Collective dynamics of actomyosin cortex endow cells with intrinsic mechanosensing properties
Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent, purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodelling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerisation at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn regulates the cell size in a force-dependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena which are of the same nature as those taking place during the contraction of a whole muscle. This explains the fact that single nonmuscle cell and whole muscle contraction both follow a Hill-like force–velocity relationship. When placed in different mechanical environments, living cells assume different shapes [1, 2, 3, 4, 5]. This behaviour is known to be strongly dependent on the contractile activity of the actomyosin network [6, 7, 8, 9, 10]. One of the cues driving the cell response to its environment is rigidity [11]. Cells are able to sense not only the local rigidity of the material they are in contact with [12], but also the one associated with distant cell-substrate contacts : that is, the amount of extra force needed in order to achieve a given displacement of microplates between which the cell is placed [13], Fig. 1c, of an AFM cantilever [14, 15], or of elastic micropillars [16]. This cell-scale rigidity sensing is totally dependent on Myosin-II activity [13]. A working model of the molecular mechanisms at play in the actomyosin cortex is available [17], where myosin contraction, actin treadmilling and actin crosslinker turnover are the main ingredients. Phenomenological models [18, 19] of mechanosensing have been proposed, but could not bridge the gap between the molecular microstructure and this phenomenology. Here, we show that the collective dynamics of actin, actin crosslinkers and myosin molecular motors are sufficient to explain cell-scale rigidity sensing. The model derivation is analogous to the one of rubber elasticity of transiently crosslinked networks [20], with the addition of active crosslinkers, accounting for the myosin. It involves four parameters only: myosin contractile stress, speed of actin treadmilling, elastic modulus, and viscoelastic relaxation time of the cortex, which arises because of crosslinker unbinding. It allows quantitative predictions of the dynamics and statics of cell contraction depending on the external stiffness. The crucial dependence of this behaviour on the fact that crosslinkers have a short life time is reminiscent of the model of muscle contraction by A. F. Huxley [21], in which the force dependence of muscle contraction rate is explained by the fact that for lower muscle force and higher contraction speed, the num∗Univ. Grenoble Alpes, LIPHY, F-38000 Grenoble, France †CNRS, LIPHY, F-38000 Grenoble, France ‡to whom correspondence should be addressed; E-mail: Jocelyn.Etienne@ujf-grenoble.fr §Université Paris-Diderot–CNRS, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057, Paris, France 1 ar X iv :1 40 7. 27 65 v2 [ ph ys ic s. bi oph ] 1 7 Ju l 2 01 4 ber of myosin heads contributing to filament sliding decreases in favour of those resisting it transiently, before they unbind. While it is known that many molecules associated with actomyosin exhibit stressdependent dynamics [22], collective effects alone can explain observations in both Huxley’s muscle contraction model and the present model. We have previously evidenced the similarity of single nonmuscle cell and muscle contraction rate [13]. In spite of very dissimilar organisation of actomyosin in muscles, where it forms well-ordered sarcomeres, and in nonmuscle cell cortex, where no large-scale patterning is observed, we show that corresponding mechanisms explain their similar motor properties. The collective dynamics we describe are consistent with the fact that the actin network behaves as a fluid at long times. We show how myosin activity can contract this fluid at a given rate that depends on external forces resisting cell contraction, arising e.g. from the stiffness of the environment. This, combined with actin protrusivity, results in both a sustained retrograde flow and a regulation of cell shape. In addition, this explains the elastic-like behaviour observed in cell-scale rigidity-sensing and justifies ad hoc models based on this observation [18].