Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.

Synopsis Shear rheological data for a wide range of nearly monodisperse linear polyisoprene melts are reported herein using the results of linear and nonlinear measurements. The number of entanglements per chain ranges from about 0.5 to 230. In order to extend the range of available frequencies and shear rates the procedure of time-temperature superposition is improved and validated in both the linear and the nonlinear regime. In the linear flow regime a detailed comparison with the tube theory by Likhtman and McLeish Macromolecules 35, 6332-6343 2002 was performed. The overall agreement was found to be satisfactory but several minor disagreements, e.g., at the crossover regime and for the steady-state compliance, were observed and have been discussed. Until now, most nonlinear models for entangled polymers were compared with shear data on solutions. However, the equivalence between solutions and melts is not well established. In this paper the results of a series of nonlinear start-up shear experiments are compared with those predicted by the tube model Graham et al., J. Rheol. 47, 1117-1200 2003 and with several literature datasets on entangled solutions having similar numbers of entanglements. The melts were found to behave in a very similar manner to the previously studied solutions and agree well with the tube theory. Disagreements are observed when the shear rate exceeds the Rouse time of one entanglement and also for chains with very small number of entanglements. For the high molecular weight samples possible instabilities and edge fracture can occur at high strains and the results are discussed in light of these effects. The extensive dataset presented here could serve as a test for future theories and models of entangled melts. © 2008 The

One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.

Biomolecular condensates, some of which are liquid-like during health, can age over time becoming gel-like pathological systems. One potential source of loss of liquid-like properties during ageing of RNA-binding protein condensates is the progressive formation of inter-proteinβ-sheets. To bridge microscopic understanding between accumulation of inter-proteinβ-sheets over time and the modulation of FUS and hnRNPA1 condensate viscoelasticity, we develop a multiscale simulation approach. Our method integrates atomistic simulations with sequence-dependent coarse-grained modelling of condensates that exhibit accumulation of inter-proteinβ-sheets over time. We reveal that inter-proteinβ-sheets notably increase condensate viscosity but does not transform the phase diagrams. Strikingly, the network of molecular connections within condensates is drastically altered, culminating in gelation when the network of strongβ-sheets fully percolates. However, high concentrations of RNA decelerate the emergence of inter-proteinβ-sheets. Our study uncovers molecular and kinetic factors explaining how the accumulation of inter-proteinβ-sheets can trigger liquid-to-solid transitions in condensates, and suggests a potential mechanism to slow such transitions down.