Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, USA.
Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, USA.
Prog Biophys Mol Biol. 2019 Jul;144:102-115. doi: 10.1016/j.pbiomolbio.2018.07.015. Epub 2018 Aug 23.
The dynamic oscillations of tropomyosin molecules in the azimuthal direction over the surface of the actin filament during thin filament activation are studied here from an energy landscape perspective. A mathematical model based on principles from nonlinear dynamics and chaos theory is derived to describe these dynamical motions. In particular, an energy potential with three wells is proposed to govern the tropomyosin oscillations between the observed regulatory positions observed during muscle contraction, namely the blocked "B", closed "C" and open "M" states. Based on the variations in both the frequency and amplitude of the environmental (surrounding the thin filament system) driving tractions, such as the electrostatic, hydrophobic, and Ca-dependent forces, the tropomyosin movements are shown to be complex; they can change from being simple harmonic oscillations to being fully chaotic. Three cases (periodic, period-2, and chaotic patterns) are presented to showcase the different possible dynamic responses of tropomyosin sliding over the actin filament. A probability density function is used as a statistical measure to calculate the average residence time spanned out by the tropomyosin molecule when visiting each (B, C, M) equilibrium state. The results were found to depend strongly on the energy landscape profile and its featured barriers, which normally govern the transitions between the B-C-M states during striated muscle activation.
从能量景观的角度研究了薄丝激活过程中肌动蛋白丝表面上原肌球蛋白分子在方位角方向上的动态振动。本文提出了一个基于非线性动力学和混沌理论原理的数学模型来描述这些动力学运动。特别是，提出了一个具有三个势阱的能量势来控制肌球蛋白在观察到的肌肉收缩期间的调节位置之间的振荡，即被阻塞的“B”、关闭的“C”和开放的“M”状态。基于环境（围绕薄丝系统）驱动力的频率和幅度的变化，如静电、疏水性和 Ca 依赖性力，肌球蛋白的运动表现出复杂性；它们可以从简单的谐波振动变为完全混沌。本文展示了三种情况（周期、双周期和混沌模式），以展示肌球蛋白在肌动蛋白丝上滑动的不同可能的动力学响应。概率密度函数用作统计量来计算肌球蛋白分子在访问每个（B、C、M）平衡态时所跨越的平均停留时间。结果发现，这些结果强烈依赖于能量景观的轮廓及其特征势垒，这些势垒通常控制横纹肌激活期间 B-C-M 状态之间的转换。
