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 function’s 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. Competing Interest Statement The authors have declared no competing interest. Footnotes (e-mail: liuqinguo{at}westlake.edu.cn) (e-mail: xren{at}eitech.edu.cn) (e-mail: xiaofangzhou{at}westlake.edu.cn) The author list has been revised to add Xinying Ren as the second author. This revision is made to appropriately acknowledge her significant contribution to the conceptual development of the project. In particular, the initial idea of the R-index was developed through discussions with her, and she also provided important insights during the early-stage discussions that helped shape the direction of the study. The author contribution statement has been updated accordingly.