We use perturbation theory to derive a continuum model for the dynamic actomyosin bundle/ring in the regime of very strong crosslinking. Actin treadmilling is essential for contraction. Linear stability analysis and numerical solutions of the model equations reveal that when the actin treadmilling is very slow, actin and myosin aggregate into equidistantly spaced peaks. When treadmilling is significant, actin filament of one polarity are distributed evenly, while filaments of the opposite polarity develop a shock wave moving with the treadmilling velocity. Myosin aggregates into a sharp peak surfing the crest of the actin wave. Any actomyosin aggregation diminishes contractile stress. The easiest way to maintain higher contraction is to upregulate the actomyosin turnover which destabilizes nontrivial patterns and stabilizes the homogeneous actomyosin distributions. We discuss the model’s implications for the experiment.

我们使用摄动理论来推导动态肌动球蛋白束/环在非常强的交联状态下的连续模型。肌动蛋白跑步机是收缩必不可少的。线性稳定性分析和模型方程的数值解表明，当肌动蛋白跑步很慢时，肌动蛋白和肌球蛋白聚集成等距的峰。当进行大量跑步运动时，一种极性的肌动蛋白丝会均匀分布，而另一种极性的肌动蛋白丝会产生随跑步速度移动的冲击波。肌球蛋白聚集在肌动蛋白波峰的尖峰上。任何肌动球蛋白的聚集都会减少收缩压力。维持较高收缩率的最简单方法是上调放线菌素周转，这会破坏非平凡模式并稳定均匀的放线菌素分布。我们讨论了该模型对实验的影响。