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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.

The large electrostatic repulsion arising from the negatively-charged backbone of RNA molecules presents a large barrier to folding. Solution counterions assist in the folding process by screening this electrostatic repulsion. While early research interpreted the effect of these counterions in terms of an empirical ligand-binding model, theories based on physical models have supplanted them and revised our view of the roles that ions play in folding. Instead of specific ion-binding sites, most ions in solution interact inside an “ion atmosphere” – a fluctuating cloud of non-specifically associated ions surrounding any charged molecule. Recent advances in experiments have begun the task of characterizing the ion atmosphere, yielding valuable data that has revealed deficiencies in Poisson-Boltzmann theory, the most widely-used theory of the ion atmosphere. The continued development of experiments will help guide the development of improved theories, with the ultimate goal of understanding RNA folding and function and nucleic acid/protein interactions from a quantitative perspective.

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 transesterification in which adenine and guanine nucleobases contributed by the interacting loops combine together in general acid-base catalysis.

We recently used computational protein design to create an extremely stable, globular protein, Top7, with a sequence and fold not observed previously in nature. Since Top7 was created in the absence of genetic selection, it provides a rare opportunity to investigate aspects of the cellular protein production and surveillance machinery that are subject to natural selection. Here we show that a portion of the Top7 protein corresponding to the final 49 C-terminal residues is efficiently mis-translated and accumulates at high levels in Escherichia coli. We used circular dichroism, size-exclusion chromatography, small-angle X-ray scattering, analytical ultra-centrifugation, and NMR spectroscopy to show that the resulting C-terminal fragment (CFr) protein adopts a compact, extremely stable, homo-dimeric structure. Based on the solution structure, we engineered an even more stable variant of CFr by disulfide-induced covalent circularisation that should be an excellent platform for design of novel functions. The accumulation of high levels of CFr exposes the high error rate of the protein translation machinery. The rarity of correspondingly stable fragments in natural proteins coupled with the observation that high quality ribosome binding sites are found to occur within E. coli protein-coding regions significantly less often than expected by random chance implies a stringent evolutionary pressure against protein sub-fragments that can independently fold into stable structures. The symmetric self-association between two identical mis-translated CFr sub-domains to generate an extremely stable structure parallels a mechanism for natural protein-fold evolution by modular recombination of protein sub-structures.

We study the early steps of amyloid formation of the seven residue peptide GNNQQNY from yeast prion-like protein Sup35 by simulating the random coil to beta-sheet and alpha-helix to beta-sheet transition both in the absence and presence of a cross-beta amyloid nucleus. The simulation method at atomic resolution employs a new implementation of a Langevin dynamics "reaction path annealing" algorithm. The results indicate that the presence of amyloid-like cross-beta-sheet strands both facilitates the transition into the cross-beta conformation and substantially lowers the free energy barrier for this transition. This model systems allows us to investigate the energetic and kinetic details of this transition, which is consistent with an auto-catalyzed, nucleation-like mechanism for the formation of beta-amyloid. In particular, we find that electrostatic interactions of peptide backbone dipoles contribute significantly to the stability of the beta-amyloid state. Furthermore, we find water exclusion and interactions of polar side-chains to be driving forces of amyloid formation: the cross-beta conformation is stabilized by burial of polar side-chains and inter-residue hydrogen bonds in the presence of an amyloid-like "seed". These findings are in support of a "dry, polar zipper model" of amyloid formation.

Summary The open/closed transition in polymerases is a crucial event in DNA replication and transcription. We hypothesize that the residues that transmit the signal for the open/closed transition are also strongly conserved. To identify the dynamically relevant residues, we use an elastic network model of polymerases and probe the residue-specific response to a local perturbation. In a variety of DNA/RNA polymerases, a network of residues spanning the fingers and palm domains is involved in the open/closed transition. The similarity in the network of residues responsible for large-scale domain movements supports the notion of a common induced-fit mechanism in the polymerase families for the formation of a closed ternary complex. Multiple sequence alignment shows that many of these residues are also strongly conserved. Residues with the largest sensitivity to local perturbations include those that are not so obviously involved in the polymerase catalysis. Our results suggest that mutations of the mechanical "hot spots" can compromise the efficiency of the enzyme.

Fibrillar deposits of insulin cause serious problems in implantable insulin pumps, commercial production of insulin, and for some diabetics. We performed a systematic investigation of the effect of urea-induced structural perturbations on the mechanism of fibrillation of insulin. The addition of as little as 0.5 m urea to zinc-bound hexameric insulin led to dissociation into dimers. Moderate concentrations of urea led to accumulation of a partially unfolded dimer state, which dissociates into an expanded, partially folded monomeric state. Very high concentrations of urea resulted in an unfolded monomer with some residual structure. The addition of even very low concentrations of urea resulted in increased fibrillation. Accelerated fibrillation correlated with population of the partially folded intermediates, which existed at up to 8 m urea, accounting for the formation of substantial amounts of fibrils under such conditions. Under monomeric conditions the addition of low concentrations of urea slowed down the rate of fibrillation, e.g. 5-fold at 0.75 m urea. The decreased fibrillation of the monomer was due to an induced non-native conformation with significantly increased α-helical content compared with the native conformation. The data indicate a close-knit relationship between insulin conformation and propensity to fibrillate. The correlation between fibrillation and the partially unfolded monomer indicates that the latter is a critical amyloidogenic intermediate in insulin fibrillation.

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.

Chaperonins use ATPase cycling to promote conformational changes leading to protein folding. The prokaryotic chaperonin GroEL requires a cofactor, GroES, which serves as a “lid” enclosing substrates in the central cavity and confers an asymmetry on GroEL required for cooperative transitions driving the reaction. The eukaryotic chaperonin TRiC/CCT does not have such a cofactor but appears to have a “built-in” lid. Whether this seemingly symmetric chaperonin also operates through an asymmetric cycle is unclear. We show that unlike GroEL, TRiC does not close its lid upon nucleotide binding, but instead responds to the trigonal-bipyramidal transition state of ATP hydrolysis. Further, nucleotide analogs inducing this transition state confer an asymmetric conformation on TRiC. Similar to GroEL, lid closure in TRiC confines the substrates in the cavity and is essential for folding. Understanding the distinct mechanisms governing eukaryotic and bacterial chaperonin function may reveal how TRiC has evolved to fold specific eukaryotic proteins.

Human insulin exists in different association states, from monomer to hexamer, depending on the conditions. In the presence of zinc the “normal” state is a hexamer. The structural properties of 20 variants of human insulin were studied by near-UV circular dichroism, fluorescence spectroscopy, and small-angle X-ray scattering (SAXS). The mutants showed different degrees of association (monomer, dimers, tetramers, and hexamers) at neutral pH. A correlation was shown between the accessibility of tyrosines to acrylamide quenching and the degree of association of the insulin mutants. The near-UV CD spectra of the insulins were affected by protein association and by mutation-induced structural perturbations. However, the shape and intensity of difference CD spectra, obtained by subtraction of the spectra measured in 20% acetic acid (where all insulin species were monomeric) from the corresponding spectra measured at neutral pH, correlate well with the degree of insulin association. In fact, the near-UV CD difference spectra for monomeric, dimeric, tetrameric, and hexameric insulin are very distinctive, both in terms of intensity and shape. The results show that the spectral properties of the insulins reflect their state of association, and can be used to predict their oligomeric state. © 2003 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 92:847–858, 2003

The pathological hallmark of Parkinson's disease is the presence of intracellular inclusions, Lewy bodies, and Lewy neurites, in the dopaminergic neurons of the substantia nigra and several other brain regions. Filamentous α-synuclein is the major component of these deposits and its aggregation is believed to play an important role in Parkinson's disease and several other neurodegenerative diseases. Two homologous proteins, β- and γ-synucleins, are also abundant in the brain. The synucleins are natively unfolded proteins. β-Synuclein, which lacks 11 central hydrophobic residues compared with its homologs, exhibited the properties of a random coil, whereas α- and γ-synucleins were slightly more compact and structured. γ-Synuclein, unlike its homologs, formed a soluble oligomer at relatively low concentrations, which appears to be an off-fibrillation pathway species. Here we show that, although they have similar biophysical properties to α-synuclein, β- And γ-synucleins inhibit α-synuclein fibril formation. Complete inhibition of α-synuclein fibrillation was observed at 4:1 molar excess of β- and γ-synucleins. No significant incorporation of β-synuclein into the fibrils was detected. The lack of fibrils formed by β-synuclein is most readily explained by the absence of a stretch of hydrophobic residues from the middle region of the protein. A model for the inhibition is proposed.

Light chain amyloidosis involves the systemic pathologic deposition of monoclonal light chain variable domains of immunoglobulins as insoluble fibrils. The variable domain LEN was obtained from a patient who had no overt amyloidosis; however, LEN forms fibrils in vitro, under mildly destabilizing conditions. The in vitro kinetics of fibrillation were investigated using a wide variety of probes. The rate of fibril formation was highly dependent on the initial protein concentration. In contrast to most amyloid systems, the kinetics became slower with increasing LEN concentrations. At high protein concentrations a significant lag in time was observed between the conformational changes and the formation of fibrils, consistent with the formation of soluble off-pathway oligomeric species and a branched pathway. The presence of off-pathway species was confirmed by small angle x-ray scattering. At low protein concentrations the structural rearrangements were concurrent with fibril formation, indicating the absence of formation of the off-pathway species. The data are consistent with a model for fibrillation in which a dimeric form of LEN (at high protein concentration) inhibits fibril formation by interaction with an intermediate on the fibrillation pathway and leads to formation of the off-pathway intermediate.

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.

Sap1 is a DNA-binding protein involved in controlling the mating type switch in fission yeast Schizosaccharomyces pombe. In the absence of any significant sequence similarity with any structurally known protein, a variety of biophysical techniques has been used to probe the solution low-resolution structure of the sap1 protein. First, sap1 is demonstrated to be an unusually elongated dimer in solution by measuring the translational diffusion coefficient with two independent techniques: dynamic light-scattering and ultracentrifugation. Second, sequence analysis revealed the existence of a long coiled-coil region, which is responsible for dimerization. The length of the predicted coiled-coil matches estimates drawn from the hydrodynamic experimental behaviour of the molecule. In addition, the same measurements done on a shorter construct with a coiled-coil region shortened by roughly one-half confirmed the localization of the long coiled-coil region. A crude T-shape model incorporating all these information was built. Third, small-angle X-ray scattering (SAXS) of the free molecule provided additional evidence for the model. In particular, the P(r) curve strikingly demonstrates the existence of long intramolecular distances. Using a novel 3D reconstruction algorithm, a low resolution 3D model of the protein has been independently constructed that matches the SAXS experimental data. It also fits the translation diffusion coefficients measurements and agrees with the first T-shaped model. This low-resolution model has clearly biologically relevant new functional implications, suggesting that sap1 is a bifunctional protein, with the two active sites being separated by as much as 120 A; a tetrapeptide repeated four times at the C terminus of the molecule is postulated to be of utmost functional importance.

There have been a number of advances in atomic resolution simulations of biomolecules during the past few years. These have arisen partly from improvements to computer power and partly from algorithmic improvements. There have also been advances in measuring time-dependent fluctuations in proteins using NMR spectroscopy, revealing the importance of fluctuations in the microsecond to millisecond time range. Progress has also been made in measuring how far the simulations are able to represent the accessible phase space that is available to the protein in its native state, in solution, at room temperature. Another area of development is the simulation of protein unfolding at atomic resolution.

Equilibrium unfolding of hen egg lysozyme as a function of urea concentration at pH 2.9 has been studied by solution X-ray scattering. Differences in the unfolding transition are observed as monitored by the radius of gyration R g , and by far and near UV CD (circular dichroism) at 222 nm and 298 nm, respectively. This suggests the existence of a third unfolding species, in addition to the native and the unfolded states. A singular value decomposition (SVD) analysis was made of the scattering curves at different urea concentrations. This analysis shows clear evidence of a third basis component in the X-ray scattering curves, thus supporting the results of the R g and CD measurements. The denaturant binding model was employed to estimate the thermodynamic parameters of denaturation for the intermediate and unfolded states. Use of these parameters to refine the SVD analysis allows us to reconstruct a scattering profile for the pure intermediate state. Simplified partially folded models, based on the crystal structure of hen lysozyme, support a working model for the intermediate, whose structure may be correlated with that of the kinetic intermediate found in the refolding pathway studied by Dobson and coworkers.

Partially folded states of proteins are found to occur with a wide variety of degrees of unfolding, ranging from the compact molten globule to the fully unfolded forms, depending on solvent conditions and the specific protein involved. Small to intermediate angle X-ray scattering from partially folded states of proteins yields low resolution scattering profiles that may be used to explore the degree of folding of a protein under given solution conditions. By Monte Carlo simulation of a highly simplified homopolymer model, we show that such partially folded states will yield a characteristic scattering profile that may be written as a linear superposition of scattering from a compact core and of scattering from random coil loops that emerge from this core. We also find a term resulting from interference of X-rays scattering from the core with those scattering from the loops. This interference term oscillates in sign and tends to enhance the core portion of the scattering profile. We compare the model calculations of the scattering profile with measurements of the scattering profile as a function of salt concentration for cytochromecat pH 2. Because of our characterization of the scattering profiles, we suggest that these results may be re-interpreted in terms of the presence of a range of partially folded states as a function of pH and salt concentration, and that the observed scattering profiles are consistent with the characterization of the partially folded states in terms of random coil loops emerging from a compact core with the loop fraction increasing as the salt concentration is decreased. This characterization is consistent with data on amide protection against H –2H exchange of compact regions within partially folded states observed for a number of proteins, including cytochromec.

Freshly-prepared blue membranes from Halobacterium halobium, previously reported to be disordered, are shown to have a distinct crystal lattice structure, slightly different from the native form. The lattice of the blue form is disrupted irreversibly when dehydrated. The disorder process was observed using time-resolved small-angle X-ray diffraction and analyzed by radial autocorrelation functions. The diffraction peaks of the in-plane lattice first sharpen and increase due to improved membrane orientation, then the trimer lattice becomes disordered and the unit cell dimension decreases by 1.8 A. In contrast, dehydration of purple membranes does not disorder the lattice, and the unit cell dimension shrinks by only 1.0 A. Comparisons of radial autocorrelation functions for the blue membrane during drying show drastic loss of inter-trimer, long-range correlation while the intra-trimer, short-range correlations remain more or less unchanged. This suggests that the deionized protein trimers can maintain their overall structure during the dehydration, even though the lattice dimension decreases appreciably and the two-dimensional crystallinity is disrupted.

We briefly summarize the basic concepts behind the terms “Kondo insulator”. We point out the importance of including band structure effects in calculating excitation spectra. A discussion of a mid-gap impurity band induced by depants leads to the suggestion of a low-temperature magnetic phase caused by departure from stoichiometry in samples of CeNiSn. This could provide an explanation for the 1/T1 ∝ T3 behavior in NMR for this material.

The nitrogenase enzyme complex, consisting of the molybdenum-iron protein and the iron protein, plays a critical role in the biological reduction of dinitrogen to ammonia (nitrogen fixation). The nitrogen-fixing site within the molybdenum-iron protein is an iron-molybdenum-sulfur cofactor (FeMoco) of roughly 1000-2000 Dalton mass. Structural aspects of FeMoco have been determined by spectroscopic and more recently by crystallographic studies. In order to determine the radius of gyration (Rg) of isolated FeMoco, we have performed small-angle x-ray scattering studies of FeMoco in N-methylformamide solution, in the absence of the molybdenum-iron protein. Model compounds of known structure have also been examined in similar solvents, N,N-dimethylformamide and acetonitrile, as controls and for calibration purposes. The Rg values obtained for the models are in good agreement with calculations based upon their respective crystal structures. However, the Rg obtained for FeMoco clearly indicates that the cofactor is not monomeric in solution, but rather aggregated and possibly polydisperse. Further, Rg values were also measured after addition of thiol, dithionite, and thiol and dithionite, to the FeMoco samples. The results indicate, surprisingly, that oxidation state and putative thiol coordination have no detectable effect on the aggregation behavior of FeMoco in solution, as determined by these measurements.

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.

The transition-metal oxides show a range of ground states of broken symmetry; for example, Mott insulators, antiferromagnetic states, charge density waves, and, more recently, high-temperature superconductors. All these properties depend essentially on electronic correlation effects induced by the Pauli effect acting on the double occupation of specific orbitals. Present first principles band theory methods using the local density approximation (LDA) do not converge to an antiferromagnetic ground state for La2-xSrxCuO4 and YBaCuO. In this paper we propose a method based on the Gutwiller projection technique to improve the treatment of the electron correlation. This method requires the reformulation of Bloch waves into localized orbitals about each site as well as a Monte Carlo method for treating the many-body Hamiltonian. We use as input to our many-body formalism the results obtained from a conventional self-consistent ASW augmented spherical wave) band calculation.

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

Using synchrotron radiation the X-ray Ca K-absorption edges have been measured with high resolution. The Ca binding site in the adenosine triphosphate (ATP) has been studied. The K edges of simple Ca model compounds CaHPO 3 , CaCO 3 , and Ca(C 2 H 3 O 2 ) 2 have been measured, for comparison with the K edge of CaATP. The calcium site in ATP is similar to Ca site in calcium hydrogen phosphate.

Self-consistent multiple scattered wave formation was used to calculate the theoretical L-absorption edges of hydrated and unhydrated erbium trichloride in both bound state and continuum regions, in order to investigate the white line behavior. The white line was found to correspond to a transition to a d-like bound state lying just below the continuum threshold.

We study a percolating network of highly hysteretic Josephson junctions in which each junction is modelled as a piecewise-Ohmic hysteretic device. At the percolation threshold, the average voltage drop across a network on a large L × L grid is assumed to fall to zero as V ∼ ( I − I c ( L )) η as the applied current is reduced to the critical current I c ( L ). Our finite-size Monte Carlo study gives the value η = 2.0±0.1. This value is remarkably close to the result η =2 obtained by a scaling analysis of a continuum version of the model.

The polarized X-ray absorption cross section of the ls → 3d transition in a square planar CuCl2−4 complex has been measured with respect to rotation about an axis normal to the CuCl4. The cross section exhibits four-fold periodicity about this axis, indicating that the transition is primarily due to coupling with the electric quadrupole component of the radiation. The vibronically allowed dipole transition is approximately one-third as the quadrupolar cross section. These observations are in agreement with SCF Xα multiple-scattered wave calculations, and may have implications for the intepretation of other X-ray absorption spectra. The half-filled d orbital is shown to have the angular characteristics of dx2−y2.

X-ray crystallographic studies of troponin C (Herzberg, O., and James, M.N.G. (1985) Nature 313, 653-659; Sundaralingam, M., Bergstrom, R., Strasburg, G., Rao, S.T., and Roychowdhury, P. (1985a) Science 227, 945-948) have revealed a novel protein structure consisting of two globular domains, each containing two Ca2+-binding sites, connected via a nine-turn alpha-helix, three turns of which are fully exposed to solvent. Since the crystals were grown at pH approximately 5, it is of interest to determine whether this structure is applicable to the protein in solution under physiological conditions. We have used small-angle x-ray scattering to examine the solution structure of troponin C at pH 6.8 and the effect of Ca2+ on the structure. The scattering data are consistent with an elongated structure in solution with a radius of gyration of approximately 23.0 A, which is quite comparable to that computed for the crystal structure. The experimental scattering profile and the scattering profile computed from the crystal structure coordinates do, however, exhibit differences at the 40-A level. A weak Ca2+-facilitated dimerization of troponin C was observed. The data rule out large Ca2+-induced structural changes, indicating rather that the molecule with Ca2+ bound is only slightly more compact than the Ca2+-free molecule.

By considering a one-dimensional analog of a system of conduction electrons exchange coupled to a localized spin in each cell of a lattice, it is suggested that a second-order transition from an antiferromagnetic to a Kondo spin-compensated ground state will occur as the exchange coupling constant J is increased to a critical value Jc. For systems in which J ≲ Jc, a very weak sublattice magnetization may occur as a result of nearly complete spin-compensation.

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.