Evaluating valid parameter regimes for biocircuits

Abstract

Biocircuit functions are often valid only in specific parameter regimes, yet these regimes are rarely made explicit. We use a holistic analysis method based on regimes to derive validity conditions and introduce the Realizability Index (R-index), quantifying the size of the valid regions in log-parameter space. The framework is applied to Michaelis-Menten kinetics, Hill functions, and enzymatic negative-feedback adaptation, showing how circuit structure and experimental control variables shape functional realizability. Our analysis shows the Hill functions R-index goes to zero in sequential binding with increasing Hill coefficient. We also resolve an active debate about whether negative-feedback adaptation is realizable when competitive binding is taken into account, and demonstrates the superiority of the holistic R-index method over numerical parameter scans that lead to incorrect conclusions. R-index defines a validity-aware language for studying and designing functional biocircuits.