Carbon-13 metabolic flux inference

Turn reviewed carbon maps, explicit tracer mixtures, and corrected labeling measurements into feasible flux estimates and evidence about which fluxes the experiment constrains. Use the bundled solver rather than reconstructing isotope balances or fitting each reaction independently. It runs mfapy's EMU forward simulator and fits fluxes in the mass-balanced feasible space with SciPy. It does not use an FBA objective.

Scope and required evidence

This implementation supports metabolic and isotopic steady state, a single shared flux state across one or more tracer experiments, nonnegative one-way reaction fluxes, and carbon-subset mass distributions. Reversible reactions are two separately mapped directions. Measurement error is Gaussian with a supplied covariance or a disclosed diagonal approximation.

Before fitting, obtain:

• The carbon network and the source of each atom assignment. Stoichiometry alone does not specify where labeled atoms go. Record compartments as separate metabolite IDs.
• Evidence for both steady-state assumptions. Stable metabolite abundance does not establish isotopic steady state. Time-course labeling requires INST-MFA with pool sizes and initial labeling; do not average it into this solver.
• Every carbon input's positional isotopomer distribution, including unlabeled supplements, bicarbonate/CO2 when assimilated, and tracer impurity.
• Fragment carbon assignments, natural-abundance correction history, and uncertainty of the reported mean. Raw peak intensities, derivatized spectra, and MS/MS transitions require validated preprocessing before these inputs can be constructed.
• Flux units, extracellular rate measurements or a stated relative-flux reference, and biologically justified bounds. Label fractions alone cannot set an absolute rate.