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 examined how white lupin (Lupinus albus) cotyledons mobilize nitrogen and minerals during early seedling growth under nitrogen‑deficient conditions, revealing that 60 % of stored proteins degrade within eight days and are redirected to support development. Proteomic analyses showed dynamic shifts in nutrient transport, amino acid metabolism, and stress responses, and premature cotyledon removal markedly impaired growth, highlighting the cotyledon's essential role in nutrient supply and transient photosynthetic activity.