We investigate the Brownian dynamics of a nanoparticle bound to a thermally undulating elastic membrane. The ligand-functionalized nanoparticle is assumed to interact monovalently with the receptor expressed on the membrane. In order to resolve the nanoparticle transient motion subject to the instantaneous membrane configuration in a consistent manner, we employ a set of coupled Langevin equations that simultaneously incorporate the hydrodynamic effects, ligand-receptor binding interaction, intramembrane elastic forces, and thermal fluctuations. We show that the presence of a deformable, elastic fluid membrane not only affects the dynamics of a bound nanoparticle but also alters the effective binding potential felt by the nanoparticle. In contrast to a nanoparticle bound to a flat surface, the oscillatory characteristics of the nanoparticle velocity autocorrelation function are suppressed and transition to an anticorrelated long-time tail. Moreover, the nanoparticle position fluctuation becomes more coherent with that of the membrane binding site, and the width of the distribution of the nanoparticle distance from the membrane decreases with increasing membrane bending rigidity. By introducing a locally harmonic, bistable potential as an effective potential for the ligand-receptor pair, the rate of nanoparticle transitioning between two bound states is facilitated by membrane undulations as a result of stronger positional variations associated with the nanoparticle.

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布朗纳米粒子与热波动膜表面的结合

我们调查绑定到热起伏的弹性膜的纳米粒子的布朗动力学。假定配体官能化的纳米颗粒与膜上表达的受体单价相互作用。为了以一致的方式解析受瞬时膜构型影响的纳米粒子瞬态运动，我们采用了一组耦合的Langevin方程，该方程同时包含了流体动力学效应，配体-受体结合相互作用，膜内弹性力和热波动。我们表明可变形的弹性流体膜的存在不仅影响结合的纳米颗粒的动力学，而且改变了纳米颗粒感受到的有效结合电位。与结合在平面上的纳米颗粒相反，纳米粒子速度自相关函数的振荡特性被抑制并转变为反相关的长时间尾巴。此外，纳米颗粒位置的波动变得与膜结合位点的波动更加一致，并且纳米颗粒到膜的距离的分布宽度随着膜弯曲刚度的增加而减小。通过引入局部谐波，双稳态电势作为配体-受体对的有效电势，由于与纳米颗粒相关的更强的位置变化，膜起伏促进了纳米颗粒在两个结合状态之间的转变速率。纳米颗粒位置的波动变得与膜结合部位的波动更加一致，并且纳米颗粒到膜的距离的分布宽度随着膜弯曲刚度的增加而减小。通过引入局部谐波，双稳态电势作为配体-受体对的有效电势，由于与纳米颗粒相关的更强的位置变化，膜起伏促进了纳米颗粒在两个结合状态之间的转变速率。纳米粒子位置的波动变得与膜结合部位的波动更加一致，并且纳米粒子到膜的距离的分布宽度随着膜弯曲刚度的增加而减小。通过引入局部谐波，双稳态电势作为配体-受体对的有效电势，由于与纳米颗粒相关的更强的位置变化，膜起伏促进了纳米颗粒在两个结合状态之间的转变速率。