# MoMA

# Minimisation of Metabolic Adjustment

MoMA is a flux-based analysis technique similar to FBA and based on the same stoichiometric constraints, but the optimal growth flux for mutants is relaxed. Instead, MoMA provides an approximate solution for a sub-optimal growth flux state, which is nearest in flux distribution to the unperturbed state. The mathematical formulation of this yields a quadratic programming problem:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \min\ ||\mathbf{v_w} - \mathbf{v_d}||^2 \qquad s. t.\quad \mathbf{S}\cdot\mathbf{v_d}=0 }**

where **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \mathbf{v_w}}**
represents the wild-type (or unperturbed state) flux distribution and **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \mathbf{v_d}}**
represents the flux distribution on gene deletion that is to be solved for. This simplifies to:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \min\ \frac{1}{2}\,{\mathbf{v_d}}^T\,\mathbf{I}\,\mathbf{v_d} + (\mathbf{-v_w})\cdot\mathbf{v_d} \qquad s. t.\quad \mathbf{S}\cdot\mathbf{v_d}=0 }**

where **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \mathbf{I}}**
is an identity matrix of size **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n \times n}**
, **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n}**
being the length of the vector **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \mathbf{v_d}}**
. An important feature of MoMA is that the wild-type flux distribution used need not be obtained by performing an FBA; an experimentally determined flux distribution could serve better. Thus, objective functions for optimisation, which may not reflect the physiological situation very accurately can be circumvented using MoMA. MoMA also does not assume optimality of growth or any other metabolic function.

# References

- Segre D, Vitkup D, Church GM. Analysis of optimality in natural and perturbed metabolic networks.
*Proc Natl Acad Sci U S A*2002;**99**:15112–15117. - Segre D, Zucker J, Katz J, et al. From annotated genomes to metabolic flux models and kinetic parameter fitting.
*OMICS*2003;**7**:301–316.