Cells as liquid motors

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.

From actin and myosin collective dynamics to motor properties and mechanosensing

Animals have muscles to act on their environment. The molecules endowing them with this faculty are actin, that forms long filaments organised in a network, and myosins, which are molecular motors able to slide actin filaments relative to one another. These molecules are also present in nonmuscle cells, and are at the origin of single cells' ability to migrate through the body to fight infection or during embryo development for instance. However, besides the difference in size, the lack of a large-scale organisation of actin and myosin filaments within nonmuscle cells is strikingly different from the crystalline structure they assume in muscles.

We show that these puzzling properties arise from a common property of nonmuscle disordered actomyosin and crystalline muscle's one: in order to change shape (or shorten), cells (or muscles) need, of course, the myosin contraction, but also need to accomodate this contraction by some relaxation of the tension created: thus, myosin needs to unbind after pulling. This unbinding allows the actomyosin to flow according to its myosin driving, it is thus well described as a liquid mechanical system—albeit a liquid which is also a motor, since it drives itself to contraction and can pull on loads. This 'liquid motor' concept allows to decipher several puzzles: why the actomyosin flows backward when the cell edge moves forward, how a cell can assume different shapes when in contact with different surroundings while still being able to resist mechanical challenges. It allows also to benchmark the cell as we do for any motor: how much power does it develop for a given rate of fuel injection, and what is the friction that dissipates away the difference?

Shape regulation through the competition of contractility and protrusion

The energy budget of a living cell. Our model focuses on what happens if the same quantity of energy is being injected by myosin motors, but the environment of the cell is changed. We find that this is representative of our experiments.
The mechanical work rate is the quantity of energy per unit time (power) that the cell effectively employs in displacing an external load. It is zero if the force needed to move that load is zero, or if the force is such that the speed of the displacement that the cell achieves is zero (force F_max).
The rest of the mechanical power injected by myosins is dissipated by three different mechanisms. First, a friction-like dissipation : if cells contract fast (in the case of low opposing force), the material of the cell itself is dissipating energy in changing its own shape. In particular, myosin motors, after having pulled on actin, will take some time to detach from them and, in the mean time, resist further deformation : this is similar to the energy loss due to a rower not lifting his oar quickly enough. This phenomenon is also what limits the speed of muscle contraction in the model by Huxley.
Second, an internal creep is responsible for losses especially when the force is so large that the cell cannot move the load. In that case, myosin motors tense the actin network without achieving any displacement (like the rowers stuck against the tree bend their oar in vain) and will eventually detach from actin without having performed any useful work: when detaching, the tension they have accumulated is lost, just as if the bent oar is lifted out of water and vibrates away all its elastic energy. Again, this is something which is also present in whole muscle dynamics.
Finally, cells regulate their size by the dynamic balance between contracting thanks to myosin and extending thanks to actin polymerisation. These competing phenomena both use energy, and myosins provide work that counterbalances the protrusive effect of polymerisation.
In the end, the efficiency of nonmuscle cells is not very high, with 0.5 fW of useful power for more than 10 fW of mechanical energy injected. However, these 10 fW represent only 1/1000 of the total cell metabolism: this is why evolution will have selected this costly but versatile liquid-motor system.