Salt-Dependent Self-Association of Trinucleotide Repeat RNA Sequences.

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.

Odd-even disparity in the population of slipped hairpins in RNA repeat sequences with implications for phase separation.

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, ΔGS, 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 ΔGS (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 ΔGS 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.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins.

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

Universal Nature of Collapsibility in the Context of Protein Folding and Evolution.

Theory and simulations predicted that the sizes of the unfolded states of globular proteins should decrease as the denaturant concentration is reduced from a high to a low value. However, small angle X-ray scattering (SAXS) data were used to assert the opposite, while interpretation of single molecule Förster resonance energy transfer experiments (FRET) supported the theoretical predictions. The disagreement between the two experiments is the SAXS-FRET controversy. By harnessing recent advances in SAXS and FRET experiments and setting these findings in the context of a general theory and simulations, which do not rely on experimental data, we establish that compaction of unfolded states under native conditions is universal. The theory also predicts that proteins rich in ß-sheets are more collapsible than α-helical proteins. Because the extent of compaction is small, experiments have to be accurate and their interpretations should be as model-free as possible. Theory also suggests that collapsibility itself could be a physical restriction on the evolution of foldable sequences, and also provides a physical basis for the origin of multidomain proteins.

Salt Effects on Protein Folding Thermodynamics.

Salts differ in their ability to stabilize protein conformations, thereby affecting the thermodynamics and kinetics of protein folding. We developed a coarse-grained protein model that can predict salt-induced changes in protein properties by using the transfer free-energy data of various chemical groups from water to salt solutions. Using this model and molecular dynamics simulations, we probed the effect of seven different salts on the folding thermodynamics of the DNA binding domain of lac repressor protein ( lac-DBD) and N-terminal domain of ribosomal protein (NTL9). We show that a salt can act as a protein stabilizing or destabilizing agent depending on the protein sequence and folded state topology. The computed thermodynamic properties, especially the m values for various salts, which reveal the relative ability of a salt to stabilize the protein folded state, are in quantitative agreement with the experimentally measured values. The computations show that the degree of protein compaction in the denatured ensemble strongly depends on the salt identity, and for the same variation in salt concentration, the compaction in the protein dimensions varies from ∼4% to ∼30% depending on the salt. The transition-state ensemble (TSE) of lac-DBD is homogeneous and polarized, while the TSE of NTL9 is heterogeneous and diffusive. Salts induce subtle structural changes in the TSE that are in agreement with Hammond's postulate. The barrier to protein folding tends to disappear in the presence of moderate concentrations (∼3-4 m) of strongly stabilizing salts.

Transient intermediates are populated in the folding pathways of single-domain two-state folding protein L.

Small single-domain globular proteins, which are believed to be dominantly two-state folders, played an important role in elucidating various aspects of the protein folding mechanism. However, recent single molecule fluorescence resonance energy transfer experiments [H. Y. Aviram et al. J. Chem. Phys. 148, 123303 (2018)] on a single-domain two-state folding protein L showed evidence for the population of an intermediate state and it was suggested that in this state, a ß-hairpin present near the C-terminal of the native protein state is unfolded. We performed molecular dynamics simulations using a coarse-grained self-organized-polymer model with side chains to study the folding pathways of protein L. In agreement with the experiments, an intermediate is populated in the simulation folding pathways where the C-terminal ß-hairpin detaches from the rest of the protein structure. The lifetime of this intermediate structure increased with the decrease in temperature. In low temperature conditions, we also observed a second intermediate state, which is globular with a significant fraction of the native-like tertiary contacts satisfying the features of a dry molten globule.

Thermodynamics and Kinetics of Single-Chain Monellin Folding with Structural Insights into Specific Collapse in the Denatured State Ensemble.

Proteins, which behave as random coils in high denaturant concentrations undergo collapse transition similar to polymers on denaturant dilution. We study collapse in the denatured ensemble of single-chain monellin (MNEI) using a coarse-grained protein model and molecular dynamics simulations. The model is validated by quantitatively comparing the computed guanidinium chloride and pH-dependent thermodynamic properties of MNEI folding with the experiments. The computed properties such as the fraction of the protein in the folded state and radius of gyration (Rg) as function of [GuHCl] are in good agreement with the experiments. The folded state of MNEI is destabilized with an increase in pH due to the deprotonation of the residues Glu24 and Cys42. On decreasing [GuHCl], the protein in the unfolded ensemble showed specific compaction. The Rg of the protein decreased steadily with [GuHCl] dilution due to increase in the number of native contacts in all the secondary structural elements present in the protein. MNEI folding kinetics is complex with multiple folding pathways and transiently stable intermediates are populated in these pathways. In strong stabilizing conditions, the protein in the unfolded ensemble showed transition to a more compact unfolded state where Rg decreased by ≈17% due to the formation of specific native contacts in the protein. The intermediate populated in the dominant MNEI folding pathway satisfies the structural features of the dry molten globule inferred from experiments.

Folding of Protein L with Implications for Collapse in the Denatured State Ensemble.

A fundamental question in protein folding is whether the coil to globule collapse transition occurs during the initial stages of folding (burst phase) or simultaneously with the protein folding transition. Single molecule fluorescence resonance energy transfer (FRET) and small-angle X-ray scattering (SAXS) experiments disagree on whether Protein L collapse transition occurs during the burst phase of folding. We study Protein L folding using a coarse-grained model and molecular dynamics simulations. The collapse transition in Protein L is found to be concomitant with the folding transition. In the burst phase of folding, we find that FRET experiments overestimate radius of gyration, Rg, of the protein due to the application of Gaussian polymer chain end-to-end distribution to extract Rg from the FRET efficiency. FRET experiments estimate ≈6 Å decrease in Rg when the actual decrease is ≈3 Å on guanidinium chloride denaturant dilution from 7.5 to 1 M, thereby suggesting pronounced compaction in the protein dimensions in the burst phase. The ≈3 Å decrease is close to the statistical uncertainties of the Rg data measured from SAXS experiments, which suggest no compaction, leading to a disagreement with the FRET experiments. The transition-state ensemble (TSE) structures in Protein L folding are globular and extensive in agreement with the Ψ-analysis experiments. The results support the hypothesis that the TSE of single domain proteins depends on protein topology and is not stabilized by local interactions alone.

Parallel versus Off-Pathway Michaelis-Menten Mechanism for Single-Enzyme Kinetics of a Fluctuating Enzyme.

Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of ß-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of ß-galactosidase.