Shape regulation through the competition of contractility and protrusion
Among the many mysteries of living cells, their ability to move and adapt their shape has attracted our attention as physicists. A combination of modelling and experiments explains two puzzling observations: first, that the cell adapts the level of force with which it pulls on its surroundings depending on how rigid they are, and second, that while a cell progresses in one direction by extending a protrusion, its internal skeleton of proteins actually flows in the other direction in what seems a counterproductive motion. This is called the retrograde flow. We show that both of these phenomena stem from the same paradoxical property of this internal skeleton of the cell, which is made of filaments of actin assembled into a network. In fact, because this assemblage is bound by short-lived connections, this network is actually a liquid that will slowly flow. This is puzzling with respect to common observations, since a liquid's shape is dictated by its environment, while cells actively deform their surroundings. However, actin is also bound with molecular motors, called myosin, which can drive this flow from the interior. We show that it is the interaction of this myosin-driven flow with the cell surroundings that defines the shape that the cell will take. This is done at the cost of continually spending energy even when the cell is globally immobile, but we show that this endows the cell with two crucial advantages: it is as fluid and versatile as a liquid, and therefore can accomplish many physiological roles, and it is as resilient as an elastic solid, that will respond instantaneously to mechanical challenges.