Band-like Stress Fiber Propagation in a Continuum and Implications for Myosin Contractile Stresses

Abstract

Abstract-Stress fibers are band-like features that form with sarcomere-like actin and myosin arrangement between cell regions, resisting myosin contractility. We consider three aspects of stress fiber formation: (1) they form by cytoskeletal actin-myosin interaction when myosin contractile forces are resisted, (2) they propagate in a band-like manner, and (3) they maintain a level of stress and material continuity with the cytoskeleton. This suggests that any description of myosin force should capture the band-like propagation of stress fibers within the constraints of a continuum model. Recent studies describe myosin force as increasing proportional to the cytoskeletal resistance in that direction, but do not capture the band-like propagation of myosin stresses in a continuum. While the spreading of myosin stresses in continuum models is commonly attributed to the elliptic nature of continuum equations, we show that it comes from an incomplete description of the myosin force. Qualitative observations of cytoskeletal actin-myosin interaction indicate the interaction to be 'zipper-like'; myosin contractile forces get transmitted by bending actin filaments in directions away from that of the cytoskeletal resistance. A simple coarse-grained implementation of the lateral myosin forces that arise from the zippering action reproduces band-like stress propagation within a continuum model for the first time. This model also shows actin packing into the stress channel and its propagation along the edge for square and triangular constrained cells; features not captured earlier. Physically, the lateral contractile forces prevent stress spreading by balancing perpendicular shear forces that arise when stress channels through a continuum. Mathematically, these forces render the continuum stress equation hyperbolic. This paper presents a theoretical argument, based on continuum mechanics principles, that it is the zippering actin-myosin action that allows for band-like stress fiber propagation within a coarse-grained cytoskeletal continuum, and that any visualization of the cytoskeletal stress field should account for lateral contractile forces accompanying the much-acknowledged contractile force along a stress fiber.

Signaling pathways that control cell migration: models and analysis

“…Theoretical work in this area has accelerated recently. Chandran et al invoked a continuum mechanical model to show how actin stress fibers emerge and spread in a band-like manner as a result of forces opposed by F-actin resistance [29]. By formulating a detailed model describing the forces generated in an actin gel as a cell forms multiple points of adhesion, Shemesh et al showed that the lamellipodia/lamella interface might arise as a consequence of high stretching stresses that dissolve the actin gel to create two distinct zones at the cell’s leading edge [30].…”

Numeric reconstruction of 2D cellular actomyosin network from substrate displacement

“…Both aspects can contribute to existing models, which considered isotropic contractions over the cytoplasm (Sen et al, 2009), for example. The contraction model implemented does not incorporate the force perpendicular to the stress fibers proposed by Chandran et al (2009), but it was still able to approximately reproduce experimental results. A refined actomyosin material model could improve this approximation.…”

“…The actomyosin contraction was modeled by Sen et al (2009) as an isotropic initial stress of the elements, Volume 31, Number 4, p. 328-333, 2015 resulting in a homogeneous contraction in all directions. Chandran et al (2009) proposed a simple model for a homogeneous isotropic actomyosin material which captures band-like propagation of stress fibers and relates a perpendicular force along with the known contractile axial force. In the present work, the actomyosin material is considered anisotropic, with the contraction modeled as an initial stress, but defined by an initial strain composed of x and y components according to an angle of contraction θ that varies over the actomyosin domain.…”

On the multiscale modeling of heart valve biomechanics in health and disease

“…This phenomenon is perhaps more relevant at the cell-scale simulations where the time scale of simulations may be of the same order as those of active response of the cells. Active, remodeling models of cell mechanics are at their infancy (Chandran et al 2009;Chandran and Mofrad 2010). Modeling heart valve biomechanics at organ-and tissue-scales has been going through generations of refinement over the past three decades; however, it has only been within the past few years that researchers have begun to identify that the need to incorporate the valve mechanics at the cell-and molecular-scale in order to fully appreciate valve biomechanics.…”