Source code for cobra.flux_analysis.loopless

# -*- coding: utf-8 -*-

"""Provides functions to remove thermodynamically infeasible loops."""

from __future__ import absolute_import

import logging

import numpy
from optlang.symbolics import Zero

from cobra.core import get_solution
from cobra.flux_analysis.helpers import normalize_cutoff
from cobra.util import create_stoichiometric_matrix, nullspace

[docs]LOGGER = logging.getLogger(__name__)
[docs]def add_loopless(model, zero_cutoff=None): """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 (default model.tolerance). 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. """ zero_cutoff = normalize_cutoff(model, zero_cutoff) 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_" +, 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_" +, ) # -(max_bound + 1) * a_i + 1 <= G_i <= -(max_bound + 1) * a_i + 1000 delta_g = prob.Variable("delta_g_" + delta_g_range = prob.Constraint( delta_g + (max_bound + 1) * indicator, lb=1, ub=max_bound, name="delta_g_range_" +, ) 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[] 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=None): """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 (default model.tolerance). 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`. """ zero_cutoff = normalize_cutoff(model, zero_cutoff) current = model.objective.value sol = get_solution(model) objective_dir = model.objective.direction # Handle a suddenly infeasible solution, # usually due to numerical instability if current is None: return None # 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 = 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