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In this case, the obtained maximum possibility flux vector is fully possible.
These provide a much more informative flux estimation than a point-wise one, such as the maximum possibility flux vector, or the interval of minimum-maximum possible values in [ 38].
Figure 3B depicts the maximum possibility flux estimation and three possibilistic intervals by means of a box-plot chart.
The simplest outcome of a PMFA problem is a point-wise flux estimation: the minimum-cost (maximum possibility) flux vector.
As expected, this time we obtained a maximum possibility flux vector with a similar shape, but higher possibility (0.88).
The marginal possibility distributions are depicted in Figure 9A, and the maximum possibility flux estimation and the flux intervals are depicted in Figure 9B.
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According to (4), the maximum possibility (minimum-cost) flux vector v mp corresponding to a given set of measurements is obtained as the solution to the linear programming (LP) optimization problem: (24) being its degree of possibility π(v mp ) = exp(J min ).
At this point, the maximum possibility (minimum-cost) flux vector v mp corresponding to a given set of measurements is obtained solving a linear programming (LP) problem: (8) min ε, μ, v J s. t. { ℳ O C ℳ ℰ C The possibility of the most possible solution being, π mp = π (v m p ) = e − J max.
If the estimation is repeated removing the flux, the maximum possibility does not increase; however, when the estimation is performed removing, the maximum possibility is significantly higher (0.7).
The interpretation of the new coefficients would, therefore, be that the same deviation from the fluxes of maximum possibility will be now be considered as a less possible fact.
Then, possibilistic MFA is able to query the flux vector of maximum possibility.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com