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.