The (un)likelihood of clock-driven lateral root priming; a modeling exploration

Lateral root formation starts with priming, predisposing subsets of pericycle cells with the potential of future lateral root formation through semi-periodic elevations in auxin (signaling). While various mechanisms have been suggested, one frequently suggested hypothesis proposes a genetic, cell-autonomous root clock akin to the clock underlying vertebrate somitogenesis. Still, although gene expression variations were observed, so far this clock has not been proven. From a functional and evolutionary perceptive, it is furthermore an open question whether lateral root priming is not more likely to arise from an emergent tissue level process similar to phyllotaxis. To help settle this debate in this study, I use general knowledge of oscillator dynamics and simple models of auxin signaling to underline the unlikelihood of a root clock driving lateral root priming. I show how, within a single cell, oscillations are limited to a small parameter domain, with constraints intensifying due to the presence of multiple AUX/IAA and ARF types as well as auxin export. Furthermore, I demonstrate how non-meristem-based oscillations, due to a lack of memory of oscillator phase, cannot drive periodic prebranch site formation, and periodic inputs are insufficient to induce phase differences. Combined, these factors underline the unlikelihood of a root clock driving lateral root priming.