Abstract
We use linear stability analysis and numerical solutions of partial differential equations to investigate pattern formation in the one-dimensional system of short dynamic polymers and one (plus-end directed) or two (one is plus-end, another minus-end directed) molecular motors. If polymer sliding and motor gliding rates are slow and/or the polymer turnover rate is fast, then the polymer-motor bundle has mixed polarity and homogeneous motor distribution. However, if motor gliding is fast, a sarcomeric pattern with periodic bands of alternating polymer polarity separated by motor aggregates evolves. On the other hand, if polymer sliding is fast, a graded-polarity bundle with motors at the center emerges. In the presence of the second, minus-end directed motor, the sarcomeric pattern is more ubiquitous, while the graded-polarity pattern is destabilized. However, if the minus-end motor is weaker than the plus-end directed one, and/or polymer nucleation is autocatalytic, and/or long polymers are present in the bundle, then a spindle-like architecture with a sorted-out polarity emerges with the plus-end motors at the center and minus-end motors at the edges. We discuss modeling implications for actin-myosin fibers and in vitro and meiotic spindles.