RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion–phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

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Although it is known that RNA undergoes liquid-liquid phase separation (LLPS), the interplay between the molecular driving forces and the emergent features of the condensates, such as their morphologies and dynamical properties, is not well understood. We introduce a coarse-grained model to simulate phase separation of trinucleotide repeat RNAs, which are implicated in neurological disorders such as Huntington disease and amyotrophic lateral sclerosis. After establishing that the simulations reproduce key experimental findings (length and concentration dependence of the phase transition in (CAG) n repeats), we show that once recruited inside the liquid droplets, the monomers transition from hairpin-like structures to extended states. Interactions between the monomers in the condensates result in the formation of an intricate and dense intermolecular network, which severely restrains the fluctuations and mobilities of the RNAs inside large droplets. In the largest densely packed high viscosity droplets, the mobility of RNA chains is best characterized by reptation, reminiscent of the dynamics in polymer melts.

Congestion is the condition of the road in the traffic networks which is characterised as slow speed and long travel time. The detection of unusual traffic patterns including congestions is an significant research problem in the data mining and knowledge discovery community. However, to the best of our knowledge, the discovery of propagation, or causal interactions among detected traffic congestions has not been appropriately investigated before. In this research, we introduce algorithms which construct causality trees based on temporal and spatial information of identified congestions. Frequent substructures of these causality trees reveal not only recurring interactions among spatio-temporal congestions, but potential bottlenecks or flaws in the design of existing traffic networks. Our algorithms are validated by experiments on a large real-time travel time data in an urban road network.