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.

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.

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.

Gold nanocrystal labels provide a sequence-to-3D structure map in SAXS reconstructions.

Small-angle x-ray scattering (SAXS) is a powerful technique to probe the structure of biological macromolecules and their complexes under virtually arbitrary solution conditions, without the need for crystallization. While it is possible to reconstruct molecular shapes from SAXS data ab initio, the resulting electron density maps have a resolution of ~1 nm and are often insufficient to reliably assign secondary structure elements or domains. We show that SAXS data of gold-labeled samples significantly enhance the information content of SAXS measurements, allowing the unambiguous assignment of macromolecular sequence motifs to specific locations within a SAXS structure. We first demonstrate our approach for site-specifically internally and end-labeled DNA and an RNA motif. In addition, we present a protocol for highly uniform and site-specific labeling of proteins with small (~1.4 nm diameter) gold particles and apply our method to the signaling protein calmodulin. In all cases, the position of the small gold probes can be reliably identified in low-resolution electron density maps. Enhancing low-resolution measurements by site-selective gold labeling provides an attractive approach to aid modeling of a large range of macromolecular systems.

Angular correlations of photons from solution diffraction at a free-electron laser encode molecular structure.

During X-ray exposure of a molecular solution, photons scattered from the same molecule are correlated. If molecular motion is insignificant during exposure, then differences in momentum transfer between correlated photons are direct measurements of the molecular structure. In conventional small- and wide-angle solution scattering, photon correlations are ignored. This report presents advances in a new biomolecular structural analysis technique, correlated X-ray scattering (CXS), which uses angular intensity correlations to recover hidden structural details from molecules in solution. Due to its intense rapid pulses, an X-ray free electron laser (XFEL) is an excellent tool for CXS experiments. A protocol is outlined for analysis of a CXS data set comprising a total of half a million X-ray exposures of solutions of small gold nanoparticles recorded at the Spring-8 Ångström Compact XFEL facility (SACLA). From the scattered intensities and their correlations, two populations of nanoparticle domains within the solution are distinguished: small twinned, and large probably non-twinned domains. It is shown analytically how, in a solution measurement, twinning information is only accessible via intensity correlations, demonstrating how CXS reveals atomic-level information from a disordered solution of like molecules.

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.

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.

Observation of correlated X-ray scattering at atomic resolution.

Tools to study disordered systems with local structural order, such as proteins in solution, remain limited. Such understanding is essential for e.g. rational drug design. Correlated X-ray scattering (CXS) has recently attracted new interest as a way to leverage next-generation light sources to study such disordered matter. The CXS experiment measures angular correlations of the intensity caused by the scattering of X-rays from an ensemble of identical particles, with disordered orientation and position. Averaging over 15 496 snapshot images obtained by exposing a sample of silver nanoparticles in solution to a micro-focused synchrotron radiation beam, we report on experimental efforts to obtain CXS signal from an ensemble in three dimensions. A correlation function was measured at wide angles corresponding to atomic resolution that matches theoretical predictions. These preliminary results suggest that other CXS experiments on disordered ensembles--such as proteins in solution--may be feasible in the future.

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.

Dependence of micelle size and shape on detergent alkyl chain length and head group.

Micelle-forming detergents provide an amphipathic environment that can mimic lipid bilayers and are important tools for solubilizing membrane proteins for functional and structural investigations in vitro. However, the formation of a soluble protein-detergent complex (PDC) currently relies on empirical screening of detergents, and a stable and functional PDC is often not obtained. To provide a foundation for systematic comparisons between the properties of the detergent micelle and the resulting PDC, a comprehensive set of detergents commonly used for membrane protein studies are systematically investigated. Using small-angle X-ray scattering (SAXS), micelle shapes and sizes are determined for phosphocholines with 10, 12, and 14 alkyl carbons, glucosides with 8, 9, and 10 alkyl carbons, maltosides with 8, 10, and 12 alkyl carbons, and lysophosphatidyl glycerols with 14 and 16 alkyl carbons. The SAXS profiles are well described by two-component ellipsoid models, with an electron rich outer shell corresponding to the detergent head groups and a less electron dense hydrophobic core composed of the alkyl chains. The minor axis of the elliptical micelle core from these models is constrained by the length of the alkyl chain, and increases by 1.2-1.5 Šper carbon addition to the alkyl chain. The major elliptical axis also increases with chain length; however, the ellipticity remains approximately constant for each detergent series. In addition, the aggregation number of these detergents increases by ∼16 monomers per micelle for each alkyl carbon added. The data provide a comprehensive view of the determinants of micelle shape and size and provide a baseline for correlating micelle properties with protein-detergent interactions.

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.

Salt dependence of the radius of gyration and flexibility of single-stranded DNA in solution probed by small-angle x-ray scattering.

Short single-stranded nucleic acids are ubiquitous in biological processes; understanding their physical properties provides insights to nucleic acid folding and dynamics. We used small-angle x-ray scattering to study 8-100 residue homopolymeric single-stranded DNAs in solution, without external forces or labeling probes. Poly-T's structural ensemble changes with increasing ionic strength in a manner consistent with a polyelectrolyte persistence length theory that accounts for molecular flexibility. For any number of residues, poly-A is consistently more elongated than poly-T, likely due to the tendency of A residues to form stronger base-stacking interactions than T residues.

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.

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).

ATP-independent reversal of a membrane protein aggregate by a chloroplast SRP subunit.

Membrane proteins impose enormous challenges to cellular protein homeostasis during their post-translational targeting, and they require chaperones to keep them soluble and translocation competent. Here we show that a novel targeting factor in the chloroplast signal recognition particle (cpSRP), cpSRP43, is a highly specific molecular chaperone that efficiently reverses the aggregation of its substrate proteins. In contrast to 'ATPases associated with various cellular activities' (AAA(+)) chaperones, cpSRP43 uses specific binding interactions with its substrate to mediate its 'disaggregase' activity. This disaggregase capability can allow targeting machineries to more effectively capture their protein substrates and emphasizes a close connection between protein folding and trafficking processes. Moreover, cpSRP43 provides the first example to our knowledge of an ATP-independent disaggregase and shows that efficient reversal of protein aggregation can be attained by specific binding interactions between a chaperone and its substrate.

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.

The ligand-free state of the TPP riboswitch: a partially folded RNA structure.

Riboswitches are elements of mRNA that regulate gene expression by undergoing structural changes upon binding of small ligands. Although the structures of several riboswitches have been solved with their ligands bound, the ligand-free states of only a few riboswitches have been characterized. The ligand-free state is as important for the functionality of the riboswitch as the ligand-bound form, but the ligand-free state is often a partially folded structure of the RNA, with conformational heterogeneity that makes it particularly challenging to study. Here, we present models of the ligand-free state of a thiamine pyrophosphate riboswitch that are derived from a combination of complementary experimental and computational modeling approaches. We obtain a global picture of the molecule using small-angle X-ray scattering data and use an RNA structure modeling software, MC-Sym, to fit local structural details to these data on an atomic scale. We have used two different approaches to obtaining these models. Our first approach develops a model of the RNA from the structures of its constituent junction fragments in isolation. The second approach treats the RNA as a single entity, without bias from the structure of its individual constituents. We find that both approaches give similar models for the ligand-free form, but the ligand-bound models differ for the two approaches, and only the models from the second approach agree with the ligand-bound structure known previously from X-ray crystallography. Our models provide a picture of the conformational changes that may occur in the riboswitch upon binding of its ligand. Our results also demonstrate the power of combining experimental small-angle X-ray scattering data with theoretical structure prediction tools in the determination of RNA structures beyond riboswitches.