From sequence to timescale: a frequency-domain control-theoretic framework linking ncRNA sequence composition to...

Non-coding RNAs (ncRNAs) are central regulators of epigenomic states, orchestrating chromatin modifications, gene silencing, and nuclear architecture through recruitment of chromatin-modifying complexes. Long noncoding RNAs (lncRNAs) such as XIST, HOTAIR, and MALAT1 exemplify these regulatory roles. Despite their importance, quantitative computational frameworks for linking ncRNA sequence composition to temporal regulatory behaviour remain limited. We introduce a frequency-domain control theory framework modelling RNA sequences as cascaded feedback systems, extending a previously established second-order negative feedback model developed for hormonal endocrine axis dynamics (1,2). This paper constitutes the molecular layer beneath that endocrine framework: where the companion paper characterises the cortisol-HPA axis at the hormonal timescale (τ ≈ 130 min, ultradian period ∼ 90 min), the present work resolves the finer-grained tier of lncRNA-mediated chromatin responses (8-24 min) that constitutes the molecular machinery through which hormonal signals are transduced into epigenetic change. Together, the two frameworks delineate a two-tier frequency hierarchy: the hormonal cascade sets the input signal timescale, and ncRNA sequence composition determines whether the downstream chromatin response is bandwidth-matched to follow it. As a proof-of-concept demonstration using one representative miRNA and one lncRNA sequence, analysis reveals that RNA length and topology encode low-pass temporal filtering properties, with ncRNAs exhibiting slower cutoff frequencies and stronger noise attenuation than short miRNAs. The parameter mapping from sequence composition to control-theoretic parameters is treated as an abstract mathematical heuristic rather than a literal physical law, and the framework is intended to generate experimentally testable hypotheses rather than quantitative physiological predictions. Mixed miRNA-ncRNA cascades show extreme phase accumulation at the stability boundary, a necessary but not sufficient condition for bistable or oscillatory epigenetic regulation. ncRNA sequence composition systematically encodes temporal response characteristics relevant to epigenetic regulation, providing a theoretical basis for predictive modelling of chromatin dynamics and RNA-mediated control systems.