Collective pulsatile expansion and swirls in proliferating tumor tissue

Understanding the dynamics of expanding biological tissues is essential to a wide range of phenomena in morphogenesis, wound healing and tumor proliferation. Increasing evidence suggests that many of the relevant phenomena originate from complex collective dynamics, inherently nonlinear, of constituent cells that are physically active. Here, we investigate thin disk layers of proliferating, cohesive, monoclonal tumor cells and report the discovery of macroscopic, periodic, soliton-like mechanical waves with which cells are collectively ratcheting, as in the traveling-wave chemotaxis of dictyostelium discodium amoeba cells. The relevant length-scale of the waves is remarkably large (similar to 1 mm), compared to the thickness of a mono-layer tissue (similar to 10 mu m). During the tissue expansion, the waves are found to repeat several times with a quite well defined period of approximately 4 h. Our analyses suggest that the waves are initiated by the leading edge that actively pulls the tissue in the outward direction, while the cells within the bulk tissue do not seem to generate a strong selfpropulsion. Subsequently, we demonstrate that a simple mathematical model chain of nonlinear springs that are constantly pulled in the outward direction at the leading edge recapitulates the observed phenomena well. As the areal cell density becomes too high, the tissue expansion stalls and the periodic traveling waves yield to multiple swirling vortices. Cancer cells are known to possess a broad spectrum of migration mechanisms. Yet, our finding has established a new unusual mode of tumor tissue expansion, and it may be equally applicable for many different expanding thin layers of cell tissues.