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Abstract The preponderance of intrinsically disordered proteins (IDPs) in the eukaryotic proteome, and their ability to interact with each other, and with folded proteins, RNA, and DNA for functional purposes, have made it important to quantitatively characterize their biophysical properties. Toward this end, we developed the transferable self‐organized polymer (SOP‐IDP) model to calculate the properties of several IDPs. The values of the radius of gyration () obtained from SOP‐IDP simulations are in excellent agreement (correlation coefficient of 0.96) with those estimated from SAXS experiments. For AP180 and Epsin, the predicted values of the hydrodynamic radii () are in nearly quantitative agreement with those from fluorescence correlation spectroscopy (FCS) experiments. Strikingly, the calculated SAXS profiles for 36 IDPs are also nearly superimposable on the experimental profiles. The dependence of and the mean end‐to‐end distance () on chain length, , follows Flory's scaling law, ( and ), suggesting that globally IDPs behave as synthetic polymers in a good solvent. This finding depends on the solvent quality, which can be altered by changing variables such as pH and salt concentration. The values of and are 0.20 and 0.48 nm, respectively. Surprisingly, finite size corrections to scaling, expected on theoretical grounds, are negligible for and . In contrast, only by accounting for the finite sizes of the IDPs, the dependence of experimentally measurable on can be quantitatively explained using . Although Flory scaling law captures the estimates for , , and accurately, the spread of the simulated data around the theoretical curve is suggestive of of sequence‐specific features that emerge through a fine‐grained analysis of the conformational ensembles using hierarchical clustering. Typically, the ensemble of conformations partitions into three distinct clusters, having different equilibrium populations and structural properties. Without any further readjustments to the parameters of the SOP‐IDP model, we also obtained nearly quantitative agreement with paramagnetic relaxation enhancement (PRE) measurements forα‐synuclein. The transferable SOP‐IDP model sets the stage for several applications, including the study of phase separation in IDPs and interactions with nucleic acids. 

Repeat RNA sequences self-associate to form condensates. Simulations of a coarse-grained single-interaction site model for (CAG)n (n = 30 and 31) show that the salt-dependent free energy gap, ΔGS, between the ground (perfect hairpin) and the excited state (slipped hairpin (SH) with one CAG overhang) of the monomer for (n even) is the primary factor that determines the rates and yield of self-assembly. For odd n, the free energy (GS) of the ground state, which is an SH, is used to predict the self-association kinetics. As the monovalent salt concentration, CS, increases, ΔGS and GS increase, which decreases the rates of dimer formation. In contrast, ΔGS for shuffled sequences, with the same length and sequence composition as (CAG)31, is larger, which suppresses their propensities to aggregate. Although demonstrated explicitly for (CAG) polymers, the finding of inverse correlation between the free energy gap and RNA aggregation is general. 

Abstract Most amino acids are encoded by multiple codons, making the genetic code degenerate. Synonymous mutations affect protein translation and folding, but their impact on RNA itself is often neglected. We developed a genetic algorithm that introduces synonymous mutations to control the diversity of structures sampled by an mRNA. The behavior of the designed mRNAs reveals a physical code layered in the genetic code. We find that mRNA conformational heterogeneity directs physical properties and functional outputs of RNA-protein complexes and biomolecular condensates. The role of structure and disorder of proteins in biomolecular condensates is well appreciated, but we find that RNA conformational heterogeneity is equally important. This feature of RNA enables both evolution and engineers to build cellular structures with specific material and responsive properties. 

Low-complexity nucleotide repeat sequences, which are implicated in several neurological disorders, undergo liquid–liquid phase separation (LLPS) provided the number of repeat units, n , exceeds a critical value. Here, we establish a link between the folding landscapes of the monomers of trinucleotide repeats and their propensity to self-associate. Simulations using a coarse-grained Self-Organized Polymer (SOP) model for (CAG) n repeats in monovalent salt solutions reproduce experimentally measured melting temperatures, which are available only for small n . By extending the simulations to large n , we show that the free-energy gap, ΔG S , between the ground state (GS) and slipped hairpin (SH) states is a predictor of aggregation propensity. The GS for even n is a perfect hairpin (PH), whereas it is a SH when n is odd. The value of ΔG S (zero for odd n ) is larger for even n than for odd n . As a result, the rate of dimer formation is slower in (CAG) 30 relative to (CAG) 31 , thus linking ΔG S to RNA–RNA association. The yield of the dimer decreases dramatically, compared to the wild type, in mutant sequences in which the population of the SH decreases substantially. Association between RNA chains is preceded by a transition to the SH even if the GS is a PH. The finding that the excitation spectrum—which depends on the exact sequence, n , and ionic conditions—is a predictor of self-association should also hold for other RNAs (mRNA for example) that undergo LLPS. 

Super-Kamiokande (SK) has observed ${}^8\mathrm{B}$solar neutrino elastic scattering at recoil electron kinetic energies ( $E_{\mathrm{kin}}$) as low as 3.49 MeV to study neutrino flavor conversion within the Sun. At SK-observable energies, these conversions are dominated by the Mikheyev-Smirnov-Wolfenstein effect. An upturn in the electron neutrino survival probability in which vacuum neutrino oscillations become dominant is predicted to occur at lower energies, but radioactive background increases exponentially with decreasing energy. New machine learning approaches provide substantial background reduction below 3.49 MeV such that statistical extraction of solar neutrino interactions becomes feasible. This article presents an analysis of the solar neutrino interaction rate at $E_{\mathrm{kin}}<3.49\mathrm{MeV}$with the full SK-IV period, using data from a wideband intelligent trigger when available and with a boosted decision tree for event selection. A solar neutrino signal is observed between $2.99\mathrm{MeV}<E_{\mathrm{kin}}<3.49\mathrm{MeV}$with $2.76\sigma$significance and a data to unoscillated Monte Carlo ratio of ${0.307}_{-0.111}^{+0.112}$. These additional low-energy data have a negligible effect on the $1\sigma$intervals of the fits to the solar neutrino energy spectrum but have a noticeable effect on the best fit when using the exponential parametrization. 

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.