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

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. laments 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.