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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.

We aim to measure substantial structural information via X-ray scattering in the absence of an ordered system. Instead of a crystal, which consists of N particles at a single orientation relative to the X-ray beam, our samples consist of N randomly oriented identical particles. Assume, in a given exposure, two (or more) photons scatter from the same particle in a time interval much less than the rotational diffusion time, i.e. while the particle orientation is fixed. These two photons are correlated via the structure of the particle. By time averaging intensity correlations from such measurements, one can hope to recover structural information of the single scatterer relative to the background of N randomly oriented scatterers. One can demonstrate the high-dimensional data obtained from such a correlation experiment exceeds that measured in small and wide angle X-ray scattering measurements.We have performed measurements on gold nanoparticle solutions at the Linac Coherent Light Source (LCLS) and are using them to identify and overcome the challenges involved in CXS experiments. Imperfections in detector geometry and electronic response can contribute to false correlations in the data; we are developing ways of identifying and removing these artifacts. We are simultaneously gauging our ability to recover protein secondary structural information from such data. Nanoparticle scattering will serve as a benchmark for an upcoming experiment at the Spring-8 Angstrom Compact free electron laser (SACLA), where we will attempt to measure correlated scattering from F-actin. Thereafter we hope to refine current models of the F-actin polymer by fitting them against our high dimensional data.

Polyelectrolytes, or charged polymers, are prevalent in biological systems, yet their physical properties are far less well understood than those of neutral polymers. We report on measurements using small angle x-ray scattering to study bulk ensemble-averaged properties of small (up to 100 bases) poly-deoxythymine (poly-dT) and poly-deoxyadenine (poly-dA) molecules. By studying homomeric single stranded DNA (ssDNA), we can observe their polymeric properties without interference from secondary structure formation. This gives us insight to the conformational space explored by single stranded nucleic acids in folding processes, and the nucleotide dependence of loop flexibility of DNA and RNA junctions. We observe, as is consistent with base-stacking of purines, that poly-dA is stiffer than poly-dT. For poly-dT, the radius of gyration (Rg) scales with the number of monomers with a Flory exponent (ν) which decreases slowly with increasing salt, but drops sharply below that expected for a self-avoiding random walk (SAW) polymer (ν ∼ 0.588) with more than 500 mM of added sodium acetate. This is perhaps due to the condensation of charges around the DNA and/or the change in solvent quality with added salt. The ratio (r) of the square of the maximum pair-wise distance (Dmax) to Rg fluctuates around 10, suggesting that ssDNA compacts locally. Assuming that Dmax is a fair estimate of the end-to-end distance of the polymer, a value of 12 is expected for r in the case of a rod, and about 6.3 for a SAW polymer. This localized clustering is consistent with the electrostatic blob model of de Gennes et al. The persistence length of poly-dT - determined by fitting the data to a worm-like chain model - increases in a sublinear fashion with increasing Debye screening length, unlike the behaviors predicted by polyelectrolyte theories.

Poisson-Boltzmann (PB) theory is among the most widely applied electrostatic theories in biological and chemical science. Despite its reasonable success in explaining a wide variety of phenomena, it fails to incorporate two basic physical effects, ion size and ion-ion correlations, into its theoretical treatment. Recent experimental work has shown significant deviations from PB theory in competitive monovalent and divalent ion binding to a DNA duplex. The experimental data for monovalent binding are consistent with a hypothesis that attributes these deviations to counterion size. To model the observed differences, we have generalized an existing size-modified Poisson-Boltzmann (SMPB) theory and developed a new numerical implementation that solves the generalized theory around complex, atomistic representations of biological molecules. The results of our analysis show that good agreement to data at monovalent ion concentrations up to approximately 150 mM can be attained by adjusting the ion-size parameters in the new size-modified theory. SMPB calculations employing calibrated ion-size parameters predict experimental observations for other nucleic acid structures and salt conditions, demonstrating that the theory is predictive. We are, however, unable to model the observed deviations in the divalent competition data with a theory that only accounts for size but neglects ion-ion correlations, highlighting the need for theoretical descriptions that further incorporate ion-ion correlations. The accompanying numerical solver has been released publicly, providing the general scientific community the ability to compute SMPB solutions around a variety of different biological structures with only modest computational resources.

Nucleic acids are central to the storage, transmission, and control of genetic information. Their cellular function is dependent not only on sequence, but also on their three-dimensional shape, mechanical properties, and conformational dynamics. Here, we discuss three recent developments that have provided unique insights into these important aspects of DNA and RNA functions.Firstly, small-angle X-ray scattering (SAXS) is emerging as an important tool to study RNA structure. We have demonstrated that SAXS can provide ab initio low-resolution 3D models of RNAs [1]. By taking into account prior information, we have succeeded to build an atomistic model of the VS ribozyme from SAXS data [2]. A particular strength of SAXS as a solution technique is that conformations under different solution conditions can be explored. We have dissected the conformations of the glycine riboswitch [3] and of a TPT riboswitch [4] in the absence and presence of Mg2+ required for folding and in the absence of presence of the functional ligands.Secondly, the highly negatively charged backbone of nucleic acids presents an important barrier to folding and packing and makes these processes strongly dependent on counterions. We show that low and intermediate resolution models derived from SAXS in combination with computational modeling can provide a rigorous framework to understand RNA-ion interactions and to distinguish the effects of electrostatic relaxation and specific ion binding [5].Finally, I will describe how single-molecule experiments can present an complementary window to study the (salt-dependent) mechanical properties of double stranded DNA and RNA [6].[1] Lipfert, et al., JAC (2007)[2] Lipfert, Ouellet, et al., Structure (2008)[3] Lipfert, et al. JMB (2007)[4] Ali, et al. JMB (2010)[5] Lipfert, Sim, et al. RNA (2010)[6] Lipfert, et al. Nature Methods, in press

Time-resolved small-angle x-ray scattering using the stopped-flow method has been applied successfully to investigate the refolding of myoglobin. This is the only method to date that yields direct information on protein physical dimensions during the folding process. It has the potential to detect and probe important processes, such as protein compaction and association, on a millisecond time scale. Initial experiments were performed with horse myoglobin denatured in high concentrations of urea. The denatured protein was diluted rapidly into a buffer containing no urea or low concentrations of urea. The time-course of the forward-scattered intensity shows a decrease in amplitude which is clearly not engendered by the compaction of the protein, but does correspond well to a dimer dissociation process. Initial and final radii of gyration correspond well to a dimer and a monomer, respectively. Kratky plots of the initial and final states also support the transient dimerization model. The apparent dissociation rate constant was obtainable directly from the data. An association rate constant and an equilibrium constant could be estimated. The dimerizing intermediate is speculated to be a globular non-native state with an exposed hydrophobic surface.

We have used anomalous small-angle x-ray scattering as a structural probe for solutions of rabbit parvalbumin labeled with terbium. This technique makes use of the large changes in the terbium scattering factor that occur when the x-ray energy is tuned around an L3 absorption edge of this heavy-atom label. These changes in scattering result in changes in the small-angle scattering curve of the labeled protein as a whole, which can then be analyzed to derive structural information concerning the distribution of labels in the protein. Based on a Gaussian model for the protein electron density, the mean distance from the terbiums to the protein center of mass is determined to be 13.2 A and is consistent with crystallographic results. Our results demonstrate the usefulness of terbium as an anomalous scattering label and provide criteria to help establish anomalous scattering as a reliable structural technique for proteins in solution.

A relatively unknown protein structure motif forms stable isolated single alpha-helices, termed ER/K alpha-helices, in a wide variety of proteins and has been shown to be essential for the function of some molecular motors. The flexibility of the ER/K alpha-helix determines whether it behaves as a force transducer, rigid spacer, or flexible linker in proteins. In this study, we quantify this flexibility in terms of persistence length, namely the length scale over which it is rigid. We use single-molecule optical trapping and small-angle x-ray scattering, combined with Monte Carlo simulations to demonstrate that the Kelch ER/K alpha-helix behaves as a wormlike chain with a persistence length of approximately 15 nm or approximately 28 turns of alpha-helix. The ER/K alpha-helix length in proteins varies from 3 to 60 nm, with a median length of approximately 5 nm. Knowledge of its persistence length enables us to define its function as a rigid spacer in a translation initiation factor, as a force transducer in the mechanoenzyme myosin VI, and as a flexible spacer in the Kelch-motif-containing protein.

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.

Functional RNAs fold into compact, well-defined tertiary structures despite strong electrostatic repulsion both within and between helices. To achieve these compact structures, many RNAs employ structural divalent cations, typically Mg2+. The simplest tertiary contact in nucleic acids is two helices, joined by some non-helical contact. To explore the fundamental characteristics of tertiary contact formation in nucleic acids we studied a system of two DNA helices tethered via a short PEG linker by both computational and experimental methods. Computationally, we predict the electrostatic repulsion between these helices as a function of Mg2+ and Na+ concentration. Experimentally, we linked the distal termini of these helices via a disulfide linker. Using small-angle x-ray scattering, we measured the fraction of intact disulfide bonds as a function of reducing strength of the buffer at a range of Mg2+ and Na+ concentration. Using these data we can extrapolate the magnitude of the strain on the disulfide bond, and thus the repulsion between the helices. Previous results show that the conformational ensemble is narrowly distributed around an extended, co-linear conformation at low salt and becomes more relaxed at high salt, but is unable to isolate a conformation in which the helices are stacked. Furthermore, previous results also suggest that specific interactions between Mg2+ and the phosphate backbone strongly are more important than simple ionic strength in determining the magnitude of the repulsive potential between the helices. In this project, we hope to experimentally demonstrate the energy of helix stacking and the different role of ionic strength and ionic specific interactions.