The Dynamics of Unfolded versus Folded tRNA: The Role of Electrostatic Interactions

Multivalent ions and biomolecules: Attempting a comprehensive perspective

Ions are ubiquitous in nature. They play a key role for many biological processes on the molecular scale, from molecular interactions, to mechanical properties, to folding, to self-organisation and assembly, to reaction equilibria, to signalling, to energy and material transport, to recognition etc. Going beyond monovalent ions to multivalent ions, the effects of the ions are frequently not only stronger (due to the obviously higher charge), but qualitatively different. A typical example is the process of binding of multivalent ions, such as Ca2+ , to a macromolecule and the consequences of this ion binding such as compaction, collapse, potential charge inversion and precipitation of the macromolecule. Here we review these effects and phenomena induced by multivalent ions for biological (macro)molecules, from the "atomistic/molecular" local picture of (potentially specific) interactions to the more global picture of phase behaviour including, e. g., crystallisation, phase separation, oligomerisation etc. Rather than attempting an encyclopedic list of systems, we rather aim for an embracing discussion using typical case studies. We try to cover predominantly three main classes: proteins, nucleic acids, and amphiphilic molecules including interface effects. We do not cover in detail, but make some comparisons to, ion channels, colloidal systems, and synthetic polymers. While there are obvious differences in the behaviour of, and the relevance of multivalent ions for, the three main classes of systems, we also point out analogies. Our attempt of a comprehensive discussion is guided by the idea that there are not only important differences and specific phenomena with regard to the effects of multivalent ions on the main systems, but also important similarities. We hope to bridge physico-chemical mechanisms, concepts of soft matter, and biological observations and connect the different communities further.

Polyelectrolyte association and solvation

There has been significant interest in the tendency of highly charged particles having the same charge to form dynamic clusters in solution, but an accepted theoretical framework that can account for this ubiquitous phenomenon has been slow to develop. The theoretical difficulties are especially great for flexible polyelectrolytes due to the additional complex coupling between the polyelectrolyte chain configurations and the spatial distribution of the ionic species in solution. For highly charged polyelectrolytes, this leads to the formation of a diffuse "polarizable" cloud of counter-ions around these polymers, an effect having significant implications for the function of proteins and other natural occurring polyelectrolytes, as emphasized long ago by Kirkwood and co-workers. To investigate this phenomenon, we perform molecular dynamics simulations of a minimal model of polyelectrolyte solutions that includes an explicit solvent and counter-ions, where the relative affinity of the counter-ions and the polymer for the solvent is tunable through the variation of the relative strength of the dispersion interactions of the polymer and ions. In particular, we find that these dispersion interactions can greatly influence the nature of the association between the polyelectrolyte chains under salt-free conditions. We calculate static and dynamic correlation functions to quantify the equilibrium structure and dynamics of these complex liquids. Based on our coarse-grained model of polyelectrolyte solutions, we identify conditions in which three distinct types of polyelectrolyte association arise. We rationalize these types of polyelectrolyte association based on the impact of the selective solvent affinity on the charge distribution and polymer solvation in these solutions. Our findings demonstrate the essential role of the solvent in the description of the polyelectrolyte solutions, as well as providing a guideline for the development of a more predictive theory of the properties of the thermodynamic and transport properties of these complex fluids.

RNA as a Complex Polymer with Coupled Dynamics of Ions and Water in the Outer Solvation Sphere

We unravel the internal and collective modes of a widely studied 58-nucleotide rRNA fragment in solvent using atomically detailed molecular dynamics simulations. The variation of lifetimes for water hydrogen bonds with nucleotide groups indicates heterogeneity of water dynamics on the RNA surface. The time scales of interactions of the discrete water molecules with RNA nucleotides extend from several hundred picoseconds to a few nanoseconds. We determine all of the association sites and the spatial distribution of residence times for Mg²⁺, K⁺, and water molecules in those sites. We provide insights into the population of Mg²⁺ and K⁺ ions and water molecules in the outer sphere and how their fluctuations are intricately linked with the kinetics of the 58-mer. We find that many of the long-lived Mg²⁺ sites identified from the simulations agree with the locations of ions in the X-ray structure. We determine the excess ion atmosphere around the rRNA and compare it with experimental data. We investigate the collective behavior of RNA, ions, and water, by performing a joint principle component analysis for the Cartesian coordinates of the RNA phosphorus atoms and for the occupation counts of the association sites. Our results indicate that the 58-mer system is a complex polymer, composed of RNA that is encased by a fluctuating network of associated counterions, co-ions, and water.

Entropic stabilization of folded RNA in crowded solutions measured by SAXS

Non-coding RNAs must fold into specific structures that are stabilized by metal ions and other co-solutes in the cell's interior. Large crowder molecules such as PEG stabilize a bacterial group I ribozyme so that the RNA folds in low Mg²⁺ concentrations typical of the cell's interior. To understand the thermodynamic origins of stabilization by crowder molecules, small angle X-ray scattering was used to measure the folding and helix assembly of a bacterial group I ribozyme at different temperatures and in different MgCl₂ and polyethylene glycol (PEG) concentrations. The resulting phase diagrams show that perturbations to folding by each variable do not overlap. A favorable enthalpy change drives the formation of compact, native-like structures, but requires Mg²⁺ ions at all temperatures studied (5–55°C). PEG reduces the entropic cost of helix assembly and increases correlations between RNA segments at all temperatures. The phase diagrams also revealed a semi-compact intermediate between the unfolded and folded ensemble that is locally more flexible than the unfolded state, as judged by SHAPE modification. These results suggest that environmental variables such as temperature and solute density will favor different types of RNA structures.

Charge screening in RNA: an integral route for dynamical enhancements

Electrostatic interactions of RNA are at the center of determining the dynamical flexibility and structural stability. By analysing neutron scattering spectroscopy, we show that fast dynamics of hydrated tRNA on ps to ns timescales increases with stronger charge screening, while its structural stability either increases or remains largely unchanged. An unprecedented electrostatic threshold for the onset of additional flexibility is induced from the correlation between the charge-screening density of counterions and the promoted dynamical properties. The results demonstrate that the enhanced dynamical flexibility of tRNA originates from local conformational relaxation coupled with stabilized charge screening rather than governed by fluctuation of hydrated counterions. The present study casts light on the specificity of electrostatic interactions in the thermodynamic balance between the dynamical flexibility and structural stability of RNA.

Dynamics and rigidity in an intrinsically disordered protein, β-casein

The emergence of intrinsically disordered proteins (IDPs) as a recognized structural class has forced the community to confront a new paradigm of structure, dynamics, and mechanical properties for proteins. We present novel data on the similarities and differences in the dynamics and nanomechanical properties of IDPs and other biomacromolecules on the picosecond time scale. An IDP, β-casein (CAS), has been studied in a calcium bound and unbound state using neutron and light scattering techniques. We show that CAS partially folds and stiffens upon calcium binding, but in the unfolded state, it is softer than folded proteins such as green fluorescence protein (GFP). We also see that some localized diffusive motions in CAS have a larger amplitude than in GFP at this time scale but are still smaller than those observed in tRNA. In spite of these differences, CAS dynamics are consistent with the classes of motions seen in folded protein on this time scale.

Influence of Sequence and Covalent Modifications on Yeast tRNA Dynamics

Modified nucleotides are prevalent in tRNA. Experimental studies reveal that these covalent modifications play an important role in tuning tRNA function. In this study, molecular dynamics (MD) simulations were used to investigate how modifications alter tRNA dynamics. The X-ray crystal structures of tRNA(Asp), tRNA(Phe), and tRNA(iMet), both with and without modifications, were used as initial structures for 333 ns explicit solvent MD simulations with AMBER. For each tRNA molecule, three independent trajectory calculations were performed, giving an aggregate of 6 μs of total MD across six molecules. The global root-mean-square deviations (RMSD) of atomic positions show that modifications only introduce significant rigidity to the global structure of tRNA(Phe). Interestingly, RMSDs of the anticodon stem-loop (ASL) suggest that modified tRNA has a more rigid structure compared to the unmodified tRNA in this domain. The anticodon RMSDs of the modified tRNAs, however, are higher than those of corresponding unmodified tRNAs. These findings suggest that the rigidity of the anticodon stem-loop is finely tuned by modifications, where rigidity in the anticodon arm is essential for tRNA translocation in the ribosome, and flexibility of the anticodon is important for codon recognition. Sugar pucker and water residence time of pseudouridines in modified tRNAs and corresponding uridines in unmodified tRNAs were assessed, and the results reinforce that pseudouridine favors the 3′-endo conformation and has a higher tendency to interact with water. Principal component analysis (PCA) was used to examine correlated motions in tRNA. Additionally, covariance overlaps of PCAs were compared for trajectories of the same molecule and between trajectories of modified and unmodified tRNAs. The comparison suggests that modifications alter the correlated motions. For the anticodon bases, the extent of stacking was compared between modified and unmodified molecules, and only unmodified tRNA(Asp) has significantly higher percentage of stacking time. Overall, the simulations reveal that the effect of covalent modification on tRNA dynamics is not simple, with modifications increasing flexibility in some regions of the structure and increasing rigidity in other regions.

Advances in the determination of nucleic acid conformational ensembles

Conformational changes in nucleic acids play a key role in the way genetic information is stored, transferred, and processed in living cells. Here, we describe new approaches that employ a broad range of experimental data, including NMR-derived chemical shifts and residual dipolar couplings, small-angle X-ray scattering, and computational approaches such as molecular dynamics simulations to determine ensembles of DNA and RNA at atomic resolution. We review the complementary information that can be obtained from diverse sets of data and the various methods that have been developed to combine these data with computational methods to construct ensembles and assess their uncertainty. We conclude by surveying RNA and DNA ensembles determined using these methods, highlighting the unique physical and functional insights obtained so far.

Temperature Dependence of Logarithmic-like Relaxational Dynamics of Hydrated tRNA

The dynamics of RNA within the β-relaxation region of 10 ps to 1 ns is crucial to its biological function. Because of its simpler chemical building blocks and the lack of the side methyl groups, faster relaxational dynamics of RNA compared to proteins can be expected. However, the situation is actually opposite. In this work, the relaxational dynamics of tRNA is measured by quasielastic neutron scattering and analyzed using the mode coupling theory, originally developed for glass-forming liquids. Our results reveal that the dynamics of tRNA follows a log-decay within the β-relaxation region, which is an important trait demonstrated by the dynamics of proteins. The dynamics of hydrated tRNA and lysozyme compared in the time domain further demonstrate that the slower dynamics of tRNA relative to proteins originates from the difference in the folded states of tRNA and proteins, as well as the influence of their hydration water.

Dynamical coupling of intrinsically disordered proteins and their hydration water: comparison with folded soluble and membrane proteins

Hydration water is vital for various macromolecular biological activities, such as specific ligand recognition, enzyme activity, response to receptor binding, and energy transduction. Without hydration water, proteins would not fold correctly and would lack the conformational flexibility that animates their three-dimensional structures. Motions in globular, soluble proteins are thought to be governed to a certain extent by hydration-water dynamics, yet it is not known whether this relationship holds true for other protein classes in general and whether, in turn, the structural nature of a protein also influences water motions. Here, we provide insight into the coupling between hydration-water dynamics and atomic motions in intrinsically disordered proteins (IDP), a largely unexplored class of proteins that, in contrast to folded proteins, lack a well-defined three-dimensional structure. We investigated the human IDP tau, which is involved in the pathogenic processes accompanying Alzheimer disease. Combining neutron scattering and protein perdeuteration, we found similar atomic mean-square displacements over a large temperature range for the tau protein and its hydration water, indicating intimate coupling between them. This is in contrast to the behavior of folded proteins of similar molecular weight, such as the globular, soluble maltose-binding protein and the membrane protein bacteriorhodopsin, which display moderate to weak coupling, respectively. The extracted mean square displacements also reveal a greater motional flexibility of IDP compared with globular, folded proteins and more restricted water motions on the IDP surface. The results provide evidence that protein and hydration-water motions mutually affect and shape each other, and that there is a gradient of coupling across different protein classes that may play a functional role in macromolecular activity in a cellular context.

Neutron Scattering Reveals Enhanced Protein Dynamics in Concanavalin A Amyloid Fibrils

Protein aggregation is one of the most challenging topics in life sciences, and it is implicated in several human pathologies. The nature and the role of toxic species is highly debated, with amyloid fibrils being among the most relevant species for their peculiar structural and functional properties. Protein dynamics and in particular the ability to fluctuate through a large number of conformational substates are closely related to protein function. This Letter focuses on amyloid fibril dynamics, and, to our knowledge, it is the first neutron scattering study on a protein (Concanavalin A) isolated in its fibril state. Our results reveal enhanced atomic fluctuations in amyloid fibrils and indicate that the protein is "softer" in the fibril state with respect to the native and amorphous aggregate states. We discuss this finding in terms of a structural interpretation and suggest that the paradigm ordered structure ↔ lower flexibility can be questioned when considering the local fast side-chain protein dynamics.