# 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
if TYPE_CHECKING:
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. https://doi.org/10.1073/pnas.232349399.
.. [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[r.id]
if linear:
components = sutil.add_absolute_expression(
model,
r.flux_expression,
name="moma_dist_" + r.id,
difference=flux,
add=False,
)
to_add.extend(components)
obj_vars.append(components.variable)
else:
dist = prob.Variable("moma_dist_" + r.id)
const = prob.Constraint(
r.flux_expression - dist,
lb=flux,
ub=flux,
name="moma_constraint_" + r.id,
)
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)
```