  We present a model of systems of cells with intracellular oscillators
(`clocks'). This is motivated by examples from developmental biology and from
the behavior of organisms on the threshold to multicellularity. Cells undergo
random motion and adhere to each other. The adhesion strength between neighbors
depends on their clock phases in addition to a constant baseline strength. The
oscillators are linked via Kuramoto-type local interactions. The model is an
advection-diffusion partial differential equation with nonlocal advection
terms. We demonstrate that synchronized states correspond to Dirac-delta
measure solutions of a weak version of the equation. To analyze the complex
interplay of aggregation and synchronization, we then perform a linear
stability analysis of the incoherent, spatially uniform state. This lets us
classify possibly emerging patterns depending on model parameters. Combining
these results with numerical simulations, we determine a range of possible
far-from equilibrium patterns when baseline adhesion strength is zero: There is
aggregation into separate synchronized clusters with or without global
synchrony; global synchronization without aggregation; or unexpectedly a
``phase wave" pattern characterized by spatial gradients of clock phases. A 2D
Lattice-Gas Cellular Automaton model confirms and illustrates these results.
