Flow-wave coupling synchronizes oscillations in growing active matter

Oscillatory biochemical signals and mechanical forces must coordinate robustly during development, yet the principles governing their mutual coupling remain poorly understood. In syncytial embryos and cell-free extracts, mitotic waves propagate across millimeter scales while simultaneously generating cytoplasmic flows, suggesting a two-way interaction between chemical oscillators and mechanics. Here, we combine experiments in Xenopus Laevis cytoplasmic extracts with a minimal particle-based model to reveal a mechanochemical feedback that stabilizes phase wave propagation. In contrast to previous models of oscillatory active matter, an asymmetric size cycle, slow growth and rapid shrinkage, combined with size-dependent mechanical interactions generates a net particle displacement and flows aligned with the wave direction, which in turn drive a synchronization transition. Our results show that mechanical forces actively maintain the coherence of biochemical waves, providing a general mechanism for long-range order in oscillating active matter.