The study introduces a hybrid modeling framework that integrates a logistic ordinary differential equation with a Long Short-Term Memory neural network to form a Physics-Informed Neural Network (PINN) for predicting wheat plant height. Using only time and temperature as inputs, the PINN outperformed other longitudinal growth models, achieving the lowest average RMSE and reduced variability across multiple random initializations. The results suggest that embedding biological growth constraints within data‑driven models can substantially improve prediction accuracy for plant traits.

The authors used a bottom‑up thermodynamic modelling framework to investigate how plants decode calcium signals, starting from Ca2+ binding to EF‑hand proteins and extending to higher‑order decoding modules. They identified six universal Ca2+-decoding modules that can explain variations in calcium sensitivity among kinases and provide a theoretical basis for interpreting calcium signal amplitude and frequency in plant cells.

The study shows that high ambient temperature triggers extensive changes in ROS homeostasis in Arabidopsis seedlings, with H2O2 balance being essential for thermomorphogenic hypocotyl elongation. PIF4 directly activates catalase genes CAT2 and CAT3 to regulate H2O2 levels, forming a PIF4‑CAT‑H2O2 module that operates alongside the PIF4‑auxin pathway, while elevated H2O2 feeds back to reduce PIF4 protein abundance.