Department of Biomedical Engineering and Center for Biomolecular Condensates, James McKelvey School of Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA.
Department of Physics, The State University of New York at Buffalo, Buffalo, New York 14260, USA.
J Chem Phys. 2024 Sep 7;161(9). doi: 10.1063/5.0223001.
Biomolecular condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model that leverages information regarding intra- and inter-chain contacts, which we extract from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations of phase separation. The key ingredient of the generalized Rouse model is a graph Laplacian that we compute from equilibrium MMC simulations. We compute two flavors of graph Laplacians, one based on a single-chain graph that accounts only for intra-chain contacts, and the other referred to as a collective graph that accounts for inter-chain interactions. Calculations based on the single-chain graph systematically overestimate the storage and loss moduli, whereas calculations based on the collective graph reproduce the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two graphs proves to be most accurate. In line with the theory of Rouse and contrary to recent assertions, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic vs dominantly viscous behaviors does not imply a single relaxation time. Instead, it is influenced by the totality of the relaxation modes. Hence, our analysis affirms that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain the relaxation time spectra that underlie the dynamics within condensates. This is of practical importance given advancements in passive and active microrheology measurements of condensate viscoelasticity.
生物分子凝聚物是粘弹性材料，其特征在于依赖时间的、序列特异性的复杂剪切模量。在这里，我们表明，可以直接使用扩展的罗瑟模型来计算粘弹性模量，该模型利用了关于链内和链间接触的信息，这些信息是从基于格子的 metropolis 蒙特卡罗（mmc）相分离平衡构型中提取的。广义罗瑟模型的关键要素是图拉普拉斯算子，我们从平衡 mmc 模拟中计算得到。我们计算了两种图拉普拉斯算子，一种基于仅考虑链内接触的单链图，另一种称为集体图，它考虑了链间相互作用。基于单链图的计算系统地高估了储能和损耗模量，而基于集体图的计算则更准确地再现了测量的模量。然而，在长时间、低频域，两种图的混合物被证明是最准确的。与罗瑟理论一致，与最近的断言相反，我们发现凝聚物中存在连续的弛豫时间分布。主要表现为弹性或粘性行为的单交叉频率并不意味着存在单一的弛豫时间。相反，它受到所有松弛模式的影响。因此，我们的分析证实了粘弹性流体状凝聚物最好被描述为广义 maxwell 流体。最后，我们表明，可以使用复剪切模量来解决反问题，以获得凝聚物动力学所依据的弛豫时间谱。考虑到被动和主动微流变学测量凝聚物粘弹性的进展，这一点具有实际意义。
