Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.
Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 8499000, Israel.
J Chem Phys. 2021 Apr 14;154(14):144901. doi: 10.1063/5.0045278.
The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.
在黏弹性材料中追踪粒子扩散的基础物理是一个有争议的话题。这类材料的机械响应中的长期记忆会导致具有记忆核的扩散运动，如分数布朗运动（fBM）。这就是微流变学能够提供聚合物网络剪切模量的原因。令人惊讶的是，在纯化蛋白质肌动蛋白的网络中，追踪粒子的扩散被发现符合连续时间随机行走类型（CTRW）。我们通过使用两种不同的示踪粒子尺寸，在不同网格尺寸的肌动蛋白网络中研究示踪粒子扩散，旨在解决这一差异。我们发现，示踪粒子尺寸与生物聚合物网络特征长度尺度的比值在确定其扩散类型方面起着关键作用。我们发现，当粒子比网格尺寸大时，示踪粒子的扩散具有 fBM 的特征，当粒子比网格尺寸小时，具有正常扩散的特征，而在这两个极限之间则具有 CTRW 的特征。基于我们的发现，我们提出并通过数值验证了一种新的示踪粒子在所有状态下运动的模型。我们的模型表明，肌动蛋白网络中的扩散由追踪粒子的 fBM 与具有幂律分布逃逸时间的笼式事件耦合而成。
