Pulsatile contractions and pattern formation in excitable actomyosin cortex

Abstract

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulate stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.

Size-dependent transition from steady contraction to waves in actomyosin networks with turnover

“…While in some cases, the function of the pulsatile dynamics is unclear, in other cases the pulsatile dynamics are essential, enabling large-scale force generation while maintaining tissue integrity 8,9 , and facilitating cellular functions such as active transport and motility 6 . Typically, these periodic or aperiodic waves emerge from complex nonlinear reactions in coupled mechano-chemical systems, involving regulators of the actomyosin machinery such as Rho GTPases 10,11,36,39,40 . Our work shows that waves can also emerge in essentially mechanical systems, with turnover but without complex biochemical regulation.…”

Pulsatory patterns in active viscoelastic fluids with distinct relaxation time scales

“…When we substitute this into equation (15), the eigenvalue λ can be calculated. Before doing so however, we first distinguish two cases: (i) equal relaxation times τ B = τ S and (ii) unequal relaxation times τ B ̸ = τ S .…”

“…The dominant eigenvalue corresponds to the mode with k 2 = 4π 2 /L 2 . For the second case with τ B ̸ = τ S , substituting equation (19) into equation (15) results in a quadratic equation for the eigenvalues. We will write this as αλ 2 + βλ + γ = 0, with the coefficients α, β, γ defined as…”

“…In particular, previous studies showed that pulsatile oscillatory time dynamics is an important feature of many morphogenetic processes [11][12][13]. Theoretical models could reproduce pulsatile patterns in active gels; one prevalent mechanism for the generation of oscillatory solutions was the incorporation of at least two molecular regulators in the model that either generate time-dynamic patterns through a Turing-like reaction-diffusion-based mechanism [14,15], through asymmetries in the regulators' influence on the active stress [16] or through distinct stress-dependent unbinding rates of both regulators [17]. Further, oscillatory time-dynamics was generated in active gels with one or no molecular regulator species by (i) combining active hydrodynamics with the dynamics of a polarisation vector field [18,19], by (ii) coupling a viscoelastic active surface with a surrounding viscous fluid [20] or by (iii) conveying the active gel with material properties of viscoelastic solids [21].…”

Pulsatory patterns in active viscoelastic fluids with distinct relaxation time scales

“…In particular, previous studies showed that pulsatile oscillatory time dynamics is an important feature of many morphogenetic processes [11,12,13]. Theoretical models could reproduce pulsatile patterns in active gels by i) incorporating at least two molecular species and nonlinearities in their mechanochemical regulation [14,15,16], or by ii) combining active hydrodynamics with the dynamics of a polarization vector field [17,18], by iii) coupling an axisymmetric viscoelastic active surface with a surrounding highly viscous fluid [19].…”