基于首次穿越的扩散过程理论研究单分子键断裂

Rupture of a Single Molecular Bond Based on the Diffusion Theory of the First Passage

细胞膜内的黏附蛋白与其对应的配体形成的分子键相互作用可用随机动力学系统描述,基于已有的单分子键随机动力学模型及首次穿越的扩散过程理论,建立了单分子键的条件可靠性函数满足的后向Kolmogorov方程及平均首次穿越时间所满足的Pontryagin方程,求解这两个方程可得分子键断裂相关的分子键残存率及分子键解离速率.将该方法应用于考虑外力作用势的分子键模型,由该方法所得的结果与数值模拟的结果吻合很好,与Freund近似公式相比具有能有效研究初始条件对分子键断裂影响的优点,并讨论了外力相关参数及分子键净势能相关参数对分子键断裂的影响,表明该方法的有效性.

The interaction between the molecular bonds formed by membrane receptors and their corresponding ligands can be described by stochastic dynamics. Based on a existing model for the stochastic dynamics of a single molecular bond and the theory of first-passage problem on diffusion process, the backward Kolmogorov equation with respect to the conditional reliability function for rupture of a single molecule bond and the Pontryagin equation with respect to the mean first-passage time were derived. Solving these two equations yielded the bond survival reliability and the rate of bond rupture. The proposed method was applied to a molecular bond under external force. The results are in good agreement with those obtained fxom the numerical simulations. In comparison with the approximate formula by Freund, this method is able to consider the effect of the initial conditions on the bond rupture. In addition, the effects of parameters related to the external force and the bond potential on the rupture of a molecular bond were investigated. The results show the efficiency of the proposed method.