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 demonstrates that a rapid increase in cytosolic Ca²⁺ is the primary and sufficient signal mediating auxin‑induced root growth inhibition in Arabidopsis. Using live imaging, microfluidics, and optogenetic control of Ca²⁺ influx, the authors show that blocking Ca²⁺ entry prevents growth responses, while light‑triggered Ca²⁺ influx from the apoplast or ER mimics inhibition, indicating that diverse stimuli converge on a Ca²⁺‑dependent mechanism.

The study uses an optogenetic ChannelRhodopsin 2 variant (XXM2.0) to generate defined cytosolic Ca²⁺ transients in Arabidopsis root cells, revealing that these Ca²⁺ signatures suppress auxin‑induced membrane depolarization, Ca²⁺ spikes, and auxin‑responsive transcription, leading to reversible inhibition of cell division and elongation. This demonstrates that optogenetically imposed Ca²⁺ signals act as dynamic regulators of auxin sensitivity in roots.