Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

Abstract

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells.

Cells as liquid motors: Mechanosensitivity emerges from collective dynamics of actomyosin cortex

“…Consistent with prior computational models (25), this equation shows that the contractile stress σ a gives rise to either the buildup of a contractile tension σ (if clamped boundary conditions allow no strain) or a contractile strain rate σ a =ð2τ α EÞ proportional to α myo =τ myo [if free boundary conditions allow strain but not tension buildup (e.g., in the case of superprecipitation in vitro) (33)] or a combination of these. We then asked whether this simple rheological law for the actomyosin cortex could explain the behavior of cells in our microplate experiments (Fig.…”

“…The crucial dependence of this behavior on the fact that cross-linkers have a short lifetime is reminiscent of the model of muscle contraction by Huxley (22), in which the force dependence of muscle contraction rate is explained by the fact that, for lower muscle force and higher contraction speed, the number of myosin heads contributing to filament sliding decreases in favor of those resisting it transiently before they unbind. Although it is known that many molecules associated with actomyosin exhibit stress-dependent dynamics (23,24) and can lead to microscale response to rigidity (25,26), collective effects govern the linear response of actomyosin and are sufficient to explain the observations in both the model by Huxley (22) and this model: we show that force-dependent binding kinetics tune the system's efficiency without essential alterations to its behavior, as Huxley (22) noted himself. Despite very dissimilar organization of actomyosin in muscles, where it forms well-ordered sarcomeres, and nonmuscle cell cortex, where no large-scale patterning is observed, we show that similar mechanisms explain their motor properties.…”

“…Indeed, for an environment (external spring) of stiffness k much beyond the critical value k c , the contractile fluid is unable to significantly strain the microplates, and equilibrium is reached when it exerts its maximal contractility σ a . In contrast to computational models (25,26) discussed in SI Text, S4.1, where such a maximum force arises because myosin molecules reach their specific stall force, the maximal contractility σ a emerges from collective dynamics: we assume a fixed rate of power strokes 1=τ myo (SI Text, S3.9 and Fig. S1), and each of them increases the stress in the network of modulus E, but the competing phenomenon of cross-linker detachment at rate 1=τ α limits the number of power strokes before the network relaxes.…”

A time-dependent phenomenological model for cell mechano-sensing

“…These stalling events may occur for several reasons such as high forces, arrival at barbed ends or blocking due to lack of binding sites. These phenomena and their role in cell mechanosensing were previously explored in (Borau et al 2012). In that work, using a Brownian dynamics computational model, we found that although the cause for motor stalling depends on the extracellular matrix (ECM) compliance, the number of stalled motors and the stalling evolution with time is practically independent of ECM stiffness.…”

“…$$\alpha :false[0,Tfalse]\to R$$ and interpret α ( t ) as the level of motor stalling, that is to say, the ratio of myosin molecules that are stalled, with α =1 meaning that the cell has reached equilibrium (Borau et al 2012). Therefore, this ratio takes on various values corresponding to the range 0 ≤ α ( t ) ≤ 1.…”