In Arabidopsis, the root clock regulates the spacing of lateral organs along the primary root through oscillating gene expression. The core molecular mechanism that drives the root clock periodicity and how it is modified by exogenous cues such as auxin and gravity remain unknown. We identified the key elements of the oscillator (AUXIN RESPONSE FACTOR 7, its auxin-sensitive inhibitor IAA18/POTENT, and auxin) that form a negative regulatory loop circuit in the oscillation zone. Through multilevel computer modeling fitted to experimental data, we explain how gene expression oscillations coordinate with cell division and growth to create the periodic pattern of organ spacing. Furthermore, gravistimulation experiments based on the model predictions show that external auxin stimuli can lead to entrainment of the root clock. Our work demonstrates the mechanism underlying a robust biological clock and how it can respond to external stimuli.

Availability of the essential macronutrient nitrogen in soil plays a critical role in plant growth, development, and impacts agricultural productivity. Plants have evolved different strategies for sensing and responding to heterogeneous nitrogen distribution. Modulation of root system architecture, including primary root growth and branching, is among the most essential plant adaptions to ensure adequate nitrogen acquisition. However, the immediate molecular pathways coordinating the adjustment of root growth in response to distinct nitrogen sources, such as nitrate or ammonium, are poorly understood. Here, we show that growth as manifested by cell division and elongation is synchronized by coordinated auxin flux between two adjacent outer tissue layers of the root. This coordination is achieved by nitratedependent dephosphorylation of the PIN2 auxin efflux carrier at a previously uncharacterized phosphorylation site, leading to subsequent PIN2 lateralization and thereby regulating auxin flow between adjacent tissues. A dynamic computer model based on our experimental data successfully recapitulates experimental observations. Our study provides mechanistic insights broadening our understanding of root growth mechanisms in dynamic environments.