Spreading of molecular mechanical perturbations on linear filaments

Abstract

Global changes in the state of spatially distributed systems can often be traced back to events resulting from local interactions. Whether the results of local interactions grow into global changes, however, depends (i) on the system geometry and (ii) the spatial spreading of the outcomes of local interactions. Here, we investigate how different spreading behaviors of local events determine their global impact in one-dimensional systems of different size. In particular, we combine in vitro experiments where groups of myosin motors propel actin filaments, single-molecule resolution simulations of these in vitro experiments, and an abstracted spin chain model. All three approaches lead to the same two conclusions. First, local events that become long-term stable only after they have spread to full system size have more impact in smaller systems. Second, local events that are relatively stable upon initial occurrence and then spread to full system size have more impact in larger systems. Our work provides highly specific predictions for future experiments that resolve actin-myosin-crosslinker interactions along actin filaments. Also, the conclusions from our work should generally apply to local-to-global spreading in finite, one-dimensional geometries.\n\nSignificance StatementWe address the fundamental question of how results of local interactions spread in one-dimensional systems of different size. To this end, we reconstituted the molecular contractile machinery of muscle, which is organized around linear actin filaments of different length and drives their forward sliding. In addition, we use detailed simulations that follow the mechanically interacting molecules individually. Lastly, we used a more abstract theoretical physics model, which transfers our results to all systems with one-dimensional geometry and local interactions. All three approaches give the same results: local interactions that persist only once they cover the whole system affect smaller systems more strongly; local interactions that are relatively stable even before spreading affect larger systems more strongly.