1.0 for v in objective_vars})
[docs]def loopless_solution(model, fluxes=None):
"""Convert an existing solution to a loopless one.
Removes as many loops as possible (see Notes).
Uses the method from CycleFreeFlux [1]_ and is much faster than
`add_loopless` and should therefore be the preferred option to get loopless
flux distributions.
Parameters
----------
model : cobra.Model
The model to which to add the constraints.
fluxes : dict
A dictionary {rxn_id: flux} that assigns a flux to each reaction. If
not None will use the provided flux values to obtain a close loopless
solution.
Returns
-------
cobra.Solution
A solution object containing the fluxes with the least amount of
loops possible or None if the optimization failed (usually happening
if the flux distribution in `fluxes` is infeasible).
Notes
-----
The returned flux solution has the following properties:
- it contains the minimal number of loops possible and no loops at all if
all flux bounds include zero
- it has an objective value close to the original one and the same
objective value id the objective expression can not form a cycle
(which is usually true since it consumes metabolites)
- it has the same exact exchange fluxes as the previous solution
- all fluxes have the same sign (flow in the same direction) as the
previous solution
References
----------
.. [1] CycleFreeFlux: efficient removal of thermodynamically infeasible
loops from flux distributions. Desouki AA, Jarre F, Gelius-Dietrich
G, Lercher MJ. Bioinformatics. 2015 Jul 1;31(13):2159-65. doi:
10.1093/bioinformatics/btv096.
"""
# Need to reoptimize otherwise spurious solution artifacts can cause
# all kinds of havoc
# TODO: check solution status
if fluxes is None:
sol = model.optimize(objective_sense=None)
fluxes = sol.fluxes
with model:
prob = model.problem
# Needs one fixed bound for cplex...
loopless_obj_constraint = prob.Constraint(
model.objective.expression,
lb=-1e32, name="loopless_obj_constraint")
model.add_cons_vars([loopless_obj_constraint])
_add_cycle_free(model, fluxes)
solution = model.optimize(objective_sense=None)
solution.objective_value = loopless_obj_constraint.primal
return solution
[docs]def loopless_fva_iter(model, reaction, solution=False, zero_cutoff=1e-6):
"""Plugin to get a loopless FVA solution from single FVA iteration.
Assumes the following about `model` and `reaction`:
1. the model objective is set to be `reaction`
2. the model has been optimized and contains the minimum/maximum flux for
`reaction`
3. the model contains an auxiliary variable called "fva_old_objective"
denoting the previous objective
Parameters
----------
model : cobra.Model
The model to be used.
reaction : cobra.Reaction
The reaction currently minimized/maximized.
solution : boolean, optional
Whether to return the entire solution or only the minimum/maximum for
`reaction`.
zero_cutoff : positive float, optional
Cutoff used for loop removal. Fluxes with an absolute value smaller
than `zero_cutoff` are considered to be zero.
Returns
-------
single float or dict
Returns the minimized/maximized flux through `reaction` if
all_fluxes == False (default). Otherwise returns a loopless flux
solution containing the minimum/maximum flux for `reaction`.
"""
current = model.objective.value
sol = get_solution(model)
objective_dir = model.objective.direction
# boundary reactions can not be part of cycles
if reaction.boundary:
if solution:
return sol
else:
return current
with model:
_add_cycle_free(model, sol.fluxes)
model.slim_optimize()
# If the previous optimum is maintained in the loopless solution it was
# loopless and we are done
if abs(reaction.flux - current) < zero_cutoff:
if solution:
return sol
return current
# If previous optimum was not in the loopless solution create a new
# almost loopless solution containing only loops including the current
# reaction. Than remove all of those loops.
ll_sol = get_solution(model).fluxes
reaction.bounds = (current, current)
model.slim_optimize()
almost_ll_sol = get_solution(model).fluxes
with model:
# find the reactions with loops using the current reaction and remove
# the loops
for rxn in model.reactions:
rid = rxn.id
if ((abs(ll_sol[rid]) < zero_cutoff) and
(abs(almost_ll_sol[rid]) > zero_cutoff)):
rxn.bounds = max(0, rxn.lower_bound), min(0, rxn.upper_bound)
if solution:
best = model.optimize()
else:
model.slim_optimize()
best = reaction.flux
model.objective.direction = objective_dir
return best
[docs]def construct_loopless_model(cobra_model):
"""Construct a loopless model.
This adds MILP constraints to prevent flux from proceeding in a loop, as
done in http://dx.doi.org/10.1016/j.bpj.2010.12.3707
Please see the documentation for an explanation of the algorithm.
This must be solved with an MILP capable solver.
"""
# copy the model and make it irreversible
model = cobra_model.copy()
convert_to_irreversible(model)
max_ub = max(model.reactions.list_attr("upper_bound"))
# a dict for storing S^T
thermo_stoic = {"thermo_var_" + metabolite.id: {}
for metabolite in model.metabolites}
# Slice operator is so that we don't get newly added metabolites
original_metabolites = model.metabolites[:]
for reaction in model.reactions[:]:
# Boundary reactions are not subjected to these constraints
if len(reaction._metabolites) == 1:
continue
# populate the S^T dict
bound_id = "thermo_bound_" + reaction.id
for met, stoic in iteritems(reaction._metabolites):
thermo_stoic["thermo_var_" + met.id][bound_id] = stoic
# I * 1000 > v --> I * 1000 - v > 0
reaction_ind = Reaction(reaction.id + "_indicator")
reaction_ind.variable_kind = "integer"
reaction_ind.upper_bound = 1
reaction_ub = Metabolite(reaction.id + "_ind_ub")
reaction_ub._constraint_sense = "G"
reaction.add_metabolites({reaction_ub: -1})
reaction_ind.add_metabolites({reaction_ub: max_ub})
# This adds a compensating term for 0 flux reactions, so we get
# S^T x - (1 - I) * 1001 < -1 which becomes
# S^T x < 1000 for 0 flux reactions and
# S^T x < -1 for reactions with nonzero flux.
reaction_bound = Metabolite(bound_id)
reaction_bound._constraint_sense = "L"
reaction_bound._bound = max_ub
reaction_ind.add_metabolites({reaction_bound: max_ub + 1})
model.add_reaction(reaction_ind)
for metabolite in original_metabolites:
metabolite_var = Reaction("thermo_var_" + metabolite.id)
metabolite_var.lower_bound = -max_ub
model.add_reaction(metabolite_var)
metabolite_var.add_metabolites(
{model.metabolites.get_by_id(k): v
for k, v in iteritems(thermo_stoic[metabolite_var.id])})
return model