Understanding nucleic acid-ion interactions.

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

Tissue- and development-stage-specific mRNA and heterogeneous CNV signatures of human ribosomal proteins in normal and cancer samples.

We give results from a detailed analysis of human Ribosomal Protein (RP) levels in normal and cancer samples and cell lines from large mRNA, copy number variation and ribosome profiling datasets. After normalizing total RP mRNA levels per sample, we find highly consistent tissue specific RP mRNA signatures in normal and tumor samples. Multiple RP mRNA-subtypes exist in several cancers, with significant survival and genomic differences. Some RP mRNA variations among subtypes correlate with copy number loss of RP genes. In kidney cancer, RP subtypes map to molecular subtypes related to cell-of-origin. Pan-cancer analysis of TCGA data showed widespread single/double copy loss of RP genes, without significantly affecting survival. In several cancer cell lines, CRISPR-Cas9 knockout of RP genes did not affect cell viability. Matched RP ribosome profiling and mRNA data in humans and rodents stratified by tissue and development stage and were strongly correlated, showing that RP translation rates were proportional to mRNA levels. In a small dataset of human adult and fetal tissues, RP protein levels showed development stage and tissue specific heterogeneity of RP levels. Our results suggest that heterogeneous RP levels play a significant functional role in cellular physiology, in both normal and disease states.

Absolute Intramolecular Distance Measurements with Angstrom-Resolution Using Anomalous Small-Angle X-ray Scattering.

Accurate determination of molecular distances is fundamental to understanding the structure, dynamics, and conformational ensembles of biological macromolecules. Here we present a method to determine the full distance distribution between small (∼7 Å radius) gold labels attached to macromolecules with very high-precision (≤1 Å) and on an absolute distance scale. Our method uses anomalous small-angle X-ray scattering close to a gold absorption edge to separate the gold-gold interference pattern from other scattering contributions. Results for 10-30 bp DNA constructs achieve excellent signal-to-noise and are in good agreement with previous results obtained by single-energy SAXS measurements without requiring the preparation and measurement of single labeled and unlabeled samples. The use of small gold labels in combination with ASAXS read out provides an attractive approach to determining molecular distance distributions that will be applicable to a broad range of macromolecular systems.

Caulobacter chromosome in vivo configuration matches model predictions for a supercoiled polymer in a cell-like confinement.

We measured the distance between fluorescent-labeled DNA loci of various interloci contour lengths in Caulobacter crescentus swarmer cells to determine the in vivo configuration of the chromosome. For DNA segments less than about 300 kb, the mean interloci distances, , scale as n(0.22), where n is the contour length, and cell-to-cell distribution of the interloci distance r is a universal function of r/n(0.22) with broad cell-to-cell variability. For DNA segments greater than about 300 kb, the mean interloci distances scale as n, in agreement with previous observations. The 0.22 value of the scaling exponent for short DNA segments is consistent with theoretical predictions for a branched DNA polymer structure. Predictions from Brownian dynamics simulations of the packing of supercoiled DNA polymers in an elongated cell-like confinement are also consistent with a branched DNA structure, and simulated interloci distance distributions predict that confinement leads to "freezing" of the supercoiled configuration. Lateral positions of labeled loci at comparable positions along the length of the cell are strongly correlated when the longitudinal locus positions differ by <0.16 µm. We conclude that the chromosome structure is supercoiled locally and elongated at large length scales and that substantial cell-to-cell variability in the interloci distances indicates that in vivo crowding prevents the chromosome from reaching an equilibrium arrangement. We suggest that the force causing rapid transport of loci remote from the parS centromere to the distal cell pole may arise from the release at the polar region of potential energy within the supercoiled DNA.

Potential for measurement of the distribution of DNA folds in complex environments using Correlated X-ray Scattering.

In vivo chromosomal behavior is dictated by the organization of genomic DNA at length scales ranging from nanometers to microns. At these disparate scales, the DNA conformation is influenced by a range of proteins that package, twist and disentangle the DNA double helix, leading to a complex hierarchical structure that remains undetermined. Thus, there is a critical need for methods of structural characterization of DNA that can accommodate complex environmental conditions over biologically relevant length scales. Based on multiscale molecular simulations, we report on the possibility of measuring supercoiling in complex environments using angular correlations of scattered X-rays resulting from X-ray free electron laser (xFEL) experiments. We recently demonstrated the observation of structural detail for solutions of randomly oriented metallic nanoparticles [D. Mendez et al., Philos. Trans. R. Soc. B360 (2014) 20130315]. Here, we argue, based on simulations, that correlated X-ray scattering (CXS) has the potential for measuring the distribution of DNA folds in complex environments, on the scale of a few persistence lengths.

Tuning micelle dimensions and properties with binary surfactant mixtures.

Detergent micelles are used in many areas of research and technology, in particular, as mimics of the cellular membranes in the purification and biochemical and structural characterization of membrane proteins. Applications of detergent micelles are often hindered by the limited set of properties of commercially available detergents. Mixtures of micelle-forming detergents provide a means to systematically obtain additional micellar properties and expand the repertoire of micelle features available; however, our understanding of the properties of detergent mixtures is still limited. In this study, the shape and size of binary mixtures of seven different detergents commonly used in molecular host-guest systems and membrane protein research were investigated. The data suggests that the detergents form ideally mixed micelles with sizes and shapes different from those of pure individual micelles. For most measurements of size, the mixtures varied linearly with detergent mole fraction and therefore can be calculated from the values of the pure detergents. We propose that properties such as the geometry, size, and surface charge can be systematically and predictably tuned for specific applications.

AquaSAXS: a web server for computation and fitting of SAXS profiles with non-uniformally hydrated atomic models.

Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural biologists and biochemists, thanks to better access to dedicated synchrotron beamlines, better detectors and the relative easiness of sample preparation. The ability to compute the theoretical SAXS profile of a given structural model, and to compare this profile with the measured scattering intensity, yields crucial structural informations about the macromolecule under study and/or its complexes in solution. An important contribution to the profile, besides the macromolecule itself and its solvent-excluded volume, is the excess density due to the hydration layer. AquaSAXS takes advantage of recently developed methods, such as AquaSol, that give the equilibrium solvent density map around macromolecules, to compute an accurate SAXS/WAXS profile of a given structure and to compare it to the experimental one. Here, we describe the interface architecture and capabilities of the AquaSAXS web server (http://lorentz.dynstr.pasteur.fr/aquasaxs.php).

Asymmetry in the peak in Covid-19 daily cases and the pandemic R-parameter.

Within the context of the standard SIR model of pandemics, we show that the asymmetry in the peak in recorded daily cases during a pandemic can be used to infer the pandemic R-parameter. Using only daily data for symptomatic, confirmed cases, we derive a universal scaling curve that yields: (i) reff, the pandemic R-parameter; (ii) Leff, the effective latency, the average number of days an infected individual is able to infect others and (iii) α, the probability of infection per contact between infected and susceptible individuals. We validate our method using an example and then apply it to estimate these parameters for the first phase of the SARS-Cov-2/Covid-19 pandemic for several countries where there was a well separated peak in identified infected daily cases. The extension of the SIR model developed in this paper differentiates itself from earlier studies in that it provides a simple method to make an a-posteriori estimate of several useful epidemiological parameters, using only data on confirmed, identified cases. Our results are general and can be applied to any pandemic.

Electrostatics of nucleic acid folding under conformational constraint.

RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.

Dissecting electrostatic screening, specific ion binding, and ligand binding in an energetic model for glycine riboswitch folding.

Riboswitches are gene-regulating RNAs that are usually found in the 5'-untranslated regions of messenger RNA. As the sugar-phosphate backbone of RNA is highly negatively charged, the folding and ligand-binding interactions of riboswitches are strongly dependent on the presence of cations. Using small angle X-ray scattering (SAXS) and hydroxyl radical footprinting, we examined the cation dependence of the different folding stages of the glycine-binding riboswitch from Vibrio cholerae. We found that the partial folding of the tandem aptamer of this riboswitch in the absence of glycine is supported by all tested mono- and divalent ions, suggesting that this transition is mediated by nonspecific electrostatic screening. Poisson-Boltzmann calculations using SAXS-derived low-resolution structural models allowed us to perform an energetic dissection of this process. The results showed that a model with a constant favorable contribution to folding that is opposed by an unfavorable electrostatic term that varies with ion concentration and valency provides a reasonable quantitative description of the observed folding behavior. Glycine binding, on the other hand, requires specific divalent ions binding based on the observation that Mg(2+), Ca(2+), and Mn(2+) facilitated glycine binding, whereas other divalent cations did not. The results provide a case study of how ion-dependent electrostatic relaxation, specific ion binding, and ligand binding can be coupled to shape the energetic landscape of a riboswitch and can begin to be quantitatively dissected.

Do conformational biases of simple helical junctions influence RNA folding stability and specificity?

Structured RNAs must fold into their native structures and discriminate against a large number of alternative ones, an especially difficult task given the limited information content of RNA's nucleotide alphabet. The simplest motifs within structured RNAs are two helices joined by nonhelical junctions. To uncover the fundamental behavior of these motifs and to elucidate the underlying physical forces and challenges faced by structured RNAs, we computationally and experimentally studied a tethered duplex model system composed of two helices joined by flexible single- or double-stranded polyethylene glycol tethers, whose lengths correspond to those typically observed in junctions from structured RNAs. To dissect the thermodynamic properties of these simple motifs, we computationally probed how junction topology, electrostatics, and tertiary contact location influenced folding stability. Small-angle X-ray scattering was used to assess our predictions. Single- or double-stranded junctions, independent of sequence, greatly reduce the space of allowed helical conformations and influencing the preferred location and orientation of their adjoining helices. A double-stranded junction guides the helices along a hinge-like pathway. In contrast, a single-stranded junction samples a broader set of conformations and has different preferences than the double-stranded junction. In turn, these preferences determine the stability and distinct specificities of tertiary structure formation. These sequence-independent effects suggest that properties as simple as a junction's topology can generally define the accessible conformational space, thereby stabilizing desired structures and assisting in discriminating against misfolded structures. Thus, junction topology provides a fundamental strategy for transcending the limitations imposed by the low information content of RNA primary sequence.

Dynamic charge interactions create surprising rigidity in the ER/K alpha-helical protein motif.

Protein alpha-helices are ubiquitous secondary structural elements, seldom considered to be stable without tertiary contacts. However, amino acid sequences in proteins that are based on alternating repeats of four glutamic acid (E) residues and four positively charged residues, a combination of arginine (R) and lysine (K), have been shown to form stable alpha-helices in a few proteins, in the absence of tertiary interactions. Here, we find that this ER/K motif is more prevalent than previously reported, being represented in proteins of diverse function from archaea to humans. By using molecular dynamics (MD) simulations, we characterize a dynamic pattern of side-chain interactions that extends along the backbone of ER/K alpha-helices. A simplified model predicts that side-chain interactions alone contribute substantial bending rigidity (0.5 pN/nm) to ER/K alpha-helices. Results of small-angle x-ray scattering (SAXS) and single-molecule optical-trap analyses are consistent with the high bending rigidity predicted by our model. Thus, the ER/K alpha-helix is an isolated secondary structural element that can efficiently span long distances in proteins, making it a promising tool in designing synthetic proteins. We propose that the significant rigidity of the ER/K alpha-helix can help regulate protein function, as a force transducer between protein subdomains.

The transmission of SARS-CoV-2 is likely comodulated by temperature and by relative humidity.

Inferring the impact of climate upon the transmission of SARS-CoV-2 has been confounded by variability in testing, unknown disease introduction rates, and changing weather. Here we present a data model that accounts for dynamic testing rates and variations in disease introduction rates. We apply this model to data from Colombia, whose varied and seasonless climate, central port of entry, and swift, centralized response to the COVID-19 pandemic present an opportune environment for assessing the impact of climate factors on the spread of COVID-19. We observe strong attenuation of transmission in climates with sustained daily temperatures above 30 degrees Celsius and simultaneous mean relative humidity below 78%, with outbreaks occurring at high humidity even where the temperature is high. We hypothesize that temperature and relative humidity comodulate the infectivity of SARS-CoV-2 within respiratory droplets.

The complete VS ribozyme in solution studied by small-angle X-ray scattering.

We have used small-angle X-ray solution scattering to obtain ab initio shape reconstructions of the complete VS ribozyme. The ribozyme occupies an electron density envelope with an irregular shape, into which helical sections have been fitted. The ribozyme is built around a core comprising a near-coaxial stack of three helices, organized by two three-way helical junctions. An additional three-way junction formed by an auxiliary helix directs the substrate stem-loop, juxtaposing the cleavage site with an internal loop to create the active complex. This is consistent with the current view of the probable mechanism of trans-esterification in which adenine and guanine nucleobases contributed by the interacting loops combine in general acid-base catalysis.

Redistribution of terbium ions across acetylcholine receptor-enriched membranes induced by agonist desensitization.

Using small-angle x-ray diffraction from centrifugally oriented acetylcholine receptor (AChR) enriched membranes coupled with anomalous scattering from terbium ions (Tb3+) titrated into presumed Ca2+ binding sites, we have mapped the distribution of Tb3+ perpendicular to the membrane plane using a heavy atom refinement algorithm. We have compared the distribution of Tb3+ in the closed resting state with that in the carbamylcholine-desensitized state. In the closed resting state we find 45 Tb3+ ions distributed in 10 narrow peaks perpendicular to the membrane plane. Applying the same refinement procedure to the data from carbamylcholine desensitized AChR we find 18 fewer Tb3+ ions in eight peaks, and slight rearrangements of Tb3+ density in the peaks near the ends of the AChR ion channel pore. These agonist dependent changes in the Tb3+ stoichiometry and distribution suggest a likely role for multivalent cations in stabilizing the different functional states of the AChR, and the changes in the Tb3+ distribution at the two ends of the pore suggest a potential role for multivalent cations in the gating of the ion channel.

Mixing and matching detergents for membrane protein NMR structure determination.

One major obstacle to membrane protein structure determination is the selection of a detergent micelle that mimics the native lipid bilayer. Currently, detergents are selected by exhaustive screening because the effects of protein-detergent interactions on protein structure are poorly understood. In this study, the structure and dynamics of an integral membrane protein in different detergents is investigated by nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopy and small-angle X-ray scattering (SAXS). The results suggest that matching of the micelle dimensions to the protein's hydrophobic surface avoids exchange processes that reduce the completeness of the NMR observations. Based on these dimensions, several mixed micelles were designed that improved the completeness of NMR observations. These findings provide a basis for the rational design of mixed micelles that may advance membrane protein structure determination by NMR.

Riboswitch conformations revealed by small-angle X-ray scattering.

Riboswitches are functional RNA molecules that control gene expression through conformational changes in response to small-molecule ligand binding. In addition, riboswitch 3D structure, like that of other RNA molecules, is dependent on cation-RNA interactions as the RNA backbone is highly negatively charged. Here, we show how small-angle X-ray scattering (SAXS) can be used to probe RNA conformations as a function of ligand and ion concentration. In a recent study of a glycine-binding tandem aptamer from Vibrio cholerae, we have used SAXS data and thermodynamic modeling to investigate how Mg(2+)-dependent folding and glycine binding are energetically coupled. In addition, we have employed ab initio shape reconstruction algorithms to obtain low-resolution models of the riboswitch structure from SAXS data under different solution conditions.

MinActionPath: maximum likelihood trajectory for large-scale structural transitions in a coarse-grained locally harmonic energy landscape.

The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using 'morphing' techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http://lorentz.dynstr.pasteur.fr/joel/index.php.

Critical assessment of nucleic acid electrostatics via experimental and computational investigation of an unfolded state ensemble.

Electrostatic forces, acting between helices and modulated by the presence of the ion atmosphere, are key determinants in the energetic balance that governs RNA folding. Previous studies have employed Poisson-Boltzmann (PB) theory to compute the energetic contribution of these forces in RNA folding. However, the complex interaction of these electrostatic forces with RNA features such as tertiary contact formation, specific ion-binding, and complex interhelical junctions present in prior studies precluded a rigorous evaluation of PB theory, especially in physiologically important Mg(2+) solutions. To critically assess PB theory, we developed a model system that isolates these electrostatic forces. The model system, composed of two DNA duplexes tethered by a polyethylene glycol junction, is an analog for the unfolded state of canonical helix-junction-helix motifs found in virtually all structured RNAs. This model system lacks the complicating features that have precluded a critical assessment of PB in prior studies, ensuring that interhelical electrostatic forces dominate the behavior of the system. The system's simplicity allows PB predictions to be directly compared with small-angle X-ray scattering experiments over a range of monovalent and divalent ion concentrations. These comparisons indicate that PB is a reasonable description of the underlying electrostatic energies for monovalent ions, but large deviations are observed for divalent ions. The validation of PB for monovalent solutions allows analysis of the change in the conformational ensemble of this simple motif as salt concentration is changed. Addition of ions allows the motif to sample more compact microstates, increasing its conformational entropy. The increase of conformational entropy presents an additional barrier to folding by stabilizing the unfolded state. Neglecting this effect will adversely impact the accuracy of folding analyses and models.

Structural transitions and thermodynamics of a glycine-dependent riboswitch from Vibrio cholerae.

Riboswitches are complex folded RNA domains found in noncoding regions of mRNA that regulate gene expression upon small molecule binding. Recently, Breaker and coworkers reported a tandem aptamer riboswitch (VCI-II) that binds glycine cooperatively. Here, we use hydroxyl radical footprinting and small-angle X-ray scattering (SAXS) to study the conformations of this tandem aptamer as a function of Mg(2+) and glycine concentration. We fit a simple three-state thermodynamic model that describes the energetic coupling between magnesium-induced folding and glycine binding. Furthermore, we characterize the structural conformations of each of the three states: In low salt with no magnesium present, the VCI-II construct has an extended overall conformation, presumably representing unfolded structures. Addition of millimolar concentrations of Mg(2+) in the absence of glycine leads to a significant compaction and partial folding as judged by hydroxyl radical protections. In the presence of millimolar Mg(2+) concentrations, the tandem aptamer binds glycine cooperatively. The glycine binding transition involves a further compaction, additional tertiary packing interactions and further uptake of magnesium ions relative to the state in high Mg(2+) but no glycine. Employing density reconstruction algorithms, we obtain low resolution 3-D structures for all three states from the SAXS measurements. These data provide a first glimpse into the structural conformations of the VCI-II aptamer, establish rigorous constraints for further modeling, and provide a framework for future mechanistic studies.