Time-dependent material properties of ageing biomolecular condensates from different viscoelasticity measurements in molecular dynamics simulations

Biomolecular condensates are important contributors to the internal organization of the cell material. While initially described as liquid-like droplets, the term biomolecular condensates is now used to describe a diversity of condensed phase assemblies with material properties extending from low to high viscous liquids, gels, and even glasses. Because the material properties of condensates are determined by the intrinsic behaviour of their molecules, characterising such properties is integral to rationalising the molecular mechanisms that dictate their functions and roles in health and disease. Here, we apply and compare three distinct computational methods to measure the viscoelasticity of biomolecular condensates in molecular simulations. These methods are the shear stress relaxation modulus integration (SSRMI), the oscillatory shear (OS) technique, and the bead tracking (BT) method. We find that, although all of these methods provide consistent results for the viscosity of the condensates, the SSRMI and OS techniques outperform the BT method in terms of computational efficiency and statistical uncertainty. We, thus, apply the SSRMI and OS techniques for a set of 12 different protein/RNA systems using a sequence-dependent high-resolution coarse-grained model. Our results reveal a strong correlation between condensate viscosity and density, as well as with protein/RNA length and the number of stickers vs. spacers in the amino-acid protein sequence. Moreover, we couple the SSRMI and the OS technique to nonequilibrium molecular dynamics simulations that mimic the progressive liquid-to-gel transition of protein condensates due to the accumulation of inter-protein {beta}-sheets. We compare the behaviour of three different protein condensates--i.e., those formed by either hnRNPA1, FUS, or TDP-43 proteins--whose liquid-to-gel transitions are associated with the onset of amyotrophic lateral sclerosis and frontotemporal dementia. We find that both SSRMI and OS techniques successfully predict the transition from functional liquid-like behaviour to kinetically arrested states once the network of inter-protein {beta}-sheets has percolated through the condensates. Overall, our work provides a comparison of different modelling rheological techniques to assess the viscosity of biomolecular condensates, a critical magnitude that provides information on the behaviour of biomolecules inside condensates.