Kinetics of stress fibers

Stress fibers are contractile cytoskeletal structures, tensile actomyosin bundles which allow sensing and production of force, provide cells with adjustable rigidity and participate in various processes such as wound healing. The stress fiber is possibly the best characterized and most accessible multiprotein cellular contractile machine. Here we develop a quantitative model of the structure and relaxation kinetics of stress fibers. The principal experimentally known features are incorporated. The fiber has a periodic sarcomeric structure similar to muscle fibers with myosin motor proteins exerting contractile force by pulling on actin filaments. In addition the fiber contains the giant spring-like protein titin. Actin is continuously renewed by exchange with the cytosol leading to a turnover time of several minutes. In order that steady state be possible, turnover must be regulated. Our model invokes simple turnover and regulation mechanisms: actin association and dissociation occur at filament ends, while actin filament overlap above a certain threshold in the myosin-containing regions augments depolymerization rates. We use the model to study stress fiber relaxation kinetics after stimulation, as observed in a recent experimental study where some fiber regions were contractile and others expansive. We find that two distinct episodes ensue after stimulation: the turnover-overlap system relaxes rapidly in seconds, followed by the slow relaxation of sarcomere lengths in minutes. For parameter values as they have been characterized experimentally, we find the long time relaxation of sarcomere length is set by the rate at which actin filaments can grow or shrink in response to the forces exerted by the elastic and contractile elements. Consequently, the stress fiber relaxation time scales inversely with both titin spring constant and the intrinsic actin turnover rate. The model's predicted sarcomere velocities and contraction-expansion kinetics are in good quantitative agreement with experiment.