Instantaneous growth: a compact measure of efficient carbon and nitrogen allocation in leaves and roots of C3 and C4 plants.

Elucidating plant functions and identifying crop productivity bottlenecks requires the accurate quantification of their performance. This task has been attained through photosynthetic models. However, their traditional focus on the leaf's capacity to uptake CO₂ is becoming increasingly restrictive. Advanced bioengineering of C₃ plants has made it possible to increase rates of CO₂ assimilation by packing photosynthetic structures more densely within leaves. The operation of mechanisms that concentrate CO₂ inside leaves can boost rates of assimilation while requiring a lower investment in carboxylating enzymes. Therefore, whether in the context of spontaneous plants or modern manipulation, considering trade-offs in resource utilization efficiency emerges as a critical necessity. I've developed a concise and versatile analytical model that simulates concurrent leaf and root growth by balancing instantaneous fluxes of carbon and nitrogen. Carbon is made available by leaf photosynthesis, encompassing all types of biochemistries, while nitrogen is either taken up by roots or remobilized after senescence. The allocation of leaf nitrogen between light or carbon reactions was determined using a fitting algorithm: growth maximisation was the only reliable fitting goal. Both the leaf nitrogen pool and the root-to-leaf ratio responded realistically to various environmental drivers (CO₂ concentration, light intensity, soil nitrogen), replicating trends typically observed in plants. Furthermore, modifying the strength of CO₂ concentrating mechanisms proved sufficient to alter the root-to-leaf ratio between C₃ and C₄ types. This direct and mechanistic one-to-one link convincingly demonstrates, for the first time, the functional dependence of a morphological trait on a single biochemical property.