Guérin T, Prost J, Joanny J-F
Physicochimie Curie (Institut Curie/CNRS-UMR168/UPMC), Institut Curie, Centre de Recherche, Paris Cedex, France,
Eur Phys J E Soft Matter. 2011 Jun;34(6):60. doi: 10.1140/epje/i2011-11060-5. Epub 2011 Jun 23.
We present a detailed analysis of the dynamical instabilities appearing in two kinetic theories for the collective behavior of molecular motors: the rigid two-state model and the two-state crossbridge (or power-stroke) model with continuous binding sites. We calculate force-velocity relations, discuss their stability, plot a diagram that summarizes the oscillation regimes, identify the location of the Hopf bifurcation with a memory effect, discuss the oscillation frequency and make a link with single-molecule experiments. We show that the instabilities present in these models naturally translate into non-linearities in force-displacement relations, and at linear order give forces that are similar to the delayed stretch activation observed in oscillating muscles. We also find that instabilities can appear for both apparent load-decelerated and load-accelerated detachment rates in a 3-state crossbridge model.
刚性二态模型和具有连续结合位点的二态横桥（或动力冲程）模型。我们计算了力-速度关系，讨论了它们的稳定性，绘制了一个总结振荡区域的图表，确定了具有记忆效应的霍普夫分岔的位置，讨论了振荡频率，并与单分子实验建立了联系。我们表明，这些模型中存在的不稳定性自然地转化为力-位移关系中的非线性，并且在线性阶数上给出的力类似于在振荡肌肉中观察到的延迟拉伸激活。我们还发现，在三态横桥模型中，表观负载减速和负载加速脱离速率都可能出现不稳定性。
