Dynamic instabilities of contractile acto-myosin rings

The actin cytoskeleton is a prototypic example of active matter and shows a wealth of dynamic phenomena alien to conventionally studied materials. In living cells, actin filaments and myosin motors often organize into dynamic rings. This is notably the case during the late stages of cell division of animal cells, where such a ring contracts and thereby cleaves the mother cell into two daughters. Similar structures are observed in dividing fission yeast, where their functional role is less clear, though. Furthermore, rings spanning several cells appear upon closure of tissues. It has been found experimentally that myosin forms stationary or moving clusters in acto-myosin rings. The mechanism underlying their formation and their role in ring dynamics remain unclear. Based on the analysis of a phenomenological theory, we show that traveling and stationary clusters are generic features of contractile actin rings. Our numerical results indicate that there is a direct transition from homogenous actin and myosin densities to chaotic dynamics along rings. We then use a mesocopic approach to study a possible molecular mechanism for the observed generic phemomena. It suggests that the transient formation of bipolar filaments provides a common mechanism underlying the experiementally observed patterns. The theory also shows that stationary myosin clusters are associated with elevated contractile stress, whereas traveling clusters are not. We compare these theoretical results to experimental observations in mammalian and fission yeast cells.