Robust statistical testing for qualitative sign-structure constraints

Develop a statistical theory that translates qualitative constraints implied by sign-structure and monotonicity in input–output biological systems (for example, the impossibility of biphasic outputs in response to monotone inputs when all directed input–output paths have the same sign) into finite-sample hypothesis tests applicable to noisy, indirect experimental measurements.

Background

A core theme of the paper is using dynamic phenotypes and sign-structure (monotonicity, incoherent feedforward/feedback motifs) to constrain model classes without detailed parameters. While these arguments are robust conceptually, practical inference requires methods that handle noisy, limited, and indirect data.

The authors explicitly pose the need for statistical frameworks that connect structural impossibility results (e.g., monotonicity forbidding biphasic responses from step inputs when initialized at equilibrium) to quantitative tests that can be applied to finite experimental datasets.

References

Developing theory that connects qualitative constraints (e.g., impossibility of biphasic responses under monotonicity assumptions) to finite-data statistical tests is an important open problem.

— Dynamic response phenotypes and model discrimination in systems and synthetic biology (2512.24945 - Sontag, 31 Dec 2025) in Concluding remarks and outlook; bullet point “Robustness of qualitative inference”