Bentil D E
Department of Mathematics and Statistics, University of Vermont, Burlington 05401, USA.
Bull Math Biol. 1998 Sep;60(5):973-95. doi: 10.1006/bulm.1998.0055.
Optical trapping is one of the most evolving technologies that measures biophysical quantities and provides insights into some of the fundamental questions in the study of molecular motor proteins such as myosin. Several laboratories have successfully used this technique to observe and score nanometre-size displacements produced by myosin on interacting with actin. We have studied the distribution of attachment events for two myosin molecules with different orientations interacting with an actin filament within the framework of a Langevin-type bidirectional mathematical model. When myosin is detached from actin, our model predicts Brownian displacements centred at 0 +/- 8 nm (mean +/- SD, n = 251,058). When attached, the time-averaged displacements of the actin filament system produced step sizes with peaks of 8 +/- 6 nm (mean +/- SD, n = 22,174) (forward displacements) and -8 +/- 6 nm (mean +/- SD, n = 26,769) (reverse displacements). We infer from our results that the population distribution of attachment events is strongly dependent on (i) the magnitude of the Brownian displacements, (ii) the location of the actin binding sites relative to the myosin molecules, (iii) the orientation of the myosin molecules, and (iv) the relative kinetics (rate constants) for the forward and reverse displacement events.
光镊技术是发展最为迅速的技术之一，它能够测量生物物理量，并为研究诸如肌球蛋白等分子运动蛋白的一些基本问题提供见解。多个实验室已成功运用该技术来观察和记录肌球蛋白与肌动蛋白相互作用时产生的纳米级位移。我们在朗之万型双向数学模型的框架内，研究了两个具有不同取向的肌球蛋白分子与一条肌动蛋白丝相互作用时的附着事件分布。当肌球蛋白与肌动蛋白分离时，我们的模型预测布朗位移以0 +/- 8纳米为中心（平均值 +/- 标准差，n = 251,058）。当附着时，肌动蛋白丝系统的时间平均位移产生的步长峰值为8 +/- 6纳米（平均值 +/- 标准差，n = 22,174）（正向位移）和 -8 +/- 6纳米（平均值 +/- 标准差，n = 26,769）（反向位移）。我们从结果中推断出，附着事件的总体分布强烈依赖于：（i）布朗位移的大小；（ii）肌动蛋白结合位点相对于肌球蛋白分子的位置；（iii）肌球蛋白分子的取向；以及（iv）正向和反向位移事件的相对动力学（速率常数）。
