Mathematical Modeling of Circadian Clock-Regulated Hypocotyl Elongation Accelerated by Artificial Photoperiods in Arabidopsis

Light–dark cycles regulate hypocotyl elongation in Arabidopsis thaliana through the circadian clock and PHYTOCHROME-INTERACTING FACTORs (PIFs), but the quantitative relationship between photoperiodic patterns, PIF4/PIF5 dynamics, and growth remains unclear. Here, we modified the circadian-clock-regulated hypocotyl elongation model by integrating a previously established Arabidopsis clock framework with PIF4/PIF5 regulatory interactions and a saturation term in the growth equation. Mathematical properties (existence, uniqueness, non-negativity and boundedness) of the model were analyzed. The model was parameterized using published PIF4 expression and hypocotyl growth datasets and evaluated against photoperiod-dependent PIF4 expression, hypocotyl length responses, and growth dynamics in wild-type and clock- or PIF4-related genetic backgrounds. The modified growth equation captured the saturating nature of hypocotyl elongation under constant darkness (DD), while simulations showed that shorter photoperiods enhance nighttime PIF4/PIF5 protein accumulation and increase hypocotyl growth rates. Bifurcation analysis indicated that sufficient expression of PSEUDO-RESPONSE REGULATOR 5 (PRR5)/TIMING OF CAB EXPRESSION 1 (TOC1) is required to induce PIF4/PIF5 transcript oscillations under the DD condition. The model further predicted that, compared with the 12 h light/12 h dark (12L:12D) condition, the 5L:5D:7L:7D and 6L:5D:6L:7D photoperiod regimes reduced the growth cycle by 23.74% and 22.18%, respectively. This framework serves as a quantitative tool for dissecting photoperiod-dependent hypocotyl elongation and screening optimized artificial light strategies.