  Notch signaling is a ubiquitous and versatile intercellular signaling system
that drives collective behaviors and pattern formation in biological tissues.
During embryonic development, Notch is involved in generation of collective
biochemical oscillations that form the vertebrate body segments, and its
failure results in embryonic defects. Notch ligands of the Delta family are key
components of this collective rhythm, but it is unclear how different Delta
ligands with distinct properties contribute to relaying information among
cells. Motivated by the zebrafish segmentation clock, in this work we propose a
theory describing interactions between biochemical oscillators, where Notch
receptor is bound by both oscillatory and nonoscillatory Delta ligands. Based
on previous in vitro binding studies, we first consider Notch activation by
Delta dimers. This hypothesis is consistent with experimental observations in
conditions of perturbed Notch signaling. Then we test an alternative hypothesis
where Delta monomers directly bind and activate Notch, and show that this
second model can also describe the experimental observations. We show that
these two hypotheses assign different roles for a non-oscillatory ligand, as a
binding partner or as a baseline signal. Finally, we discuss experiments to
distinguish between the two scenarios. Broadly, this work highlights how a
multiplicity of ligands may be harnessed by a signaling system to generate
versatile responses.
