Performs a heuristic version of the parsimonious FBA algorithm. See details.
Arguments
- model
Model of class ModelOrg
- costcoeffw, costcoefbw
A numeric vector containing cost coefficients for all variables/reactions (forward direction: 'costcoeffw'; backward direction: 'costcoefbw'). If set to NULL, all cost coefficients are set to 1, so that all variables have the same impact on the objective function.
- pFBAcoeff
Numeric value to weight the minimization of total flux within the combined objective function. See details.
Details
The exact-solution pFBA algorithm described by Lewis et al. 2010 consists of
two optimization steps: (1) A basic flux balance analysis is performed to
obtain the optimal value of the objective function (e.g., growth rate). (2)
The objective function from (1) is transformed into a constraint where the
value of the function is fixed to the determined optimal value. A new
objective is defined that minimizes the absolute sum of fluxes through the
metabolic network.
The here implemented heuristic pFBA performs only one optimization step.
Therefore, the original objective function is combined with a term that
minimizes the absolute (weighted) sum of fluxes:
$$max: \sum_{i=1}^{n}(c_i v_i) - p \sum_{i=1}^{n}(w_i |v_i|)$$
for maximization direction or
$$min: \sum_{i=1}^{n}(c_i v_i) + p \sum_{i=1}^{n}(w_i |v_i|)$$
if the original objective function is minimized.
Here,
\(c_i\) is the original objective coefficient of reaction \(i\),
\(v_i\) the flux through reaction \(i\),
\(n\) the number of reactions in the model, and
\(w_i\) the weight of reaction \(i\) (see arguments 'costcoeffw',
'costcoefbw').
The scalar parameter \(p\) (argument 'pFBAcoeff') defines the weighting of
the total flux minimization. Increasing this value increases the weight of
total flux minimization, possibly at costs for the value of the objective
function defined in 'model' (e.g., flux through biomass reaction).
This heuristic implementation of a pFBA is the core of the gap-filling
algorithm of 'gapseq' (Zimmermann et al. 2021).
References
N. E. Lewis et al., “Omic data from evolved E. coli are consistent with computed optimal growth from genome‐scale models,” Molecular Systems Biology, vol. 6, no. 1. EMBO, Jan. 2010. doi: 10.1038/msb.2010.47.
J. Zimmermann, C. Kaleta, and S. Waschina, “gapseq: informed prediction of bacterial metabolic pathways and reconstruction of accurate metabolic models,” Genome Biology, vol. 22, no. 1. Springer Science and Business Media LLC, Mar. 10, 2021. doi: 10.1186/s13059-021-02295-1.