  Rhythmic and sequential subdivision of the elongating vertebrate embryonic
body axis into morphological somites is controlled by an oscillating
multicellular genetic network termed the segmentation clock. This clock
operates in the presomitic mesoderm (PSM), generating dynamic stripe patterns
of oscillatory gene-expression across the field of PSM cells. How these spatial
patterns, the clock's collective period, and the underlying cellular-level
interactions are related is not understood. A theory encompassing temporal and
spatial domains of local and collective aspects of the system is essential to
tackle these questions. Our delayed coupling theory achieves this by
representing the PSM as an array of phase oscillators, combining four key
elements: a frequency profile of oscillators slowing across the PSM; coupling
between neighboring oscillators; delay in coupling; and a moving boundary
describing embryonic axis elongation. This theory predicts that the
segmentation clock's collective period depends on delayed coupling. We derive
an expression for pattern wavelength across the PSM and show how this can be
used to fit dynamic wildtype gene-expression patterns, revealing the
quantitative values of parameters controlling spatial and temporal organization
of the oscillators in the system. Our theory can be used to analyze
experimental perturbations, thereby identifying roles of genes involved in
segmentation.
