# 17.1.1.2.1.7. cobra.flux_analysis.moma¶

Provide minimization of metabolic adjustment (MOMA).

## 17.1.1.2.1.7.1. Module Contents¶

### 17.1.1.2.1.7.1.1. Functions¶

 moma(model, solution=None, linear=True) Compute a single solution based on (linear) MOMA. add_moma(model, solution=None, linear=True) Add constraints and objective representing for MOMA.
cobra.flux_analysis.moma.moma(model, solution=None, linear=True)[source]

Compute a single solution based on (linear) MOMA.

Compute a new flux distribution that is at a minimal distance to a previous reference solution. Minimization of metabolic adjustment (MOMA) is generally used to assess the impact of knock-outs. Thus the typical usage is to provide a wildtype 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 (wildtype) reference solution.

• linear (bool, optional) – Whether to use the linear MOMA formulation or not (default True).

Returns

A flux distribution that is at a minimal distance compared to the reference solution.

Return type

cobra.Solution

add_moma()

cobra.flux_analysis.moma.add_moma(model, solution=None, linear=True)[source]

Add constraints and objective representing for MOMA.

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.

• 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 <= v^d_i <= 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 <= v^d_i <= 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.

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.