Source code for cobra.flux_analysis.moma

"""Provide minimization of metabolic adjustment (MOMA)."""

from typing import TYPE_CHECKING, Optional

from optlang.symbolics import Zero, add

from ..util import solver as sutil
from .parsimonious import pfba

    from cobra.core import Model, Solution

[docs]def moma( model: "Model", solution: Optional["Solution"] = None, linear: bool = True ) -> "Solution": """Compute a single solution based on (linear) MOMA. Compute a new flux distribution that is at a minimal distance to a previous reference solution `solution`. Minimization of metabolic adjustment (MOMA) is generally used to assess the impact of knock-outs. Thus, the typical usage is to provide a wild-type flux distribution as reference and a model in knock-out state. Parameters ---------- model : cobra.Model The model state to compute a MOMA-based solution for. solution : cobra.Solution, optional A (wild-type) reference solution (default None). linear : bool, optional Whether to use the linear MOMA formulation or not (default True). Returns ------- cobra.Solution A flux distribution that is at a minimal distance compared to the reference solution. See Also -------- add_moma : add MOMA constraints and objective """ with model: add_moma(model=model, solution=solution, linear=linear) solution = model.optimize() return solution
[docs]def add_moma( model: "Model", solution: Optional["Solution"] = None, linear: bool = True ) -> None: r""" Add MOMA constraints and objective representing to the `model`. This adds variables and constraints for the minimization of metabolic adjustment (MOMA) to the model. Parameters ---------- model : cobra.Model The model to add MOMA constraints and objective to. solution : cobra.Solution, optional A previous solution to use as a reference. If no solution is given, one will be computed using pFBA (default None). linear : bool, optional Whether to use the linear MOMA formulation or not (default True). Notes ----- In the original MOMA [1]_ specification, one looks for the flux distribution of the deletion (v^d) closest to the fluxes without the deletion (v). In math this means: minimize: \sum_i (v^d_i - v_i)^2 s.t. : Sv^d = 0 lb_i \le v^d_i \le ub_i Here, we use a variable transformation v^t := v^d_i - v_i. Substituting and using the fact that Sv = 0 gives: minimize: \sum_i (v^t_i)^2 s.t. : Sv^d = 0 v^t = v^d_i - v_i lb_i \le v^d_i \le ub_i So, basically we just re-center the flux space at the old solution and then find the flux distribution closest to the new zero (center). This is the same strategy as used in cameo. In the case of linear MOMA [2]_, we instead minimize \sum_i abs(v^t_i). The linear MOMA is typically significantly faster. Also, quadratic MOMA tends to give flux distributions in which all fluxes deviate from the reference fluxes a little bit whereas linear MOMA tends to give flux distributions where the majority of fluxes are the same reference with few fluxes deviating a lot (typical effect of L2 norm vs L1 norm). The former objective function is saved in the optlang solver interface as ``"moma_old_objective"`` and this can be used to immediately extract the value of the former objective after MOMA optimization. See Also -------- pfba : parsimonious FBA References ---------- .. [1] Segrè, Daniel, Dennis Vitkup, and George M. Church. “Analysis of Optimality in Natural and Perturbed Metabolic Networks.” Proceedings of the National Academy of Sciences 99, no. 23 (November 12, 2002): 15112. .. [2] Becker, Scott A, Adam M Feist, Monica L Mo, Gregory Hannum, Bernhard Ø Palsson, and Markus J Herrgard. “Quantitative Prediction of Cellular Metabolism with Constraint-Based Models: The COBRA Toolbox.” Nature Protocols 2 (March 29, 2007): 727. """ if "moma_old_objective" in model.solver.variables: raise ValueError("The model is already adjusted for MOMA.") # Fall back to default QP solver if current one has no QP capability if not linear and sutil.interface_to_str(model.problem) not in sutil.qp_solvers: model.solver = sutil.choose_solver(model, qp=True) if solution is None: solution = pfba(model) prob = model.problem v = prob.Variable("moma_old_objective") c = prob.Constraint( model.solver.objective.expression - v, lb=0.0, ub=0.0, name="moma_old_objective_constraint", ) to_add = [v, c] model.objective = prob.Objective(Zero, direction="min", sloppy=True) obj_vars = [] for r in model.reactions: flux = solution.fluxes[] if linear: components = sutil.add_absolute_expression( model, r.flux_expression, name="moma_dist_" +, difference=flux, add=False, ) to_add.extend(components) obj_vars.append(components.variable) else: dist = prob.Variable("moma_dist_" + const = prob.Constraint( r.flux_expression - dist, lb=flux, ub=flux, name="moma_constraint_" +, ) to_add.extend([dist, const]) obj_vars.append(dist**2) model.add_cons_vars(to_add) if linear: model.objective.set_linear_coefficients({v: 1.0 for v in obj_vars}) else: model.objective = prob.Objective(add(obj_vars), direction="min", sloppy=True)