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 study reveals that REMORIN protein evolution is primarily driven by diversification of their conserved C-terminal domain, defining four major clades. Structural bioinformatics predicts a common membrane‑binding interface with diverse curvatures and lengths, and suggests that some REMs can form C‑terminal‑mediated oligomers, adding complexity to membrane organization.