Flux–species sampling enables holistic exploration of biocircuit behavior

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Abstract
Summary: Biocircuit behavior is usually discovered by drawing uncertain kinetic parameters and simulating, but the scored phenotypes are functions of steady-state species, catalytic fluxes, dominance relations, and local response matrices. We introduce flux–species sampling (FSS), which samples that functional layer directly and algebraically inverts to parameters. This coordinate change turns regulatory modes into simple dominance chambers, gives every full-dimensional behavior-realizing regime positive measure, and can replace the sampling stage of existing pipelines without changing downstream stability or phenotype tests. A sequestration toy shows how a large species regime can collapse into a narrow parameter strip. In an enzymatic feedback motif, FSS rescues free- A * adaptation missed by parameter sampling and identifies the regime as non-Michaelian and complex-dominated. In MultiFate- N , FSS separates a sampling limitation from a structural limitation and rescues parameter sets realizing all 2 N states. Highlights: Flux–species sampling (FSS) draws the control/function layer where biocircuit behavior is read FSS boxes intersect every full-dimensional behavior-realizing regime with positive measure FSS is no slower than parameter-space sampling and is a hot fix for existing pipelines FSS rescues non-Michaelian free- A * adaptation missed by parameter sampling FSS rescues the all-2 N symmetric MultiFate regime missed by fixed parameter boxes eTOC blurb: This study reframes biocircuit exploration by sampling steady-state species and fluxes rather than raw parameters. The resulting flux–species coordinate exposes regulatory dominance regimes, rescues adaptation and multistability regimes missed by parameter sampling, and gives finite sampling nulls an explicit scope.

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